Sevenoaks School - IB prized writing 2016 by sevenoaks school

Sevenoaks School was one of the first schools in the UK to introduce the International Baccalaureate, and the first UK school to move exclusively to the IB at Sixth Form. The school now enjoys world-class academic status, with an average IB score ten points above the world average. The IB has rapidly established itself as the international gold standard of education. Its single vision is an attempt to prepare young people for a life of learning in an unpredictable future. While having a proven track record in its ability to prepare students better for undergraduate studies, its educational vision is premised on a notion of what being well-educated means: an 18-year-old school-leaver should be numerate, literate, able to apply rigorous scientific and mathematical thinking to the world, while being able to engage in foreign cultures. These are the basic requirements of living in the multifaceted world of the 21st century, regardless of the university destination or degree. In this book, we have a collection of ten of our IB Extended Essays from our 2016 cohort of students â&#x20AC;&#x201C; these typify the depth, breadth and subject nature of the studies that form an integral part of the IB. We hope you enjoy reading them!

Prized Writing - Sevenoaks School International Baccalaureate Extended Essays 2016

Celebrating the achievements of Sevenoaks students

Sevenoaks School

Prized writing

International Baccalaureate Extended Essays 2016 Cornelia Bentsen - Geography

Bolurin Edun - Mathematics

Theresa Grillo - German

Cecilia Jay - Psychology

Eloise Robson - History

Freya Sackville-West - Visual Arts

Miranda Stevens - Biology

Hugo Sunnucks - Philosophy

Nanako Watanabe - Economics

Sevenoaks School High Street, Sevenoaks, Kent TN13 1HU directdesign.co.uk

www.sevenoaksschool.org

Felix Wood - Physics 1

Prized Writing 2016

- Prized Writing Sevenoaks School International Baccalaureate Extended Essays 2016

Prized Writing 2016

Introduction from Nigel Haworth, Director of IB, Sevenoaks School Every year in March each of our, over 200, Lower Sixth students embarks on a journey which will be the one of the biggest challenges of their young academic careers: the IB extended essay. It is undoubtedly a daunting task: a 4000-word independently researched essay on a topic of their own choosing, often in a subject that they’ve only been studying for six months. Every year, however, all of our students reach their goal having produced a remarkable piece of original research. I say ‘independent’ and genuinely mean it. The IB is clear in its expectations: supervisors are to spend no more than five hours over a six-month process working directly with the student and at no point are we allowed to edit the student’s writing or compel them into any particular direction. It is without doubt the most difficult academic work in which they will have engaged. It is also the extended essay which seems to most prepare them for the rigour and independence of undergraduate study. Again and again we hear from our visiting OS that it was the extended essay that prepared them most for undergraduate research and has given them a clear advantage among their peers at university.

The collection of essays contained in this, our third edition of Prized Writing are genuinely that – prized. We, their supervisors and teachers, think they stand out solely on basis of the originality of their topics, the levels of commitment and enthusiasm of the authors whilst demonstrating the ability of these student to overcome whatever difficulties they encountered in the research and writing process. They were purposely chosen before they received any external marks from IB examiners. We are, undoubtedly, proud of each of the essays submitted to the IB in May 2016 and would stand by any one of them, but these seemed to be first among equals, so we share them with you. The students’ essays are included in exactly the way that they submitted to the IB, so there may be some idiosyncrasies within, but this is what makes them so special. They’ve been written by real students doing their absolute best, and we applaud them.

Prized Writing 2016

Contents Cornelia Bentsen - Geography

Bolurin Edun - Mathematics

Theresa Grillo - German

Cecilia Jay - Psychology

Eloise Robson - History

Freya Sackville-West - Visual Arts

113

Miranda Stevens - Biology

145

Hugo Sunnucks - Philosophy

191

Nanako Watanabe - Economics

203

Felix Wood - Physics

221

Prized Writing 2016

Cornelia Bentsen - Geography

To what extent is Harringay Gentrified?

Cornelia Bentsen - Geography

Cornelia Bentsen - Geography Writing my Extended Essay was definitely a challenge and in particular I struggled to find accurate and reliable data for the gentrification indicators I was examining. Given that no gentrification indices existed already, I had to devise my own index and then find data from the UK Census to input into each component. This process highlighted to me the importance of academic research, especially seeing as so many geographic issues are critical to policy making. Moreover my investigation in Harringay prompted me to reflect more broadly on the changing nature of gentrification itself, both in terms of who was participating in the process and in the locations in which it occurred. This conclusion brought me to the forefront of geographical research, something that encapsulates the unique opportunity presented by the Extended Essay.

Supervisor: Paul Thompson Cornelia chose to base her essay around the topic of ‘Gentrification’ and her focus was the small scale residential area of Harringay within the London borough of Haringey. Gentrification is a multi-faceted process thus choosing, justifying and evaluating appropriate ‘Gentrification’ criteria was a key aspect of her research methodology. Using census manipulated data, she examined changes in different gentrification indicators to assess the her research question. Secondary data included temporal changes in the percentage of full-time students, median house prices, environmental quality and residents academic qualifications. Cornelia produced her own composite index of Gentrification. Spatial emphasis and the application of geographical theory and methodology is essential to a good Geography EE so Cornelia at the lower super output area (LSOA) level choropleth mapped her results using Google Fusion tables and mapping software. Written analysis, interpretation and evaluation were sound throughout. Her in-depth geographical study showed that even within a small area there were significant spatial inequalities and degrees of gentrification. Cornelia concluded her outcomes using a ‘traffic light’ indicator of gentrification summary.

Cornelia Bentsen - Geography

Contents Introduction 8 Investigation 13 Analysis 15 Conclusions 32 Appendix

Bibliography 37

Abstract The debate surrounding gentrification is controversial and widely discussed â&#x20AC;&#x201C; How do you define it? What are the effects? Should governments encourage it as a means to regenerate deprived urban areas or intervene against it as a force that causes mass-eviction and homelessness? The eruption of gentrification riots across the globe have forced gentrification to the forefront of the media and made it a relevant issue to 21st Century society. Consequently this essay investigated the occurrence of gentrification, specifically within a small area of North London called Harringay. This area was chosen because of numerous journal articles commenting on its ascent in status relative to other areas in London (stemming from the various merits of the great value housing in Harringay and the high quality services opening up in the area) (Homes and Property 2012, Evening Standard 2014) resulting in the research question â&#x20AC;&#x153;To what extent is Harringay gentrified?â&#x20AC;? Through the use of UK census data, changes in numerous different indicators of gentrification in Harringay were examined. This examination used a range of different scale geographies including lower super output areas (LSOAs), which are spatial units of around 1500 residents living in a compact area. Social homogeneity was taken into account when creating these small statistic areas meaning that areas usually have one common land use and show relatively little internal variation. Throughout the investigation data comparisons were made to other similar outer London boroughs, and to London itself, as a kind of control. The analysis has shown that there are gentrification processes occurring in Harringay but they are still in motion. This means that the answer to the research question is that at present is only gentrified to a limited extent. However some areas are significantly more gentrified than others.

Cornelia Bentsen - Geography

Cornelia Bentsen Sevenoaks School Extended Essay: Geography To what extent is Harringay gentrified? 1. Introduction: The exact definition of the term gentrification is debated due to the concept’s abstract nature and intangibility. However to answer the research question “To what extent is Harringay Gentrified?” the definition of gentrification as “the transformation of a working-‐class or vacant area of the central city to a middle class residential and/or commercial use area” will be used. (Slater, Wyly & Lees, 2010) Whilst this definition has come close to being universal, the impacts of gentrification are more uncertain as they depend largely on the specific circumstances of the area being gentrified. Some common impacts are summarized in the diagram below. Wealthier residents move into an area. The area becomes even less run down.

They improve the housing stock and urban environmental quality.

The local culture is diluted and displaced, poorer residents become dissatisjied and potentially violent. (3)

Property values rise.

Poorer residents are forced to leave as the area becomes more expensive (=social displacement.) Gentrification has been evident in many parts of London over the last 60 years including Fulham, Notting Hill and more recently Brixton. (Economist, 2014) In London gentrification has typically taken the form of affluent individuals buying Victorian housing in the inner city and improving its aesthetics. The presence of these “middle class” gentrifiers has then stimulated high-‐end businesses such as boutique clothing stores and gourmet restaurants to open up, increasing the affluence and desirability of an area. However patterns of gentrification are changing. Gentrification is classified as a centripetal movement occuring at the 8

Cornelia Bentsen - Geography

Cornelia Bentsen Sevenoaks School Extended Essay: Geography To what extent is Harringay gentrified? “urban centre” of a place. (N, Smith, 2000: 294) However the majority of inner London has been heavily gentrified, with some exceptions in East London, meaning that gentrifiers have begun to look outwards for prospective areas to invest in. This phenomenon changes the definition of gentrification and poses the question of whether it is a centrifugal or centripetal movement because the process is now attracting people out of the inner city into more suburban areas rather than the other way around. This can be seen with the case study of this essay, Harringay, a relatively suburban ward located 8.9 km from the centre of London in the borough of Haringey. (Wikipedia, 2015.) Diagram 1: The location of the London Borough of Haringey (London Councils Directory) Haringey Diagram 2: Wards in the London Borough of Haringey. (Haringey Green Party, 2014) Harringay 9

Cornelia Bentsen - Geography

Cornelia Bentsen Sevenoaks School Extended Essay: Geography To what extent is Harringay gentrified? Harringay (not to be confused with the borough Haringey which it lies within) is predominantly comprised of the Harringay Ladder, a residential area of 20 streets between Green Lanes, Wightman Road and Finsbury Park. The area’s potential to be gentrified is derived from the summation of the following factors; • Victorian housing • Accessibility (3 different over ground train stations, 3 underground tube stations) • Proximity to central London (its in zone 3) • Good local shops and services • Having the large, attractive open area Finsbury Park

Cornelia Bentsen - Geography

Cornelia Bentsen Sevenoaks School Extended Essay: Geography To what extent is Harringay gentrified?

Hornsey Overground Station

Harringay Overground Station

Turnpike Lane Underground Station

The area boxed in by orange is the Harringay Ladder. The rows of parallel streets form the ladder shape.

Manor House Underground Station

Finsbury Park

Finsbury Park Overground and Underground Station

7 11

Cornelia Bentsen - Geography

Cornelia Bentsen Sevenoaks School Extended Essay: Geography To what extent is Harringay gentrified? The map above (Neighbourhood statistics, 2015) shows the LSOAs that this essay will use to answer this essay’s research question. They will either be used separately or as part of an average for the ward of Harringay. 12

Cornelia Bentsen - Geography

Cornelia Bentsen Sevenoaks School Extended Essay: Geography To what extent is Harringay gentrified? 2. Investigation: Given the multifaceted nature of gentrification, a number of visible indicators that it affects can be used to measure it holistically. These are outlined in the table below.

Aspect of Gentrjication

Poorer residents are forced to leave as the area becomes more expensive (=social displacement.)

Property values rise. Wealthier residents move into an area.

Wealthier residents move into an area.

Wealthier residents move into an area. Poorer residents are forced to leave the area. Poorer residents are forced to leave the area. Wealthier residents improve the urban environmental quality. Wealthier residents improve the housing stock.

Indicator of Gentrijication

Changes in the percentage of full time students and migrants.

Changes in median house prices.

Changes in the percentage of people employed in Higher Managerial, Professional or Administrative occupations..

Changes in the percentage of people with level 4 or 5 qualijications.

Changes in the percentage of people doing skilled labour.

Changes in the percentage of people employed in routine occupations. Changes in the percentage of people claimaing jobseeker's allowance.

Relative differences in the environmental quality of Harringay and surrounding wards. Relative differences in the number of properties undergoing renovation between Harringy and surrounding wards.

Data Source

Neighbourhood Statistics

London Datastore

Neighbourhood Statistics

Environmental quality survey.

Housing renovation survey.

Cornelia Bentsen - Geography

Cornelia Bentsen Sevenoaks School Extended Essay: Geography To what extent is Harringay gentrified? An environmental quality survey, which can be seen in Appendix 1, was conducted on a transect going along Seymour Street (a residential street in the centre of Harringay), across Harringay high street into the adjacent ward of St Ann’s via St Ann’s road (a map of this route is shown on page 21.) The survey’s purpose was to provide primary data allowing the comparison of environmental quality in Harringay and St Ann’s. Additionally a survey into the number of houses being renovated was undertaken along the same transect route. 14

Cornelia Bentsen - Geography

Cornelia Bentsen Sevenoaks School Extended Essay: Geography To what extent is Harringay gentrified? 3. Analysis In order to look at the aspects of gentrification as described in the table on page 9 the following hypotheses were formulated. They then formed the core of this essay’s analysis. -‐ Hypothesis 1 – “The percentage of full-‐time students and immigrants in Harringay will have decreased between 2001 to 2011.” As established earlier on in the essay, when gentrification occurs the percentage of “middle or upper class” residents (categorized as the ONS’s social grades A, B and C1) increases whilst the percentage of “lower class” residents (defined as the ONS’ social grades C2, D and E) decreases. This is because poorer, lower class residents are driven out of the area being gentrified by higher costs of living (social displacement.) Normally students (those in higher education) and immigrants (defined as people born in other countries) are categorized as lower class because students have no source of income, and therefore live in the cheapest possible way. Similarly the majority of immigrants have unskilled jobs and are often exploited as a source of cheap labour. (Shelley, T, 2007) Therefore by looking at changes in student and immigrant populations, conclusions can be formed about whether this aspect of gentrification is occurring. As shown in the graphs below, the percentage of immigrants and full-‐time students has decreased by more than 10% in Harringay between 2001 and 2011. This change is even more extreme considering that the trend for London as a whole is a rapid increase. Similarly other comparable boroughs have all experienced an increase in their immigrant and student populations, with the exception of Haringey (although the change that happened here was over 10% slower than in Harringay.) This means that social displacement has occurred, as hypothesised, and this would suggest that gentrification has taken place, at least to some extent, due to the correlation (and causation) between gentrification and social displacement.

Cornelia Bentsen - Geography

Percentage change in the immigrant population

Cornelia Bentsen Sevenoaks School Extended Essay: Geography To what extent is Harringay gentrified?

Percentage change in immigrant populations between 2001 and 2011 in various areas across London

70 60 50 40 30 20 10 0

-‐10 -‐20 -‐30

Percentage change in the student population

-‐

The percentage change in full-‐time student populations between 2001 and 2011 in various areas across London 50 40 30 20 10 0

-‐10 -‐20

Hypothesis 2 – “The percentage of people employed in routine occupations will have decreased between 2001 and 2011.”

Analysing the occupational composition of the population is another means of seeing whether social displacement has occured. If gentrification were indeed happening the proportion of residents in routine occupations would decrease

Cornelia Bentsen - Geography

Cornelia Bentsen Sevenoaks School Extended Essay: Geography To what extent is Harringay gentrified? and the number of young professionals and middle class families would increase. This is because people employed in routine occupations form one of the lowest income groups in society and are therefore highly sensitive to changes in price (that result from gentrification.) Contrary to hypothesis 2, the trend for the percentage of people employed in routine occupations has been upwards in the ward of Harringay. All the LSOAs within Harringay fit this upward trend although the rate of change varies between LSOAs. This evidence implies that there has been an increase in the percentage of lower class persons living in Harringay and contradicts the findings of hypothesis 1’s. This evidence also suggests that gentrification is taking place at variable rates in different parts of Harringay.

Percentage

Percentage change of people employed in routine occupations between 2001 and 2011

10 9 8 7 6 5 4 3 2 1 0

Haringey 031B experienced the smallest increase (and to the lowest level) of people employed in routine occupations.

-‐

Apr-‐01

Mar-‐11

Haringey 023C experienced one of the largest increases to the highest level of people employed in routine occupations.

Hypothesis 3 – “The percentage of jobseeker’s allowance claimants will have decreased between 2004 and 2014.”

The last population group likely to be displaced by gentrification is the unemployed. They are among the poorest in society so they will be one of the first groups of people to be forced out of Harringay if it is being gentrified. Alternatively a few unemployed people may find jobs, working for local shops for example, as a result of the regeneration and economic boom in Harringay created by gentrification (and the associated influx of wealthy residents.) Thus, regardless of whether the unemployed in Harringay re-‐enter the job market or are evicted, the percentage of jobseeker’s allowance claimants should decrease if Harringay is being gentrified.

Cornelia Bentsen - Geography

Cornelia Bentsen Sevenoaks School Extended Essay: Geography To what extent is Harringay gentrified? The following line graph depicts how the jobseeker’s claimant rate (a proxy for unemployment) in Harringay has been exceedingly high relative to all other comparison areas since 2004. However, since 2011, where unemployment peaked in Harringay at a level greater than 1.5% higher than other areas, the decrease in unemployment has been very rapid. This means that the outcome of hypothesis 3’s investigation does not support either side of Harringay’s gentrification debate.

Unemployment in different London geographies between 2004 and 2014

8.0 7.0 6.0

Brent

4.0

Newham

5.0

Haringey

3.0

Waltham Forest

1.0

London

2.0 0.0

-‐

Harringay July July July July July July July July July July July 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 2014

-‐Hypothesis 4 -‐ “The percentage change of people employed in Higher Managerial, Administrative or Professional Occupations will have increased between 2001 and 2011.”

As an extension of this essay’s inquiry into changes in Harringay’s occupational structure trends in the proportion of people employed in Higher Managerial, Administrative or Professional Occupations were examined. People employed in these occupations, ranked as the highest paid and most skilled by the UK census, represent the majority of the middle/upper class and an increase in their population will support the view that Harringay is being gentrified. As demonstrated by the graphs below the percentage of people employed in Harringay employed in these occupations only increased by 0.6% between 2001 and 2011. In contrast, London experienced an increase of 8.5%. On the grounds that London is being used as a control in this investigation (because gentrification processes need to be occurring faster in Harringay than the London average for Harringay to be said to be gentrified) this would provide further evidence that Harringay is not being gentrified. 18

Cornelia Bentsen - Geography

Cornelia Bentsen Sevenoaks School Extended Essay: Geography To what Beentsen xtent is Harringay gentrified? Extended Essay: Geography Cornelia Sevenoaks S chool Cornelia Bentsen Sevenoaks School Extended Essay: Geography To what extent is Harringay gentrified? To what extent is Harringay gentrified? Conversely it is worth noting that the boroughs Newham and Waltham Forest, which are also being used as points of comparison in this investigation, actually Conversely is worth noting the boroughs Newham and Waltham Conversely it is it worth noting that that the boroughs Newham and Waltham Forest, Forest, faced percentage decreases. This doesn’t change the fact that Harringay can’t be which are also being used as points of comparison in this investigation, actually which are also being used as points of comparison in this investigation, actually completely gentrified due to its miniscule increase in people employed in Higher faced percentage decreases. This doesn’t change the fact that Harringay can’t be faced percentage decreases. This doesn’t change the fact that Harringay can’t be Managerial, Occupations, but it to completely gAdministrative entrified ue to mand its mProfessional iniscule increase in people employed in help Higher completely gentrified due dto its iniscule increase in people employed in does Higher stop the changes in Harringay’s occupational structure serving to disprove that Managerial, Administrative Professional Occupations, it help does to help to Managerial, Administrative and and Professional Occupations, but it but does any g entrification h as h appened i n H arringay a s s uch t rends a re n ot u nusual. stop the changes in Harringay’s occupational structure serving to disprove that stop the changes in Harringay’s occupational structure serving to disprove that any gentrification happened in Harringay as strends uch trends are not unusual. any gentrification has hhas appened in Harringay as such are not unusual. 10 10 10 % Change % C% hange Change

5 0

5 5 0 0

Percentage change in people employed in Higher Percentage change in pieople employed in Higher Percentage change n people employed in Higher Managerial, Professional and Administrative Managerial, Professional and aA2nd dministrative Managerial, Professional Administrative Occupations between 001 and 2011 Occupations between 2001 and 2 Occupations between 2001 a011 nd 2011

Harringay London Harringay average London Harringay London -‐5 average average -‐5 -‐5

-‐10 -‐10 -‐10

Brent Haringey Newham Waltham Brent Haringey Newham Waltham Forest Brent Haringey Newham Forest Waltham Forest

-‐15 -‐15 -‐15

Again large inequalities between LSOAs existed. Haringey showed large Again inequalities between LSOAs existed. Haringey 023C 023C showed the the largest percentage decrease in middle/upper class persons. On the showed other Again large inequalities between LSOAs class existed. Haringey 023C the largest percentage decrease in middle/upper persons. On the other hand hand Haringey and and 023D experienced at least a 10% increase, which is more Haringey 023A 023D experienced at least a 10% increase, which is more largest 023A percentage decrease in middle/upper class persons. On the other hand than all all the the outer London boroughs investigated and a London itself. itself. This would than outer London boroughs investigated and This Haringey 023A and 023D experienced at least 10% London increase, which is would more suggest that some areas are are being gentrified whilst others are either being suggest that some areas being gentrified whilst others are either being than all the outer London boroughs investigated and London itself. This would gentrified ess loess r nare ot t ot all. gentrified considerably or anbeing at agentrified ll. suggest considerably that some lareas whilst others are either being gentrified considerably less or not at all.

Cornelia Bentsen - Geography

Cornelia Bentsen Sevenoaks School Extended Essay: Geography Cornelia Bentsen Sevenoaks School Extended Essay: Geography To what extent is Harringay gentrified? To what extent is Harringay gentrified?

Percentage change in people employed in Higher Percentage change in people employed in Higher Managerial, Professional or Administrative Occupations Managerial, Professional or Administrative Occupations between 2001 2011 within Harringay between 2001 and a2nd 011 within Harringay

30 30 10 10

0 Haringey Haringey Haringey Haringey Haringey Haringey Haringey Haringey Haringey Haringey Haringey Haringey Haringey Haringey -‐10 -‐10 031C 031C 031B 031B 031A 031A 023B 023B 023D 023D 023A 023A 023C 023C 0

% Change

20 20

-‐20 -‐20 -‐30 -‐30 -‐40 -‐40 -‐50

-‐50

However for this indicator of gentrification there was a problem with collecting However for this indicator of gentrification there was a problem with collecting the data because the census categories were slightly different in 2001 and 2011. the data because the census categories were slightly different in 2001 and 2011. In 2001 there were the following two categories, amongst others, under National In 2001 there were the following two categories, amongst others, under National Statistics Socio-‐economic Classification (NS-‐SeC); Large Employers and Higher Statistics Socio-‐economic (NS-‐SeC); OLarge Employers Managerial Occupations as well Classification as Higher Professional ccupations. In 2011 and this Higher Managerial O ccupations a s w ell a s H igher P rofessional O ccupations. I n 2011 this had changed so there was only one category called Higher Managerial, had changed so there was only one category called Higher Managerial, Administrative and Professional Occupations. In an attempt to account for these Administrative and Professional Occupations. In an attempt to account for these changes the two categories in 2001 were merged and then renamed as was changes the two categories in 2001 were merged customary for the 2011 NS-‐SeC. Therefore the 2001 and and 2011 then data renamed categories as was customary for the 2011 NS-‐SeC. Therefore the 2001 and 2011 data categories are similar but by no means the same and will have consequently caused are similar but by for no this means the osame and will have consequently caused inaccuracies in the data indicator f gentrification. inaccuracies i n t he d ata f or t his i ndicator o f gentrification. -‐ Hypothesis 5 -‐ “ The percentage of people doing “skilled labour” will -‐have Hypothesis 5etween -‐ “ The 2p001 ercentage of p eople doing “skilled labour” will increased b and 2011 in Harringay.” have increased between 2001 and 2011 in Harringay.” Other than Higher Managerial, Administrative or Professional Occupations, gentrifiers are commonly employed in SAdministrative killed Trades Occupations (as defined by Other than Higher Managerial, or Professional Occupations, the gentrifiers ONS’s 2010 Standard Occupational The Osubsequent are commonly employed Classification.) in Skilled Trades ccupations (column as defined by graphs make evident, not only has the percentage of people employed in skilled the ONS’s 2010 Standard Occupational Classification.) The subsequent column trades occupations increased rapidly in Harringay between 2001 and 2011, but graphs make evident, not only has the percentage of people employed in skilled the trades occupations increased rapidly in Harringay between 2001 and 2011, but rate of change in Harringay is also considerably faster than the London average. the rate of change in Harringay is also considerably faster than the London average. Despite this, two out of the eight boroughs being used for comparison have faster rates of increase than Harringay. One of these is Haringey, which makes Despite this, two out of the eight boroughs being used for comparison have faster Harringay’s rate of increase relatively unimpressive and Harringay’s rates of increase than Harringay. One of these is Haringey, which makes gentrification status more debatable. Harringay’s rate of increase relatively unimpressive and Harringay’s gentrification status more debatable.

Cornelia Bentsen - Geography

% C% hange Change

Cornelia Bentsen Sevenoaks School Extended Essay: Geography To w hat e xtent i s H arringay g entrified? Extended Essay: Geography Cornelia Bentsen Sevenoaks S chool To what extent is Harringay gentrified? Percentage change of people employed in Skilled Trade Occupations etween 2001 and Percentage change of pbeople employed in 2S011 killed Trade Occupations between 2001 and 2011 40

35 40 30 35 25 30 20 25 15 20 10 15 5 10 0 5 -‐5 0 -‐5

Hypothesis 6 -‐ “The percentage of people with a level 4 or 5 qualification have ipercentage ncreased between 2001 with and 2a 011.” Hypothesis 6 will -‐ “The of people level 4 or 5 qualification will have increased between 2001 and 2011.” As foreshadowed by the table in the investigation plan on page 9, the qualification level of was used as plan a proxy for average As foreshadowed by Harringay the table residents in the investigation on page 9, the income. This is because those with a graduate degree earn on average £200,000 qualification level of Harringay residents was used as a proxy for average more than those without a degree in the UK throughout the course of their income. This is because those with a graduate degree earn on average £200,000 lifetimes (Graduates, 2013.) Consequently if the percentage of people with level more than those without a degree in the UK throughout the course of their 4/5 qualifications in Harringay has increased the average income of Harringay lifetimes (Graduates, 2013.) Consequently if the percentage of people with level residents would have increased. has 4/5 qualifications in Harringay increased the average income of Harringay residents would have increased. The bar chart details the 13.3% increase in the percentage of people who have a level b4ar ocr hart 5 qualification Harringay. This nearly double otf he rate ow f ho change The details the i1n 3.3% increase in its he percentage people have in a the borough of Haringey, in indicating that Harringay is ouble being the gentrified. The fact level 4 or 5 qualification Harringay. This is nearly d rate of change in that borough Harringay didn’t change as fast that as London is less significant because the the of Haringey, indicating Harringay is being gentrified. The fact comparison is less valid than as that outer London boroughs because the that Harringay didn’t change fast with as London is less significant because the London average includes inner London, which has a very different socio-‐ comparison is less valid than that with outer London boroughs because the economic average climate includes to Harringay. Similarly which the comparison Newham is London inner London, has a very with different socio-‐ unreliable because Newham was so deprived in 2001, that barely any residents economic climate to Harringay. Similarly the comparison with Newham is had level 4/5 qualifications. This means that any increase in the qualification unreliable because Newham was so deprived in 2001, that barely any residents level in Newham was exaggerated onsiderably when put in a in percentage format. had level 4/5 qualifications. This cmeans that any increase the qualification level in Newham was exaggerated considerably when put in a percentage format. -‐ -‐

Cornelia Bentsen - Geography

Cornelia Bentsen Sevenoaks School Extended Essay: Geography To what extent is Harringay gentrified?

Percentage change in people with level 4/5 quali_ications between 2001 and 2011

45 40 35 30 25 20 15 10 5 0

-‐

H LSOA average % change

London % change

Haringey % Brent % Change Newham % Waltham Forest Change Change % Change

Hypothesis 7 – “The median house prices in Harringay will have risen and at a faster rate than London as well as other comparable London Boroughs between 1991 and 2011.”

When gentrification occurs middle class homeowners invest in property improvement, resulting in higher quality properties. This has the knock on effect of stimulating demand and changing the perception of the area. The result is significantly higher house prices, with house prices increasing rapidly initially and slowing down as the area becomes more heavily gentrified. This theory forms the foundations of hypothesis 8. The line graph below shows hypothesis 7 to be correct, as the median house price in Harringay has augmented precipitously between 1995 and 2014 from under £100,000 to over £450,000. Initially the growth of house prices experienced by houses in Harringay was slightly slower than that of London and roughly average relative to other outer London boroughs, indicating that gentrification had not yet taken effect in Harringay. However in 2004 the median house price in Harringay overtook the median house price in Outer London, before going on to overtake the median house price in London as a whole in 2005. Furthermore with the exception of 2008 and 2009 (post global financial crisis,) house prices in Harringay have experienced indisputably faster, albeit less steady, growth than all other areas being used for comparison on the graph. Growth in 2013 and 2014 has been especially rapid, with house prices increasing by over £125000 in just 2 years and this trend looks set to continue. This demonstrates that the processes being experienced in Harringay are an exception to other similar areas in London and this, because gentrification is relative, proves Harringay is being gentrified. 22

Cornelia Bentsen - Geography

Cornelia Bentsen Sevenoaks School Extended Essay: Geography To what extent is Harringay gentrified?

Median House Prices 1995 -‐ 2014

500,000 450,000 400,000 350,000 300,000 250,000

The median house price in Harringay has increased fastest and to the highest level. All house prices dropped temporarily post jinancial crisis.

Ealing

Greenwich Haringey

Lewisham

150,000

Newham Median(£)-‐1995 Median(£)-‐1996 Median(£)-‐1997 Median(£)-‐1998 Median(£)-‐1999 Median(£)-‐2000 Median(£)-‐2001 Median(£)-‐2002 Median(£)-‐2003 Median(£)-‐2004 Median(£)-‐2005 Median(£)-‐2006 Median(£)-‐2007 Median(£)-‐2008 Median(£)-‐2009 Median(£)-‐2010 Median(£)-‐2011 Median(£)-‐2012 Median(£)-‐2013 Median(£)-‐2014

100,000 0

Barnet Brent

200,000 50,000

Barking And Dagenham

Redbridge

Waltham Forest Outer London London

Harringay Average

The following graph makes evident the large inequalities between LSOAs in Harringay. The largest disparity in median house prices, between Haringey 023D and Haringey 023B, is over £300,000. This highlights how, although there might be overarching trends in Harringay, there is variation between LSOAs in terms of the extent to which the trends are present.

Median House Prices in Harringay

700,000 600,000 500,000

Haringey 023A

400,000

Haringey 023B

300,000

Haringey 031A

200,000 0

Haringey 031B Median(£)-‐1995 Median(£)-‐1996 Median(£)-‐1997 Median(£)-‐1998 Median(£)-‐1999 Median(£)-‐2000 Median(£)-‐2001 Median(£)-‐2002 Median(£)-‐2003 Median(£)-‐2004 Median(£)-‐2005 Median(£)-‐2006 Median(£)-‐2007 Median(£)-‐2008 Median(£)-‐2009 Median(£)-‐2010 Median(£)-‐2011 Median(£)-‐2012 Median(£)-‐2013 Median(£)-‐2014

100,000

Haringey 031C Haringey 023C

Haringey 023D

Cornelia Bentsen - Geography

Cornelia Bentsen Sevenoaks School Extended Essay: Geography To what extent is Harringay gentrified? The chloropleth map below reinforces this idea by showing the most (darkest) to least gentrified LSOAs (palest) in Harringay in terms of percentage changes in house prices between 1995 and 2014. Turnpike Surprisingly gentrification Lane occurred faster in Haringey 023B and 023D than in Haringey 031A, 031B and 023A because they are closer to the Haringey 023C was the busy, noisy and often congested least gentrified LSOA in road Harringay Green Lanes. Harringay – house price Reasons for this could be that percentage change was they are further away from the relatively slow at 230%. all the stations, meaning they This is due to its proximity experience less traffic. to Hornsey Train Depot and the heavy traffic flow along Turnpike Lane. Harringay Green Lanes

A typical view from a house on Endymion road of Finsbury Park.

Haringey 013C was the most gentrified LSOA – it experienced an 800% percentage increase in house prices between 1995 and 2014. This can be explained by the views residents in Haringey 013C have of Finsbury park. Moreover houses surrounding the park are the largest in the area, causing them to be popular for families moving out of central London in search of more space. 24

Cornelia Bentsen - Geography

Cornelia Bentsen Sevenoaks School Extended Essay: Geography To what extent is Harringay gentrified? -‐ Hypothesis 8 – “The environmental quality of Harringay will higher than that of St Ann’s.” Environmental quality is an alternative indicator that can be used to reflect improvements to the quality of the Harringay area. Using the sampling technique described on page 10, an environmental quality survey was conducted along the transect represented on the map by the orange line. Using a random generator a street in Harringay was selected and then followed linearly into St Ann’s to create the transect route along Seymour Lane and then St Ann’s road. The results of Hypothesis 8’s examination are shown on the map, where the recorded environmental quality index score at each point on the transect is indicated (data points are at intervals of 20 housing units.) The maximum possible score for the index is 34, meaning that the houses in Harringay had a moderately high score, but more so in relative than absolute terms. The average index score in Harringay was 27.5. In relation to this the average index score St Ann’s was 15.5 – 12 points lower than in Harringay. This data therefore supports hypothesis 8 that the environmental quality of Harringay is higher than that of St Ann’s and proves that aesthetically Harringay is gentrified.

Cornelia Bentsen Sevenoaks Extended Essay: Geography Cornelia Bentsen - Geography School To what extent is Harringay gentrified?

The transect route is shown in orange. It then carries on slightly further into St Ann’s in the direction specified.

Cornelia Bentsen - Geography

Cornelia Bentsen Sevenoaks School Extended Essay: Geography To what extent is Harringay gentrified?

15/06/2015

This photograph (letter A on the map above) was taken looking down Seymour street and displays the typical qualities of streets on the Harringay ladder. In contrast St Ann’s road is dirtier with more litter and poorly maintained buildings, as portrayed in the photographs below (letter B in the map above.)

15/06/2015

Cornelia Bentsen - Geography

Cornelia Bentsen Sevenoaks School Extended Essay: Geography To what extent is Harringay gentrified?

15/06/2015

The reason for higher environmental quality in Harringay is increased affluence in the area (from gentrifiers) increasing the wealth of the local council and providing demand for improved public services to maintain and improve Harringay. The result is Harringay becoming smarter, cleaner and more attractive. -‐ Hypothesis 9 – “The number of properties undergoing renovation will be higher in Harringay than in St Ann’s.” This housing renovation survey based its judgements on whether the house had scaffolding on it or whether there was some form of industrial waste disposal unit outside the house. The prediction of hypothesis 9 was derived from the idea that renovation proves the houses in Harringay are being improved and gentrified. On Seymour Lane, 1 in every 20 houses was undergoing renovation but in St Ann’s no houses on the transect route were being renovated. This is represented visually on the graph below and provides clear evidence to say Harringay is being gentrified.

Cornelia Bentsen - Geography

Cornelia Bentsen Sevenoaks School Extended Essay: Geography To what extent is Harringay gentrified?

Number of houses undergoing renovation

4.5 4

3.5 3

2.5 2

1.5 1

0.5 0

West Harringay

East Harringay

St Ann's

-‐ Hypothesis 10 -‐“ The qualitative data resulting from telephone interviews with Harringay estate agents will provide evidence that Harringay is gentrified.” During telephone interviews with numerous Harringay estate agents (including the branch manager of Bairstow Eves and estate agents from Teepee Properties and Anthony Peep & Co,) it was apparent that people in Harringay thought it was being gentrified. According to Navide Kazi, branch manager of Bairstow Eves, the price of a four bedroom Victorian house on the ladder has gone up by over £300,000 in the last 2 years and he does not think these phenomenal increases in house prices are going to slow down. In fact Mr Kazi’s can see prices as “only going up” in the future. All of the estate agents shared the view that the Harringay housing market is very “buoyant” at the moment and that demand has picked up significantly over the last 10 years, although more recent years have shown the fastest rises in demand. “5 years ago a run down property would stay vacant for as long as 3 years in some cases, today they are sold within months or picked up for renovation by the local council,” says an estate agent at Teepee Properties. A large proportion of buyers entering the market have been young, middle class professionals (yuppies) attracted to the ladder by the reasonable prices (relative to inner London,) its accessibility, abundance of local services and “trendy” reputation. Many have reached the stage in the family life cycle model where they are looking to start families and need more space than can be found in central London. These are exactly the kind of people that one would expect to see when gentrification happens in an area. However this was not reflected in the the census data relating to the changes in occupational structure in Harringay. Nevertheless Harringay has changed. New residents have dispersed local culture as social displacement has occurred. On the plus side the environmental quality has improved as the local council has started to take better care of the public

Cornelia Bentsen - Geography

Cornelia Bentsen Sevenoaks School Extended Essay: Geography To what extent is Harringay gentrified? spaces. There is less litter, more greenery and the area “feels” safer. Despite these positive changes to Harringay, one estate agent went as far as to say that Harringay had peaked and demand has spilled over into surrounding wards where good value housing is not a myth. These side effects of gentrification observed by Harringay estate agents, among other information from the interviews, support Hypothesis 10. Where in Harringay is the most gentrified? The analysis presented above demonstrates the overall level of gentrification within Harringay. However, there are significant spatial inequalities within Harringay which can be examined further by analysing results from the seven different LSOAs which make up the study area. In order to assess these differences, a gentrification index was created using four indicators; – Percentage change in median house prices between 2001 and 2011; – Percentage change in the proportion of people employed in Higher Managerial, Professional and Administrative occupations between 2001 and 2011; – Percentage change in the proportion of people with level 4/5 qualifications between 2001 and 2011; – Percentage change in the proportion of students and immigrants living in Harringay between 2001 and 2011. The score of each LSOA for a given indicator was classified as either very high, high, average, low and very low. Each grade was awarded a different number of points ranging from 5 (very high) to 1 (very low.) Thus the maximum score for each LSOA is 20. Evidently there are significant disparities in Harringay because 4 LSOAs have an index score of 15 or over, and are therefore definitely experiencing gentrification, whilst the least gentrified LSOAs have scores as low as 4 points, meaning they are barely gentrified. The reasons for these internal disparities in Harringay are due to variations in noise and traffic levels, as explained on page 21. The raw data is shown in the table below and is also represented visually on the chloropleth map on page 26. Lower Super Output Area Index Score Haringey 023D 18 Haringey 023B 17 Haringey 031C 16 Haringey 031B 15 Haringey 031A 12 Haringey 023A 7 Haringey 023C 4 30

Cornelia Bentsen Sevenoaks School Extended Essay: Geography To what extent is Harringay gentrified? Cornelia Bentsen - Geography Haringey 023C ranks as the least gentrified LSOA and this essay would argue that gentrification has not occurred here because it predominantly experienced worse or similar scores to London in the analysis.

Haringey 023D is the most gentrified LSOA in Harringay because it is located in the middle of the ladder on relatively quiet streets.

27 31

Cornelia Bentsen - Geography

Cornelia Bentsen Sevenoaks School Extended Essay: Geography To what extent is Harringay gentrified? 4. Conclusion: The following table below presents the outcomes of the investigation. A traffic light colour scheme is used to signify the level of gentrification for each indicator. INDICATOR OF GENTRIFICATION OUTCOME – GENTRIFIED OR NOT? Migrant and student population changes.

House prices.

Percentage of people employed in routine occupations.

Percentage of people employed in Higher Managerial, Administrative or Professional occupations. Percentage of people with a level 4 or 5 qualification.

Percentage of people classified as skilled labour.

Cornelia Bentsen - Geography

Cornelia Bentsen Sevenoaks School Extended Essay: Geography To what extent is Harringay gentrified? Environmental quality.

Number of renovation.

houses

undergoing

Percentage of jobseeker’s allowance claimants.

Telephone interviews with Harringay estate agents.

The majority of evidence supports the overall hypothesis of this investigation that Harringay has been gentrified. The outcomes of 6 different hypotheses suggest gentrification has, and still is, occurring in Harringay while only 1 contradict this and 3 are neutral. However, now that it has been established that Harringay is being gentrified the extent to which Harringay is gentrified must be deduced in order to answer the research question. Due to the fact that the rates of change in Harringay have been so high, this essay concludes that Harringay is gentrified to a limited extent because the process of gentrification is still in motion in Harringay. If Harringay were gentrified to a significant extent then very fast rates of change would have been expected between 1991 and 2001 and then much slower rates of change, comparable to the average London level, as the process comes to an end between 2001 and 2011. This has not been the case because rates of change in Harringay have been exceptionally high between 2001 and 2011. 33

Cornelia Bentsen - Geography

Cornelia Bentsen Sevenoaks School Extended Essay: Geography To what extent is Harringay gentrified? The conclusion of the sub investigation into varying rates of gentrification within Harringay has resulted the following outcomes; Harringay LSOA Gentrified or not? Haringey 023B

Haringey 023D

Haringey 031C

Haringey 031B

Haringey 031A

Haringey 023A

Haringey 023C

The same key was used as above meaning that Haringey 023B, 023D, 031B and 031C are gentrified whilst Haringey 031A is to a limited extent and Haringey 023A and 023C are not gentrified. The conclusion of this investigation, that Harringay is being gentrified, has an impact on the theory behind gentrification as stated in the introduction on page 4. This is because it proves that gentrification can be a centrifugal urban movement, attracting people out of the inner city into more suburban areas that

Cornelia Bentsen - Geography

Cornelia Bentsen Sevenoaks School Extended Essay: Geography To what extent is Harringay gentrified? are being gentrified. Additionally it highlights a subtle shift in the nature of gentrification. The gentrification of Victorian housing in Harringay has resulted in the overall uplift of all house prices across Harringay. This has incentivized numerous modern infill developments and the regeneration of the notoriously deprived Woodsberry Down estate (located in the North of Hackney, bordering Harringay) (The Guardian (1), 2014) from which developers stand to make significant amounts of profit. Subsequently it can be concluded that the property mix of areas being gentrified is changing and patterns of gentrification are getting harder to discern across London. (Butler, T, 2007) This reflects the fragmentation of the term gentrification and makes it less useful in an academic context because its definition and connotations are considerably broader. The validity of this study’s outcomes would be enhanced by doing more primary fieldwork in order to gain a deeper insight into the social climate of Harringay and its housing market. Such fieldwork could include more extensive environmental quality studies that covered a wider area as well as qualitative interviews with Harringay residents. This would allow more accurate conclusions to be drawn.

Cornelia Bentsen - Geography

Cornelia Bentsen Sevenoaks School Extended Essay: Geography To what extent is Harringay gentrified? Appendix: (1): Qualities being assessed

1. Well designed / pleasing to the eye 2. In good condition 3. Evidence of maintenance / improvement 4. Outside – land, gardens or open space are in good condition 5. No vandalism evident 6. Roads have no traffic congestion 7. Parking is easy; garages or spaces provided 8. No traffic noise 9. Safeforpeople 10. No smell from traffic or other pollution 11. Large gardens or open space outside house 12. Trees and shrubs visible from close by 13. Public parks within easy distance 14. No litter 15. Roads well maintained with paving etc. well kept 16. Close to public transport 17. Close to shops, amenities or services

High Generally +2 fine +1

Av. Generally 0 poor -1

Very poor -2

Poorly designed / ugly In poor condition Poorly maintained / no improvement Outside – no gardens, or land / open space in poor condition Extensive vandalism Streets badly congested Parking is very difficult; no parking provision High noise volume from traffic Dangerous for people Obvious smell from traffic or other pollution No garden / open space – door opens to street No greenery visible from house No public parks easily accessible Much litter Roads poorly maintained with paving etc. broken Long way from public transport Remote from shops, amenities / services

Cornelia Bentsen - Geography

Cornelia Bentsen Sevenoaks School Extended Essay: Geography To what extent is Harringay gentrified? Bibliography: – Homes and property. 2012. Harringay Ladder is urban, diverse -‐ and still great value. [ONLINE] Available at: http://www.homesandproperty.co.uk/area-‐guides/greater-‐ london/harringay-‐ladder-‐urban-‐diverse-‐and-‐still-‐great-‐value. [Accessed 10 September 15]. – Evening Standard. 2014. London's hottest hipster hangouts all begin with H. [ONLINE] Available at: http://www.standard.co.uk/goingout/attractions/londons-‐hottest-‐ hipster-‐hangouts-‐all-‐begin-‐with-‐h-‐9175905.html. [Accessed 10 September 15]. – Lees, L. Slater, T. Wyly, E, 2007. Gentrification. 1st ed. Milton: Routledge. – Cortright, J, 2015. The Perils of Conflating Gentrification and Displacement: A Longer and Wonkier Critique of Governing’s Gentrification Issue. City Observatory, [Online]. Available at: http://cityobservatory.org/longer-‐governing-‐response/ [Accessed 28 July 2015] – The Economist. 2014. Chasing Cool. [ONLINE] Available at: http://www.economist.com/blogs/blighty/2014/04/gentrification-‐ london. [Accessed 10 June 15]. – Smith, N. (2000) “Gentrification” in R.J. Johnston, D. Gregory, G. Pratt and M. Watts (eds.) The Dictionary of Human Geography 4th ed. (Oxford: Blackwell) 294-‐296. – Wikipedia. 2015. Harringay. [ONLINE] Available at: https://en.wikipedia.org/wiki/Harringay. [Accessed 11 July 15]. – London Councils Directory, (2014), Borough Map [ONLINE]. Available at: http://directory.londoncouncils.gov.uk [Accessed 12 July 15]. – The Smart School Councils, (2014), Haringey Ward Map [ONLINE]. Available at: http://www.haringeygreens.org.uk/haringey_green_party_get_the_word_ out [Accessed 12 July 15]. – Neighbourhood Statistics, 2015. Harringay. [ONLINE] Available at: http://www.neighbourhood.statistics.gov.uk/dissemination/AreaListMa pSelection.do. [Accessed 01 August 15]. – Shelley, T, 2007. Exploited: Migrant Labour in the New Global Economy. 1st ed. London: Zed Books. – Graduates. 2013. The Graduate Premium: Graduates Earn £200,000 more than those without a degree. [ONLINE] Available at: http://www.graduates.co.uk/the-‐graduate-‐premium/. [Accessed 22 July 15]. – The Guardian. 2014. The truth about gentrification: regeneration or con trick? [ONLINE] Available at: http://www.theguardian.com/society/2014/may/18/-‐sp-‐truth-‐about-‐ gentrification-‐how-‐woodberry-‐down-‐became-‐woodberry-‐park. [Accessed 24 September 15]. – BUTLER, T. (2007), Re-‐urbanizing London Docklands: Gentrification, Suburbanization or New Urbanism?. International Journal of Urban and Regional Research, 31: 759–781. doi: 10.1111/j.1468-‐2427.2007.00758.x

Cornelia Bentsen - Geography

Bolurin Edun - Mathematics

How significant is the effect of a constant horizontal air resistance on projectile path?

39 39

Bolurin Edun - Mathematics

Bolurin Edun - Mathematics I chose a question on projectile motion because it is a topic in Physics that I find interesting, and I was curious about how particles behave once one disregards some of the assumptions of the model – like the presence of air resistance and a launch height. I worked with a model for air resistance that determined the size of the resistive force with a constant ‘k’. I found it difficult to determine the equations that define the particle’s motion, and present them on a graph in a simple, straightforward way. However, I really enjoyed finding out how the air resistance affected projectile path, and I learned how difficult it is to actually form an accurate model for air resistance.

Supervisor: Gillian Williams Bolurin wrote a superb Mathematics Extended Essay; looking at projectile behaviour he was able to outline the key concepts with clarity getting to grips with the fundamental theories from the outset. Bolurin approached his work with maturity and independence. Solving the flight path can yield interesting results, and Bolurin displayed plenty of initiative and perseverance to consider the effects of different parameters. With the addition of air resistance, these equations can become very intriguing and quite complex, and it takes considerable endeavour in order to first, understand the concepts and second, put the mathematical techniques into action. Bolurin showed great mastery in his interpretation ultimately producing a sophisticated piece of work.

Bolurin Edin - Mathematics

Contents Introduction

Projectile path in ideal conditions

Projectile with launch height

Projectile with horizontal air resistance

Different variations of projectile path

Summary

Conclusion

Bibliography

Abstract The research question of this essay is â&#x20AC;&#x153;How significant is the effect of constant horizontal air resistance on projectile path?â&#x20AC;? I start by mapping the path in simple ideal conditions; that is where air resistance is negligible and the projectile is launched from level ground. I then go on to include launch height and then air resistance acting in the horizontal direction alone, and compare them to the initial path observed to see the differences. To do this, I insert certain values into the equations for projectile path and map the graphs produced using Wolfram Mathematica. Analysing the different graphs allowed me to draw the conclusion that constant air resistance has the considerable effect of distorting the simple parabolic path of a projectile, making the flight path oblique in shape.

the Â initial Â path Â observed Â to Â see Â the Â differences. Â To Â do Â this, Â I Â insert Â certain Â values Â into Â the Â equations Â for Â projectile Â path Â and Â map Â the Â graphs Â produced Â using Â Wolfram Â Mathematica. Â Analysing Â the Â different Â graphs Â allowed Â me Â to Â draw Â the Â conclusion Â that Â constant Â air Â resistance Â has Â the Â considerable Â effect Â of Â distorting Â the Â simple Â parabolic Â pBolurin ath Â oEdun f Â a Â p-rojectile, Â Mathematicsmaking Â the Â flight Â path Â oblique Â in Â shape. Â Â Word Â Count: Â 130 Â Â

Introduction Â I Â came Â across Â the Â idea Â for Â my Â research Â question Â in Â my Â mechanics Â extension Â course, Â where Â we Â go Â into Â more Â detail Â with Â the Â mathematics Â involved Â in Â solving Â physics Â problems Â than Â is Â done Â in Â the Â Higher Â Level Â Physics Â course. Â Projectile Â motion Â is Â one Â of Â the Â topics Â we Â covered Â extensively Â in Â the Â course, Â so Â I Â had Â a Â good Â background Â on Â which Â to Â base Â my Â investigation. Â Furthermore, Â throughout Â the Â course Â we Â neglected Â the Â effects Â of Â air Â resistance Â on Â the Â trajectory Â of Â a Â projectile. Â In Â real Â life, Â however, Â air Â resistance Â does Â have Â quite Â an Â important Â effect Â on Â projectiles Â and Â needs Â to Â be Â taken Â into Â account Â when Â designing Â objects Â that Â fly Â through Â the Â air, Â for Â example: Â missiles, Â golf Â balls Â and Â planes. Â The Â knowledge Â of Â air Â resistance Â is Â used Â everyday, Â and Â is Â quite Â important Â as Â miscalculations Â in Â the Â designing Â of Â an Â airplane Â wing, Â for Â example, Â could Â mean Â the Â loss Â of Â many Â lives. Â Thus, Â I Â was Â persuaded Â to Â investigate Â the Â effect Â of Â air Â resistance Â on Â projectile Â motion Â to Â further Â extend Â my Â knowledge Â of Â projectiles. Â Â A Â mechanics Â STEP Â question Â asked Â to Â find Â the Â shape Â of Â the Â flight Â path Â of Â a Â projectile Â that Â is Â affected Â by Â a Â constant Â horizontal Â air Â resistance Â that Â is Â proportional Â to Â gravity. Â This Â presented Â a Â good Â starting Â point Â for Â my Â essay Â that Â would Â investigate Â how Â significant Â this Â effect Â is Â on Â projectile Â path. Â Â Â Â Projectile Â path Â Â Â The Â path Â of Â a Â projectile Â is Â graphed Â by Â obtaining Â an Â equation Â for Â the Â flight Â path Â using Â Newtonâ&#x20AC;&#x2122;s Â equations Â of Â motion. Â To Â start, Â I Â shall Â derive Â the Â equations Â of Â motion Â for Â constant Â acceleration Â â&#x20AC;&#x201C; Â the Â first Â assumption Â I Â make Â in Â my Â investigation Â is Â that Â acceleration Â is Â always Â constant. Â Â Â đ?&#x2018;&#x17D;đ?&#x2018;&#x17D; =

đ?&#x2018;&#x2018;đ?&#x2018;&#x2018;đ?&#x2018;&#x2018;đ?&#x2018;&#x2018; Â đ?&#x2018;&#x2018;đ?&#x2018;&#x2018;đ?&#x2018;&#x2018;đ?&#x2018;&#x2018;

Acceleration, Â â&#x20AC;&#x2DC;aâ&#x20AC;&#x2122;, Â is Â the Â rate Â of Â change Â of Â velocity Â with Â respect Â to Â time, Â so Â to Â get Â the Â equation Â for Â velocity, Â we Â integrate Â acceleration Â with Â respect Â to Â time. Â Â đ?&#x2018;Łđ?&#x2018;Ł =

đ?&#x2018;&#x17D;đ?&#x2018;&#x17D; Â Â đ?&#x2018;&#x2018;đ?&#x2018;&#x2018;đ?&#x2018;&#x2018;đ?&#x2018;&#x2018; = đ?&#x2018;&#x17D;đ?&#x2018;&#x17D;đ?&#x2018;&#x17D;đ?&#x2018;&#x17D; + đ?&#x2018;?đ?&#x2018;? Â

3 Â

Bolurin Edun - Mathematics

At Â time Â t Â = Â 0 Â the Â velocity Â is Â equal Â to Â c, Â so Â c Â is Â the Â initial Â velocity Â u. Â Thus Â the Â formula Â is Â written Â as: Â At Â time Â t Â = Â 0 Â the Â velocity Â is Â equal Â to Â c, Â so Â c Â is Â the Â initial Â velocity Â u. Â Thus Â the Â formula Â is Â written Â as: Â đ?&#x2018;Łđ?&#x2018;Ł = đ?&#x2018;&#x17D;đ?&#x2018;&#x17D;đ?&#x2018;&#x17D;đ?&#x2018;&#x17D; + đ?&#x2018;˘đ?&#x2018;˘ Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â (1) Â đ?&#x2018;Łđ?&#x2018;Ł = đ?&#x2018;&#x17D;đ?&#x2018;&#x17D;đ?&#x2018;&#x17D;đ?&#x2018;&#x17D; + đ?&#x2018;˘đ?&#x2018;˘ Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â (1) Â The Â velocity Â â&#x20AC;&#x2DC;vâ&#x20AC;&#x2122;, Â is Â the Â rate Â of Â change Â of Â the Â distance Â from Â a Â fixed Â point Â with Â respect Â to Â time, Â so Â to Â get Â the Â equation Â for Â distance, Â we Â integrate Â velocity. Â The Â velocity Â â&#x20AC;&#x2DC;vâ&#x20AC;&#x2122;, Â is Â the Â rate Â of Â change Â of Â the Â distance Â from Â a Â fixed Â point Â with Â respect Â to Â time, Â so Â to Â

get Â the Â equation Â for Â distance, Â we Â integrate Â velocity. Â 1 đ?&#x2018; đ?&#x2018; = đ?&#x2018;˘đ?&#x2018;˘ + đ?&#x2018;&#x17D;đ?&#x2018;&#x17D;đ?&#x2018;&#x17D;đ?&#x2018;&#x17D; Â đ?&#x2018;&#x2018;đ?&#x2018;&#x2018;đ?&#x2018;&#x2018;đ?&#x2018;&#x2018; = đ?&#x2018;˘đ?&#x2018;˘đ?&#x2018;˘đ?&#x2018;˘ + đ?&#x2018;&#x17D;đ?&#x2018;&#x17D;đ?&#x2018;Ąđ?&#x2018;Ą ! + đ?&#x2018;?đ?&#x2018;? Â 2 1 đ?&#x2018; đ?&#x2018; = đ?&#x2018;˘đ?&#x2018;˘ + đ?&#x2018;&#x17D;đ?&#x2018;&#x17D;đ?&#x2018;&#x17D;đ?&#x2018;&#x17D; Â đ?&#x2018;&#x2018;đ?&#x2018;&#x2018;đ?&#x2018;&#x2018;đ?&#x2018;&#x2018; = đ?&#x2018;˘đ?&#x2018;˘đ?&#x2018;˘đ?&#x2018;˘ + đ?&#x2018;&#x17D;đ?&#x2018;&#x17D;đ?&#x2018;Ąđ?&#x2018;Ą ! + đ?&#x2018;?đ?&#x2018;? Â 2 At Â time Â t Â = Â 0, Â the Â distance Â is Â zero Â as Â the Â particle Â will Â have Â not Â moved. Â Therefore Â the Â constant Â c Â is Â equal Â to Â t Â zero, Â o Â the Â general Â is Â formula Â At Â time Â = Â 0, Â sthe Â distance Â zero Â as Â is: Â the Â particle Â will Â have Â not Â moved. Â Therefore Â the Â constant Â c Â is Â equal Â to Â zero, Â so Â the Â general Â formula Â is: Â

đ?&#x2018; đ?&#x2018; = đ?&#x2018;˘đ?&#x2018;˘đ?&#x2018;˘đ?&#x2018;˘ + đ?&#x2018;&#x17D;đ?&#x2018;&#x17D;đ?&#x2018;Ąđ?&#x2018;Ą ! Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â (2) Â ! !

Â Â

Ideal Â Conditions Â Ideal Â Conditions Â

The Â most Â basic Â path Â of Â a Â projectile Â is Â observed Â when Â we Â assume Â it Â is Â launched Â from Â level Â ground, Â without Â spin Â and Â air Â of Â resistance Â is Â neglected. Â When Â a Â we Â projectile Â at Â an Â angle, Â initial Â The Â most Â basic Â path Â a Â projectile Â is Â observed Â when Â assume Â is Â it Â launched Â is Â launched Â from Â level Â its Â ground, Â velocity Â i s Â a Â v ector Â q uantity; Â i t Â h as Â m agnitude Â a nd Â d irection. Â A dding Â t wo Â v ectors Â t ogether Â p roduces Â a Â without Â spin Â and Â air Â resistance Â is Â neglected. Â When Â a Â projectile Â is Â launched Â at Â an Â angle, Â its Â initial Â resultant Â vector. Â Since Â this Â is Â true, Â the Â converse Â can Â be Â done, Â so Â it Â is Â possible Â to Â divide Â a Â vector Â into Â velocity Â is Â a Â vector Â quantity; Â it Â has Â magnitude Â and Â direction. Â Adding Â two Â vectors Â together Â produces Â a Â separate Â components Â which Â when Â added, Â will Â produce Â the Â initial Â vector1. Â When Â a Â projectile Â is Â resultant Â vector. Â Since Â this Â is Â true, Â the Â converse Â can Â be Â done, Â so Â it Â is Â possible Â to Â divide Â a Â vector Â into Â launched Â at Â an Â angle, Â its Â initial Â velocity Â vector Â can Â be Â divided Â into Â vertical Â separate Â components Â which Â when Â added, Â will Â produce Â the Â initial Â vector1. Â Where: Â When Â Â a Â projectile Â is Â and Â horizontal Â components. Â This Â is Â for Â ease Â of Â calculation, Â as Â vectors Â that Â launched Â at Â an Â angle, Â its Â initial Â velocity Â vector Â can Â be Â divided Â into Â vertical Â Where: Â Â are Â perpendicular Â to Â one Â another Â do Â not Â interact. Â So Â when Â a Â projectile Â is Â and Â horizontal Â components. Â This Â is Â for Â ease Â of Â calculation, Â as Â vectors Â that Â Sy Â = Â vertical Â distance Â / Â metres Â (m) Â launched Â at Â an Â angle Â đ?&#x153;&#x192;đ?&#x153;&#x192; Â to Â the Â horizontal, Â the Â formulae Â for Â the Â distance Â in Â are Â perpendicular Â to Â one Â another Â do Â not Â interact. Â So Â when Â a Â projectile Â is Â Sy Â = Â vertical Â distance Â / Â metres Â (m) Â Sx Â = Â horizontal Â d istance Â / Â m Â the Â vertical Â and Â horizontal Â directions Â respectively Â are Â given Â by: Â launched Â at Â an Â angle Â đ?&#x153;&#x192;đ?&#x153;&#x192; Â to Â the Â horizontal, Â the Â formulae Â for Â the Â distance Â in Â S Â = Â horizontal Â d istance Â / Â m Â t Â x= Â time Â / Â seconds Â (s) Â the Â vertical Â and Â horizontal Â directions Â respectively Â are Â given Â by: Â ! ! đ?&#x2018;&#x2020;đ?&#x2018;&#x2020;! = đ?&#x2018;˘đ?&#x2018;˘ sin đ?&#x153;&#x192;đ?&#x153;&#x192; đ?&#x2018;Ąđ?&#x2018;Ą â&#x2C6;&#x2019; đ?&#x2018;&#x201D;đ?&#x2018;&#x201D;đ?&#x2018;Ąđ?&#x2018;Ą Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â (3) Â ! t Â = Â time Â / Â seconds Â (s) Â -Ââ&#x20AC;?1 ! ! đ?&#x2018;&#x2020;đ?&#x2018;&#x2020;! = đ?&#x2018;˘đ?&#x2018;˘ sin đ?&#x153;&#x192;đ?&#x153;&#x192; đ?&#x2018;Ąđ?&#x2018;Ą â&#x2C6;&#x2019; đ?&#x2018;&#x201D;đ?&#x2018;&#x201D;đ?&#x2018;Ąđ?&#x2018;Ą Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â (3) Â u Â = Â initial Â velocity Â / Â ms Â ! đ?&#x2018;&#x2020;đ?&#x2018;&#x2020;! = đ?&#x2018;˘đ?&#x2018;˘ cos đ?&#x153;&#x192;đ?&#x153;&#x192; đ?&#x2018;Ąđ?&#x2018;Ą Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â (4) Â u Â = Â initial Â velocity Â / Â ms-Ââ&#x20AC;?1 Â g Â = Â acceleration Â due Â to Â gravity Â / Â ms-Ââ&#x20AC;?2 Â đ?&#x2018;&#x2020;đ?&#x2018;&#x2020;! = đ?&#x2018;˘đ?&#x2018;˘ cos đ?&#x153;&#x192;đ?&#x153;&#x192; đ?&#x2018;Ąđ?&#x2018;Ą Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â (4) Â g Â = Â acceleration Â due Â to Â gravity Â / Â ms-Ââ&#x20AC;?2 Â To Â obtain Â the Â flight Â path, Â we Â substitute Â for Â t Â into Â the Â Sy Â equation. Â Â Â To Â obtain Â the Â flight Â path, Â we Â substitute Â for Â t Â into Â the Â Sy Â equation. Â Â Â đ?&#x2018;&#x2020;đ?&#x2018;&#x2020;! Â đ?&#x2018;&#x2020;đ?&#x2018;&#x2020;! = đ?&#x2018;˘đ?&#x2018;˘ cos đ?&#x153;&#x192;đ?&#x153;&#x192; đ?&#x2018;Ąđ?&#x2018;Ą Â â&#x2020;&#x2019; đ?&#x2018;Ąđ?&#x2018;Ą = đ?&#x2018;˘đ?&#x2018;˘ cos đ?&#x2018;&#x2020;đ?&#x2018;&#x2020;! đ?&#x153;&#x192;đ?&#x153;&#x192; Â đ?&#x2018;&#x2020;đ?&#x2018;&#x2020;! = đ?&#x2018;˘đ?&#x2018;˘ cos đ?&#x153;&#x192;đ?&#x153;&#x192; đ?&#x2018;Ąđ?&#x2018;Ą Â â&#x2020;&#x2019; đ?&#x2018;Ąđ?&#x2018;Ą = đ?&#x2018;˘đ?&#x2018;˘ cos đ?&#x153;&#x192;đ?&#x153;&#x192;! đ?&#x2018;&#x201D;đ?&#x2018;&#x201D;đ?&#x2018;&#x2020;đ?&#x2018;&#x2020;! đ?&#x2018;&#x2020;đ?&#x2018;&#x2020;! đ?&#x2018;&#x2020;đ?&#x2018;&#x2020;! = đ?&#x2018;˘đ?&#x2018;˘ sin đ?&#x153;&#x192;đ?&#x153;&#x192; â&#x2C6;&#x2019; ! !! Â đ?&#x2018;˘đ?&#x2018;˘ cos 2đ?&#x2018;˘đ?&#x2018;˘đ?&#x2018;&#x201D;đ?&#x2018;&#x201D;đ?&#x2018;&#x2020;đ?&#x2018;&#x2020; cos đ?&#x2018;&#x2020;đ?&#x2018;&#x2020;! đ?&#x153;&#x192;đ?&#x153;&#x192; ! đ?&#x153;&#x192;đ?&#x153;&#x192; đ?&#x2018;&#x2020;đ?&#x2018;&#x2020;! = đ?&#x2018;˘đ?&#x2018;˘ sin đ?&#x153;&#x192;đ?&#x153;&#x192; â&#x2C6;&#x2019; ! Â đ?&#x2018;˘đ?&#x2018;˘ cos đ?&#x153;&#x192;đ?&#x153;&#x192; 2đ?&#x2018;˘đ?&#x2018;˘ cos ! đ?&#x153;&#x192;đ?&#x153;&#x192; This Â can Â be Â simplified Â to: Â This Â can Â be Â simplified Â to: Â

đ?&#x2018;&#x201D;đ?&#x2018;&#x201D;đ?&#x2018;Ľđ?&#x2018;Ľ ! Â ! ! đ?&#x153;&#x192;đ?&#x153;&#x192; 2đ?&#x2018;˘đ?&#x2018;˘ !đ?&#x2018;&#x201D;đ?&#x2018;&#x201D;đ?&#x2018;Ľđ?&#x2018;Ľ cos đ?&#x2018;Śđ?&#x2018;Ś = đ?&#x2018;Ľđ?&#x2018;Ľ tan đ?&#x153;&#x192;đ?&#x153;&#x192; â&#x2C6;&#x2019; ! Â 2đ?&#x2018;˘đ?&#x2018;˘ cos ! đ?&#x153;&#x192;đ?&#x153;&#x192; đ?&#x2018;Śđ?&#x2018;Ś = đ?&#x2018;Ľđ?&#x2018;Ľ tan đ?&#x153;&#x192;đ?&#x153;&#x192; â&#x2C6;&#x2019;

Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â 1

Â Â Â Â H Â Â Â omer, Â Â Â Â Â Â Â Â Â Â Â Â Â Â D Â Â Â . Â Â Â Â 2 Â Â 014 Â Â Â Â Â Â Â Â Â Â P Â Â hysics Â Â Â Â Â Â Â Â Â Â Â Â Â Â C Â Â Â ourse Â Â Â Â Â Â Â Companion, Â Oxford Â

2 1 Â McLester, Â J. Â 2008, Â Applied Â Biomechanics; Â concepts Â and Â connections, Â Thompson Â 2

Â Â

Â Homer, Â D. Â 2014 Â Physics Â Course Â Companion, Â Oxford Â Â McLester, Â J. Â 2008, Â Applied Â Biomechanics; Â concepts Â and Â connections, Â Thompson Â 43

4 Â 4 Â

Bolurin Edun - Mathematics

Where Â y Â is Â the Â vertical Â distance Â and Â x Â is Â the Â horizontal Â distance. Â This Â equation Â is Â identical Â to Â that Â of Â a Â basic Â parabola: Â đ?&#x2018;Śđ?&#x2018;Ś = đ?&#x2018;&#x17D;đ?&#x2018;&#x17D;đ?&#x2018;&#x17D;đ?&#x2018;&#x17D; + đ?&#x2018;?đ?&#x2018;?đ?&#x2018;Ľđ?&#x2018;Ľ ! Â

So Â the Â path Â produced Â by Â a Â projectile Â in Â this Â scenario Â is Â described Â as Â parabolic. Â !

To Â graph Â the Â path, Â I Â take Â the Â value Â of Â Î¸ Â to Â be Â Â radians Â â&#x20AC;&#x201C; Â because Â I Â would Â later Â come Â to Â express Â !

values Â in Â terms Â of Â tan đ?&#x153;&#x192;đ?&#x153;&#x192; Â so Â having Â it Â equal Â 1 Â makes Â it Â easy Â to Â determine Â values Â for Â plotting Â graphs Â â&#x20AC;&#x201C;, Â u Â to Â be Â 30 Â ms-Ââ&#x20AC;?1 Â and Â g Â to Â be Â 9.81 Â ms-Ââ&#x20AC;?2. Â This Â gives Â the Â equation: Â đ?&#x2019;&#x161;đ?&#x2019;&#x161; = đ?&#x2019;&#x2122;đ?&#x2019;&#x2122; đ??đ??đ??đ??đ??đ?? Which Â has Â the Â graph Â below. Â

đ?&#x;&#x2014;đ?&#x;&#x2014;. đ?&#x;&#x2013;đ?&#x;&#x2013;đ?&#x;&#x2013;đ?&#x;&#x2013;đ?&#x2019;&#x2122;đ?&#x2019;&#x2122;đ?&#x;?đ?&#x;? đ??&#x2026;đ??&#x2026; â&#x2C6;&#x2019; Â đ?&#x;&#x2019;đ?&#x;&#x2019; đ?&#x;?đ?&#x;?đ?&#x;?đ?&#x;?đ?&#x;?đ?&#x;?đ?&#x;?đ?&#x;? Â đ??&#x153;đ??&#x153;đ??&#x153;đ??&#x153;đ??&#x153;đ??&#x153; đ?&#x;?đ?&#x;? đ??&#x2026;đ??&#x2026; đ?&#x;&#x2019;đ?&#x;&#x2019;

Flight Â path Â in Â ideal Â conditions Â y 0.8 0.6 0.4 0.2

0.5

1.0

1.5

2.0

2.5

3.0

0.2

Â As Â is Â seen Â above, Â the Â graph Â is Â symmetrical Â about Â the Â maximum Â height. Â This Â would Â be Â a Â key Â point Â of Â comparison Â for Â the Â other Â projectile Â graphs. Â The Â maximum Â height Â is Â reached Â at Â half Â the Â range Â of Â the Â projectile. Â We Â know Â this Â because; Â 1 đ?&#x2018;&#x2020;đ?&#x2018;&#x2020;! = đ?&#x2018;˘đ?&#x2018;˘ sin đ?&#x153;&#x192;đ?&#x153;&#x192; đ?&#x2018;Ąđ?&#x2018;Ą â&#x2C6;&#x2019; đ?&#x2018;&#x201D;đ?&#x2018;&#x201D;đ?&#x2018;Ąđ?&#x2018;Ą ! Â 2

At Â full Â flight Â time Â the Â projectile Â would Â have Â reached Â the Â ground Â again, Â so Â the Â vertical Â distance Â between Â the Â projectile Â and Â the Â ground Â Sy Â would Â be Â zero. Â 1 0 = đ?&#x2018;˘đ?&#x2018;˘ sin đ?&#x153;&#x192;đ?&#x153;&#x192; đ?&#x2018;Ąđ?&#x2018;Ą â&#x2C6;&#x2019; đ?&#x2018;&#x201D;đ?&#x2018;&#x201D;đ?&#x2018;Ąđ?&#x2018;Ą ! Â 2

To Â solve Â the Â equation Â for Â t, Â we Â factor Â it Â out Â

1 0 = đ?&#x2018;˘đ?&#x2018;˘ sin đ?&#x153;&#x192;đ?&#x153;&#x192; â&#x2C6;&#x2019; đ?&#x2018;&#x201D;đ?&#x2018;&#x201D;đ?&#x2018;&#x201D;đ?&#x2018;&#x201D; đ?&#x2018;Ąđ?&#x2018;Ą Â 2

This Â gives Â us Â two Â possible Â values Â for Â t. Â We Â can Â however Â eliminate Â t=0 Â because Â the Â time Â cannot Â equal Â zero Â when Â the Â projectile Â has Â completed Â its Â flight. Â This Â leaves Â us Â with: Â Â

5 Â 44

Bolurin Edun - Mathematics

1 0 = đ?&#x2018;˘đ?&#x2018;˘ sin đ?&#x153;&#x192;đ?&#x153;&#x192; â&#x2C6;&#x2019; đ?&#x2018;&#x201D;đ?&#x2018;&#x201D;đ?&#x2018;&#x201D;đ?&#x2018;&#x201D; Â 2

Rearranging Â this Â gives Â the Â full Â flight Â time Â as: Â

đ?&#x2018;Ąđ?&#x2018;Ą =

2đ?&#x2018;˘đ?&#x2018;˘ sin đ?&#x153;&#x192;đ?&#x153;&#x192; Â đ?&#x2018;&#x201D;đ?&#x2018;&#x201D;

When Â the Â projectile Â is Â at Â its Â maximum Â height, Â the Â velocity Â in Â the Â vertical Â direction Â is Â zero. Â

So Â the Â value Â of Â t Â at Â maximum Â height Â is: Â

0 = đ?&#x2018;˘đ?&#x2018;˘ sin đ?&#x153;&#x192;đ?&#x153;&#x192; â&#x2C6;&#x2019; đ?&#x2018;&#x201D;đ?&#x2018;&#x201D;đ?&#x2018;Ąđ?&#x2018;Ą Â đ?&#x2018;Ąđ?&#x2018;Ą =

đ?&#x2018;˘đ?&#x2018;˘ sin đ?&#x153;&#x192;đ?&#x153;&#x192; Â đ?&#x2018;&#x201D;đ?&#x2018;&#x201D;

This Â proves Â that Â the Â maximum Â height Â is Â reached Â at Â half Â the Â flight Â time Â of Â the Â projectile. Â

Launch Â from Â a Â height Â â&#x20AC;&#x2DC;hâ&#x20AC;&#x2122; Â The Â graph Â for Â the Â projectile Â launched Â from Â a Â height Â is Â rather Â similar. Â The Â equation Â for Â flight Â path Â has Â the Â same Â derivation Â as Â above, Â except Â that Â the Â distance Â in Â the Â vertical Â direction Â has Â the Â equation, Â Â 1 đ?&#x2018;&#x2020;đ?&#x2018;&#x2020;! = đ?&#x2018;˘đ?&#x2018;˘ sin đ?&#x153;&#x192;đ?&#x153;&#x192; đ?&#x2018;Ąđ?&#x2018;Ą â&#x2C6;&#x2019; đ?&#x2018;&#x201D;đ?&#x2018;&#x201D;đ?&#x2018;Ąđ?&#x2018;Ą ! + â&#x201E;&#x17D; Â 2

Therefore Â the Â formula Â for Â the Â flight Â path Â is Â given Â by: Â đ?&#x2018;Śđ?&#x2018;Ś = đ?&#x2018;Ľđ?&#x2018;Ľ tan đ?&#x153;&#x192;đ?&#x153;&#x192; â&#x2C6;&#x2019;

đ?&#x2018;&#x201D;đ?&#x2018;&#x201D;đ?&#x2018;Ľđ?&#x2018;Ľ ! + â&#x201E;&#x17D; Â 2đ?&#x2018;˘đ?&#x2018;˘ ! cos ! đ?&#x153;&#x192;đ?&#x153;&#x192;

It Â is Â evident Â from Â the Â equation Â that Â the Â graph Â produced Â will Â simply Â be Â a Â vertical Â shift Â of Â the Â original Â graph. Â If Â we Â insert Â a Â value Â of Â 10 Â for Â h Â and Â keep Â the Â same Â values Â for Â the Â other Â variables, Â we Â get Â the Â equation: Â đ?&#x2019;&#x161;đ?&#x2019;&#x161; = đ?&#x2019;&#x2122;đ?&#x2019;&#x2122; đ??đ??đ??đ??đ??đ?? Which Â has Â the Â graph Â below. Â

đ??&#x2026;đ??&#x2026; đ?&#x;&#x2014;đ?&#x;&#x2014;. đ?&#x;&#x2013;đ?&#x;&#x2013;đ?&#x;&#x2013;đ?&#x;&#x2013;đ?&#x2019;&#x2122;đ?&#x2019;&#x2122;đ?&#x;?đ?&#x;? â&#x2C6;&#x2019; + đ?&#x;?đ?&#x;?đ?&#x;?đ?&#x;? Â đ?&#x;&#x2019;đ?&#x;&#x2019; đ?&#x;?đ?&#x;?đ?&#x;?đ?&#x;?đ?&#x;?đ?&#x;?đ?&#x;?đ?&#x;? Â đ??&#x153;đ??&#x153;đ??&#x153;đ??&#x153;đ??&#x153;đ??&#x153; đ?&#x;?đ?&#x;? đ??&#x2026;đ??&#x2026; đ?&#x;&#x2019;đ?&#x;&#x2019;

Flight Â path Â with Â a Â starting Â height Â Â

Â 5

Â 4

6 Â 45

Bolurin Edun - Mathematics

As Â can Â be Â seen Â above, Â the Â entire Â graph Â is Â still Â a Â parabola Â and Â is Â symmetrical Â about Â the Â maximum Â height. Â However, Â if Â we Â consider Â the Â positive Â section Â alone, Â the Â graph Â is Â no Â longer Â symmetrical. Â

y 10

When Â we Â focus Â on Â only Â the Â positive Â section Â â&#x20AC;&#x201C; Â the Â path Â the Â projectile Â actually Â travels Â â&#x20AC;&#x201C; Â we Â can Â see Â that Â there Â is Â a Â clear Â difference Â between Â the Â path Â obtained Â from Â launching Â a Â projectile Â from Â a Â height Â and Â launching Â a Â projectile Â from Â the Â ground. Â This Â is Â because Â when Â a Â projectile Â is Â launched Â from Â a Â height, Â the Â maximum Â height Â is Â not Â reached Â at Â half Â the Â flight Â time. Â Â At Â the Â time Â the Â projectile Â reaches Â maximum Â height, Â the Â velocity Â in Â the Â vertical Â direction Â is Â zero. Â So, Â as Â with Â the Â projectile Â launched Â from Â the Â ground, Â the Â time Â is Â given Â by: Â đ?&#x2018;Ąđ?&#x2018;Ą =

đ?&#x2018;˘đ?&#x2018;˘ sin đ?&#x153;&#x192;đ?&#x153;&#x192; Â đ?&#x2018;&#x201D;đ?&#x2018;&#x201D;

When Â the Â projectile Â lands, Â its Â displacement Â from Â the Â point Â at Â which Â it Â was Â thrown Â is Â â&#x20AC;&#x2DC;-Ââ&#x20AC;?hâ&#x20AC;&#x2122;. Â Â 1 â&#x2C6;&#x2019;â&#x201E;&#x17D; = đ?&#x2018;˘đ?&#x2018;˘ sin đ?&#x153;&#x192;đ?&#x153;&#x192; đ?&#x2018;Ąđ?&#x2018;Ą â&#x2C6;&#x2019; đ?&#x2018;&#x201D;đ?&#x2018;&#x201D;đ?&#x2018;Ąđ?&#x2018;Ą ! Â 2

This Â can Â be Â rearranged Â as Â

1 ! đ?&#x2018;&#x201D;đ?&#x2018;&#x201D;đ?&#x2018;Ąđ?&#x2018;Ą â&#x2C6;&#x2019; Â đ?&#x2018;˘đ?&#x2018;˘ sin đ?&#x153;&#x192;đ?&#x153;&#x192; đ?&#x2018;Ąđ?&#x2018;Ą â&#x2C6;&#x2019; â&#x201E;&#x17D; = 0 Â 2

Using Â the Â quadratic Â formula Â to Â solve Â for Â t, Â we Â get: Â đ?&#x2018;Ąđ?&#x2018;Ą =

u sin Î¸ Âą (đ?&#x2018;˘đ?&#x2018;˘ sin đ?&#x153;&#x192;đ?&#x153;&#x192;)! + 2đ?&#x2018;&#x201D;đ?&#x2018;&#x201D;â&#x201E;&#x17D; Â g

This Â gives Â two Â possible Â solutions Â for Â the Â flight Â time. Â However, Â we Â can Â restrict Â this Â to Â only Â one Â because Â if Â we Â were Â to Â take Â the Â solution Â with Â u sin Î¸ â&#x2C6;&#x2019; (đ?&#x2018;˘đ?&#x2018;˘ sin đ?&#x153;&#x192;đ?&#x153;&#x192;)! + 2đ?&#x2018;&#x201D;đ?&#x2018;&#x201D;â&#x201E;&#x17D;, Â we Â would Â get Â a Â negative Â time Â as Â the Â root Â of Â the Â discriminant Â would Â be Â greater Â than Â u sin Î¸. Â Thus Â the Â only Â possible Â flight Â time Â is: Â

7 Â

Bolurin Edun - Mathematics

đ?&#x2018;Ąđ?&#x2018;Ą =

u sin Î¸ + (đ?&#x2018;˘đ?&#x2018;˘ sin đ?&#x153;&#x192;đ?&#x153;&#x192;)! + 2đ?&#x2018;&#x201D;đ?&#x2018;&#x201D;â&#x201E;&#x17D; Â g

This Â shows Â that Â the Â lack Â of Â symmetry Â of Â the Â flight Â path Â is Â due Â to Â the Â maximum Â height Â time Â not Â being Â half Â the Â full Â flight Â time, Â as Â is Â the Â case Â with Â the Â projectile Â launched Â from Â the Â ground. Â Â

Air Â resistance Â in Â horizontal Â direction Â When Â a Â projectile Â moves Â through Â the Â air, Â it Â displaces Â air Â particles Â in Â order Â to Â move Â forward. Â This Â means Â that Â a Â force Â is Â applied Â to Â these Â air Â particles Â to Â cause Â them Â to Â move. Â Newtonâ&#x20AC;&#x2122;s Â third Â law Â of Â motion Â mandates Â that Â an Â equal Â and Â oppositely Â directed Â force Â must Â be Â applied Â to Â the Â projectile Â by Â the Â air Â particles. Â The Â resistive Â force Â in Â the Â horizontal Â direction Â is Â called Â drag Â force2. Â This Â opposing Â force Â causes Â deceleration, Â so Â is Â therefore Â also Â known Â as Â air Â resistance. Â Many Â factors Â affect Â the Â resistive Â force Â caused Â by Â drag; Â the Â mathematical Â representation Â of Â these Â factors Â is: Â

Where: Â

đ??šđ??š! =

1 đ??śđ??ś đ?&#x153;&#x152;đ?&#x153;&#x152;đ??´đ??´ đ?&#x2018;Łđ?&#x2018;Ł ! Â 2 ! !

Â đ??šđ??š! = Â Drag Â force Â đ??śđ??ś! = Â Coefficient Â of Â drag Â đ?&#x153;&#x152;đ?&#x153;&#x152; Â = Â The Â density Â of Â the Â air Â through Â which Â the Â projectile Â is Â flying Â đ??´đ??´! = Â The Â area Â of Â the Â projectile Â oriented Â parallel Â to Â air Â flow Â đ?&#x2018;Łđ?&#x2018;Ł ! = Â Velocity Â of Â the Â projectile Â relative Â to Â air Â flow Â Â Â There Â are Â various Â models Â for Â air Â resistance Â that Â are Â used Â to Â predict Â how Â a Â projectile Â would Â behave Â in Â real Â life Â situations, Â and Â the Â model Â I Â will Â be Â working Â with Â came Â out Â of Â a Â STEP Â question Â on Â projectiles. Â It Â proposes Â that Â air Â resistance Â is Â proportional Â to Â gravity, Â with Â a Â constant Â of Â proportionality Â â&#x20AC;&#x2DC;kâ&#x20AC;&#x2122; Â and Â acts Â solely Â in Â the Â horizontal Â direction. Â It Â also Â proposed Â variations Â of Â the Â constant Â which Â when Â explored, Â bring Â about Â bizarre Â mathematical Â solutions. Â Â As Â will Â be Â shown Â below, Â this Â air Â resistance Â has Â the Â effect Â of Â reducing Â the Â velocity Â of Â the Â projectile Â at Â a Â constant Â rate. Â If Â the Â velocity Â of Â the Â projectile Â reaches Â zero, Â it Â would Â start Â to Â accelerate Â in Â the Â opposite Â direction Â to Â which Â it Â was Â launched. Â That Â is, Â in Â the Â direction Â of Â the Â resistive Â force. Â Since Â this Â is Â the Â case, Â air Â resistance Â also Â potentially Â has Â the Â effect Â of Â causing Â the Â projectile Â to Â turn Â around Â horizontally. Â This Â depends Â on Â the Â magnitude Â of Â the Â constant Â of Â proportionality, Â as Â well Â as Â the Â time Â for Â which Â the Â projectile Â is Â in Â the Â air Â and Â under Â the Â effect Â of Â air Â resistance. Â We Â will Â look Â at Â how Â this Â affects Â the Â path Â of Â a Â projectile Â launched Â from Â the Â ground. Â The Â equations Â for Â distance Â in Â the Â vertical Â and Â horizontal Â directions Â respectively Â are: Â !

đ?&#x2018;&#x2020;đ?&#x2018;&#x2020;! = đ?&#x2018;˘đ?&#x2018;˘ sin đ?&#x153;&#x192;đ?&#x153;&#x192; đ?&#x2018;Ąđ?&#x2018;Ą â&#x2C6;&#x2019; đ?&#x2018;&#x201D;đ?&#x2018;&#x201D;đ?&#x2018;Ąđ?&#x2018;Ą ! Â Â Â Â !

Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â

(5) Â

Â McLester, Â J. Â 2008, Â Applied Â Biomechanics; Â concepts Â and Â connections, Â Thompson Â Wadsworth Â Â

8 Â 47

Bolurin Edun - Mathematics

đ?&#x2018;&#x2020;đ?&#x2018;&#x2020;! = đ?&#x2018;˘đ?&#x2018;˘ cos đ?&#x153;&#x192;đ?&#x153;&#x192; đ?&#x2018;Ąđ?&#x2018;Ą â&#x2C6;&#x2019; đ?&#x2018;&#x2DC;đ?&#x2018;&#x2DC;đ?&#x2018;&#x2DC;đ?&#x2018;&#x2DC;đ?&#x2018;Ąđ?&#x2018;Ą ! Â Â !

(6) Â

A Â number Â of Â things Â can Â be Â deduced Â from Â these Â equations. Â Since Â the Â equation Â for Â distance Â in Â the Â vertical Â direction Â is Â the Â same Â as Â in Â the Â first Â case, Â where Â the Â projectile Â was Â launched Â from Â the Â ground Â with Â no Â air Â resistance, Â the Â maximum Â height Â is Â reached Â at Â half Â the Â full Â flight Â time Â â&#x20AC;&#x201C; Â as Â shown Â on Â page Â 6. Â Â Where: Â

đ?&#x2018;&#x2021;đ?&#x2018;&#x2021;! =

đ?&#x2018;˘đ?&#x2018;˘ sin đ?&#x153;&#x192;đ?&#x153;&#x192; Â Â , đ?&#x2018;&#x201D;đ?&#x2018;&#x201D;

đ?&#x2018;&#x2021;đ?&#x2018;&#x2021;! =

2đ?&#x2018;˘đ?&#x2018;˘ sin đ?&#x153;&#x192;đ?&#x153;&#x192; Â Â đ?&#x2018;&#x201D;đ?&#x2018;&#x201D;

đ?&#x2018;&#x2021;đ?&#x2018;&#x2021;! Â = Â Maximum Â height Â time Â đ?&#x2018;&#x2021;đ?&#x2018;&#x2021;! = Â Full Â flight Â time Â

The Â formula Â for Â horizontal Â distance, Â however, Â is Â different Â from Â the Â one Â shown Â for Â ideal Â conditions Â on Â page Â 4. Â With Â the Â previous Â case, Â the Â horizontal Â distance Â constantly Â increased Â with Â increments Â in Â time Â i.e. Â the Â equation Â for Â the Â horizontal Â on Â its Â own Â represents Â a Â linear Â graph. Â However, Â with Â this Â case, Â the Â formula Â is Â that Â of Â a Â parabola. Â This Â means Â that Â for Â half Â the Â portion Â of Â the Â graph, Â the Â distance Â is Â increasing Â and Â for Â the Â other Â half, Â it Â is Â decreasing. Â This Â means Â that Â if Â the Â projectile Â were Â airborne Â for Â a Â long Â enough Â time, Â it Â would Â eventually Â change Â direction Â horizontally. Â The Â deceleration Â due Â to Â air Â resistance Â is Â constant, Â so Â for Â algebraic Â simplicity Â we Â will Â let Â đ?&#x2018;?đ?&#x2018;? = đ?&#x2018;&#x2DC;đ?&#x2018;&#x2DC;đ?&#x2018;&#x2DC;đ?&#x2018;&#x2DC;. Â Thus Â the Â horizontal Â distance Â at Â any Â given Â time Â is: Â !

đ?&#x2018;&#x2020;đ?&#x2018;&#x2020;! = đ?&#x2018;˘đ?&#x2018;˘ cos đ?&#x153;&#x192;đ?&#x153;&#x192; đ?&#x2018;Ąđ?&#x2018;Ą â&#x2C6;&#x2019; đ?&#x2018;?đ?&#x2018;?đ?&#x2018;Ąđ?&#x2018;Ą ! Â Â Â !

(7) Â

When Â we Â compare Â this Â to Â equation Â (4), Â we Â can Â see Â that Â as Â t Â increases Â and Â all Â other Â values Â are Â kept Â constant, Â the Â horizontal Â distance Â with Â air Â resistance Â will Â always Â be Â less Â than Â without Â it. Â Using Â equation Â (2), Â the Â velocity Â in Â the Â horizontal Â direction Â is: Â đ?&#x2018;Łđ?&#x2018;Ł = đ?&#x2018;˘đ?&#x2018;˘ cos đ?&#x153;&#x192;đ?&#x153;&#x192; â&#x2C6;&#x2019; đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;? Â

At Â the Â time Â at Â which Â the Â projectile Â turns Â around Â in Â the Â horizontal Â direction, Â the Â horizontal Â component Â of Â its Â velocity Â is Â zero. Â 0 = đ?&#x2018;˘đ?&#x2018;˘ cos đ?&#x153;&#x192;đ?&#x153;&#x192; â&#x2C6;&#x2019; đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;? Â

This Â can Â be Â rearranged Â to Â give Â the Â horizontal Â â&#x20AC;&#x2DC;turnaround Â timeâ&#x20AC;&#x2122; Â as: Â đ?&#x2018;Ąđ?&#x2018;Ą =

đ?&#x2018;˘đ?&#x2018;˘ cos đ?&#x153;&#x192;đ?&#x153;&#x192; Â đ?&#x2018;?đ?&#x2018;?

The Â air Â resistance Â acting Â against Â the Â horizontal Â velocity Â is Â given Â by Â the Â constant Â â&#x20AC;&#x2DC;kgâ&#x20AC;&#x2122;. Â The Â value Â of Â g Â is Â a Â known Â constant, Â whereas Â k Â is Â an Â undefined Â constant. Â This Â means Â that Â very Â different Â graphs Â can Â arise Â depending Â on Â the Â value Â assigned Â to Â k. Â Â To Â examine Â the Â different Â graphs Â that Â can Â arise, Â we Â could Â relate Â the Â turnaround Â time Â to Â the Â maximum Â height Â time Â and Â the Â full Â flight Â time Â to Â see Â at Â what Â point Â in Â its Â path Â the Â projectile Â turns Â around, Â or Â even Â if Â at Â all Â it Â turns Â around. Â By Â doing Â so Â we Â can Â determine Â how Â the Â value Â of Â k Â affects Â the Â flight Â path. Â

9 Â

Bolurin Edun - Mathematics

Using Â the Â trigonometric Â identity, Â tan đ?&#x153;&#x192;đ?&#x153;&#x192; =

We Â can Â rewrite Â the Â turnaround Â time Â as: Â đ?&#x2018;Ąđ?&#x2018;Ą =

sin đ?&#x153;&#x192;đ?&#x153;&#x192; Â cos đ?&#x153;&#x192;đ?&#x153;&#x192;

đ?&#x2018;˘đ?&#x2018;˘ sin đ?&#x153;&#x192;đ?&#x153;&#x192; 1 Â đ?&#x2018;&#x201D;đ?&#x2018;&#x201D; đ?&#x2018;&#x2DC;đ?&#x2018;&#x2DC; tan đ?&#x153;&#x192;đ?&#x153;&#x192;

This Â is Â a Â multiple Â of Â the Â maximum Â height Â time Â â&#x20AC;&#x201C; Â which Â is Â half Â the Â full Â flight Â time Â in Â this Â scenario. Â By Â relating Â the Â turnaround Â time Â to Â the Â maximum Â height Â time Â and Â the Â full Â flight Â time, Â we Â can Â determine Â a Â range Â of Â values Â for Â k Â for Â which Â the Â path Â has Â some Â unique Â characteristics. Â

Interesting Â variations Â For Â the Â purpose Â of Â this Â investigation, Â I Â will Â look Â at Â four Â variations Â of Â the Â path Â of Â the Â projectile. Â They Â occur Â when Â the Â turnaround Â time Â is: Â â&#x20AC;˘ â&#x20AC;˘ â&#x20AC;˘ â&#x20AC;˘

Greater Â than Â the Â landing Â time Â Greater Â than Â the Â maximum Â height Â time Â but Â smaller Â than Â the Â landing Â time Â Smaller Â than Â the Â maximum Â height Â time Â Equal Â to Â the Â maximum Â height Â time Â

Turnaround Â time Â greater Â than Â landing Â time Â In Â this Â scenario Â the Â turnaround Â time Â is Â greater Â than Â the Â landing Â time. Â So, Â

This, Â rewritten, Â is: Â

đ?&#x2018;˘đ?&#x2018;˘ cos đ?&#x153;&#x192;đ?&#x153;&#x192; 2đ?&#x2018;˘đ?&#x2018;˘ sin đ?&#x153;&#x192;đ?&#x153;&#x192; > Â đ?&#x2018;&#x201D;đ?&#x2018;&#x201D; đ?&#x2018;&#x2DC;đ?&#x2018;&#x2DC;đ?&#x2018;&#x2DC;đ?&#x2018;&#x2DC;

This Â mandates Â that Â

1 2đ?&#x2018;˘đ?&#x2018;˘ sin đ?&#x153;&#x192;đ?&#x153;&#x192; đ?&#x2018;˘đ?&#x2018;˘ sin đ?&#x153;&#x192;đ?&#x153;&#x192; Ă&#x2014; > Â Â đ?&#x2018;&#x2DC;đ?&#x2018;&#x2DC; tan đ?&#x153;&#x192;đ?&#x153;&#x192; đ?&#x2018;&#x201D;đ?&#x2018;&#x201D; đ?&#x2018;&#x201D;đ?&#x2018;&#x201D;

! !"# !

Â be Â greater Â than Â 2, Â or Â that: Â

1 đ?&#x2018;&#x2DC;đ?&#x2018;&#x2DC; tan Î¸ < Â 2

As Â I Â stated Â earlier, Â I Â will Â be Â keeping Â the Â value Â of Â Î¸ Â constant Â for Â the Â purpose Â of Â comparison, Â so Â what Â is Â really Â changing Â here Â is Â the Â value Â of Â k. Â For Â this Â particular Â range Â of Â values, Â the Â projectile, Â when Â launched, Â would Â have Â its Â turnaround Â time Â occur Â after Â the Â landing Â time Â so Â would Â not Â turnaround Â during Â flight. Â This Â is Â probably Â the Â most Â common Â of Â the Â four Â scenarios, Â as Â we Â never Â really Â see Â projectiles Â turning Â back Â on Â themselves Â due Â to Â air Â resistance. Â Â If Â we Â keep Â the Â same Â values Â as Â before, Â and Â assign Â k Â a Â value Â of Â 0.25 Â because Â it Â is Â within Â the Â required Â range Â and Â would Â produce Â an Â example Â of Â the Â required Â path Â shape, Â the Â parametric Â equations Â we Â plot Â are: Â

10 Â

1 đ?&#x2018;&#x2DC;đ?&#x2018;&#x2DC; tan Î¸ < Â 2

As Â I Â stated Â earlier, Â I Â will Â be Â keeping Â the Â value Â of Â Î¸ Â constant Â for Â the Â purpose Â of Â comparison, Â so Â what Â is Â Bolurin Edun - Mathematics really Â changing Â here Â is Â the Â value Â of Â k. Â For Â this Â particular Â range Â of Â values, Â the Â projectile, Â when Â launched, Â would Â have Â its Â turnaround Â time Â occur Â after Â the Â landing Â time Â so Â would Â not Â turnaround Â during Â flight. Â This Â is Â probably Â the Â most Â common Â of Â the Â four Â scenarios, Â as Â we Â never Â really Â see Â projectiles Â turning Â back Â on Â themselves Â due Â to Â air Â resistance. Â Â If Â we Â keep Â the Â same Â values Â as Â before, Â and Â assign Â k Â a Â value Â of Â 0.25 Â because Â it Â is Â within Â the Â required Â Â range Â and Â would Â produce Â an Â example Â of Â the Â required Â path Â shape, Â the Â parametric Â equations Â we Â plot Â are: Â Â Â

đ??&#x2026;đ??&#x2026; đ?&#x153;&#x2039;đ?&#x153;&#x2039; đ?&#x2018;Śđ?&#x2018;Ś = 30 sin đ?&#x2018;Ąđ?&#x2018;Ą â&#x2C6;&#x2019; 0.5Ă&#x2014;9.81đ?&#x2018;Ąđ?&#x2018;Ą ! â&#x;š đ?&#x2019;&#x161;đ?&#x2019;&#x161; = đ?&#x;&#x2018;đ?&#x;&#x2018;đ?&#x;&#x2018;đ?&#x;&#x2018; đ??Źđ??Źđ??Źđ??Źđ??Źđ??Ź đ?&#x2019;&#x2022;đ?&#x2019;&#x2022; â&#x2C6;&#x2019; đ?&#x;&#x2019;đ?&#x;&#x2019;. đ?&#x;&#x2014;đ?&#x;&#x2014;đ?&#x;&#x2014;đ?&#x;&#x2014;đ?&#x;&#x2014;đ?&#x;&#x2014;đ?&#x2019;&#x2022;đ?&#x2019;&#x2022;đ?&#x;?đ?&#x;? Â đ?&#x;&#x2019;đ?&#x;&#x2019; 4

10 Â

đ??&#x2026;đ??&#x2026; đ?&#x153;&#x2039;đ?&#x153;&#x2039; đ?&#x2018;Ľđ?&#x2018;Ľ = 30 cos đ?&#x2018;Ąđ?&#x2018;Ą â&#x2C6;&#x2019; 0.5Ă&#x2014;0.25Ă&#x2014;9.81đ?&#x2018;Ąđ?&#x2018;Ą ! â&#x;š đ?&#x2019;&#x2122;đ?&#x2019;&#x2122; = đ?&#x;&#x2018;đ?&#x;&#x2018;đ?&#x;&#x2018;đ?&#x;&#x2018; đ??&#x153;đ??&#x153;đ??&#x153;đ??&#x153;đ??&#x153;đ??&#x153; đ?&#x2019;&#x2022;đ?&#x2019;&#x2022; â&#x2C6;&#x2019; đ?&#x;?đ?&#x;?. đ?&#x;?đ?&#x;?đ?&#x;?đ?&#x;?đ?&#x;?đ?&#x;?đ?&#x;?đ?&#x;?đ?&#x;?đ?&#x;?đ?&#x2019;&#x2022;đ?&#x2019;&#x2022;đ?&#x;?đ?&#x;? Â đ?&#x;&#x2019;đ?&#x;&#x2019; 4

Where Â t Â is Â the Â parameter Â and Â represents Â time, Â so Â the Â graph Â shows Â a Â parametric Â plot Â of Â how Â the Â distances Â in Â the Â horizontal Â and Â vertical Â directions Â change Â with Â time. Â I Â made Â the Â decision Â to Â use Â parametric Â equations Â in Â this Â case Â for Â ease Â of Â plotting Â the Â graphs. Â Â

Flight Â path Â with Â turnaround Â time Â greater Â than Â landing Â time Â

Â As Â can Â be Â seen Â on Â the Â graph, Â the Â projectile Â does Â not Â turn Â around Â during Â its Â flight. Â Although Â the Â flight Â path Â may Â look Â similar Â to Â that Â of Â the Â projectile Â launched Â from Â the Â ground Â with Â no Â air Â resistance, Â it Â is Â very Â different. Â The Â shape Â of Â the Â path Â is Â oblique Â rather Â than Â parabolic. Â Velocity Â in Â the Â horizontal Â direction Â is Â decreasing Â â&#x20AC;&#x201C; Â as Â opposed Â to Â being Â constant Â â&#x20AC;&#x201C; Â due Â to Â the Â presence Â of Â air Â resistance. Â đ?&#x2018;Łđ?&#x2018;Ł = đ?&#x2018;˘đ?&#x2018;˘ cos đ?&#x153;&#x192;đ?&#x153;&#x192; â&#x2C6;&#x2019; đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;? Â

So Â as Â the Â time, Â t, Â increases, Â the Â velocity Â decreases. Â If Â the Â projectile Â were Â allowed Â to Â fly Â for Â long Â enough, Â we Â would Â eventually Â see Â the Â projectile Â turnaround Â on Â itself, Â then Â start Â to Â accelerate Â in Â the Â opposite Â horizontal Â direction, Â which Â is Â the Â direction Â the Â air Â resistance Â acts Â in. Â Â

11 Â

Bolurin Edun - Mathematics

From Â this, Â it Â can Â be Â proved Â that Â whenever Â air Â resistance Â acts Â to Â oppose Â a Â projectileâ&#x20AC;&#x2122;s Â motion, Â the Â horizontal Â distance Â in Â ideal Â conditions Â would Â always Â be Â greater Â than Â when Â air Â resistance Â is Â considered. Â

Turnaround Â time Â greater Â than Â maximum Â height Â time Â but Â less Â than Â landing Â time Â In Â this Â scenario, Â the Â projectile Â turns Â around Â during Â its Â flight; Â it Â turns Â around Â after Â the Â projectile Â reaches Â its Â maximum Â height Â â&#x20AC;&#x201C; Â half Â the Â flight Â time Â in Â this Â case Â â&#x20AC;&#x201C; Â and Â before Â the Â projectile Â lands. Â Â đ?&#x2018;˘đ?&#x2018;˘ sin đ?&#x153;&#x192;đ?&#x153;&#x192; đ?&#x2018;˘đ?&#x2018;˘ cos Î¸ 2đ?&#x2018;˘đ?&#x2018;˘ sin Î¸ < < Â đ?&#x2018;&#x201D;đ?&#x2018;&#x201D; đ?&#x2018;&#x2DC;đ?&#x2018;&#x2DC;đ?&#x2018;&#x2DC;đ?&#x2018;&#x2DC; đ?&#x2018;&#x201D;đ?&#x2018;&#x201D;

Â Rewriting Â this Â as: Â

For Â this Â to Â happen, Â

! !"# !

1 2đ?&#x2018;˘đ?&#x2018;˘ sin Î¸ đ?&#x2018;˘đ?&#x2018;˘ sin đ?&#x153;&#x192;đ?&#x153;&#x192; đ?&#x2018;˘đ?&#x2018;˘ sin đ?&#x153;&#x192;đ?&#x153;&#x192; < Ă&#x2014; < Â đ?&#x2018;&#x2DC;đ?&#x2018;&#x2DC; tan đ?&#x153;&#x192;đ?&#x153;&#x192; đ?&#x2018;&#x201D;đ?&#x2018;&#x201D; đ?&#x2018;&#x201D;đ?&#x2018;&#x201D; đ?&#x2018;&#x201D;đ?&#x2018;&#x201D;

Â must Â be Â between Â 1 Â and Â 2, Â or: Â

1 < đ?&#x2018;&#x2DC;đ?&#x2018;&#x2DC; tan đ?&#x153;&#x192;đ?&#x153;&#x192; < 1 Â 2

When Â the Â constant Â is Â within Â these Â bounds, Â the Â projectile Â turns Â around Â on Â itself Â during Â its Â flight. Â Assigning Â k Â the Â value Â of Â proof. Â

Â will Â provide Â an Â example Â of Â such Â a Â path Â and Â leaves Â scope Â for Â my Â next Â

đ?&#x2019;&#x161;đ?&#x2019;&#x161; = đ?&#x;&#x2018;đ?&#x;&#x2018;đ?&#x;&#x2018;đ?&#x;&#x2018; đ??Źđ??Źđ??Źđ??Źđ??Źđ??Ź

đ??&#x2026;đ??&#x2026; đ?&#x2019;&#x2022;đ?&#x2019;&#x2022; â&#x2C6;&#x2019; đ?&#x;&#x2019;đ?&#x;&#x2019;. đ?&#x;&#x2014;đ?&#x;&#x2014;đ?&#x;&#x2014;đ?&#x;&#x2014;đ?&#x;&#x2014;đ?&#x;&#x2014;đ?&#x2019;&#x2022;đ?&#x2019;&#x2022;đ?&#x;?đ?&#x;? Â đ?&#x;&#x2019;đ?&#x;&#x2019;

đ?&#x153;&#x2039;đ?&#x153;&#x2039; 7 đ??&#x2026;đ??&#x2026; đ?&#x2018;Ľđ?&#x2018;Ľ = 30 cos đ?&#x2018;Ąđ?&#x2018;Ą â&#x2C6;&#x2019; 0.5Ă&#x2014;0.25Ă&#x2014; Ă&#x2014;9.81đ?&#x2018;Ąđ?&#x2018;Ą ! â&#x;š đ?&#x2019;&#x2122;đ?&#x2019;&#x2122; = đ?&#x;&#x2018;đ?&#x;&#x2018;đ?&#x;&#x2018;đ?&#x;&#x2018; đ??&#x153;đ??&#x153;đ??&#x153;đ??&#x153;đ??&#x153;đ??&#x153; đ?&#x2019;&#x2022;đ?&#x2019;&#x2022; â&#x2C6;&#x2019; đ?&#x;?đ?&#x;?. đ?&#x;&#x2013;đ?&#x;&#x2013;đ?&#x;&#x2013;đ?&#x;&#x2013;đ?&#x;&#x2013;đ?&#x;&#x2013;đ?&#x;&#x2013;đ?&#x;&#x2013;đ?&#x;&#x2013;đ?&#x;&#x2013;đ?&#x2019;&#x2022;đ?&#x2019;&#x2022;đ?&#x;?đ?&#x;? Â 4 12 đ?&#x;&#x2019;đ?&#x;&#x2019;

Again, Â the Â parameter Â t Â represents Â time, Â so Â the Â equations Â give Â the Â graph Â below. Â

Flight Â path Â with Â turnaround Â time Â between Â maximum Â height Â and Â landing Â time Â

12 Â

Bolurin Edun - Mathematics

Â Â As Â can Â be Â seen Â on Â the Â graph, Â the Â projectile Â turns Â around Â during Â its Â flight Â and Â its Â horizontal Â distance Â at Â the Â maximum Â height Â is Â less Â than Â its Â horizontal Â distance Â when Â it Â lands. Â From Â this, Â I Â found Â myself Â asking Â if Â there Â is Â a Â range Â of Â values Â for Â which Â the Â horizontal Â distance Â at Â maximum Â height Â is Â greater Â than Â the Â distance Â when Â it Â lands. Â The Â sub-Ââ&#x20AC;?section Â below Â answers Â this Â question. Â Â

Projectileâ&#x20AC;&#x2122;s Â horizontal Â distance Â at Â maximum Â height Â greater Â than Â at Â landing Â time Â The Â horizontal Â distance Â is Â determined Â using Â equation Â (2). Â The Â distance Â at Â the Â maximum Â height Â is: Â đ?&#x2018;Ľđ?&#x2018;Ľ = đ?&#x2018;˘đ?&#x2018;˘ cos đ?&#x153;&#x192;đ?&#x153;&#x192;

1 đ?&#x2018;˘đ?&#x2018;˘ sin đ?&#x153;&#x192;đ?&#x153;&#x192; đ?&#x2018;˘đ?&#x2018;˘ sin đ?&#x153;&#x192;đ?&#x153;&#x192; â&#x2C6;&#x2019; đ?&#x2018;&#x2DC;đ?&#x2018;&#x2DC;đ?&#x2018;&#x2DC;đ?&#x2018;&#x2DC; 2 đ?&#x2018;&#x201D;đ?&#x2018;&#x201D; đ?&#x2018;&#x201D;đ?&#x2018;&#x201D;

We Â can Â open Â up Â the Â brackets Â and Â make Â a Â common Â denominator: Â

We Â can Â further Â simplify Â this Â to: Â

đ?&#x2018;Ľđ?&#x2018;Ľ =

2đ?&#x2018;˘đ?&#x2018;˘ ! sin đ?&#x153;&#x192;đ?&#x153;&#x192; cos đ?&#x153;&#x192;đ?&#x153;&#x192; â&#x2C6;&#x2019; đ?&#x2018;&#x2DC;đ?&#x2018;&#x2DC;đ?&#x2018;˘đ?&#x2018;˘ ! sin! đ?&#x153;&#x192;đ?&#x153;&#x192; Â 2đ?&#x2018;&#x201D;đ?&#x2018;&#x201D;

đ?&#x2018;Ľđ?&#x2018;Ľ =

đ?&#x2018;˘đ?&#x2018;˘ ! sin đ?&#x153;&#x192;đ?&#x153;&#x192; (2 cos đ?&#x153;&#x192;đ?&#x153;&#x192; â&#x2C6;&#x2019; đ?&#x2018;&#x2DC;đ?&#x2018;&#x2DC; sin đ?&#x153;&#x192;đ?&#x153;&#x192;) Â 2đ?&#x2018;&#x201D;đ?&#x2018;&#x201D;

đ?&#x2018;Ľđ?&#x2018;Ľ =

đ?&#x2018;˘đ?&#x2018;˘ ! sin đ?&#x153;&#x192;đ?&#x153;&#x192; cos đ?&#x153;&#x192;đ?&#x153;&#x192; (2 â&#x2C6;&#x2019; đ?&#x2018;&#x2DC;đ?&#x2018;&#x2DC; tan đ?&#x153;&#x192;đ?&#x153;&#x192;) Â 2đ?&#x2018;&#x201D;đ?&#x2018;&#x201D;

We Â can Â rewrite Â đ?&#x2018;&#x2DC;đ?&#x2018;&#x2DC; sin đ?&#x153;&#x192;đ?&#x153;&#x192; Â as Â đ?&#x2018;&#x2DC;đ?&#x2018;&#x2DC; tan đ?&#x153;&#x192;đ?&#x153;&#x192; cos đ?&#x153;&#x192;đ?&#x153;&#x192;, Â and Â thus Â can Â further Â simplify Â to: Â

Similarly, Â the Â horizontal Â distance Â when Â the Â projectile Â lands Â is: Â đ?&#x2018;Ľđ?&#x2018;Ľ = đ?&#x2018;˘đ?&#x2018;˘ cos đ?&#x153;&#x192;đ?&#x153;&#x192;

1 2đ?&#x2018;˘đ?&#x2018;˘ sin đ?&#x153;&#x192;đ?&#x153;&#x192; 2đ?&#x2018;˘đ?&#x2018;˘ sin đ?&#x153;&#x192;đ?&#x153;&#x192; â&#x2C6;&#x2019; đ?&#x2018;&#x2DC;đ?&#x2018;&#x2DC;đ?&#x2018;&#x2DC;đ?&#x2018;&#x2DC; 2 đ?&#x2018;&#x201D;đ?&#x2018;&#x201D; đ?&#x2018;&#x201D;đ?&#x2018;&#x201D;

As Â with Â the Â previous Â distance, Â this Â simplifies Â to: Â Â đ?&#x2018;Ľđ?&#x2018;Ľ =

4đ?&#x2018;˘đ?&#x2018;˘ ! sin đ?&#x153;&#x192;đ?&#x153;&#x192; cos đ?&#x153;&#x192;đ?&#x153;&#x192; (1 â&#x2C6;&#x2019; đ?&#x2018;&#x2DC;đ?&#x2018;&#x2DC; tan đ?&#x153;&#x192;đ?&#x153;&#x192;) Â 2đ?&#x2018;&#x201D;đ?&#x2018;&#x201D;

So Â our Â two Â equations Â for Â horizontal Â distance Â are: Â đ?&#x2018;Ľđ?&#x2018;Ľ! = đ?&#x2018;Ľđ?&#x2018;Ľ! =

!! !"# ! !"# ! !!

(2 â&#x2C6;&#x2019; đ?&#x2018;&#x2DC;đ?&#x2018;&#x2DC; tan đ?&#x153;&#x192;đ?&#x153;&#x192;) Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â (8) Â

!!! !"# ! !"# ! !!

(1 â&#x2C6;&#x2019; đ?&#x2018;&#x2DC;đ?&#x2018;&#x2DC; tan đ?&#x153;&#x192;đ?&#x153;&#x192;) Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â (9) Â

Where Â đ?&#x2018;Ľđ?&#x2018;Ľ! = Â Horizontal Â distance Â at Â maximum Â height Â đ?&#x2018;Ľđ?&#x2018;Ľ! Â = Â Horizontal Â distance Â at Â landing Â time Â

We Â want Â to Â find Â the Â range Â of Â values Â where Â the Â distance Â at Â maximum Â height Â is Â greater Â than Â the Â distance Â at Â landing Â time. Â So: Â

13 Â

Bolurin Edun - Mathematics

4đ?&#x2018;˘đ?&#x2018;˘ ! sin đ?&#x153;&#x192;đ?&#x153;&#x192; cos đ?&#x153;&#x192;đ?&#x153;&#x192; đ?&#x2018;˘đ?&#x2018;˘ ! sin đ?&#x153;&#x192;đ?&#x153;&#x192; cos đ?&#x153;&#x192;đ?&#x153;&#x192; (2 â&#x2C6;&#x2019; đ?&#x2018;&#x2DC;đ?&#x2018;&#x2DC; tan đ?&#x153;&#x192;đ?&#x153;&#x192;) > (1 â&#x2C6;&#x2019; đ?&#x2018;&#x2DC;đ?&#x2018;&#x2DC; tan đ?&#x153;&#x192;đ?&#x153;&#x192;) Â 2đ?&#x2018;&#x201D;đ?&#x2018;&#x201D; 2đ?&#x2018;&#x201D;đ?&#x2018;&#x201D;

Now Â as Â we Â are Â only Â observing Â the Â flight Â path, Â we Â can Â restrict Â this Â to Â the Â positive Â values Â of Â đ?&#x2018;Ľđ?&#x2018;Ľ. Â We Â know Â that Â the Â values Â outside Â the Â brackets Â are Â all Â positive Â â&#x20AC;&#x201C; Â as Â đ?&#x153;&#x192;đ?&#x153;&#x192; Â is Â between Â zero Â and Â ninety Â degrees Â and Â the Â initial Â velocity Â is Â positive. Â From Â this, Â we Â can Â already Â determine Â one Â of Â the Â bounds Â to Â be: Â đ?&#x2018;&#x2DC;đ?&#x2018;&#x2DC; tan đ?&#x153;&#x192;đ?&#x153;&#x192; < 1 Â

Because Â otherwise, Â we Â would Â get Â a Â negative Â value Â for Â the Â distance, Â which Â is Â not Â possible Â during Â the Â projectileâ&#x20AC;&#x2122;s Â flight. Â The Â other Â bound Â is Â obtained Â by Â solving Â the Â inequality. Â The Â inequality Â simplifies Â to: Â 2 â&#x2C6;&#x2019; Â đ?&#x2018;&#x2DC;đ?&#x2018;&#x2DC; tan đ?&#x153;&#x192;đ?&#x153;&#x192; > 4(1 â&#x2C6;&#x2019; đ?&#x2018;&#x2DC;đ?&#x2018;&#x2DC; tan đ?&#x153;&#x192;đ?&#x153;&#x192;) Â

If Â we Â open Â the Â brackets Â and Â rearrange, Â we Â get: Â

4đ?&#x2018;&#x2DC;đ?&#x2018;&#x2DC; tan đ?&#x153;&#x192;đ?&#x153;&#x192; â&#x2C6;&#x2019; đ?&#x2018;&#x2DC;đ?&#x2018;&#x2DC; tan đ?&#x153;&#x192;đ?&#x153;&#x192; > 4 â&#x2C6;&#x2019; 2 Â

Which Â is: Â

Therefore Â the Â other Â bound Â is Â

3đ?&#x2018;&#x2DC;đ?&#x2018;&#x2DC; tan đ?&#x153;&#x192;đ?&#x153;&#x192; > 2 Â 2 đ?&#x2018;&#x2DC;đ?&#x2018;&#x2DC; tan đ?&#x153;&#x192;đ?&#x153;&#x192; > Â 3

Since Â đ?&#x2018;&#x2DC;đ?&#x2018;&#x2DC; tan đ?&#x153;&#x192;đ?&#x153;&#x192; Â has Â to Â always Â satisfy Â these Â two Â inequalities Â simultaneously Â â&#x20AC;&#x201C; Â as Â the Â horizontal Â distance Â cannot Â be Â negative Â and Â the Â distance Â at Â maximum Â height Â must Â be Â greater Â than Â the Â distance Â at Â landing Â â&#x20AC;&#x201C; Â the Â range Â of Â values Â is Â given Â by Â 2 < đ?&#x2018;&#x2DC;đ?&#x2018;&#x2DC; tan đ?&#x153;&#x192;đ?&#x153;&#x192; < 1 Â 3

We Â can Â assign Â k Â the Â value Â of Â 0.75 Â as Â it Â is Â within Â the Â required Â range, Â the Â parametric Â equations Â for Â this Â flight Â path Â are: Â đ?&#x2019;&#x161;đ?&#x2019;&#x161; = đ?&#x;&#x2018;đ?&#x;&#x2018;đ?&#x;&#x2018;đ?&#x;&#x2018; đ??Źđ??Źđ??Źđ??Źđ??Źđ??Ź

đ?&#x153;&#x2039;đ?&#x153;&#x2039; đ??&#x2026;đ??&#x2026; đ?&#x2018;Ľđ?&#x2018;Ľ = 30 cos đ?&#x2018;Ąđ?&#x2018;Ą â&#x2C6;&#x2019; 0.5Ă&#x2014;0.75Ă&#x2014;9.81đ?&#x2018;Ąđ?&#x2018;Ą ! â&#x;š đ?&#x2019;&#x2122;đ?&#x2019;&#x2122; = đ?&#x;&#x2018;đ?&#x;&#x2018;đ?&#x;&#x2018;đ?&#x;&#x2018; đ??&#x153;đ??&#x153;đ??&#x153;đ??&#x153;đ??&#x153;đ??&#x153; đ?&#x2019;&#x2022;đ?&#x2019;&#x2022; â&#x2C6;&#x2019; đ?&#x;&#x2018;đ?&#x;&#x2018;. đ?&#x;&#x201D;đ?&#x;&#x201D;đ?&#x;&#x201D;đ?&#x;&#x201D;đ?&#x;&#x201D;đ?&#x;&#x201D;đ?&#x;&#x201D;đ?&#x;&#x201D;đ?&#x;&#x201D;đ?&#x;&#x201D;đ?&#x2019;&#x2022;đ?&#x2019;&#x2022;đ?&#x;?đ?&#x;? Â 4 đ?&#x;&#x2019;đ?&#x;&#x2019;

Bolurin Edun - Mathematics

Again, Â the Â parameter Â t Â represents Â time, Â so Â the Â equations Â give Â the Â graph Â below. Â

As Â can Â be Â seen Â on Â this Â graph, Â the Â projectile Â turns Â around Â during Â its Â flight Â and Â the Â horizontal Â distance Â at Â maximum Â height Â is Â greater Â than Â the Â distance Â when Â the Â projectile Â lands. Â

Turnaround Â time Â smaller Â than Â maximum Â height Â time Â In Â this Â scenario, Â the Â turnaround Â time Â of Â the Â projectile Â would Â be Â smaller Â than Â its Â maximum Â height Â time, Â so Â the Â projectile Â would Â land Â at Â a Â point Â in Â the Â opposite Â direction Â of Â which Â it Â was Â launched. Â Â đ?&#x2018;˘đ?&#x2018;˘ cos đ?&#x153;&#x192;đ?&#x153;&#x192; đ?&#x2018;˘đ?&#x2018;˘ sin đ?&#x153;&#x192;đ?&#x153;&#x192; < Â đ?&#x2018;&#x201D;đ?&#x2018;&#x201D; đ?&#x2018;&#x2DC;đ?&#x2018;&#x2DC;đ?&#x2018;&#x2DC;đ?&#x2018;&#x2DC;

This Â is: Â

Which Â means Â that: Â

đ?&#x2018;˘đ?&#x2018;˘ sin đ?&#x153;&#x192;đ?&#x153;&#x192; đ?&#x2018;&#x201D;đ?&#x2018;&#x201D;

đ?&#x2018;˘đ?&#x2018;˘ sin đ?&#x153;&#x192;đ?&#x153;&#x192; 1 < Â đ?&#x2018;&#x201D;đ?&#x2018;&#x201D; đ?&#x2018;&#x2DC;đ?&#x2018;&#x2DC; tan đ?&#x153;&#x192;đ?&#x153;&#x192; đ?&#x2018;&#x2DC;đ?&#x2018;&#x2DC; tan đ?&#x153;&#x192;đ?&#x153;&#x192; > 1 Â

If Â I Â assign Â k Â the Â value Â of Â 2.5 Â and Â keep Â all Â other Â values Â constant, Â I Â will Â obtain Â an Â example Â of Â this Â graph Â that Â can Â be Â compared Â to Â the Â other Â graphs. Â The Â parametric Â equations Â for Â this Â plot Â are: Â Â đ?&#x2019;&#x161;đ?&#x2019;&#x161; = đ?&#x;&#x2018;đ?&#x;&#x2018;đ?&#x;&#x2018;đ?&#x;&#x2018; đ??Źđ??Źđ??Źđ??Źđ??Źđ??Ź

đ?&#x153;&#x2039;đ?&#x153;&#x2039; đ??&#x2026;đ??&#x2026; đ?&#x2018;Ľđ?&#x2018;Ľ = 30 cos đ?&#x2018;Ąđ?&#x2018;Ą â&#x2C6;&#x2019; 0.5Ă&#x2014;2.5Ă&#x2014;9.81đ?&#x2018;Ąđ?&#x2018;Ą ! â&#x;š đ?&#x2019;&#x2122;đ?&#x2019;&#x2122; = đ?&#x;&#x2018;đ?&#x;&#x2018;đ?&#x;&#x2018;đ?&#x;&#x2018; đ??&#x153;đ??&#x153;đ??&#x153;đ??&#x153;đ??&#x153;đ??&#x153; đ?&#x2019;&#x2022;đ?&#x2019;&#x2022; â&#x2C6;&#x2019; đ?&#x;?đ?&#x;?đ?&#x;?đ?&#x;?. đ?&#x;?đ?&#x;?đ?&#x;?đ?&#x;?đ?&#x;?đ?&#x;?đ?&#x;?đ?&#x;?đ?&#x2019;&#x2022;đ?&#x2019;&#x2022;đ?&#x;?đ?&#x;? Â 4 đ?&#x;&#x2019;đ?&#x;&#x2019;

Which Â give Â the Â graph Â shown Â below. Â Â Â

15 Â

Bolurin Edun - Mathematics

Flight Â path Â with Â turnaround Â time Â smaller Â than Â maximum Â height Â time Â

Â As Â is Â seen Â on Â the Â graph, Â the Â projectile Â turns Â around Â before Â reaching Â its Â maximum Â height, Â and Â so Â spends Â more Â than Â half Â its Â flight Â time Â moving Â in Â the Â opposite Â direction Â to Â which Â it Â was Â launched. Â Therefore, Â the Â projectile Â lands Â behind Â its Â starting Â point. Â Another Â thing Â to Â note Â about Â this Â graph Â is Â that Â the Â maximum Â height Â occurs Â behind Â the Â projectileâ&#x20AC;&#x2122;s Â starting Â point. Â However, Â for Â some Â values Â of Â k, Â the Â maximum Â height Â would Â occur Â in Â front Â of Â the Â start Â point. Â So Â the Â question Â raised Â here Â is Â for Â what Â range Â of Â values Â does Â the Â maximum Â height Â occur Â in Â front Â of Â the Â projectileâ&#x20AC;&#x2122;s Â launch Â point? Â Â

Projectile Â reaches Â maximum Â height Â before Â returning Â to Â horizontal Â launch Â position Â At Â the Â projectileâ&#x20AC;&#x2122;s Â launch Â position, Â its Â horizontal Â distance Â is Â zero. Â So Â from Â equation Â (8) Â on Â page Â 13, Â we Â know Â the Â projectile Â will Â be Â at Â the Â same Â horizontal Â position Â as Â when Â it Â was Â launched Â when: Â đ?&#x2018;˘đ?&#x2018;˘ ! sin đ?&#x153;&#x192;đ?&#x153;&#x192; cos đ?&#x153;&#x192;đ?&#x153;&#x192; (2 â&#x2C6;&#x2019; đ?&#x2018;&#x2DC;đ?&#x2018;&#x2DC; tan đ?&#x153;&#x192;đ?&#x153;&#x192;) = 0 Â 2đ?&#x2018;&#x201D;đ?&#x2018;&#x201D;

Here Â either Â đ?&#x2018;˘đ?&#x2018;˘ ! sin đ?&#x153;&#x192;đ?&#x153;&#x192; cos đ?&#x153;&#x192;đ?&#x153;&#x192; Â or Â (2 â&#x2C6;&#x2019; đ?&#x2018;&#x2DC;đ?&#x2018;&#x2DC; tan đ?&#x153;&#x192;đ?&#x153;&#x192;) Â could Â equal Â zero, Â but Â since Â the Â latter Â contains Â the Â independent Â variable Â â&#x20AC;&#x201C; Â that Â is Â the Â one Â that Â has Â been Â changed Â during Â the Â investigation Â â&#x20AC;&#x201C; Â we Â will Â take Â the Â solution Â where Â it Â equals Â zero. Â Â 2 â&#x2C6;&#x2019; đ?&#x2018;&#x2DC;đ?&#x2018;&#x2DC; tan đ?&#x153;&#x192;đ?&#x153;&#x192; = 0 Â

So Â at Â the Â point Â where Â đ?&#x2018;&#x2DC;đ?&#x2018;&#x2DC; tan đ?&#x153;&#x192;đ?&#x153;&#x192; = 2, Â the Â maximum Â height Â would Â be Â in Â line Â with Â the Â start Â point. Â If Â we Â take Â the Â launch Â direction Â as Â positive, Â for Â the Â range Â of Â values Â where Â đ?&#x2018;&#x2DC;đ?&#x2018;&#x2DC; tan đ?&#x153;&#x192;đ?&#x153;&#x192; > 2, Â the Â horizontal Â distance Â of Â the Â maximum Â height Â relative Â to Â the Â start Â point Â would Â be Â negative, Â so Â would Â be Â behind Â the Â start Â point. Â This Â means Â that Â the Â maximum Â height Â would Â occur Â in Â front Â of Â the Â launch Â point Â of Â the Â projectile Â where: Â đ?&#x2018;&#x2DC;đ?&#x2018;&#x2DC; tan đ?&#x153;&#x192;đ?&#x153;&#x192; < 2 Â

16 Â

Bolurin Edun - Mathematics

However Â đ?&#x2018;&#x2DC;đ?&#x2018;&#x2DC; tan đ?&#x153;&#x192;đ?&#x153;&#x192; Â also Â has Â to Â satisfy Â the Â inequality Â that Â pertains Â to Â this Â family Â of Â projectile Â paths Â â&#x20AC;&#x201C; Â where Â the Â projectile Â turns Â around Â before Â reaching Â maximum Â height. Â So Â the Â range Â of Â values Â where Â the Â maximum Â height Â occurs Â in Â front Â of Â the Â start Â point Â and Â the Â projectile Â turns Â around Â before Â the Â maximum Â height Â is: Â 1 < đ?&#x2018;&#x2DC;đ?&#x2018;&#x2DC; tan đ?&#x153;&#x192;đ?&#x153;&#x192; < 2 Â

Assigning Â k Â the Â value Â of Â 1.5, Â we Â can Â show Â an Â example Â of Â such Â a Â path. Â The Â parametric Â equations Â are: Â đ?&#x2019;&#x161;đ?&#x2019;&#x161; = đ?&#x;&#x2018;đ?&#x;&#x2018;đ?&#x;&#x2018;đ?&#x;&#x2018; đ??Źđ??Źđ??Źđ??Źđ??Źđ??Ź

đ??&#x2026;đ??&#x2026; đ?&#x153;&#x2039;đ?&#x153;&#x2039; đ?&#x2018;Ľđ?&#x2018;Ľ = 30 cos đ?&#x2018;Ąđ?&#x2018;Ą â&#x2C6;&#x2019; 0.5Ă&#x2014;1.5Ă&#x2014;9.81đ?&#x2018;Ąđ?&#x2018;Ą ! â&#x;š đ?&#x2019;&#x2122;đ?&#x2019;&#x2122; = đ?&#x;&#x2018;đ?&#x;&#x2018;đ?&#x;&#x2018;đ?&#x;&#x2018; đ??&#x153;đ??&#x153;đ??&#x153;đ??&#x153;đ??&#x153;đ??&#x153; đ?&#x2019;&#x2022;đ?&#x2019;&#x2022; â&#x2C6;&#x2019; đ?&#x;&#x2022;đ?&#x;&#x2022;. đ?&#x;&#x2018;đ?&#x;&#x2018;đ?&#x;&#x2018;đ?&#x;&#x2018;đ?&#x;&#x2018;đ?&#x;&#x2018;đ?&#x;&#x2018;đ?&#x;&#x2018;đ?&#x2019;&#x2022;đ?&#x2019;&#x2022;đ?&#x;?đ?&#x;? Â đ?&#x;&#x2019;đ?&#x;&#x2019; 4

This Â gives Â the Â graph Â below. Â

Â This Â clearly Â shows Â that Â the Â maximum Â height Â occurs Â in Â front Â of Â the Â projectileâ&#x20AC;&#x2122;s Â launch Â point. Â

Turnaround Â time Â equal Â to Â the Â maximum Â height Â time Â In Â this Â scenario, Â the Â projectile Â has Â its Â turnaround Â time Â equal Â to Â the Â maximum Â height Â time. Â

This Â means Â that: Â

đ?&#x2018;˘đ?&#x2018;˘ sin đ?&#x153;&#x192;đ?&#x153;&#x192; 1 = Â đ?&#x2018;&#x201D;đ?&#x2018;&#x201D; đ?&#x2018;&#x2DC;đ?&#x2018;&#x2DC; tan đ?&#x153;&#x192;đ?&#x153;&#x192;

đ?&#x2018;˘đ?&#x2018;˘ sin đ?&#x153;&#x192;đ?&#x153;&#x192; đ?&#x2018;&#x201D;đ?&#x2018;&#x201D;

đ?&#x2018;&#x2DC;đ?&#x2018;&#x2DC; tan đ?&#x153;&#x192;đ?&#x153;&#x192; = 1 Â

When Â we Â insert Â this Â value Â into Â the Â equation Â for Â horizontal Â distance, Â we Â get: Â đ?&#x2018;Ľđ?&#x2018;Ľ = đ?&#x2018;˘đ?&#x2018;˘ cos đ?&#x153;&#x192;đ?&#x153;&#x192; đ?&#x2018;Ąđ?&#x2018;Ą â&#x2C6;&#x2019;

Setting Â đ?&#x2018;Ľđ?&#x2018;Ľ Â to Â zero Â and Â solving Â for Â time, Â we Â get: Â Â

đ?&#x2018;&#x201D;đ?&#x2018;&#x201D; đ?&#x2018;Ąđ?&#x2018;Ą ! Â 2 tan đ?&#x153;&#x192;đ?&#x153;&#x192; 17 Â

Bolurin Edun - Mathematics

đ?&#x2018;&#x201D;đ?&#x2018;&#x201D; đ?&#x2018;Ąđ?&#x2018;Ą ! = 0 Â 2 tan đ?&#x153;&#x192;đ?&#x153;&#x192;

đ?&#x2018;˘đ?&#x2018;˘ cos đ?&#x153;&#x192;đ?&#x153;&#x192; đ?&#x2018;Ąđ?&#x2018;Ą â&#x2C6;&#x2019;

So Â the Â two Â solutions Â are: Â

đ?&#x2018;Ąđ?&#x2018;Ą đ?&#x2018;˘đ?&#x2018;˘ cos đ?&#x153;&#x192;đ?&#x153;&#x192; â&#x2C6;&#x2019;

đ?&#x2018;&#x201D;đ?&#x2018;&#x201D; đ?&#x2018;Ąđ?&#x2018;Ą = 0 Â 2 tan đ?&#x153;&#x192;đ?&#x153;&#x192;

đ?&#x2018;Ąđ?&#x2018;Ą = 0 Â Â Â Â Â , Â Â Â Â Â Â đ?&#x2018;Ąđ?&#x2018;Ą =

The Â second Â solution Â can Â be Â simplified Â to Â be: Â

đ?&#x2018;Ąđ?&#x2018;Ą =

2đ?&#x2018;˘đ?&#x2018;˘ cos đ?&#x153;&#x192;đ?&#x153;&#x192; tan đ?&#x153;&#x192;đ?&#x153;&#x192; Â đ?&#x2018;&#x201D;đ?&#x2018;&#x201D;

2đ?&#x2018;˘đ?&#x2018;˘ sin đ?&#x153;&#x192;đ?&#x153;&#x192; Â đ?&#x2018;&#x201D;đ?&#x2018;&#x201D;

This Â is Â the Â same Â as Â the Â landing Â time Â of Â the Â projectile. Â So Â the Â two Â times Â where Â the Â horizontal Â distance Â is Â zero Â are Â when Â the Â projectile Â is Â launched Â and Â when Â the Â projectile Â lands. Â This Â means Â that Â in Â this Â scenario, Â the Â projectile Â only Â goes Â up Â and Â down. Â

Summary Â The Â results Â from Â the Â various Â scenarios Â so Â far Â can Â be Â summarised Â in Â the Â table Â below. Â Â Turnaround Â time Â is Â greater Â than Â landing Â time Â

1 đ?&#x2018;&#x2DC;đ?&#x2018;&#x2DC; tan đ?&#x153;&#x192;đ?&#x153;&#x192; < Â 2

Turnaround Â time Â is Â less Â than Â landing Â time Â but Â greater Â than Â maximum Â height Â time Â

1 < đ?&#x2018;&#x2DC;đ?&#x2018;&#x2DC; tan đ?&#x153;&#x192;đ?&#x153;&#x192; < 1 Â 2

Turnaround Â time Â is Â smaller Â than Â maximum Â height Â time Â

đ?&#x2018;&#x2DC;đ?&#x2018;&#x2DC; tan đ?&#x153;&#x192;đ?&#x153;&#x192; > 1 Â

2 < đ?&#x2018;&#x2DC;đ?&#x2018;&#x2DC; tan đ?&#x153;&#x192;đ?&#x153;&#x192; < 1 Â 3

1 < đ?&#x2018;&#x2DC;đ?&#x2018;&#x2DC; tan đ?&#x153;&#x192;đ?&#x153;&#x192; < 2 Â Turnaround Â time Â is Â equal Â to Â maximum Â height Â time Â Â

đ?&#x2018;&#x2DC;đ?&#x2018;&#x2DC; tan đ?&#x153;&#x192;đ?&#x153;&#x192; = 1 Â

The Â projectile Â does Â not Â change Â direction Â during Â its Â flight Â The Â projectile Â changes Â direction Â horizontally Â before Â landing Â Â The Â projectile Â changes Â direction Â horizontally, Â and Â its Â horizontal Â distance Â at Â maximum Â height Â is Â greater Â than Â at Â landing Â The Â projectile Â turns Â around Â before Â reaching Â maximum Â height Â The Â projectile Â reaches Â maximum Â height Â in Â front Â of Â its Â launch Â point Â The Â projectile Â only Â goes Â vertically Â up Â and Â down Â

From Â this, Â we Â can Â observe Â a Â trend Â between Â the Â value Â of Â the Â constant Â k Â and Â the Â position Â of Â the Â maximum Â height Â relative Â to Â the Â start Â point Â of Â the Â projectile. Â As Â k Â increases, Â the Â horizontal Â position Â of Â the Â maximum Â height Â decreases Â due Â to Â the Â projectile Â experiencing Â air Â resistance. Â Â Â Â

18 Â

Bolurin Edun - Mathematics

Conclusion The research question is “how significant is the effect of a constant horizontal air resistance on projectile path?” This essay has shown that the answer to the research question is that a constant horizontal air resistance has a considerable effect on altering the path taken by a projectile in ideal conditions. It has the effect of decreasing the horizontal range of a projectile when it is opposing the projectile’s direction of motion, and of distorting the initially symmetrical parabolic path into an unsymmetrical, oblique path. We have seen the different categories of graphs that arise from varying the constant that determines air resistance. Furthermore, by answering the sub-‐questions that arose during the investigation, we have also seen that as the value of the constant ‘k’ increases, the maximum height of the projectile occurs farther and farther away from the initial position of the projectile. However, due to some of the bizarre solutions that arise due to the simplicity of this model, relative to the drag force explained on page 8, it does not reflect all the factors that determine horizontal air resistance that acts on a projectile. An extension to this model could possibly be to consider one that takes the velocity or the surface area of the projectile into account.

Bibliography 1. John McLester and Peter St. Pierre [2008] Applied Biomechanics; Concepts and Connections 2. Sixth Term Examination Papers Mathematics 1 [June 2014] Mechanics section, question 9 3. Wolfram Alpha; Wolfram Mathematica

19 58

Bolurin Edun - Mathematics

Theresa Grillo - German

Wie zeichnet sich die neue Schuldverarbeitung und VergangenheitsbewĂ¤ltigung der Geschehnisse des Dritten Reiches in der Literatur in Bernhard Schlinks Roman Der Vorleser aus?

Theresa Grillo - German

Theresa Grillo - German I have always been very interested in literature and especially in literature about the Second World War. I had realised that the early post-war literature after 1945 is characterized by a silence from the authors about the cruelties of the war. From 1960 onwards there was a new era of coping with the guilt since the authors did not try to euphemise the happenings of the Third Reich any longer. Therefore I chose the topic of my Extended Essay to be: How is the new processing of guilt and coping with the past of events of the Third Reich reflected in the literature of Bernhard Schlink’s novel “The reader”? From the beginning onwards I knew that this would be a challenge since I examined the development of post-war literature from the 1940s onwards and also analysed the novel and Bernhard Schlink’s way of addressing the guilt of National Socialism activists and their descendants. Therefore I had to read literature from numerous authors from different times. Nevertheless I really enjoyed my topic and the opportunity to dive into this aspect of literature and its history.

Supervisor: Alexandra Schmaller Theresa’s Extended Essay is a sophisticated analytical piece examining contemporary concepts within German literature. It ranks amongst the best pieces of work I have seen from any student, and would easily pass for an undergraduate linguistic analysis. Theresa has tackled a difficult and important theme for Germans: How contemporary German literature portrays, and deals with, guilt post-World War Two. Theresa has used Bernard Schlink’s (1995) Der Vorleser (engl. The Reader), in the centre of her analysis supported by several other important works from the modern, avant-garde and postmodern eras. Schlink’s Der Vorleser is a semi-autobiographical novel involving the responsibility, collective guilt and morals associated with the Nuremberg Trials in post-world war Germany. Theresa uses this work to convincingly conclude that more modern German literature now attempts to deal with the terrors and guilt associated with the war and the Holocaust, rather than simply ignoring it as the directly post-World War Two literature does. Theresa’s Extended Essay is a brilliant, thoughtful and captivating analysis of this very complex topic.

Theresa Grillo - German

Contents Einleitung

Die Phasen der Schuldverarbeitung und Vergangenheitsbewältigung nach 1945 in der Literatur

Zum Autor Bernhard Schlink

Der Roman der Vorleser 69 Fazit 74 Quellenverzeichnis 76

Abstract In der vorliegenden Arbeit wird analysiert, was die neue Schuldverarbeitung und Vergangenheitsbewältigung der Geschehnisse des Dritten Reiches in der Literatur auszeichnet. Dies wird anhand von Bernhard Schlinks Roman Der Vorleser illustriert. Um die Frage zu beantworten, geht diese Arbeit in die Geschichte der Literatur zurück. Das Ziel ist es, die wichtigsten Eigenschaften der Literatur aufzuzeigen, die ab 1945 mit dem Ende des Zweiten Weltkrieges bis zu den neunziger Jahren entstand. Dabei wird die Entwicklung von der Literatur des Kahlschlags über die der sechziger Jahre bis hin zu der Literatur der neunziger Jahre, zu der auch Bernhard Schlinks Roman gehört, veranschaulicht. Am Beispiel Bernhard Schlinks wird daraufhin gezeigt, wodurch sich nun die moderne Schuldverarbeitung auszeichnet und welche Absichten sich dahinter verbergen. Dies wird eingeleitet durch die Biografie des Autors und einer Auflistung seiner bekanntesten Werke. Um dem Leser ein Beispiel für den Stil Bernhard Schlinks als Vertreter der modernen Nachkriegsliteratur zu zeigen, wurde der Roman Der Vorleser ausgewählt. Dabei wird zunächst der Inhalt wiedergegeben und der Protagonist Michael Berg und seine Geliebte Hanna Schmitz werden charakterisiert, damit die weitere Analyse nachvollzogen werden kann. Daraufhin wird die Schuldverarbeitung und Vergangenheitsbewältigung in dem Roman analysiert. Die Überlegungen werden abschließend in einer Schlussfolgerung zusammengetragen. Bernhard Schlink, als Vertreter seiner Generation der Nachkriegsliteratur des Zweiten Weltkrieges, unterscheidet sich in seinem Stil sehr stark von der Literatur der direkten Nachkriegszeit, die unmittelbar nach Ende des Krieges erschien. Die Literatur der direkten Nachkriegszeit hatte es sich zum Ziel gemacht, die Grausamkeiten des Dritten Reiches zu vergessen und zu verdrängen, anstatt über diese zu schreiben. Schlinks Schreibstil hingegen zeichnet aus, dass über die Ereignisse wahrheitsgemäß berichtet wird und die Schuld von Vertretern der ersten Nachkriegsgeneration aufgearbeitet wird. 63

Theresa Grillo - German

1. Einleitung

Die Vergangenheitsbewältigung und Schuldverarbeitung Deutschlands in Bezug auf die Geschehnisse des Dritten Reiches sind seit Jahrzehnten ein wichtiges Thema in der Literatur

und

kulturellen

Diskussionen.

Schuldverarbeitung

ist

die

Auseinandersetzung und das Bewusstwerden der eigenen Schuld in Bezug auf ein Ereignis aus der Vergangenheit, wohingegen Vergangenheitsbewältigung als „die

wiederholte Auseinandersetzung mit belastender, in Gegenwart und Zukunft eines Staates hinein wirkender Vergangenheit“ (Konradin Medien GmbH, 2014) definiert wird. Peter Reichel sagte, dass Vergangenheitsbewältigung als ein „offener, in der

Zeiten-‐ und Generationsfolge immer wieder erneut und unter veränderten Bedingungen

stattfindender Prozess der Annäherung an die Vergangenheit verstanden werden“ (Reichel in Weber & Steinbach, 1984, S.147f) müsse. Ob es in der Schule ist oder im alltäglichen Leben, man wird immer mit der Geschichte des Dritten Reiches konfrontiert. Auch zahlreiche Vertreter der Enkelgeneration, die nur durch ihre Großeltern mit den Verbrechen verbunden sind, interessiert es, von den Ereignissen der Vergangenheit zu

erfahren. Es stellt sich fortlaufend die Frage, wie es soweit kommen und wie der Holocaust Wirklichkeit werden konnte. Daher interessiert besonders Literatur, die sich

mit den Verbrechen des Dritten Reiches befasst und in der die Schuld der Generationen

offengelegt und verarbeitet wird. Diese Schuld betrifft nicht nur die direkten Aktivisten des nationalsozialistischen Regimes, sondern auch deren Tochtergeneration, was im Folgenden noch weiter ausgeführt wird.

Der Roman Der Vorleser fasziniert besonders durch die Art, wie es Schlink gelingt, dem Leser die Thematik der Vergangenheitsbewältigung nahezubringen. Schlink verschönert

die Situation der Konzentrationslager nicht, doch der Leser begreift an der Person

Hanna Schmitz, wie schwer es ist, einige Aktivisten des Dritten Reiches zu verurteilen, ohne sie wenigstens auch in gewisser Weise zu verstehen. Schlinks Form der Vergangenheitsbewältigung unterscheidet sich zum Beispiel fundamental von einem

Großteil der direkten Nachkriegsliteratur nach 1945. So werden beispielsweise der

Nationalsozialismus oder Holocaust im Roman Sansibar oder der letzte Grund von Alfred

Andersch nie direkt beim Namen genannt und Aspekte des Dritten Reiches chiffriert. Ein historischer Diskurs wird bewusst vermieden, verallgemeinernd wird lediglich von

einer Bedrohung durch „die Anderen“ (Andersch, 1957, S. 26) gesprochen. Ein Grund für

Theresa Grillo - German

diesen signifikanten Unterschied könnte die Tatsache sein, dass Schlink seinen Roman

Mitte der neunziger Jahre schrieb und etwa Andersch sein Werk im Jahr 1957 veröffentlichte. Das motiviert, der Frage nachzugehen, wie sich diese neue

Schuldverarbeitung und Vergangenheitsbewältigung in der Literatur von Schlink

auszeichnet, und inwieweit sie sich von der Literatur der direkten Nachkriegsjahre unterscheidet. Diesem Vorhaben folgend werden zunächst wesentliche Merkmale der unmittelbaren Nachkriegsliteratur von 1945 bis zu den 1960er Jahren aufgezeigt,

welche im Anschluss einem Vergleich mit den zentralen Besonderheiten der modernen

Nachkriegsliteratur ab den sechziger Jahren unterzogen werden. Die Ausgangsfrage wird durch die Art der Thematisierung von Schuld in Schlinks Roman Der Vorleser beantwortet werden.

Die Hypothese liegt nahe, dass die moderne Nachkriegsliteratur sich dadurch auszeichnet, dass die Autoren die Verbrechen des Dritten Reiches nicht ignorieren, da „das Reden über die Vergangenheit selbstverständlich (...) ist.“ (Schlink, 2002, S. 148)

2. Die Phasen der Schuldverarbeitung und Vergangenheitsbewältigung nach 1945 in der Literatur

2.1.

Die Phase der unmittelbaren Nachkriegsliteratur

Die Phase der unmittelbaren Nachkriegsliteratur, die nach Ende des Zweiten Weltkrieges entstand, war geprägt vom Schweigen, denn es „gewannen Verleugnung

und Rationalisierung die Oberhand“ (Schlant, 2001, S.35). Die Trümmerliteratur und

Heimkehrliteratur prägten eine Zeit, die als die Zeit des „Kahlschlags“ bezeichnet wird.

Die Werke dieser Zeit wurden von den Involvierten und Betroffenen der Begebenheiten verfasst. Die Trümmerliteratur entstand, denn „während die deutschen Städte in Schutt und Asche lagen, suchte die Trümmerliteratur nach Mitteln und Wegen, um das Leiden

der deutschen Bevölkerung während und nach dem Krieg zu beschreiben“ (Schlant, 2001, S.37). In der Heimkehrerthematik ging es um „die schrecklichen Erlebnisse der

Kriegsheimkehrer oder der entlassenen Kriegsgefangenen“ (Feuchert & Hofmann, 2005, S.61). Die Verbrechen und das Ausmaß der eigenen Schuld wurden nicht beim Namen

genannt, da die Bevölkerung Scham darüber empfand und mit dem Wiederaufbau der

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Städte beschäftigt war. Besonders der Holocaust wurde in der Literatur verschwiegen

oder verdrängt, und die Mitglieder der Gruppe 47 dachten, es sei unmöglich, die

Schandtaten der Konzentrationslager in literarischen Texten auszuformulieren. Die

Gruppe 47 war ein Zusammenschluss mehrerer Schriftsteller, die aus dem Krieg

heimgekehrt waren. Mitglieder dieser Gruppe waren berühmte Schriftsteller wie Andersch, Günter Grass, Heinrich Böll, Hans Werner Richter und viele weitere. Ihr Ziel

war es, die Sprache der Literatur von der nationalsozialistischen Sprache zu befreien, die durch Lüge und Propaganda gekennzeichnet war (Wecker, n.d.). Auch wenn zum Beispiel der Begriff der Schuld in Werken von Böll (Billiard um halbzehn, Essays zur deutschen Wehrmacht, Todesursache: Hakennase) deutlich zur Sprache kommt und beispielsweise Autoren und Dramatiker, wie etwa Berthold Brecht, den Faschismus

deutlich anprangern, setzen sich viele nicht mit den wirklichen Verbrechen des nationalsozialistischen Regimes auseinander. Die Trümmerliteratur machte später einer

Literatur Platz, die das sogenannte deutsche Wirtschaftswunder der 1950er Jahre beschrieb. Die Deutschen steckten ihre Energie in den Wiederaufbau und es fand

abermals keine Reflexion darüber statt, wie es zu dem nationalsozialistischen Staat und dessen Verbrechen überhaupt kommen konnte.1

2.2.

Die Nachkriegsliteratur in der Moderne zwischen Avantgarde und Postmoderne

Am Anfang der sechziger Jahre begann eine neue Form der Auseinandersetzung mit der Vergangenheit. Durch den Auschwitz-‐Prozess im Jahre 1968, in dem es um Gräueltaten

der Konzentrationslager ging, konnte die Vergangenheit nicht mehr verschwiegen werden. Die Studentengemeinschaft der sechziger Jahre kritisierte die „widerstandslose, geradezu willfährige Beteiligung am Nationalsozialismus“ (Möckel, 2013, S.20) und fragte nach der „Verantwortung, Verdrängung und Versagen der Elterngeneration“

(ibid.). Die Literatur dieser Generation ist sehr dokumentarisch und setzt auf Konfrontation mit den Schandtaten der Elterngeneration.

1 „Niemand stellte Fragen nach den Ursachen der Konsolidierung von Hitlers Macht oder

nach den Gründen des Krieges, nach der Rolle des einzelnen deutschen Staatsbürgers“ (Schlant, 2001, S.38)

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Die nächste entscheidende Phase markieren die neunziger Jahre. Die Autoren dieser

Generation sind nicht mehr persönlich in die Geschehnisse des Zweiten Weltkrieges

involviert und ihre Literatur zeichnet sich dadurch aus, dass die Vergangenheit von der Generation der Nachgeborenen aufgearbeitet wird. Der Tonfall ist weniger kritisch, als

der der vorhergehenden Literaturphase und es wird eine „allgemeinere Ebene der

Auseinandersetzung mit menschlichen Verhaltensweisen, Fragen von Schuld und Sühne, Egoismus und anderen Unzulänglichkeiten erreicht“ (Möckel, 2013, S. 23). Außerdem

charakterisiert diese Literatur, die von den meisten Autoren gewählte Ich-‐Perspektive als Erzählform. Der Grund liegt darin, besondere Nähe zwischen Leser und

Protagonisten schaffen zu wollen. Zu dieser modernen Phase gehört auch Schlink und

noch heute zeichnen sich Werke durch derartige Züge aus.

3. Zum Autor Bernhard Schlink

3.1.

Leben und Werke

Bernhard Schlink wurde am 6.Juli 1944 in Bielefeld geboren und wuchs in Heidelberg

und Mannheim auf. Bis zu seinem 30. Lebensjahr studierte er Rechtswissenschaften in Heidelberg und Berlin und verfasste als Jurist zahlreiche fachkundliche Lehrbücher. Seit

1992 ist er Juraprofessor an der Humboldt-‐Universität Berlin und arbeitete zwischenzeitlich von 1992 bis 2006 als Verfassungsrichter in Nordrhein-‐Westfalen.

Neben seiner Lehrtätigkeit schrieb er etliche Romane und im Jahre 1995 erschien das

erfolgreichste Werk Schlinks Der Vorleser. Der Roman war ein außergewöhnlicher Verkaufserfolg und wurde 1997 als englischsprachige Ausgabe The Reader auf den

internationalen Markt gebracht. Nur zwei Jahre später belegte der Roman Platz eins der

Bestsellerlisten und war der erste Roman Schlinks, der nicht der Gattung des Kriminalromans zugeordnet wird (Möckel, 2013, S.10ff). 3.2. Auffälligkeiten in Bezug auf den Schreibstil des Autors

Der literarische Stil des Autors ist durch seine Profession stark geprägt, denn viele seiner Protagonisten arbeiten wie Schlink selbst in der Justiz und in allen Werken wird

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der Aspekt der Schuld aufgegriffen. Als Vertreter der Nachkriegsgeneration, ohne direkten Kontakt zum Krieg und mit zeitlicher Distanz zu den Geschehnissen, setzt sich Schlink anders mit dem Thema der Schuld auseinander als die Autoren der direkten Nachkriegsjahre, wie zum Beispiel die Gruppe 47. Schlink nennt die Verbrechen des

deutschen Volkes beim Namen und versucht keine Entschuldigungen für die Geschehnisse des Zweiten Weltkrieges zu finden. Er schreibt nicht nur schlicht von den

Verbrechen des Krieges selbst, sondern hebt hervor, wie die Charaktere damit umgehen.

Er gehört zu einer „neue(n) Phase der Auseinandersetzung mit dem Holocaust“ (Möckel,

2013, S.20). Doch diese Literatur hatte es erst nicht leicht sich durchzusetzen, denn „als

Drittes Reich und Holocaust in den sechziger Jahren thematisiert wurden, musste das Thema gegen Widerstände durchgesetzt und behauptet werden“ (Schlink, 2002, S.146).

Schlink charakterisiert die Literatur seiner Generation als „tonangebend“ (Schlink, 2002, S.146), besonders „nach einer Generation, in der gerade die Opfer und Täter Scheu

hatten, von der Vergangenheit zu reden“ (ibid.). Mit dem von ihm gewählten Begriff der Scheue bezieht er sich auf die Autoren der direkten Nachkriegsgeneration, die nicht den Mut hatten, die Begebenheiten des zweiten Weltkrieges offenzulegen.

Ein Aspekt, der die Werke Schlinks besonders auszeichnet, ist die Vermenschlichung der

Täter. Er versucht sie nicht als Monster darzustellen, sondern lädt den Leser ein, sich mit ihren Motiven auseinanderzusetzen und so ihr Handeln zu verstehen.2 Ein Beispiel dafür

ist die ehemalige KZ-‐Aufseherin Hanna Schmitz in Der Vorleser, die sogar als Opfer ihres Analphabetismus beschrieben wird. Diese Identifikation mit den Tätern ist wichtig, denn Schlink fragt, „was man selbst in dieser oder jener vergangenen Situation getan hätte“

(Schlink, 2002, S.149). Die Werke des Autors sind durch das „unerwartete und unvorhersehbare Einbrechen der Vergangenheit in das gegenwärtige Leben“ (Feuchert

& Hofmann, 2005, S.59) der Protagonisten geprägt. Protagonisten wie Hanna Schmitz in

Der Vorleser oder Gerhard Selb in dem Kriminalroman Selbs Justiz (Schlink, 1987) sind plötzlich wieder mit ihrer eigenen Vergangenheit konfrontiert und werden somit aus

der Phase des Vergessens geholt. Eine weitere Parallele zwischen seinen Werken

besteht darin, dass die Protagonisten ihre Geschichte am Ende aufschreiben, um mit ihr 2 „Aber wenn die Täter immer Monster wären, wäre die Welt einfach. Sie sind es nicht. Meine Generation hat das vielfach erlebt, beim Lehrer oder Professor, beim Pfarrer oder Arzt, beim Onkel oder sogar Vater, über deren Vergangenheit eines Tages offenbart wurde, was ganz und gar nicht zum Respekt, zur Bewunderung oder sogar zur Liebe passte, die das Verhältnis bestimmt hatte.“ (Kilb, 2009)

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zu leben. Ihnen wird bewusst, dass es keinen Sinn hat, die Vergangenheit zu verdrängen. Schlink schreibt über den Holocaust, die Ereignisse des Zweiten Weltkrieges und ihre Bewältigung „nicht nur weil ihre Furchtbarkeiten so furchtbar sind, dass sie nie

vergessen werden können“ (Schlink, 2002, S.154), sondern auch, weil er erinnern möchte, zu welchen Verbrechen der deutsche Staat mit seinen Bürgern schon einmal

fähig war.3 Dies zeigt, dass er es sich zum Ziel gesetzt hat, die Menschen zu warnen, denn

er möchte verhindern, dass es noch einmal zu Verbrechen in derartiger Weise kommen kann. 4. Der Roman Der Vorleser

4.1.

Das Handlungsgerüst des Romans

Das Werk Der Vorleser gilt „als erster wirklich gelungener deutscher Versuch, die

Auseinandersetzung mit dem Holocaust beziehungsweise den Tätern in fiktionaler Form literarisch zu verarbeiten“ (Feuchert & Hofmann, 2005, S. 64). Es handelt sich um einen

Roman, der die Geschichte des Protagonisten Michael Berg, einem Vertreter der ersten Nachkriegsgeneration, in drei Abschnitten seines Lebens erzählt. Als Jugendlicher geht

er ein Verhältnis mit der deutlich älteren Hanna Schmitz ein. Ihre Treffen bestehen aus

einem „Ritual des Vorlesens, Duschens, Liebens und Beieinanderliegens“ (Schlink, 1995, S. 51), doch plötzlich verschwindet Hanna ohne eine Nachricht zu hinterlassen.

Michael begegnet ihr erst Jahre später wieder im Gerichtssaal. Es stellt sich heraus, dass

Hanna eine ehemalige Aufseherin der SS ist und angeklagt wird, zahlreiche

Menschenleben auf dem Gewissen zu haben. Außerdem erfährt Michael von Hannas

Analphabetismus, den sie jahrelang versteckt hat. Diese Wahrheit hätte Hanna vor der lebenslangen Gefängnisstrafe retten können, doch weder sie, noch Michael erzählen dem

Gericht von ihrer Schwäche. Während Hannas Inhaftierung schickt Michael ihr

Kassetten mit Vorgelesenem, wodurch es ihr ermöglicht wird, sich selbst das Lesen und Schreiben beizubringen. Michael besucht Hanna erstmals im Gefängnis nach 28 Jahren, 3 „Wenn damals das Eis, auf dem man sich kulturell und zivilisatorisch sicher wähnte, in Wahrheit so dünn war – wie sicher ist das Eis, auf dem wir heute leben?“ (Schlink, 2002, S.148)

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aber kann in ihr nicht mehr die alte Geliebte wiedererkennen. Am Tag ihrer Entlassung begeht Hanna letztendlich Selbstmord. 4.2. Person Michael Berg

Der Protagonist Michael Berg wird 1943 geboren und wächst in Heidelberg auf. Sein Vater ist ein Philosophieprofessor und hat ein eher distanziertes Verhältnis zu seinen Kindern.4 Michaels erste Begegnung mit der 22 Jahre älteren Hanna Schmitz erfolgt mit

15 Jahren. In dem Verhältnis mit Hanna scheint Michael sich der älteren und reiferen Frau geradezu unterzuordnen, und er nimmt freiwillig jede Schuld auf sich, sobald es zu einem Streit zwischen den beiden kommt 5. Als Hanna abrupt verschwindet, ist er

zutiefst betrübt. Michael studiert Jura und versucht mit seinen Kommilitonen die Vergangenheit aufzuarbeiten. Erst dann begegnet er Hanna wieder in einem NS-‐Prozess,

in dem sie angeklagt wird. Michael fühlt sich schuldig, eine ehemalige Verbrecherin

geliebt zu haben, kann sie aber auch den Rest seines Lebens nicht vergessen. 6 Die

Beziehung zu Hanna bestimmt sein ganzes Leben, denn jede Frau vergleicht er mit Hanna. Er ist ein sehr ambivalenter Charakter und beschreibt seine Gemütslage als ein

„Nebeneinander von Kaltschnäuzigkeit und Empfindsamkeit“ (Schlink, 1995, S.85). Er

steht stellvertretend für die erste Nachkriegsgeneration, die keinen direkten Kontakt zum Zweiten Weltkrieg hat.

4.3. Person Hanna Schmitz

Hanna Schmitz taucht erstmals in dem Roman als 37-‐jährige Frau auf, als sie eine Beziehung mit Michael beginnt. Im zweiten Teil des Buches erfährt der Leser von ihrem Analphabetismus und ihrer ehemaligen Profession als Siemensmitarbeiterin. Der Analphabetismus prägt ihr ganzes Leben, da sie in ständiger Angst lebt, jemand könne

ihre Schwäche herausfinden. Dieses Schicksal hatte auch einst dazu geführt, dass sie

4 „Mein Vater war verschlossen, konnte weder uns Kindern seine Gefühle m itteilen noch

etwas mit den Gefühlen anfangen, die wir ihm entgegenbrachten.“ (Schlink, 1995, S.134)

5 „ ... und ich erniedrigte und entschuldigte mich“ (Schlink, 1995, S.71)

6 „Ich wollte von Hanna frei sein. Aber das Gefühl, dass es nicht stimmt hat sich nie

verloren.“ (Schlink, 1995, S.165)

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eine Beförderung bei Siemens ablehnte und die Stelle als KZ-‐Aufseherin annahm. In

einem Prozess wird sie angeklagt, den Befehl gegeben zu haben, die Inhaftierten des Lagers in einer Bombennacht in einer brennenden Kirche eingeschlossen und sie somit dem sicheren Tod ausgesetzt zu haben. Beweis dafür soll ein von ihr unterzeichnetes Dokument sein, aber Hanna klärt nicht auf, dass sie dieses aufgrund des

Analphabetismus nicht unterschrieben haben konnte und wird somit zu einer lebenslänglichen Gefängnisstrafe verurteilt. Ihre Bemühungen um Geheimhaltung ihrer

Unfähigkeit zehren nicht nur an ihr, sondern führen auch dazu, dass sie alle Menschen in ihrem Umfeld auf Distanz hält (Schlink, 1995, S.70). Selbst Michael weiht Hanna nicht in

ihr Geheimnis ein und obwohl „sie auf der einen Seite hilfsbereit und zärtlich Michael gegenüber sein kann“ (Möckel, 2013, S.57), schlägt die Ambivalenz ihres Charakters und

ihre Erschöpfung durch das konstante Versteckspiel auch manchmal in Härte und Brutalität um (Schlink, 1995, S.54).

4.4.

Schuldverarbeitung und Vergangenheitsbewältigung in dem Roman

Der Vorleser gehört zu der Phase der literarischen Aufarbeitung des Holocausts und den

Geschehnissen des Zweiten Weltkriegs in der Moderne, die sich ab den sechziger Jahren entwickelte. Es wird die Schuld der individuellen Geschichten der handelnden Personen

mit der Schuld der Verbrechen des Zweiten Weltkrieges verbunden. Schlinks Art mit den

Begebenheiten der Kriegs-‐ und Nachkriegsjahre umzugehen, wird dadurch

charakterisiert, dass er die Verbrechen beim Namen nennt und nicht versucht, sie zu

beschönigen. Mit den beiden Protagonisten Michael und Hanna gelingt es dem Autor, die

Schuldgefühle zweier Generationen zu illustrieren. Michael ist ein Vertreter der zweiten Generation, der zwar nicht in direktem Kontakt mit dem Krieg steht, aber durch seine Eltern und die Beziehung zu Hanna in die Verbrechen verstrickt ist. Hanna Schmitz

hingegen ist eine Angehörige der ersten Generation, die als aktives Mitglied bei den Verbrechen der nationalsozialistischen Regierung mithalf. Die Frage nach Schuld und Unschuld erfährt keine Antwort, aber beide Protagonisten schrecken nicht davor zurück,

sich am Ende des Romans mit ihrer Schuld auseinanderzusetzen, sowie die

Vergangenheit aufzuarbeiten.

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Michael begeht Unrecht und nimmt Schuld auf sich, indem er Hannas Analphabetismus

verschweigt, und sie somit nicht vor ihrer Gefängnisstrafe retten kann. Er entwickelt Schuldgefühle, da er eine Verbrecherin des Naziregimes liebt. Michael steht

stellvertretend für die Kindergeneration des Krieges, die sich mit der Schuld der

Elterngeneration konfrontiert sieht durch den „überheblichen Eifer beim Zur-‐Kenntnis-‐

Nehmen und Aufklären der Furchtbarkeiten der NS-‐Zeit“ (Möckel, 2013, S.104) und die Verbindung zu den Eltern. Er gehört zu der Generation, die sich als „Avantgarde der

Aufarbeitung“ (Schlink, 1995, S.87) sieht. „Aufarbeitung der Vergangenheit!“ (Schlink,

1995, S.87) ist ihr Ziel, denn sie „rissen die Fenster auf, ließen die Luft herein, den Wind, der endlich den Staub aufwirbelte, den die Gesellschaft über die Furchtbarkeiten der Vergangenheit hatte sinken lassen“ (Schlink, 1995, S.87). Vor dem Prozess Hannas meint Michael zwischen Recht und Unrecht unterscheiden zu können, doch es fällt ihm immer

schwerer sie zu verurteilen, da er merkt, dass auch die Verbrecher Menschen sind und keine Unmenschen. In diesem Punkt kann man nicht einfach zwischen schwarz und

weiß unterscheiden, denn manchmal gibt es Gründe, die einen Menschen dazu bewegen, etwas Grausames zu tun. Dies kann deswegen natürlich nicht entschuldigt, aber

möglicherweise bis zu einem gewissen Punkt verstanden werden. Dieser Aspekt

zeichnet Schlinks Werk aus, denn ihm gelingt es die Täterin Hanna in gewisser Weise auch als Opfer darzustellen, mit dem man Mitleid bekommt.7 Michael befindet sich in

einem moralischen Konflikt, denn er „wollte Hannas Verbrechen zugleich verstehen und verurteilen. Aber es war dafür zu furchtbar“ (Schlink, 1995, S.151). Zuerst bemüht sich Michael seine Vergangenheit zu verdrängen, doch im Nachhinein will er seine Schuld

wiedergutmachen, indem er Kassetten für Hanna bespricht und diese die Schwäche des Analphabetismus somit besiegt. Michael erkennt auch, dass die einzige Möglichkeit der Verarbeitung der Begebenheiten in seinem Leben darin liegt, diese niederzuschreiben

und er verfasst ein Buch.

Eine weitere Besonderheit in Der Vorleser ist die gewählte Erzählperspektive, die zwischen dem Erlebenden Ich und dem Erzählenden Ich wechselt. Die Stellen des Erlebenden Ichs werden von dem jungen Michael erzählt, der unsicher ist und im

inneren Monolog viele Fragen stellt. Durch das Erzählende Ich wird gezeigt, wie Michael 7 „Wenn es nicht die menschliche Sicht auf die Täter gäbe, hätten wir kein Problem mit ihnen. Erst die menschliche Nähe zu ihnen macht das, was sie getan haben, so furchtbar“ (Schlink in Doerry&Hage, 2000)

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sich im Laufe seines Lebens weiterentwickelt und Situationen und seine Schuld somit retrospektiv besser beurteilen kann. Am Beispiel Michaels erkennt man, wie eng die

zweite Generation mit der Schuld der ersten Generation zusammenhängt. Diese zweite Generation versucht sich durch „Anklagen, Verurteilen und Ausstoßen der Täter, Mittäter und Zuschauer der ersten Generation“ (Schlink in Salatgarten, 1998, S.44) aus

der Schuld zu befreien, doch Michael versteht, dass die Elterngeneration in der

Gemeinschaft aufgenommen wurde und somit die Schuld an den Verbrechen kollektiv

geteilt wird. In der Vergangenheitsbewältigung des eigenen Lebens des Protagonisten Michael kann eine Parallele zu der Vergangenheitsbewältigung in der Geschichte der

Nachkriegsliteratur gesehen werden. Zuerst flüchtet er vor seiner Vergangenheit und

versucht die Erlebnisse zu verschweigen, was der direkten Nachkriegsliteratur nach 1945 entspricht. Doch dann merkt er, dass dies auch seine Vergangenheit ist und er sie

nicht verschweigen kann, was mit der Nachkriegsliteratur der Moderne übereinstimmt.

Hanna wird schuldig als Aufseherin im Konzentrationslager und steht damit für die

Zeitgenossen der NS-‐Zeit. Die Schuld dieser Generation liegt darin, dass sie dem Regime aktiv half und die Verbrechen durch wenig oder gar keinen Widerstand geschehen ließ. In der Figur Hanna Schmitz lassen sich Übereinstimmungen mit der bekannten

Aufseherin Hermine Braunsteiner feststellen, die in dem Majdanek Prozess verurteilt wurde. Genau wie Hanna es am Anfang des Romans versucht, ließ auch Hermine Braunsteiner die Vergangenheit ruhen und zog nach New York. Doch trotz dieser

Parallelen wird im Roman offensichtlich, dass Hanna nur als Modell für Involvierte des Zweiten Weltkrieges steht und es kein direktes Vorbild gibt. Hanna lässt sich in dem

Roman zu Schulden kommen, dass sie zahlreiche Menschenleben auf dem Gewissen hat,

sowohl durch die monatlichen Selektionen im Lager, als auch durch die in der Bombennacht verbrannten Opfer in der Kirche. Am Beispiel Hannas kann erkannt

werden, dass sie sich, genau wie viele Aktivisten des Zweiten Weltkrieges, nach Ende des Krieges nicht an ihre Vergangenheit erinnern und diese vergessen will. Sie spricht

nie mit Michael darüber, doch plötzlich holt ihre Vergangenheit sie im Prozess wieder ein. Anfangs kämpft sie im Prozess noch für ihr Recht, irgendwann gibt sie jedoch auf,

denn „sie redete nur noch, wenn sie gefragt wurde, sie antwortete kurz, dürftig, manchmal fahrig“ (Schlink, 1995, S.131). Der Grund könnte darin liegen, dass sie einerseits erschöpft ist von dem ewigen Widersprechen und andererseits aber auch ihre

Strafe akzeptieren und für ihre Verbrechen sühnen möchte. Dies würde einen wichtigen

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Teil ihrer Vergangenheitsbewältigung darstellen, denn sie bekennt sich zu ihrer Vergangenheit und bereitet der Zeit des Wegsehens ein Ende. Ein weiterer Schritt in

diese Richtung kann nachher in ihrem Verhalten im Gefängnis erkannt werden. Sie träumt viel von den Opfern der NS-‐Zeit und „nachdem Frau Schmitz lesen gelernt hat, hat sie gleich angefangen, über KZs zu lesen“ (Schlink, 1995, S.194).

Beide Protagonisten zeigen wie attraktiv es zunächst erscheint, seine Schuld einfach zu verdrängen oder zu vergessen. Schlink erklärt den Aspekt der individuellen Schuld und Kollektivschuld, denn in seinem Roman will er darstellen, welch schlimme Dinge

Menschen einander antun.8 Des Weiteren wird nicht nur die Schuld der ersten und zweiten Generation in seinem Roman diskutiert, sondern Schlink geht auch auf die Frage nach der Schuld der dritten Generation ein, denn Michael fragt sich: „Was sollte und soll

meine Generation der Nachlebenden eigentlich mit den Informationen über die

Furchtbarkeiten der Vernichtung der Juden anfangen?“ (Schlink, 1995, S. 99) Schlink erwähnt, dass die dritte Generation „nicht vor der Wahl steht, Solidarität mit den Tätern der ersten Generation zu üben“. Es sei aber wichtig, dass die Geschehnisse als

Geschichte in die Biografie Deutschlands eingehen. (Schlink, 1998, Auszug in Möckel, 2013, S.15) 5. Fazit

In Schlinks Roman Der Vorleser kann eindeutig erkannt werden, wie der Autor die

Schuld der nationalsozialistischen Gesellschaft verarbeitet. Die Ereignisse werden aus

der Sicht eines Jungen erzählt, der zu der zweiten Nachkriegsgeneration gehört. Die individuelle Schuld der Protagonisten wird mit der Schuld des Dritten Reiches

verwoben. Schlink schreckt nicht davor zurück, die Verbrechen in den Konzentrationslagern in brutaler Wahrheit zu illustrieren, doch die Täterin Hanna

Schmitz ist auch Opfer in seinem Roman und wird nicht als das Monster dargestellt, das

8 „was Menschen einander antun und einander schuldig bleiben können, wie sie, ohne Monster zu sein, die furchtbarsten Verbrechen begehen können, wie politische und gesellschaftliche Institutionen versagen und wie eine moralische Kultur zusammenbrechen kann, schließlich auch wie man sich zu denen verhält, die die furchtbarsten Verbrechen begangen haben“ (Schlink, 1998, Auszug in Möckel, 2013, S.15)

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die Gesellschaft gerne in einer Aufseherin der Konzentrationslager sehen würde.

Dadurch erscheint es dem Leser nahezu unmöglich, sie ohne Mitleid zu verurteilen. Schlink steht damit stellvertretend für die Literatur von Autoren einer zweiten Nachkriegsgeneration, die sich ab den neunziger Jahren entwickelte. Diese Autoren unterscheiden sich in ihren Absichten und der Art und Weise, wie die Verbrechen des

Dritten Reiches beschrieben und verarbeitet werden von der Literatur der unmittelbaren Nachkriegsjahre.

Schlink hat wie die anderen Autoren dieser modernen literarischen Phase erkannt, dass historische Dimensionen nicht ignoriert oder plakativ abgebildet werden dürfen, sondern dass die Vergangenheits-‐ und Schuldbewältigung sowie der Schuldbegriff

differenzierter betrachtet werden müssen. Seine Absicht ist nicht das Vergessen des Krieges, sondern vielmehr der Appell an die Gesellschaft, bewusst mit der Vergangenheit zu leben.

In diesem Sinne formuliert Schlink: „Es gibt keine Bewältigung. Aber es gibt das bewusste Leben mit dem, was die Vergangenheit gegenwärtig an Fragen und Emotionen

auslöst“ (Schlink, 2002, S.153). Die Ergebnisse dieser Arbeit werfen also die Frage auf, ob es überhaupt eine vollständige Vergangenheitsbewältigung geben kann und wie

rigoros diese vorangetrieben werden darf. In einem Interview der Frankfurter Allgemeinen Zeitung sagte Schlink, dass trotz aller Effizienz des gegenwärtigen

öffentlichen Diskurses, dennoch ein „Gefühl des Unheimlichen“ (Kilb, 2009) bliebe und

eine „behutsamere Bewältigung vielleicht auch bedeutet, die Unmöglichkeit der

Bewältigung (...) abzubilden.“ (ibid.) Dies zeigt uns, dass die Verbrechen und Begebenheiten des Holocausts und Zweiten Weltkrieges immer ein bedeutendes Thema in der Literatur sein werden und eine vollständige Bewältigung trotz aller gegenwärtigen Mühen nicht möglich ist.

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6. Quellenverzeichnis Andersch, A., 1957. Sansibar oder der letzte Grund. Zürich: Diogenes Verlag Braese, S., 1999. Bestandsaufnahme – Studien zur Gruppe 47. Berlin: Erich Schmidt Verlag Doerry, M. & Hage, V., 2000. Ich lebe in Geschichten. (Online) Verfügbar unter: http://www.spiegel.de/spiegel/print/d-‐15502682.html (aufgerufen am 15.7.2015) Feuchert, S. & Hofmann, L., 2005. Lektüreschlüssel Bernhard Schlink Der Vorleser. Stuttgart: Philipp Reclam jun. GmbH & Co. KG Kilb, A., 2009. Herr Schlink, ist „Der Vorleser“ Geschichte? (Online) Verfügbar unter: http://www.faz.net/aktuell/feuilleton/buecher/im-‐gespraech-‐bernhard-‐schlink-‐herr-‐ schlink-‐ist-‐der-‐vorleser-‐geschichte-‐1100720-‐p4.html (aufgerufen am 22.8.2015) Konradin Medien GmbH., 2014 Wissen.de Lexikon (Online) Verfügbar unter: http://www.wissen.de/lexikon/vergangenheitsbewaeltigung (aufgerufen am 29.9.2015) Möckel, M., 2013. Königs Erläuterungen Bernhard Schlink Der Vorleser. Hollfeld: C. Bange Verlag Schlant, E., 2001. Die Sprache des Schweigens. Die deutsche Literatur und der Holocaust. München: C.H. Beck OHG Verlag Schlink, B., 1995. Der Vorleser. Zürich: Diogenes Verlag Schlink, B., 1987. Selbs Justiz. Zürich: Diogenes Verlag Schlink, B., 1998. Salatgarten Heft 1. Seenlandschaft: Hans-‐Fallada-‐Gesellschaft Schlink, B., 2001. Auf dem Eis, (Online) Verfügbar unter: http://www.spiegel.de/spiegel/print/d-‐19120366.html (aufgerufen am 8.7.2015) Schlink, B., 2007. Vergangenheitsschuld. Zürich: Diogenes Verlag Schmitz, T. & Fuchs, A., 1996. Die Stute von Majdanek. Süddeutsche Zeitung (Download) Verfügbar unter: http://sz-‐magazin.sueddeutsche.de/texte/anzeigen/43081/101-‐bis-‐ 120 Moment 106: 1966 (aufgerufen am 8.7.2015) Weber, J. & Steinbach, P., 1984. Vergangenheitsbewältigung durch Strafverfahren? NS-‐ Prozesse in der Bundesrepublik Deutschland. München: Olzog Verlag Wecker, A., n.d. Die Gruppe 47. (Online) Verfügbar unter: http://www.uni-‐ulm.de/LiLL/senior-‐info-‐mobil/module/Lit47.htm (aufgerufen am 16.7.2015)

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To what extent does our understanding of the risk factors of Alzheimerâ&#x20AC;&#x2122;s Disease assist prevention?

Cecilia Jay - Psychology

Cecilia Jay - Psychology When approaching my Extended Essay, I knew I wanted to research a topic of relevance and importance in the field of the biomedical sciences; Alzheimer’s seemed to me a clear overlap of science, medicine, psychology and sociology. I wanted to better understand this disease that affects so many people, but is seemingly incurable - or even overlooked by many as inevitable. One of the challenges I faced with this essay was the obvious fact that ageing cannot be prevented, yet I felt this was not an adequate excuse to ignore the other risk factors and turn my interest to other healthcare issues that are perhaps more dynamic and affect people of all ages. Writing this essay, I learnt that the development of Alzheimer’s is not inevitable by any means, and the continuation of research into the area is just as important as any other scientific or medical pursuit.

Supervisor: Ian Campbell Cecilia followed in her sisters footsteps by studying Psychology and it became an area she soon grew to love. This was partly because modern Psychology integrates significant biological and medical components especially in the Abnormal part of the course, and so this essay on Alzheimer’s disease allowed for the perfect blend of Psychology and medicine. With the alarming statistics regarding the prevalence of Alzheimer’s disease, this essay is highly relevant to today’s aging population and by specifically looking at risk factors there were clear and obvious applications we can take from her research. Such is the importance and contemporary nature of her work that I can only feel it should reach wider publication and readership, and then perhaps many real lives could be enhanced.

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Contents Introduction 80 Section A: Cardiovascular Health

Section B: Traumatic Brain Injury

Section C: Gender

Section A: Genetics

Conclusion

Bibliography and References

Abstract This essay explores how scientific research into Alzheimer’s disease, and a growing understanding of its risk factors, may facilitate prevention. Alzheimer’s disease is common in the ageing community, and a subject of interest due to its debilitating effects and lack of cure. My research question is as follows: To what extent does our understanding of the risk factors of Alzheimer’s Disease assist prevention? The investigation considers four major risk factors as uncovered by recent research; specifically cardiovascular health, traumatic brain injuries, gender and genetics. I am exploring these topics using data mainly from recent scientific publications by experts in the field of neurology. I find that maintaining a healthy cardiovascular system can prevent the onset of Alzheimer’s disease. In addition, brain injuries from physical trauma are another risk factor that should be protected against with helmets in dangerous activities in order to reduce incidence of Alzheimer’s. I also explore how low oestrogen levels in post-menopausal women can increase their risk, further evaluating the use of hormone-replacement therapy as a preventative measure. Finally, I find which genes have been isolated as linked to Alzheimer’s disease, and discuss how we could genetically engineer in the future to reduce their frequency. After evaluating and comparing the studies presented in the publications, as well as analysing their reliability and validity, I find that, with present research available, we are able to focus on risk factors that can be avoided, such as lifestyle and traumatic brain injury, rather than genetics or gender. I end by stressing the importance of further research into the field of Alzheimer’s disease, in order to reduce the effect of weak or contradictory evidence and make definitive statements on preventative measures that can be put in place for the general public.

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To what extent does our understanding of the risk factors of Alzheimer’s Disease assist prevention?

Introduction Alzheimer’s disease (AD) is responsible for 60,000 deaths a year in the United Kingdom; but more importantly, it significantly reduces the quality of life for those 520,000 sufferers who struggle with the daily symptoms.1 These are not limited to memory loss alone. Problems with judging distances, depth perception, decision-making and mood changes such as irritability, anxiety and depression can also be accredited to the onset of the disease. Memory loss is caused by damage to the temporal lobe, and it can range from losing track of information and forgetting how to do daily tasks, to being unable to recognise close family and friends, or even losing one’s own identity. The average life expectancy of a person who has AD is usually eight to ten years after initial symptoms.

Our understanding of the direct causes of AD is limited, but it is accepted that organic changes in the brain involve the buildup of the β-amyloid protein in ‘plaques’ around nerve endings, reducing connectivity and leading to the death of neurones and the loss of brain tissue. This can lead to increased size of sulci – the seemingly random array of grooves covering the brain. Another hypothesis states that a protein known as tau accumulates inside cells and creates insoluble neurofibrillary ‘tangles’, affecting the cell’s ability to function.2 Both the amyloid and tau hypotheses are feasible and supported by experimental evidence, but are considerably descriptive and not as explanatory as would be ideal. Why do these plaques and tangles form? To help us answer this question - and thus take us closer to the question of prevention - we can look at the factors that increase a person’s susceptibility to AD. Obvious correlations between a certain lifestyle choice or allele of a gene and incidence of the disease can serve as signposts for possible causation.

1 Alzheimer’s

Society, ‘About Alzheimer’s - Statistics’, http://www.alzheimers.org.uk, 2008, (accessed 30 August 2015)

2 Edinformatics, ‘Alzheimer’s Update 2015’ http://www.edinformatics.com/news/alzheimers_update.htm, 2015, (accessed 30 August 2015) 4

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Our inability to cure AD is not for want of trying. Drug treatments such as Cholinesterase inhibitors (Donepezil, Rivastigmine and Galantamine) for mild cases and Memantine for severe cases are available as a means of slowing the progression of the disease. These drugs work by acting on receptors in the brain and increasing communication between cells. In most cases however, symptoms improve temporarily then exacerbate, with the addition of a large number of side effects. It can be seen therefore that understanding the risk-factors of this disease, rather than acting on the organic causes to slow down symptoms, may have a more notable effect on incidence of AD. It would allow research into new preventative treatments such as hormone replacement therapy. In addition, understanding individual risk would allow the assessment of any possible changes in your lifestyle, or in deterministic cases, the possibility of early retirement and a carpe-diem approach to life. The risk factors to be explored in this essay include cardiovascular health such as obesity and smoking, traumatic brain injuries, the female gender and genetic predisposition. Although increased age can be seen as the single most influential risk factor, our inability to reverse the body’s natural ageing process means age as a risk factor does not lend itself to be assessed on preventability, and is therefore irrelevant in this essay. Prevention of genetic risks is similarly difficult. However, modern research alludes to future possibilities of genetic modification in humans, and therefore genetics will be evaluated in this essay.

Section A - Cardiovascular Health Unlike many ailments such as heart disease, lung cancer and diabetes, AD does not have a clear lifestyle factor which is known to dramatically increase a person’s risk. However, evidence suggests that the ‘healthy heart, healthy brain’ idea is rooted in truth. This hypothesis states that a risk of suffering from AD is augmented by an unhealthy lifestyle, characterised by lack of exercise,

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smoking, drinking alcohol, an unhealthy diet and hypertension.3 If this link is valid, it highlights a clear possibility of preventative measures in those predisposed to AD, simply through lifestyle changes. Martins et al published an article in 2006 containing an agglomeration of studies in relation to the possible link between AD and factors such as cholesterol levels, incidence of Coronary Artery disease (CAD) and obesity.4 A 1990 study charted the prevalence of AD-typical amyloid plaques in CAD patients compared to unaffected participants, all non-demented. 75% of CAD patients showed an occurrence of these plaques, with only 12% of non-CAD patients affected. Similarly, further studies showed higher abundance of low-density lipoprotein (also known as ‘bad cholesterol’) and lower levels of high-density lipoprotein (or ‘good cholesterol’) in AD patients compared to healthy participants. The results of both these studies suggest a link between incidence of AD and cardiovascular diseases. In 1964, Whitmer et al carried out a longitudinal study of 6,583 participants in California who were initially grouped according to their sagittal abdominal diameter (SAD), i.e the diameter of the lower abdomen, often used as an indicator of obesity. An average of 36 years later, 15.9% of participants were diagnosed with dementia. The most overweight ⅕ of all participants had triple the abundance of dementia in comparison with the lowest ⅕. It was then concluded that central obesity increased the risk of dementia significantly.5 However, this conclusion was relevant for all types of dementia, and not only limited to AD. From the aforementioned studies, evidence suggests a correlation between cardiovascular diseases and obesity, and AD. It is hard to confidently assume causation in these instances. However, the correlation alone gives reason to believe that those without cardiovascular symptoms are less likely to suffer from AD later in life.

Mayo Clinic, ‘Alzheimer’s disease - Risk factors’, www.mayoclinic.org/diseases-conditions/alzheimers-disease/ basics/risk-factors/con-20023871, 2014, (accessed 30 August 2015) 3

Martins et al, ‘Apolipoprotein E, cholesterol metabolism, diabetes, and the convergence of risk factors for Alzheimer’s disease and cardiovascular disease’, Molecular Psychiatry, vol. 11, no. 8, 2006, p721-736

5 Whitmer et al, ‘Central obesity and increased risk of dementia more than three decades later.’, Neurology, vol 71, no. 14, 2008, Available from PubMed, (accessed 30 August 2015) 6

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Controversially, a recent study by Qizilbash et al seems to completely contradict these findings.6 In investigating the link between BMI and dementia, almost 2,000,000 participants aged 40+ were measured by their BMI, with their health then tracked for around a decade. Those with a BMI of underweight had a risk of dementia 34% higher than those who were declared as normal weight. This does not necessarily contradict previously-held beliefs; it could be that dementia risk increased with variance from a normal weight in both directions. However, the results also showed that those with a BMI of over 40 were 29% less likely to suffer from dementia. Dr Simon Ridley, from Alzheimer’s Research UK, commented that the study “doesn’t tell us that being underweight causes dementia”. However, it reduces our confidence in previous studies due to the low test-retest reliability. In addition to obesity, drinking alcohol regularly and smoking have been argued to exacerbate a risk of AD. For example, Ott et al carried out a population-based study of participants aged 55 and older, both smokers and non-smokers, all without a diagnosis of dementia.7 Results showed smoking doubled the risk of AD. However, many other studies on the effect of tobacco and alcohol on AD are inconclusive, shown in Graves et al’s meta-analysis of case-control studies in 1991. 8 In evaluating these studies, it is important to accept that theories may not be mutually exclusive, and confounding variables could be discovered that allow these studies to be valid in their own right. In this way, it is possible that the contradictory results of the studies were affected by other factors that only further research would illuminate. Nevertheless, both studies on obesity do show

6 Qizilbash et al, ‘BMI and risk of dementia in two million people over two decades: a retrospective cohort study’, The Lancet - Diabetes and Endocrinology, vol. 3, no. 6, 2015, p431-436, www.thelancet.com/journals, (accessed 30 August 2015)

Ott et al, ‘Smoking and risk of dementia and Alzheimer’s disease in a population-based cohort study: the Rotterdam study’ The Lancet, vol. 351, no. 9119, 1998, p1840-1843, http://www.sciencedirect.com/science/article/pii/ S0140673697075417, (accessed 11 September 2015) 7

Graves et al, ‘Alcohol and Tobacco Consumption as Risk Factors for Alzheimer’s Disease: A Collaborative ReAnalysis of Case-Control Studies’, International Journal of Epidemiology, vol. 20, no. 2, 1991, p48-57, http:// ije.oxfordjournals.org/content/20/Supplement_2/S48.short, (accessed 11 September 2015) 8

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cardiovascular health as having a certain degree of impact on one’s likelihood to develop AD. This cardiovascular health as having a certain degree of impact on one’s likelihood to develop AD. This

could contain important information on methods of prevention, namely changes to lifestyle if one is could contain important information on methods of prevention, namely changes to lifestyle if one is predisposed to the disease. For example, if the obesity-AD link is valid, the obvious preventative predisposed to the disease. For example, if the obesity-AD link is valid, the obvious preventative treatment would be weight loss. However, a flaw with this idea is that people suffering from obesity treatment would be weight loss. However, a flaw with this idea is that people suffering from obesity are most likely already encouraged by their doctor to lose weight, and the fact that many obese are most likely already encouraged by their doctor to lose weight, and the fact that many obese people do not follow this advice does not bode well for preventative measures for AD. In addition, people do not follow this advice does not bode well for preventative measures for AD. In addition, it could be that those who are genetically predisposed to develop AD also contain an allele for it could be that those who are genetically predisposed to develop AD also contain an allele for obesity, which would accommodate the correlation between the two, but make any prevention obesity, which would accommodate the correlation between the two, but make any prevention impossible. The growing idea of obesity as a mental illness, as well as the mental element of impossible. The growing idea of obesity as a mental illness, as well as the mental element of addiction to nicotine or alcohol, adds another layer of complexity to the possibility of prevention, addiction to nicotine or alcohol, adds another layer of complexity to the possibility of prevention, especially considering there is currently no active weight-loss drug in use in the United Kingdom, especially considering there is currently no active weight-loss drug in use in the United Kingdom, meaning these lifestyle changes can only be made independently. Taking these points into meaning these lifestyle changes can only be made independently. Taking these points into consideration, one could argue that changes to lifestyle in order to prevent AD could be useful, yet consideration, one could argue that changes to lifestyle in order to prevent AD could be useful, yet more research is needed into its efficacy. Despite this, simple lifestyle changes such as diet, exercise more research is needed into its efficacy. Despite this, simple lifestyle changes such as diet, exercise and quitting smoking could be administered easily and without the use of drugs or expensive and quitting smoking could be administered easily and without the use of drugs or expensive treatment, making it a potentially convenient and effective measure. treatment, making it a potentially convenient and effective measure.

Section B - Traumatic Brain Injury Section B - Traumatic Brain Injury A similar confirmed risk factor for AD is Traumatic brain injury (TBI), where an impact to the head A similar confirmed risk factor for AD is Traumatic brain injury (TBI), where an impact to the head interrupts normal brain functioning. Its symptoms include memory loss, confusion, and lack of interrupts normal brain functioning. Its symptoms include memory loss, confusion, and lack of coordination.9 Awareness of a link between TBI and AD could lead to adjustments in safety coordination.9 Awareness of a link between TBI and AD could lead to adjustments in safety regulations as a way of preventing the disease. In order to investigate the proposed correlation regulations as a way of preventing the disease. In order to investigate the proposed correlation between TBI and AD, Wang et al published a study in 2012 following the health of over 200,000 between TBI and AD, Wang et al published a study in 2012 following the health of over 200,000

Alzheimer’s Association, ‘Alzheimer’s and Dementia - Traumatic Brain Injury’, http://www.alz.org/dementia/traumatic-brainInjury’, http://www.alz.org/dementia/traumatic-braininjury-head-trauma-symptoms.asp, 2015, (accessed: 30 August 2015) 9injury-head-trauma-symptoms.asp, 2015,and (accessed: 30 August 2015) Alzheimer’s Association, ‘Alzheimer’s Dementia - Traumatic Brain

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individuals.10 The retrospective cohort experiment followed patients for000102-0079 5 years.

TBI and non-TBI individuals.10 The retrospective cohort experiment followed patients for 5 years. Over this course of time, 2.66% of TBI patients developed dementia, whereas only 1.53% of nonOver this course of time, 2.66% of TBI patients developed dementia, whereas only 1.53% of nonTBI individuals developed the disease. After factoring in sociodemographic variables, it was found TBI individuals developed the disease. After factoring in sociodemographic variables, it was found that TBI patients had a 1.68 times greater risk of developing dementia than non-TBI participants. that TBI patients had a 1.68 times greater risk of developing dementia than non-TBI participants. This correlation suggests that following TBI, patients are more likely to suffer from dementia in the This correlation suggests that following TBI, patients are more likely to suffer from dementia in the future. However, the study does not differentiate between types of dementia so it cannot be assumed future. However, the study does not differentiate between types of dementia so it cannot be assumed that AD follows this pattern. that AD follows this pattern. Theories for the explanation of why TBI is a risk factor of AD refer back to the β-amyloid Theories for the explanation of why TBI is a risk factor of AD refer back to the β-amyloid hypothesis of aetiology. A study by Emmerling et al in 2006 found elevated levels of the amyloid hypothesis of aetiology. A study by Emmerling et11al in 2006 found elevated levels of the amyloid protein in the cerebrospinal fluid of TBI patients. This suggests that the link between AD and TBI protein in the cerebrospinal fluid of TBI patients.11 This suggests that the link between AD and TBI is caused by the increase in this protein that is seen as a marker for AD patients, reducing cell is caused by the increase in this protein that is seen as a marker for AD patients, reducing cell communication and leading to nerve cell death. Similarly, Sivanandam et al observed amyloid communication and leading to nerve cell death. Similarly, Sivanandam et al observed amyloid plaques in 30% of patients who had died of TBI, following epidemiological studies published in plaques in 30% of patients who had died of TBI, following epidemiological studies published in 2012. Their explanation for this correlation was based on epigenetics; it could be argued that 2012. Their explanation for this correlation was based on epigenetics; it could be argued that following TBI, certain genes are expressed which increase the levels of β-amyloid in the brain. This following TBI, certain genes are expressed which increase the levels of β-amyloid in the brain. This would lead to the formation of plaques observed post-mortem in the patient’s brains. would lead to the formation of plaques observed post-mortem in the patient’s brains. These studies confirm TBI as a risk factor for AD. From this, it is possible to put preventative These studies confirm TBI as a risk factor for AD. From this, it is possible to put preventative measures into place for those who, due to family history or otherwise, are predisposed or likely to measures into place for those who, due to family history or otherwise, are predisposed or likely to suffer from AD. The most common cause of TBI are general falls, which are common in the suffer from AD. The most common cause of TBI are general falls, which are common in the

Wang et al, ‘Population based study on patients with traumatic brain injury suggests increased risk of dementia’, Journal of Neurology, Neurosurgery and Psychiatry, vol. 83, no. 11, 2012, http://jnnp.bmj.com (accessed: 30 August 10 Wang et al, ‘Population based study on patients with traumatic brain injury suggests increased risk of dementia’, 2015) Journal of Neurology, Neurosurgery and Psychiatry, vol. 83, no. 11, 2012, http://jnnp.bmj.com (accessed: 30 August 11 Emmerling et al, ‘Traumatic brain injury elevates the Alzheimer’s amyloid peptide A beta 42 in human CSF. A 2015) possible role for nerve cell injury.’, 2000, Available from PubMed, (accessed 30 August 2015) 11 Emmerling et al, ‘Traumatic brain injury elevates the Alzheimer’s amyloid peptide A beta 42 in human CSF. A 9 possible role for nerve cell injury.’, 2000, Available from PubMed, (accessed 30 August 2015) 9 10

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elderly. 12 This combination of age as a risk factor as well as TBI would put someone at a high chance of developing the disease. To reduce this, elderly citizens with balance or mobility issues could use walking frames or other supportive devices to prevent falls. Those with vision problems should have frequent check-ups to ensure they keep up with their current prescription, as sight difficulties could answer for many of the 56,000 head injuries in elderly patients in the UK per year. In addition to this, general road safety precautions such as seat belts would reduce the danger of TBI following road accidents. Lifestyle elements also come into play in this instance; reconsidering careers in contact sports or dangerous practices such as construction work where head injury is likely would also prevent the risk of AD as a consequence of TBI. Thus, it is possible to help prevent TBI - however, it is likely that precautions to reduce head injuries are already in place. This suggests that despite best efforts to prevent TBI, it remains prevalent.

Section C - Gender According to recent statistics, two thirds of AD sufferers in the UK are female.13 This can be partly attributed to the increased life expectancy in women compared to men - however, there must also be other mechanisms in play due to this ratio still being prevalent in age-matched groups. A recent article by J. Shepherd in the Journal of American Pharmacists Association outlines oestrogen as playing a major role in maintaining brain health in women.14 This includes protecting nerve cells from the β-amyloid protein present in AD patients, as well as increasing growth and repair of neurones. Shepherd wrote that the pathology of AD as well as normal brain ageing shows ‘an imbalance between neuronal injury and repair’. Following from this, we can conclude that the

Alzheimer’s Association, ‘Traumatic Brain Injury (TBI)’, http://www.alz.org/dementia/traumatic-brain-injury-head-traumasymptoms.asp, 2015, (accessed: 30 August 2015) 13 Alzheimer’s Society, ‘About Alzheimer’s - Statistics’, http://www.alzheimers.org.uk, 2008, (accessed 30 August 2015)

J. Shepherd, ‘Effects of Estrogen on Cognition, Mood and Degenerative Brain Diseases’, Journal of the American Pharmacists Association, vol. 41, no. 2, 2001, http://www.medscape.com/viewarticle/406718_2, (accessed: 30 August 2015) 10 14

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deficiency of oestrogen in postmenopausal women may have a detrimental effect on brain health, deficiency of oestrogen in postmenopausal women may have a detrimental effect on brain health, with an increased risk of AD. with an increased risk of AD.

This enables us to consider hormone-replacement therapy (HRT) using oestrogen as a possible This enables us to consider hormone-replacement therapy (HRT) using oestrogen as a possible treatment or preventative measure. Tang et al (1996) studied the effect of oestrogen on the age of treatment or preventative measure. Tang et al (1996) studied the effect of oestrogen on the age of onset of AD in women over a period of five years.15 The relative risk of developing the disease in onset of AD in women over a period of five years.15 The relative risk of developing the disease in oestrogen users was 5.8% compared to non-users who had a 16.3% chance, considering other oestrogen users was 5.8% compared to non-users who had a 16.3% chance, considering other factors also such as ethnicity, genes and level of education. They also found that women who had factors also such as ethnicity, genes and level of education. They also found that women who had been taking HRT for over a year, as well as women taking HRT before the trial began, had a smaller been taking HRT for over a year, as well as women taking HRT before the trial began, had a smaller risk of AD. From this data, the researchers concluded that oestrogen use ‘may delay the onset and risk of AD. From this data, the researchers concluded that oestrogen use ‘may delay the onset and decrease the risk of Alzheimer’s disease’. However, they also noted that further study would be decrease the risk of Alzheimer’s disease’. However, they also noted that further study would be necessary to confirm this. Overall, this suggests that oestrogen therapy could be effective as a necessary to confirm this. Overall, this suggests that oestrogen therapy could be effective as a method of prevention of AD. method of prevention of AD. However, similar studies deducing whether oestrogen therapy could be of use as a treatment postHowever, similar studies deducing whether oestrogen therapy could be of use as a treatment postdiagnosis show opposite results. A study by Mulnard et al (1999) in the Journal of the American diagnosis show opposite results. A study by Mulnard et al (1999) in the Journal of the American Medical Association investigated the efficacy of oestrogen as a treatment for mild to moderate Medical Association investigated the efficacy of oestrogen as a treatment for mild to moderate AD.16 Following a placebo-controlled trial of oestrogen in AD patients, results showed a worsening AD.16 Following a placebo-controlled trial of oestrogen in AD patients, results showed a worsening of symptoms in 80% of patients on the drug, versus 74% of patients taking a placebo. The drug had of symptoms in 80% of patients on the drug, versus 74% of patients taking a placebo. The drug had no effect on cognition, nor were there any organic changes observed in the brain. These results were no effect on cognition, nor were there any organic changes observed in the brain. These results were echoed by the Cache County study of 2002 by Zandi et al, which concluded no significant changes echoed by the Cache County study of 2002 by Zandi et al, which concluded no significant changes

15 Tang et al, ‘Effect of oestrogen during menopause on risk and age at onset of Alzheimer’s disease ’, The Lancet, vol. 348, no.et9025, 1996, of p429-432, (accessed 30 August 2015) 15 Tang al, ‘Effect oestrogenwww.thelancet.com/journals, during menopause on risk and age at onset of Alzheimer’s disease ’, The Lancet, vol. 348, no. 9025, 1996, p429-432, www.thelancet.com/journals, (accessed 30 August 2015) 16 Mulnard et al, ‘Estrogen Replacement Therapy for Treatment of Mild to Moderate Alzheimer Disease’, The Journal of Mulnard the American Association’, vol. 283, no. 2000, http://jama.jamanetwork.com/article.aspx? 16 et al, Medical ‘Estrogen Replacement Therapy for8,Treatment of Mild to Moderate Alzheimer Disease’, The Journal articleid=192426, (accessed 30 August vol. 2015) of the American Medical Association’, 283, no. 8, 2000, http://jama.jamanetwork.com/article.aspx? articleid=192426, (accessed 30 August 2015) 11 11

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in the progression of the disease following oestrogen therapy as a treatment, yet a reduced risk in participants who had taken HRT previously.17

These results suggest oestrogen therapy as a possible preventative measure for AD. However, the therapy in itself comes with several risks that may negate the positive effects of the treatment. These risks include stroke, ovarian cancer, blood clots and breast cancer.18 In addition, oestrogen has been shown to increase the risk of endometrial cancer by up to 14 times in postmenopausal women.19 The gravity of these possible side effects weaken the argument of using HRT as a preventative measure. However, if one is genetically predisposed to the disease and has a stronger chance of suffering from it than of any possible side effects of HRT, it could be considered as a preventative drug if necessary. This is a strong instance of where our understanding of the female gender as a risk factor for AD lends itself for use in preventative methods.

Section D - Genetics In addition to gender, another seemingly invariable risk factor for AD is the human genome. Researches have isolated single genes which can predispose an individual for the disease - known as risk genes - and those that will ensure the eventual development of AD, known as deterministic genes. In particular, the risk gene apolipoprotein E-e4 (APOE-e4), has been found to play a role in up to 25% of all instances of the disease. 20 The e4 form of the gene, when inherited by one or both parents, has the ability to increase an individual’s susceptibility to the disease, as well as reducing

Zandi et al, ‘Hormone Replacement Therapy and Incidence of Alzheimer Disease in Older Women’, The Journal of the American Medical Association’, vol. 288, no. 17, 2002, http://jama.jamanetwork.com/article.aspx?articleid=195464, (accessed 30 August 2015) 17

eMedicineHealth, ‘Estrogen Therapy (ET)’, http://www.emedicinehealth.com/script/main/mobileart-emh.asp? articlekey=129364&ref=129366, (accessed 30 August 2015) 18

19 Premarin, ‘Estrogen: General information and side effects’, http://www.premarin.org/estrogen.html, (accessed 30 August 2015) 20 Alzheimer’s Association, ‘Alzheimer’s Disease - Risk Factors’, http://www.alz.org/alzheimers_disease_causes_risk_factors.asp, 2015, (accessed 30 August 2015)

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the age of onset. However, the development of the disease is not inevitable. With genes such as amyloid precursor protein (APP), presenilin-1 (PS-1) and presenilin-2 (PS-2), the inheritance of one of these genes guarantees a diagnosis of what is known as familial AD. However, this only accounts for 5% of all diagnoses.

These genes have been isolated by various studies including that of Myers et al (2007), in which over 500,000 samples of brain tissue from past sufferers of the disease were extracted and analysed using SNP genotyping. 21 Results showed that the APOE-e4 allele of the gene had a ‘significant association with late-onset AD’. Furthermore, epidemiological studies have illuminated a correlation between early-onset AD and Down’s syndrome.22 As Down’s syndrome is a genetic disorder, this lends itself to the idea of AD being similarly genetically determined. Amyloid plaques typical of AD patients have been found in the majority of brains of those with Down’s syndrome, as investigated by Masters et al in 1985.23 After chemical analysis of the amyloid proteins in both AD and Down’s syndrome patients, researchers concluded a ‘common origin’ of the protein after finding the substances ‘almost identical’. This suggests, due to no other common variables, that genes have a similar impact on AD as they do on Down’s syndrome, a genetic disorder. A study by Wisniewski et al confirmed this correlation following examination of brains of Down’s syndrome patients post-mortem.24 They also concluded that AD was over three times more common in individuals with Down’s syndrome. 21 Myers et al, ‘A High-Density Whole-Genome Association Study Reveals that APOE is the Major Susceptibility Gene for Sporadic Late-Onset Alzheimer’s Disease’, The Journal of Clinical Psychiatry, vol. 68, no. 4, 2007, http:// www.researchgate.net/publication/6355004_A_High-Density_WholeGenome_Association_Study_Reveals_That_APOE_Is_the_Major_Susceptibility_Gene_for_Sporadic_LateOnset_Alzheimer%27s_Disease, (accessed 30 August 2015) 22

Alzheimer’s Association, ‘Down Syndrome and Alzheimer’s Disease’, http://www.alz.org/dementia/down-syndrome-alzheimerssymptoms.asp, 2015, (accessed 30 August 2015) 23 Masters et al, ‘Amyloid plaque core protein in Alzheimer disease and Down Syndrome’, Proceedings of the National Academy of Sciences, vol. 82, no. 12, 1985, http://www.pnas.org/content/82/12/4245.short, (accessed 30 August 2015)

Wisniewski et al, ‘Occurrence of neuropathological changes and dementa of Alzheimer’s disease in Down’s syndrome’, Annals of Neurology, vol. 17, no. 3, 1985, http://onlinelibrary.wiley.com/doi/10.1002/ana.410170310/ abstract, (accessed 30 August 2015) 13 24

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These studies, through investigating the link between AD and Down’s syndrome, confirm the idea of a genetic factor increasing the risk of AD. From this, it would be possible to undergo genome screening to discover whether one is predisposed by risk genes or confirmed by deterministic genes to develop the disease. If predisposed, an individual would be able to make the aforementioned lifestyle changes such as a healthier diet, as well as hormone therapies such as oestrogen therapy in the case of women. While the discovery of a deterministic gene would not lend itself to prevention, it could however assist in ensuring a higher quality of life before symptoms appeared, such as early retirement. In the future, there may be a possibility of prenatal altering of genes to prevent the disease before birth in familial cases, as has been done in bacterial cells since 1973 by Boyer and Cohen.25 This idea would also be supported by the information researched by Stefansson et al from deCODE genetics in Iceland, who discovered a mutation of the previously deterministic APP gene. This mutation may reduce the risk of AD by up to seven times. 26 Following this, the switching of a single nucleotide in the base pairing of the APP gene in a foetus may make their previously high risk of developing AD virtually nonexistent. However, these claims rely on continuous technological advances in the future, as well as changes in ethical considerations and legislation regarding genetic engineering. To conclude, the idea of genes playing a part in AD allow various adjustments to be made to an individual’s lifestyle, as well as underlining the possibility for future research into altering the human genome.

Morrow, Cohen et al, ‘Replication and Transcription of Eukaryotic DNA in Esherichia coli’, Proceedings of the National Academy of Sciences of the United States of America, vol. 71, no. 5, 1974, http://www.pnas.org/content/ 71/5/1743.short, (accessed 11 September 2015) 25

G. Miller., ‘Gene Mutation Protects Against Alzheimer’s’, ScienceMag, 2012, http://news.sciencemag.org/health/ 2012/07/gene-mutation-protects-against-alzheimers, (accessed 30 August 2015) 14 26

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Conclusion Considering the aforementioned research into risk factors of AD, there is overwhelming evidence that some people have a higher chance of developing the disease than others - it is not simply a case of dividing the number of patients by the total population. Isolating the reasons for this have given us greater insight into not only why AD occurs, but how it may be possible to prevent it. Of course, these risk factors are not all mutually exclusive, and when interacting could lead to a complex system of probabilities that would have to be carefully evaluated before making judgements on how to prevent the incidence of the disease. As well as this, risk factors such as an unhealthy lifestyle and traumatic brain injuries are negative in themselves, and thus should be avoided anyway. Although this may reduce our ability to avoid them further, their ability to increase the risk of AD are not controversial and would be accepted by the public as a sensible and understandable finding. In comparing the risk factors explored in this essay and their possible prevention, a hierarchy clearly forms of how influential the factor is, and how easily it can be prevented. The seemingly most preventable risk factor detailed in this essay is cardiovascular health, which is a lifestylerelated determinant, and therefore able to be changed. In sharp contrast is an individual’s genome, which doctors are currently unable to edit - however, there is no ‘maybe’ element in deterministic genes, and even risk genes can be seen to dramatically increase the chance of developing AD, and therefore play a highly influential role in its aetiology. Gender is similarly important and seemingly unalterable. However, the idea of hormone therapy allows this problem to be approached without changing the individual’s gender, increasing its preventability. TBI is similarly preventable to a certain extent, yet may not be one of the most dominant risk factors.

The importance of preventing a disease as opposed to treating it may be underestimated - if the chance is small anyway, why should somebody undergo measures that may be unnecessary and 15

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cause stress or pain, such as HRT or dieting? The idea of developing AD may not cross an individual’s mind until they become too old to prevent it’s occurrence. Other fears could be dominant - cancer, heart attack, or stroke. Be that as it may, with ameliorated medical care, the population is ageing. Despite the obvious positives of living longer, the fact is that degenerative age-related diseases are become more prevalent, and not only AD is becoming an epidemic. Parkinson’s disease, as well as other forms of dementia, are ruining the lives that technology and healthcare have worked so hard to elongate. What is important now is to sensitise the public to how they can reduce their risk of this disease, as opposed to others such as cardiovascular diseases, where methods of prevention are common knowledge. It may not be widely understood that measures can be taken that would reduce the chance of AD developing, and with increasing studies confirming these theories, this misconception must be corrected. To continue this momentum of understanding, additional research is required into investigating contradictory evidence, and further recognising exactly how certain risk factors may be reduced, for example, altering genes. Fortunately, the increasing incidence of AD has spurred such a movement into researching the disease. Recent discoveries, such as the possibility of blood transfusions leading to accumulations of amyloid protein during medical procedures,27 the medicinal properties of the antioxidant resveratrol,28 and changes in the brain’s blood vessels,29 may illuminate other risk factors and therefore preventative measures. If research can meet these expectations, then prevention of AD could become an altogether more fathomable idea that could significantly reduce its incidence. From the information considered in this essay, it is possible to

27 S. Knapton, ‘Alzheimer’s disease may be caught through medical accidents’, The Telegraph, 9 September 2015, http://www.telegraph.co.uk/news/science/science-news/11853619/Alzheimers-disease-may-be-caught-through-medicalaccidents.html, (accessed 20 September 2015)

C. Storrs, ‘For Alzheimer’s patients, resveratrol brings new hope’, CNN, 11 September 2015, http://edition.cnn.com/ 2015/09/11/health/resveratrol-hope-for-alzheimers-patients/, (accessed 20 September 2015) 28

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draw the inference that our continuous understanding of the risk factors associated with AD has great potential to assist in its prevention.

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Bibliography Books Dickerson, B. and Atri, A., Dementia: Comprehensive Principles and Practise, Boston, Oxford University Press, 2014 Swaab, D., We Are Our Brains: From the Womb to Alzheimer’s, London, Allen Lane, 2014 Websites Alzheimer’s Association, ‘Alzheimer’s Disease and Dementia’, http://www.alz.org/, 2015, (accessed: 30 August 2015) Alzheimer’s Association, ‘Down Syndrome and Alzheimer’s Disease’, http://www.alz.org/ dementia/down-syndrome-alzheimers-symptoms.asp, 2015, (accessed 30 August 2015) Alzheimer’s Society, ‘Alzheimer’s’, http://www.alzheimers.org.uk, 2008, (accessed 30 August 2015) Edinformatics, ‘Alzheimer’s Update 2015’ http://www.edinformatics.com/news/ alzheimers_update.htm, 2015, (accessed 30 August 2015) eMedicineHealth, ‘Estrogen Therapy (ET)’, http://www.emedicinehealth.com/script/main/ mobileart-emh.asp?articlekey=129364&ref=129366, (accessed 30 August 2015) Knapton, S., ‘Alzheimer’s disease may be caught through medical accidents’, The Telegraph, 9 September 2015, http://www.telegraph.co.uk/news/science/science-news/11853619/Alzheimersdisease-may-be-caught-through-medical-accidents.html, (accessed 20 September 2015) Mayo Clinic, ‘Alzheimer’s disease - Risk factors’, www.mayoclinic.org/diseases-conditions/ alzheimers-disease/basics/risk-factors/con-20023871, 2014, (accessed 30 August 2015) Whitmer et al, ‘Central obesity and increased risk of dementia more than three decades later.’, Neurology, vol 71, no. 14, 2008, Available from PubMed, (accessed 30 August 2015) Miller, G., ‘Gene Mutation Protects Against Alzheimer’s’, ScienceMag, 2012, http:// news.sciencemag.org/health/2012/07/gene-mutation-protects-against-alzheimers, (accessed 30 August 2015) Premarin, ‘Estrogen: General information and side effects’, http://www.premarin.org/estrogen.html, (accessed 30 August 2015) Storrs, C., ‘For Alzheimer’s patients, resveratrol brings new hope’, CNN, 11 September 2015, http:// edition.cnn.com/2015/09/11/health/resveratrol-hope-for-alzheimers-patients/, (accessed 20 September 2015) 18 94

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Trinity College Dublin, ‘Major breakthrough in understanding Alzheimer’s disease’, ScienceDaily, 18 September 2015, http://www.sciencedaily.com/releases/2015/09/150918152000.htm, (accessed 20 September 2015) References Emmerling et al, ‘Traumatic brain injury elevates the Alzheimer’s amyloid peptide A beta 42 in human CSF. A possible role for nerve cell injury.’, 2000, Available from PubMed, (accessed 30 August 2015) Graves et al, ‘Alcohol and Tobacco Consumption as Risk Factors for Alzheimer’s Disease: A Collaborative Re-Analysis of Case-Control Studies’, International Journal of Epidemiology, vol. 20, no. 2, 1991, p48-57, http://ije.oxfordjournals.org/content/20/Supplement_2/S48.short, (accessed 11 September 2015) Morrow, Cohen et al, ‘Replication and Transcription of Eukaryotic DNA in Esherichia coli’, Proceedings of the National Academy of Sciences of the United States of America, vol. 71, no. 5, 1974, http://www.pnas.org/content/71/5/1743.short, (accessed 11 September 2015) Mulnard et al, ‘Estrogen Replacement Therapy for Treatment of Mild to Moderate Alzheimer Disease’, The Journal of the American Medical Association’, vol. 283, no. 8, 2000, http:// jama.jamanetwork.com/article.aspx?articleid=192426, (accessed 30 August 2015) Myers et al, ‘A High-Density Whole-Genome Association Study Reveals that APOE is the Major Susceptibility Gene for Sporadic Late-Onset Alzheimer’s Disease’, The Journal of Clinical Psychiatry, vol. 68, no. 4, 2007, http://www.researchgate.net/publication/6355004_A_HighDensity_WholeGenome_Association_Study_Reveals_That_APOE_Is_the_Major_Susceptibility_Gene_for_Sporad ic_Late-Onset_Alzheimer%27s_Disease, (accessed 30 August 2015) National Institute on Aging, ‘Alzheimer’s Disease: Unraveling the Mystery’, https:// www.nia.nih.gov/alzheimers/publication/part-1-basics-healthy-brain/changing-brain-healthy-aging, 2008, (accessed: 30 August 2015) Ott et al, ‘Smoking and risk of dementia and Alzheimer’s disease in a population-based cohort study: the Rotterdam study’ The Lancet, vol. 351, no. 9119, 1998, p1840-1843, http:// www.sciencedirect.com/science/article/pii/S0140673697075417, (accessed 11 September 2015) Qizilbash et al, ‘BMI and risk of dementia in two million people over two decades: a retrospective cohort study’, The Lancet - Diabetes and Endocrinology, vol. 3, no. 6, 2015, p431-436, www.thelancet.com/journals, (accessed 30 August 2015) Shepherd, J., ‘Effects of Estrogen on Cognition, Mood and Degenerative Brain Diseases’, Journal of the American Pharmacists Association, vol. 41, no. 2, 2001, http://www.medscape.com/ viewarticle/406718_2, (accessed: 30 August 2015)

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Swerdlow et al, ‘Brain aging, Alzheimer’s disease, and mitochondria’, Biochemica et Biophysica Acta (BBA) - Molecular Basis of Disease, vol 1812, no. 12, 2011, Available from PubMed, (accessed 30 August 2015) Tang et al, ‘Effect of oestrogen during menopause on risk and age at onset of Alzheimer’s disease ’, The Lancet, vol. 348, no. 9025, 1996, p429-432, www.thelancet.com/journals, (accessed 30 August 2015) Wang et al, ‘Population based study on patients with traumatic brain injury suggests increased risk of dementia’, Journal of Neurology, Neurosurgery and Psychiatry, vol. 83, no. 11, 2012, http:// jnnp.bmj.com (accessed: 30 August 2015) Wisniewski et al, ‘Occurrence of neuropathological changes and dementia of Alzheimer’s disease in Down’s syndrome’, Annals of Neurology, vol. 17, no. 3, 1985, http://onlinelibrary.wiley.com/doi/ 10.1002/ana.410170310/abstract, (accessed 30 August 2015) Zandi et al, ‘Hormone Replacement Therapy and Incidence of Alzheimer Disease in Older Women’, The Journal of the American Medical Association’, vol. 288, no. 17, 2002, http:// jama.jamanetwork.com/article.aspx?articleid=195464, (accessed 30 August 2015)

Eloise Robson - History

To what extent and with what reasons was the evacuation of Dunkirk presented inaccurately to the British public in May/June 1940?

Eloise Robson - History

Eloise Robson - History In April 2015, when the Extended Essay process began, the media was consumed with the 75th anniversary of Dunkirk. Learning about World War II had stimulated my original fascination with history and so I was immediately drawn to this. Having entered my local book shop, I soon found that the actual event of Dunkirk had been too widely written about for an essay on it to add to the historiographical debate. However, continued research provided me with conflicting information about the event and, as such, I became increasingly curious about how, and for what reasons, the interpretations of Dunkirk might have changed over time. The extended essay process enabled me to immerse myself in a topic that both interested and surprised me, and provided me with invaluable experience in independent research.

Supervisor: Nigel Haworth Eloise came up with a very interesting idea for her Extended Essay – examining the accuracy of media’s portrayal of the Dunkirk Evacuation of May and June 1940. Eloise started with a “hunch” that the public were probably not being told the whole truth. This, once established, opened up a whole new, perhaps even more interesting, area of research. Eloise went on to investigate whether this inaccurate “story” presented to the public was due to the media themselves being largely in the dark or was it perhaps due to a sense of national pride encouraging journalists to present a positive spin on events? Eloise tackled her essay with fierce determination and showed that she was able to research in a mature and well considered manner. The work she produced is both academically impressive and an engaging read. Eloise is going on to read History at university and I am sure that the skills she has developed during her Extended Essay will stand her in very good stead.

Eloise Robson - History

Contents Introduction 100 Investigation 102 Conclusion 109 Appendix

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Abstract In May 1940 the British and French troops were desperately retreating from the oncoming German forces. Eventually the situation became so desperate that the troops had to be evacuated from Dunkirk, in an operation labelled ‘Dynamo’. Although this was a military defeat, it was presented as a resounding success to the British public in many respects by the media. The public were not, therefore, fully aware of what was really happening to their troops. It is hence important to consider ‘to what extent and with what reasons was the evacuation of Dunkirk presented inaccurately to the British public in May/June 1940?’ In order to answer this question newspapers, cartoons and radio broadcasts from the time will be looked at (these were the principal ways through which the public acquired information) alongside government memoranda and contemporary sources. By doing this it will be possible to draw a comparison between both what facts were known at the time and what was actually published as well as what may not have been known rivalled with the speculation that was circulated. Given that the evacuation was comprised of many aspects, this essay will be separated into four main sections in order to assess the accuracy of the presentation of each and have a holistic overview. The conclusion of the investigation will find that the British public were not presented with entirely accurate information about the evacuation for two main reasons. The first is the lack of information known to the media and the second is the desire to preserve a high morale. The different aspects of the evacuation were presented with varying degrees of accuracy as a result of the above dependents but also due to the different presenters of the information having contrasting access to the knowledge and motives in publishing it.

Eloise Robson - History

Eloise Robson

History

Extended Essay

INTRODUCTION Dunkirk was the location of a major operation during World War Two in which an estimated 338,000 British and French troops were evacuated1 by 222 warships and 665 other vessels2, including the famous ‘little ships’, between the 26th and 4th June 19403. It occurred out of necessity following the German penetration of Belgium, Holland, Luxembourg and France4. The apparent success of what was officially known as Operation Dynamo solidified that this was to be a total war, marked the end of the ‘Phoney War’ and has since been recognised as a significant milestone, with many of the ‘little ships’ being used for commemorative purposes since ad well as more recently. Due to the attention that Dunkirk has received, the question ‘to what extent and with what reasons was Dunkirk presented inaccurately to the British public in May/June 1940?’ is one that must be addressed in order to fully understand the significance of the event and the accuracy of its portrayal. Although the evacuation was part of a desperate retreat from the fast-approaching Germans, it was widely recognised as a victory. This was most probably due to the fact that the number of men who returned to the British shores vastly exceeded even the more ambitious expectations5 with the help of the ‘little ships’6 and the inadvertent help of the Fuhrer himself7. However, the personnel and equipment losses to Britain were catastrophic: almost all the weapons, transport and armoured vehicles had to be left behind for the Germans to take as their own8 and many of the battalions of the British Expeditionary Force (BEF) who bravely defended the perimeter were brutally murdered by the Nazis9. The British public were not, however, made aware of all of this information, particularly the negative aspects, by the media and other forms of intelligence. It does not seem likely that the press were being strictly censored in spite of government attempts to rebuttal ‘Lord Haw-Haw’s’ (William Joyce) anti-British propaganda from Berlin, which attracted millions of British listeners10. In fact the BBC issued a statement declaring that they did not want to ‘undermine the trust of the audience’ by being selective in their broadcasts11. Accordingly, the lack of information being presented to the

Report from the War Office on Operation Dynamo. 3rd May 1941. National Archives Memorandum: weekly resume 30/05/1940. From National Archives 3 Summerfield, Penny. Dunkirk and the Popular Memory of Britain at War, 1940-58. Journal of Contemporary History. 4 McKay, Sinclair. Dunkirk: From disaster to deliverance, testimonies of the last survivors p72 5 Churchill, Winston. ‘The finest hour’ speech given 04/06/1940 6 Priestly, JB. Postscript from the BBC archives 7 Sebag-Montefoire, Hugh. Dunkirk, Fight to the last man. P247 8 Churchill, Winston. Speech made on 4th June 1940 9 Sebag-Montefoire, Hugh. Dunkirk – Fight to the last man. P 297 10 BBC documentary The BBC at War, Presented by Jonathan Dimbleby 14/06/2015 11 http://www.mylearning.org/censorship-and-propaganda-in-wwii/p-3979/ 1 2

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History

Extended Essay

public was unlikely to have been simply part of an attempt to boost morale, but very much also because the information was simply unknown. Whichever the case, with seventy-five years of hindsight, it is clear that the British public did not have an accurate representation of the situation in Dunkirk until many years after the war had ended12 as a combined consequence of lack of information and effort to boost public morale.

Sebag-Montefoire, Hugh Dunkirk â&#x20AC;&#x201C; Fight to the last man. P 297

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Extended Essay

INVESTIGATION I.

THE ‘LITTLE SHIPS’

Perhaps one of the most poignant aspects of the evacuation and that which is best remembered is the role of the ‘little ships’; symbols of the triumph and strength during the evacuation. At the time, with a plethora of reports being published about them, they were seen by many as the means through which ‘victory’ was accomplished. However with hindsight, historians have argued that this may not have been the case to such an extent and their significance may have been more apparent than it was real. Cartoonists, such as Sidney ‘George’ Strube and David Lowe, awarded great significance to the little ships in their works1314. In their cartoons15 little boats are bombarded by explosions, though significantly none are hit, and in Strube’s a civilian is carrying a soldier to his boat with the caption ‘all in the day’s work’, therein highlighting the role of the ordinary civilian. The BBC’s JB Priestley also greatly commended the ‘little pleasure steamers’ by seeming to suggest their superiority over the warships (‘as magnificent though they were’). In one broadcast he attributed the success to them, speaking of them sailing ‘into the inferno: to defy bombs, shells, magnetic mines, torpedoes, machine gunfire, to rescue our soldiers’ and to return ‘glorious’16. This presentation was designed to be uplifting; the BBC had specifically brought Priestley in to ‘warm the hearts of his listeners’ and ‘go head-to-head with ‘Lord Haw-Haw’’ who was acquiring millions of British listeners in spite of his Nazi stance17. Priestley’s emphatic appraisal of the vessels was therefore part of his role as a broadcaster and his ambiguity of the losses suffered (‘some of them, alas, will never return...’) can be explained by this and indicates that intentional added emphasis had been placed on these vessels. Since then their impact has been regarded by some as more of a ‘myth’18 than reality as they were not used to make the full journey as JB Priestley seemed to be implying, but to transport soldiers from the French shores to the larger destroyers, as the water was too shallow for the latter.19 Additionally, the cartoonists’ impressions were rather misleading because over seventy of these vessels were sunk on their voyage, which seems to be a significant number compared to Priestley’s

Strube, Sydney. ‘All in the days work’, published in the Daily Express 05/06/1940. From cartoon archives. See appendix 14 Lowe, David. ‘To fight another day’, published in the Evening Standard, 08/06/1940. ibid 15 See appendix 16 JB Priestly postscript 05/06/1940. From BBC archives 17 The BBC at War, Presented by Jonathon Dimbleby 144/06/2015 18 Wilson, Patrick. ‘Dunkirk: Victory or Defeat’ published in History Review, 31/9/2000 19 McKay, Sinclair. Dunkirk: From disaster to deliverance, testimonies of the last survivors’ p125-126 13

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History

Extended Essay

‘some’.20 In spite of this, the fact remains that an extraordinary number of little boats, which were not built to cross such a large passage, face torpedoes and other German weapons, nor carry the number of people that they did, bravely assisted in the rescuing of so many thousands of troops and perhaps this positive portrayal did help to ‘bring a nation together’.21 In spite of this, the desire to rebuttal anti-British propaganda catalysed the British media’s exaggerated perception of the little ships and therefore the British public, though their moral may have been lifted, were not given accurate accounts of the role nor the losses of the small vessels.

II.

‘SNATCHING GLORY OUT OF DEFEAT’22

Unsurprisingly, Dunkirk was predominantly presented to the public as a success. A carton by David Lowe published in the Evening Standard on June 6th with the caption “We have gone too far, Adolf. Der British have declared war...”23 exemplifies this. The cartoon was most likely in response to Churchill’s inspiring words that had been spoken to the nation two days prior to this24 and it asserted that Britain was very much still in the war and that the Germans would not obliterate them as they had done others. This would have suggested to the public that Britain had been victorious in the events of the past week. The most anticipated if not most important, piece of information that was to be related to the British public was the number of men who had been returned safely during the operation. On the 6th of June 1940, two days after the end of Operation Dynamo, the government’s weekly resume stated that ‘a grand total of 335,490’ troops had returned safely to English shores25. As this memorandum is an official document made in order to analyse the success of the operation, it is the most reliable source for the known number of troops at this time. This figure, however, was not the one circulated by the press. On the 3rd June the BBC reported that ‘no less than 338,000’ troops had been rescued26 and on the 6th June, George Orwell commented that the figures he had read were ‘of nearly 350,000 men’27. Although both of the latter figures exceed the government estimates and may be perceived to be inaccurate, they are not grossly disproportionate to the official document and indeed the estimate of the BBC is remarkably close to the figure issued by the war office the following year

http://www.rania.co.uk/dunkirk/html/history.htm Wilson, Patrick. ‘Dunkirk: Victory or Defeat’ published in History Review, 31/9/2000 22 Quote from JB Priestly’s postscript 05/06/1940. From BBC archives 23 Lowe, David cartoon published in the Evening Standard 06/06/1940. From the cartoon archives. See appendix 24 Churchill, Winston. ‘The finest hour’ speech given 04/06/1940 25 From a memorandum of the weekly resume of 6/6/1940 26 From ‘BBC on this day’ Article, titled ‘Dunkirk rescue is over, Churchill defiant’. Published 3/6/1940 27 Orwell, George. The Collected Essays, Journalism and Letters, Volume 2 p386-391 20 21

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History

Extended Essay

(337,131)28, as well as that which is now supposed (338,266)29. Additionally, the government document would not have been released at this time (due to a 30 year rule30, which shows that the media’s figures must have been assumptions, hereby eliminating the possibility of total accuracy. Furthermore George Orwell was notorious for his scepticism in the information published in newspapers, suggesting that evidence from him may not be wholly truthful and thus not reliable. But, given that the figures of the media were essentially educated guesses, the exaggeration is not enough to infer that the presentation was intentionally inaccurate. We may conclude that Dunkirk’s success in the number of troops returned was presented as accurately as possible to the British public. Though the figures given to the public may have been accurate, how this astonishing feat was accomplished was not. The little ships, the Royal Navy and the Royal Air Force were accredited to Britain’s success and in many ways, rightly so. However, one aspect that was not presented to the public at all was the misjudgement of Germany’s Commander in Chief. On 24th May Adolf Hitler officially ordered his troops not to continue the advance on the allied troops, hereby giving the latter forty-eight hours of ‘breathing space’31. The first restraint from attack had begun on May 22nd when von Rundstedt demanded that the advance should be postponed and it was only on the 26th May that Hitler agreed to resume the attack32. First-hand accounts illustrate the significance of this decision. General Wilhelm von Thoma, Chief of the Tank Section of the Oberkommando des Heeres (OKH), observed that “Hitler spoilt the chance of victory” and Paul Ludwig Ewald von Kleist, the German Field Marshal, noted that “the English managed to escape... only with the help of Hitler”33. The German officers and soldiers were aware of this command and were unsurprisingly frustrated; however it does not seem that Britons were aware of it in the same way and there were no references to any holding back by the Germans in British newspapers34 nor cabinet documents. It therefore seems as though Hitler’s halt order was not known to Britain until long after the operation had been accomplished. This means that, inevitably, the presentation of it to the public was not existent and therefore inaccurate. The overwhelmingly positive attitude of the media towards the BEF implies that the answer would be no, in order to ensure the highest appraisal for the armed forces, civilians and the little ships. Neither the media’s presentation of the success nor

Report from the War Office on Operation Dynamo, 3/05/1941. From the National Archives Thompson, Julian (2011). Dunkirk: Retreat to Victory p306 30 http://www.nationalarchives.gov.uk/cabinetpapers/cabinet-gov/meetings-papers.htm 31 Roberts, Adam A miracle of war. Published in The Telegraph 25/07/2009 32 Sebag-Montefoire, Hugh Dunkirk, fight to the last man p245 and 247 33 Roberts, Adam A miracle of war. Published in The Telegraph 25/07/2009 34 The British archives had no results for any searches related to Hitler’s halt order. 28 29

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History

Extended Essay

Churchill’s appraisal of a ‘miracle of deliverance achieved by valour, by perseverance, by perfect discipline35’ were, even if unintentionally, correct. Therefore, due to a lack in knowledge and subsequent inaccuracy of the portrayal, in 1940 the British public were not aware of the whole truth in Dunkirk.

III.

‘A COLOSSAL MILITARY DISASTER’ i. Vessel losses

In perhaps his most famous war-time speech, on June 4th 1940, Churchill denounced the evacuation from Dunkirk as a ‘colossal military disaster’36. The German media took this approach as well, with Der Adler writing on the 5th June 1940 that “for the British and French who were there [the word ‘Dunkirchen’] will remind them, for the rest of their lives, of a defeat that was heavier than any army had suffered before”.37 Though this is an explicit example of anti-British propaganda, the confirmation of the event being a ‘defeat’ by Winston Churchill illustrates that Dunkirk was by no means a total success, especially when considering the equipment and vessel losses. Given that so many vessels were deployed to assist in the evacuation it was almost inevitable that a substantial number of them would be lost to the Luftwaffe. With hindsight, it is now thought that ‘6 naval destroyers, 5 minesweepers, 8 transport ships and a further 200 vessels were sunk’.38 These high numbers illustrate the severity of the defeat within the operation. However, on the 6th June, two days after the evacuation had ended, the government had found that ‘in total, 3 naval vessels were sunk and 34 were damaged’. Although the government memoranda are considered to be amongst the most reliable sources from the time, even this is far from the figures that have since been acquired. As a result, it would appear that at the time of the event the scale of the losses were not known at all. George Orwell noted that his newspaper reported that ‘6 destroyers and about 25 other boats of other kind’s had been lost on the same date.39 This is far from the current estimations but quite similar to the government’s statistic even though the latter were not available to the public thus suggesting that it must have been guesswork by both parties. Because of the disparity of the government’s knowledge compared with the knowledge now, it is clear that there was great inaccuracy in the presentation of the losses of vessels. It is equally as clear, however, that this was not done purposefully as the government memoranda were honest in Churchill, Winston. ‘The finest hour’ speech given 04/06/1940 ibid 37 Wilson, Patrick Dunkirk: Victory or Defeat. History Review Issue 37 30/07/2000 38 ibid 39 Orwell, George. The Collected Essays, Journalism and Letters, Volume 2 p386-391 35 36

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their intent and, as they would not be seen by the public, had no reason to hold back figures or be more modest in them. The presentation was, therefore, inaccurate but as a result of lack of knowledge than of desire to withhold the truth.

ii. Losses on the perimeter a) Troops It would not have been possible to evacuate so many thousands of troops without defence against the German tanks and oncoming soldiers and hence this must be examined due to its significance. A perimeter was formed that was seven miles deep around Dunkirk with the British responsible for the eastern sector and the French for the west.40 Some of the most horrific crimes of war and losses to the British army occurred at this perimeter. Two of the most notorious of these were at Wormhoudt and Le Paradis-Lestrem on consecutive days. At the former, troops from the 4th Battalion Cheshire Regiment and the 2nd Battalion Royal Warwickshire Regiment were taken as prisoners of war after fighting to protect their fellow soldiers inside the perimeter.41 Victims speak of being marched into an unbearably crowded barn only to have grenades thrown in by the ruthless enemy. One such victim, Gunner Brian Fahey, commented that ‘it was apparent they were going to murder us all’.42 At Le-Paradis, the War Crime Interrogation Unit found that ninety-seven British POWs had been murdered in equally as brutal a manner. The report went on to reveal that witnesses had mentioned other massacres but these could not be prosecuted as there were no survivors.43 Even now, it is not possible to know the scale of the breach of the Geneva Convention of 1929, where prisoners are to be treated with respect and honour. It was because of the lack of knowledge of these tragedies that no accounts were depicted to the public at the time and hereby ensured that they were not aware of the true horrors of Dunkirk. Their perception of event was inaccurate due to the unintentional though perhaps fortunate lack of information they were presented with.

b) Weapons These acts of violence were not the only losses that would affect the British. Weapon losses were immense and would hinder the war efforts of the near future44 but this was due to logistical impracticalities rather than ruthless illegalities. The destroyers, as mentioned previously, were not Sebag-Montefoire, Hugh Dunkirk, fight to the last man p261 McKay, Sinclair Dunkirk, From disaster to deliverance – testimonies of the last survivors p171 42 Levine, Joshua Forgotten voices of Dunkirk p147-8 43 Sebag-Montefoire, Hugh Dunkirk, Fight to the last man p297 44 Churchill, Winston. ‘The finest hour’ speech given 04/06/1940 40 41

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able to get close to the shores45 and the only way of reaching them was via the ‘little ships’. The name of the latter highlights their inability to transport large vehicles such as tanks, and given that human lives were the greatest priority, space was not to be wasted with unnecessary weaponry. As a result of this equipment was left around Northern France for the Germans to take as their own. Generally, this was presented truthfully to the public. The BBC wrote that ‘The BEF had to leave behind all its heavy armour and equipment’46 while Churchill tried to be more specific, announcing that nearly one thousand guns had been lost as well as ‘all transport’ and ‘all armoured vehicles’. He went so far as to indicate that it would hinder the expansion of British military strength.47 The above quotes are extremely honest as indeed all of the transport and vehicles were left behind. The only way to report this inaccurately would have been to ignore it entirely, which is what many newspapers did. In spite of this, so many British people would have relied on radio broadcasts from the Prime Minister and the BBC that their perception of this aspect of the evacuation was likely to be accurate. The accurate representation of the staggering equipment losses, especially by the Prime Minister, illustrate that the public were aware of at least a small portion of the losses from the evacuation as well as of the triumphs. However, the losses of material objects would not have been as disturbing to the public as news of thousands of lost men would have been, so perhaps this is why the media and Churchill felt they were able to be honest and accurate in this aspect of the evacuation.

IV.

THE FRENCH

Dunkirk lies in France, 10km from the Belgian boarder and so naturally this was as much an evacuation for the French as it was for the British. In spite of this, cooperation was not always as successful and harmonious as the media projected. The lack of unity between these two allied forces can perhaps be exemplified by the separation regarding the perimeter around Dunkirk, with the French taking one end, the British the opposite.48 A report from the War Office dated the 3rd May 1941, which would not be known to the public, showed that the number of British troops evacuated almost doubled the number of the French. It subsequently argued that the main reason for this disparity was the ‘failure of the French to make any effort to assist in the evacuation’.49 Though written a year after the evacuation the frustration of McKay, Sinclair. Dunkirk: From disaster to deliverance, testimonies of the last survivors’ p125-126 From ‘BBC on this day’ Article, titled ‘Dunkirk rescue is over, Churchill defiant’. Published 3/6/1940 47 Churchill, Winston. ‘The finest hour’ speech given 04/06/1940 48 Lord, Walter The Miracle of Dunkirk p78 49 From a report by the War Office on Operation Dynamo, 03/05/1941. Catalogue ref: WO 106/1618. National archives 45 46

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the war office is tangible consequently suggesting that the French were perceived as uncooperative. Indeed at the time, the chief naval staff said that the vessels the French had offered never showed up50, Britain’s Colonel Whitfield complained that France’s Admiral Le Clerc’s attitude towards him ‘was not even bordering on one of cordiality’ and there were reports of the French commander, Abrial protesting that the British soldiers were misbehaving.51 These reports imply that, although blame cannot solely be attributed to the French who had their own grievances with Britain, the relationship between the allies was unstable. In spite of this antagonistic and depleting relationship the British public were presented with a very different account. On May 29th 1940 The Times newspaper reported that ‘the French Navy, in defending the ports and lines of communication, is lending [the British] powerful support’.52 Similarly the Hartlepool Mail wrote: ‘the British and French are working in the closest unity, with steadiness never excelled in military history’ on June 1st 1940.53 Churchill himself spoke of severed communications between the two armies but never hostility54. This exemplifies the interpretation of the alliance and therefore the presentation of it to the British public as very strong and as such contradicts the first-hand accounts of the men at Dunkirk at the time. Due to the juxtaposition between what can be presumed to be a hostile and antagonistic reality and the much more praising and optimistic version by the media, it may be inferred that the presentation to the British public was inaccurate due to its optimistic emphasis on a strong alliance. The journalists, especially from smaller newspapers, would not have been present at Dunkirk and so their sweeping comments would not have been based on evidence. Yet even after the troops had returned the animosity was not reported. This suggests that the presentation of the French was intentionally inaccurate in order to depict the evacuation in the best possible light.

From a minutes report from the War Cabinet 01/06/1940: CAB 65/7/46. National Archives Hastings, Max Finest Years, Churchill as a Warlord 1940-45 p375-6 52 Articled titled ‘The Defence of Dunkirk’ 29/05/1940. From The Times newspaper archives 53 Hartlepool Mail, 01/0/1940. From the British newspaper archives 54 Churchill, Winston. ‘The finest hour’ speech given 04/06/1940 50 51

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CONCLUSION The evacuation of troops from Dunkirk was not presented entirely accurately to the British public in May/June of 1940. In the majority of cases the inaccuracy of the depiction was due to a lack of information rather than falsehood or fabrication. The knowledge that was somewhat possible to acquire, such as the number of returned troops, was relayed most accurately. However, many aspects of the evacuation, such as the relationship between the British and French, were rather more fictitious and therefore more grossly inaccurate. Though there was no strict censorship, the media would not have wanted to create a disheartening and pessimistic atmosphere in the midst of war. This partially justifies why the presentation of equipment losses was far more accurate than the losses of men. It is also important to consider that even the contemporary historiography, which has been used in order to determine the accuracy of the original presentation, may be subjective in itself especially as the majority were of British historians. However, the contemporary facts match each other so much that it would be reasonable to presume they are accurate. Therefore, it seems that overall the British public were given a more optimistic and reassuring account of Dunkirk than was real and thus it must be concluded that the presentation, though not always deliberately so, was inaccurate.

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APPENDIX Artist: Sydney Strube Published: Daily Express, 05/06/1940 Caption: All in the days work

Artist: David Lowe Published: Evening Standard, 06/06/1940 Caption: We have gone too far, Adolf. Der British have declared war...

Artist: David Lowe Published: Evening Standard, 08/06/1940 Caption: To fight another day

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Bibliography: Books Brown, Judith (1998). The Twentieth Century, the Oxford History of the British Empire Volume IV. Oxford University Press. McKay, Sinclair (2014) Dunkirk, from disaster to deliverance – testimonies of the last survivors. Great Britain Orwell, George (1970) The Collected Essays, Journalism and Letters: My Country, Right or Left,

1940-43 v. 2

Sebag-Montefoire, Hugh (2015) Dunkirk, fight to the last man. Great Britain: Clays Ltd Thompson, Julian (2001) Dunkirk: Retreat to Victory. New York: Arcade Journals The Telegraph 25/07/2009 – Dunkirk: A miracle of War, by Adam Roberts From History Review Issue 37 September 2000, by Patrick Wilson, Dunkirk: Victory or Defeat Dunkirk and the Popular Memory of Britain at War, 1940-58 by Penny Summerfield, Journal of Contemporary History Archives http://www.cartoons.ac.uk/browse/cartoon_item/anytext=evacuation%201940?page=21 http://www.cartoons.ac.uk/browse/cartoon_item/Dunkirk?page=3 The Yorkshire Evening Post, Tuesday 18th June 1940:http://www.britishnewspaperarchive.co.uk/viewer/bl/0000378/19400601/126/0004 Hartlepool Mail, 01.06.1940: http://www.britishnewspaperarchive.co.uk/viewer/bl/0000273/19400618/177/0007 The Times, June 6 1940: http://discovery.nationalarchives.gov.uk/details/r/C9034262 The Times Newspaper Archives. ‘The Defence of Dunkirk’ Paris, May 29th 1940 page 6 ‘BBC ON THIS DAY’ Article titled Dunkirk rescue is over – Churchill defiant. 3/6/1940: http://news.bbc.co.uk/onthisday/hi/dates/stories/june/4/newsid_3500000/3500865.stm Memorandum Weekly Resume: May 30th 1940: http://discovery.nationalarchives.gov.uk/details/r/C9034252#imageViewerLink Memorandum weekly resume: June 6th 1940: http://discovery.nationalarchives.gov.uk/details/r/C9034262 Minutes report prior to the evacuation of the War Cabinet on June 1st 1940: CAB 65/7/46 Report from the War Office on Operation Dynamo, dated 3rd May 1941. Catalogue ref: WO 106/1618 – National Archives.

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Derby Daily Telegraph 25 October 1948: http://www.britishnewspaperarchive.co.uk/viewer/bl/0000521/19481025/050/0008 Nottingham Evening Post 21 June 1940: http://www.britishnewspaperarchive.co.uk/viewer/bl/0000321/19400621/028/0005 Websites http://news.bbc.co.uk/1/hi/england/dorset/8692057.stm http://www.winstonchurchill.org/resources/speeches/1940-the-finest-hour/we-shall-fight-on-thebeaches (accessed 16/06/2015) http://www.bbc.co.uk/archive/dunkirk/14310.shtml

Other BBC documentary The BBC at War, Presented by Jonathan Dimbleby http://www.bbc.co.uk/iplayer/episode/b05zqtkn/the-bbc-at-war-presented-by-jonathan-dimbleby-1the-war-of-words

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To what extent is it possible to speculate on the intentions of Master John and Duncan Grant in their depictions of Mary I and Vanessa Bell?

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Freya Sackville-West - Visual Arts Writing about two portraits painted 400 years apart may seem like a curious task. However, the more I looked at each paintings and researched their context; I was able to examine the extent to which the role of portraiture reflects the society in which it was painted. My IB Visual Arts Course helped me to examine the portraits closely, and to articulate the way in which the different painting techniques convey the artistsâ&#x20AC;&#x2122; relationship with their sitters. I began writing my essay with the intention of reading History of Art at university. Undertaking this piece of research and writing has confirmed this; it combines my love for both history and art.

Supervisor: Charley Openshaw This Extended Essay explores the relationship between two portraits that are separated by 400 years but are visually, remarkably similar. It is an authoritative investigation into the motives and preoccupations of the artists concerned, using the format of the essay to both exploit traditional art historical analysis and pursue personal interests. The high degree of rigour in the visual analysis and the command of the historical contexts result in a compelling piece of research. A conclusion is argued persuasively, revealing an instinctive understanding of visual language and artistsâ&#x20AC;&#x2122; approaches to communication, informed by the author own creative practice. It is satisfying that sixteenth century painting still has resonance and relevance to contemporary image making.

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Contents Introduction 117 Queen Mary I, by Master John, 1544

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Vanessa Bell, by Duncan Grant, 1918

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Conclusion 131 Appendix 133 Bibliography 141

Abstract The aim of this essay is to investigate to what extent it is possible to speculate on the intentions of Master John and Duncan Grant in their depictions of Mary I1 and Vanessa Bell2. Visits to the National Portrait Gallery, where both works are on display, allowed me to make primary, visual observations on the two portraits in question: Queen Mary I, by Master John, 1544 and Vanessa Bell, by Duncan Grant, 1918. I combined these observations with research surrounding the context in which the two works were produced, including a discussion with Charlotte Bolland,3 in order to develop my investigation. The scope of this essay is only concerned with the two portraits in question, and not the wider intentions of the respective artists. Although the two respective contexts are explored, this investigation is limited to the two individual pieces, and so does not include analysis of work by other contemporary artists, nor other artworks by the same artists. The essay concludes that although both artists intended to convey a relationship involving the sitter, the long period between the two portraits draws attention not only to the different type of relationship, but also to the change in the role of the artist. However, there are challenges when speculating on the artists’ intentions: a lack of historical information about Master John and the difficulty in understanding the relationship between Duncan Grant and Vanessa Bell. Despite the apparent visual connections between the two portraits, Master John’s passive role in depicting the reconciliation between Mary I and her father, Henry VIII, is a contrast to Duncan Grant’s intimate role in reinforcing his love for Vanessa Bell.

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Appendix

Candidate Name: Freya Sackville-‐West Candidate No.: fph561 (000102 -‐0159)

Fig. 2 Duncan Grant, Vanessa Bell, 1918, oil on canvas, 94 × 60.6 cm., National Portrait Fig. 1 Master John, Queen Mary I, 1544, oil on panel, 71.1 × 50.8 cm., National Portrait Gallery, London. Gallery, London

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To what extent is it possible to speculate on the intentions of Master John and Duncan Grant in their depictions of Mary I and Vanessa Bell?

Introduction

My initial interest in the Bloomsbury Group was sparked by a talk I attended

about Virginia Woolf’s novel Orlando. This led me to read several books about

the art and culture of the Bloomsbury Group, including three essays in Richard

Shone’s The Art of Bloomsbury,4 the catalogue that accompanied an exhibition at

the Tate Gallery in London in 1999. Whilst flicking through the catalogue, I came across a page which showed a painting by Duncan Grant of Vanessa Bell 5 and a

Tudor portrait of Queen Mary I (painted before she became Queen) by Master

John6. I was struck by how similar, yet how different, the two portraits were and when I read the information about Grant’s portrait, it was suggested that, perhaps, the Tudor portrait had influenced Grant.7

Recent visits to the National Portrait Gallery confirmed the similar size,

composition and colours of the two portraits. However, their respective locations in the NPG highlighted the almost four-‐century gap between them and therefore how much had changed: not only the technique of the artists, but also how both the role of portraiture and the artists had changed. The different demands of

‘official’ portraiture (Mary I) and ‘intimate’ portraits (Vanessa Bell) can still be seen in contemporary works of art. In the NPG, one has only to compare the

controversial, commissioned portrait of HRH The Duchess of Cambridge8 and the

more personal, revealing portrait of Germaine Greer9.

4 R. Shone, The Art of Bloomsbury: Roger Fry, Vanessa Bell and Duncan Grant (London:

Tate Gallery Publishing, 1999). 5 Grant, Vanessa Bell, 1918. 6 Master John, Queen Mary I, 1544. 7 Shone, The Art of Bloomsbury, p. 192. 8 P. Emsley, HRH The Duchess of Cambridge, 2012, oil on canvas, 115.2 × 96.5 cm., National Portrait Gallery, London (see Appendix Fig. 3). 9 P. Rego, Germaine Greer, 1995, pastel on paper laid on aluminium, 120 × 111.1 cm., National Portrait Gallery, London (see Appendix Fig. 4). 117

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All this inspired the research question for my investigation: to what extent is it Freya Sackville-West - Visual Arts

possible to speculate on the intentions of Master John and Duncan Grant in their depictions of Mary I and Vanessa Bell?

My investigation will be formed of the analysis of the two portraits separately.

Firstly, I will consider the formal qualities of Master John’s portrait of Mary and

the context in which it was painted. Master John was painting at a time when the

artists’ intentions were surpassed by those of the sitters’.10 Then, as with the first portrait, I will examine the formal qualities of Duncan Grant’s portrait of Vanessa Bell. I will evaluate the context surrounding this portrait, particularly the

relationship between Grant and Vanessa Bell as well as the significance of the Bloomsbury Group, who wanted to reject restricting Victorian social

responsibilities, replacing them with private and personal relationships.11

In order to keep my investigation focused, I will only concentrate on these two

portraits. I make no attempt to introduce other genres of contemporary painting nor do I look at the work of other artists or other works by Master John and

Grant, unless they are directly relevant to and enhance the point I am making.

Nor will I be looking at either the artistic or contextual changes that occurred in

the period between the painting of these two portraits, as this would encompass critical analysis of almost four hundred years of artistic, social, political and cultural development.

The contexts of the two respective portraits are vital in order to understand them. Although both are single sitter portraits, this analytical investigation

reveals how each of the artists intended to portray a relationship. However, both the way in which they go about doing this and the type of relationship they show are different.

10 C. MacLeod, Tudor Portraits in the National Portrait Gallery Collection (London: National Portrait Gallery Publications, 1996), p. 2. 11 F. Spalding, The Bloomsbury Group (London: National Portrait Gallery Publications, 1997; repr. London: National Portrait Gallery Publications, 2013), pp. 5-‐24.

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Master John, Queen Mary I, 1544 Materials and technique

Before the oil paint was applied, Master John completed an underdrawing on the panel12

that emerges through the relatively thin

layers of oil. When one stands in front of this painting, the underdrawing is most

noticeable around Mary’s facial features: her eyes, nose, lips, chin and jaw giving them more definition. The small, smooth

brushstrokes used to paint Mary’s skin are incredibly well blended and her hair is

painted in a similar manner with the strands of highlights added later.

Master John, Queen Mary I, 1544

Mary’s painted dress uses a mixture of gilding gold and silver leaf and precise

painting.13 The expense of the materials used suggests that Master John wanted to please his sitter. The orange/red glaze sits on top of an undercoat of yellow ochre and gilded gold leaf.14 The viewer is astonished by the delicacy and

precision of the perfectly ordered and parallel silver leaf threads with loops of white paint.15 Mary’s red lower sleeves are painted with a looser, yet still

smooth, brushstroke, which give it a velvet-‐like texture. The cuffs of her sleeves are decorated with a faint pattern of red Tudor roses – applied with a very fine brush – suggesting the significance of the family dynasty.

12 ‘Queen Mary I’, Tudor and Jacobean Portraits Database (London: National Portrait

Gallery, 2015 (copyright date)), <http://www.npg.org.uk/collections/search/portraitConservation/mw04264/Queen-‐ Mary-‐I?> [accessed 19 August 2015]. 13 S. Plender and T. Cooper, ‘English Workshops: work in progress on 'Master John' & other 1540s native painters’, Making Art in Tudor Britain (London: National Portrait Gallery, 2015 (copyright date)), <http://www.npg.org.uk/research/programmes/making-‐art-‐in-‐tudor-‐ britain/workshops/workshop-‐2-‐abstract-‐3.php> [accessed 19 August 2015]. 14 ‘Queen Mary I’, Tudor and Jacobean Portraits Database. 15 Ibid. 119

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Candidate Name: Freya Sackville-‐West Candidate No.: fph561 (000102 -‐0159) Composition and scale

Mary is almost life-‐sized in her portrait, which makes it easier for the viewer to

relate to her. The background is flat and the lettering does not attempt to deepen it. This is not uncommon in Tudor portraiture: it was not essential to accurately depict space; artists were more concerned with presenting the sitter’s elevated position in society.16

Although her figure takes up most of the picture plane (and is the central focus of the portrait), the gilded letters are prominent in the background: ‘ANNO DÑI

1544 LADI MARI DOVGHTER TO THE MOST VERTVOVS PRINCE KING HENRI THE EIGHT THE AGE OF XXVIII YERES’. This has the effect of introducing a

second subject to the portrait: Mary’s father. It elevates Mary’s status – she is of royal blood – yet also undermines her own character – she is defined by her

father’s position. Her face appears to have little significance in the picture plane

as it is sandwiched between the gilded lettering as well as between her elaborate headdress and outfit; her tilted stare seems detached from the viewer, who, perhaps, is more drawn to the extravagance of her clothing.

Mary’s posture is stiff and looks very formal which is enhanced by the central

vertical axis acting as a line of symmetry throughout the composition. Even the embroidered pattern in her bodice is beautifully equal, giving the portrait a sense of balance. The centre point of the picture plane is the large jeweled

broach pinned to her dress, which is slightly camouflaged, surrounded by the

elaborate bodice. However, as the viewer’s eyes glance up, just above this central point, one’s eyes are lured to the jeweled flower pendant with five diamonds,

two rubies and an emerald17 framed by Mary’s pale skin, emphasising her status.

16 M. Howard, The Tudor Image (London: Tate Publishing, 1995), p. 7.

17 C. Bolland and T. Cooper, The Real Tudors: Kings and Queens Rediscovered (London: National Portrait Gallery Publications, 2014), p. 109.

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Candidate Name: Freya Sackville-‐West Candidate No.: fph561 (000102 -‐0159) Light and tone

The light source is not immediately obvious; it comes from the left of the portrait – where Mary is looking. The glistening pearls and jewels reflect this light giving them a life-‐like appearance, catching the viewer’s eyes. The shadows and

highlights in the folds of her lower sleeves enhance the luscious nature of the material.

The subtle manipulation of light and tone on Mary’s skin is an indication of the social importance of pale skin during the Tudor period.18 The changes in tone

around her face – along her neck, jaw line and forehead – give her face a more

rounded look. The relatively harsh outlines, particularly around her mouth and eyes, also reflect the stiffness of her posture.

Colour Mary’s skin is painted as white as the pearls she wears, giving her a statuesque

appearance. However, the slight blushes on her cheeks, along with the subtle yellow tones around her nose, bring her pale face to life.

Her pale skin is a contrast to the vibrant colours of her outfit. The sumptuous red lower sleeves make her figure more animate, especially as they are set against the cooler blue background. The intricate details of her bodice are visually

exciting and almost distract the viewer away from Mary’s rather plainer face.

Context In Master John’s portrait Mary seems unaffected by her distressing upbringing. Although, as a child, her father cherished Mary,19 Henry VIII was disappointed

that Katherine of Aragon, Mary’s mother, had not produced a male heir.20 This

led to their divorce as well as England’s break from Rome in 1533; Henry

18 T. Cooper, A Guide to Tudor & Jacobean Portraits (London: National Portrait Gallery,

2008), p. 14. 19 A. Whitelock, Mary Tudor: England’s First Queen (London: Bloomsbury, 2009), Amazon Kindle e-‐book (Prologue, location 94). 20 Whitelock, Mary Tudor, Amazon Kindle e-‐book (Chapter 7, location 565). 121

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became the Head of the Church of England.21 Also in that year, Henry declared Mary illegitimate and she lost her claim to the throne.22 Mary reluctantly

accepted her father as both King and Head of the Church, recognized that her parent’s marriage was invalid23 and, after Henry’s fifth wife was executed in

1542,24 her relationship with her father was rekindled. In 1543 Henry married Katherine Parr, with whom Mary (only four years younger) got on very well.25 The two women shared a love for clothes and a 1545 portrait of Katherine

Parr26, also by Master John, shows Katherine dressed in similar style27 with

affluent dresses of cloth of gold and silver. The wide, square neckline that both women exhibit was highly fashionable, exposing their pale skin. Mary was

dressing like the Queen, showing she had finally been re-‐accepted by her father. In February 1544, Henry, encouraged by Katherine, restored Mary (and her stepsister, Elizabeth) to the line of succession.28 The portrait: The Family of

Henry VIII29 celebrated the reconciliation between not only Mary and her father,

but between the whole family.30 Mary (left) and Elizabeth (right), although not

the main focus of the portrait, are still included. Their fashionable and expensive jewels and dresses distinguish them as the King’s legitimate children. In the

portrait of Mary I, the flower jewel that hangs from her neck is thought to be a

gift from Henry,31 which reinforces this idea that the portraits signify the King’s acceptance of his daughter.

In Tudor portraits the sitter and the portrait itself tend to have more significance than the artist, which is why little is known about ‘Master John’. It is thought that

21 Whitelock, Mary Tudor, Amazon Kindle e-‐book (Chapter 10, location 829). 22 Ibid. (Chapter 12, location 995).

23 Ibid. (Chapter 18, location 1615). 24 Ibid. (Chapter 23, location 1989). 25 Ibid. (Chapter 23, location 2009).

26 Master John, Katherine Parr, 1545, oil on panel, 180.3 × 94 cm., National Portrait Gallery, London (see Appendix, Fig. 5). 27 Bolland and Cooper, The Real Tudors, pp. 109-‐110. 28 Whitelock, Mary Tudor, Amazon Kindle e-‐book (chapter 24, location 2048). 29 Unknown artist, The Family of Henry VIII, 1545, oil on canvas, 144.5 × 355.9 cm., The Queen’s Gallery, Buckingham Palace, London (see Appendix, Fig. 6). 30 Whitelock, Mary Tudor, Amazon Kindle e-‐book (chapter 24, location 2057). 31 Bolland and Cooper, The Real Tudors, p. 109.

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he was an Englishman who may have worked in Holbein’s studio,32 which may be why the portrait33 is painted in a Holbeinesque, almost formulaic, style,

similar to the way in which he portrayed Katherine Parr34. It is not unusual to have so little information about a Tudor artist; unless they were particularly distinguished, they had the same status in society as craftsmen.35

Towards the end of the 15th century, portraiture was becoming increasingly

popular in the royal courts of Europe. The best painters were commissioned to portray the monarchs, aristocrats and clergy as well as wealthy merchants in

their most flattering light,36 and therefore, the sitters had a significant influence

over the final outcome of these portraits. The artist’s job was not only to present what the sitter looked like, but also to show how the sitter wanted to be

remembered:37 they wanted to show off their wealth and status. Portraiture did

not thrive in England until the reign of Henry VIII.38 Tudor portraits very much

adopted the northern European style,39 and the most eminent artists came to

England from the Low Countries.40 When the German artist, Hans Holbein, came

to England in 1526, he became the ‘King’s Painter’.41 Master John may have

picked up his trade in Holbein’s workshop42 and after Holbein’s death in 1543,

he may (like other artists at the time) have imitated Holbein’s style in order to continue his legacy.43

32 ‘Queen Mary I’, Tudor and Jacobean Portraits Database. 33 Master John, Queen Mary I, 1544.

34 Master John, Katherine Parr, 1545.

35 Cooper, A Guide to Tudor & Jacobean Portraits, p. 42. 36 Bolland and Cooper, The Real Tudors, p. 8.

37 Cooper, A Guide to Tudor & Jacobean Portraits, p. 4. 38 Ibid.

39 Howard, The Tudor Image, p. 27.

40 Cooper, A Guide to Tudor & Jacobean Portraits, p. 42

41 S. Foister, ‘Holbein as a Court Painter’, in Henry VIII: A European Court in England, ed.

by D. Starkey (London: Collins & Brown, 1991), p. 58. 42 ‘Queen Mary I’, Tudor and Jacobean Portraits Database. 43 Howard, The Tudor Image, p. 27. 123

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It is likely that Mary I commissioned her own portrait, as the payment to Master John is listed in her Privy Purse expenses.44 From a young age, Henry had used

the potential marriage of Mary as a way of securing foreign policy success. This

was no different in 1545 when a marriage was negotiated with France, to Charles V, as a sign of peace.45 During this period, Henry kept the circulation of images of his daughter under tight control and her portrait could only be painted with his permission.46 In addition to this, Mary’s pose is similar to marriage portraits

painted by Holbein.47 Although the purpose of the portrait is unclear, one could speculate that the portrait was commissioned with marriage negotiations in

mind.48 As the marriage negotiations eventually fell through, Mary’s portrait49

remained in England and Henry kept it; it was recorded in an inventory of

Whitehall Palace the year after he died,50 suggesting that it may have only been intended for private viewing.

44 Madden, Privy Purse Expenses of the Princess Mary, p. 176.

45 Whitelock, Mary Tudor, Amazon Kindle e-‐book (chapter 24, location 2104).

46 Correspondance Politique de MM. de Castillon et de Marillac, ed. by M. J. Kaulek

(Geneva: Slatkine Reprints, 1971), p. 350. 47 MacLeod, Tudor Portraits in the National Portrait Gallery Collection (London: National Portrait Gallery Publications, 1996), p. 18. 48 In conversation with Charlotte Bolland. 49 Master John, Queen Mary I, 1544. 50 Bolland and Cooper, The Real Tudors, p. 77. 124

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Candidate Name: Freya Sackville-‐West Candidate No.: ame: Freya (000102 Sackville-‐West fph561 -‐0159) ame: Freya (000102 Sackville-‐West Candidate No.: fph561 -‐0159) Duncan Grant, anessa (B000102 ell, 1918 Candidate No.: Vfph561 -‐0159) Duncan Grant, Vanessa Bell, 1918 Materials and tV echnique anessa Bell, 1918 Duncan Grant, Materials and technique By using oail nd paints, Grant is able to Materials technique By using oil paints, Grant is able to manipulate paint freely. he tuo nblended By using oil tphe aints, Grant is aTble manipulate the paint freely. The unblended skin tones gtive skin a blotchy ook, manipulate he tphe aint freely. The ulnblended skin tones give the skin a blotchy look, enriching features, particularly skin tones Vganessa’s ive the skin a blotchy look, in enriching Vanessa’s features, particularly in her face. TVhe paisley fp attern opn her dress iin s enriching anessa’s eatures, articularly her face. The paisley pattern on her dress is mostly painted with lpoose brushstrokes; her face. The paisley attern on her dress is mostly painted with loose brushstrokes; however, a finer rush was sed to enhance mostly painted wbith loose bu rushstrokes; however, a finer brush was used to enhance the pattern’s definition around her however, a finer brush w as used to bereasts. nhance the pattern’s definition around her breasts. The rhythm of the abround rushstrokes, a the ploose attern’s definition her breasts. The loose rhythm of the brushstrokes, a quality that can only e abppreciated when The loose rhythm of tbhe rushstrokes, a quality that can only be appreciated when standing close to the bpe ortrait itself, aw nd the quality that can only appreciated hen standing close to the portrait itself, and the pattern echo the ay pin which Vanessa’s standing close to w the ortrait itself, and the pattern echo the way in which Vanessa’s dress is escho lipping her pattern the owff ay in swhoulder, hich Vanessa’s dress is slipping off her shoulder, emphasising the ointimacy of the portrait. The Duncan Grant, Vanessa Bell, 1918 dress is slipping ff her shoulder, emphasising the intimacy of the portrait. The Duncan Grant, Vanessa Bell, 1918 much longer b rushstrokes background subtler and Vanessa more sBet emphasising the intimacy om f take he pthe ortrait. The Duncan Grant, ell, b1ack, 918 much longer brushstrokes make the background subtler and more set back, giving t he v iewer a s ense o f d epth. T here a re t wo d istinct p lanes; a lthough the much longer brushstrokes make the background subtler and more set back, giving the viewer a sense of depth. There are two distinct planes; although the background is relatively stresses anessa’s role as ptlanes; he main focus otf he the giving the viewer a sense flat of dthis epth. There V are two distinct although background is relatively flat this stresses Vanessa’s role as the main focus of the painting. background is relatively flat this stresses Vanessa’s role as the main focus of the painting. painting. Composition and scale Composition and scale The portrait a is nd larger Composition scale than life size, which invites the viewer to take Grant’s The portrait is larger than life size, which invites the viewer to take Grant’s position, painting Vanessa. Her figure takes up the majority f tthe picture plane. The portrait is larger than life size, which invites the viewer oto ake Grant’s position, painting Vanessa. Her figure takes up the majority of the picture plane. The viewer’s eye is ed up the portrait’s vertical axis which oaf lso acts as a lpine of position, painting Vlanessa. Her figure takes up the m(ajority the picture lane. The viewer’s eye is led up the portrait’s vertical axis (which also acts as a line of symmetry), from two hands clasped up tahe bauttons her of The viewer’s eye iVs anessa’s led up the portrait’s vertical together, axis (which lso cts as oaf line symmetry), from Vanessa’s two hands clasped together, up the buttons of her dress and up her sVeductively exposed Her cleavage marks the ocentral symmetry), from anessa’s two hands ccleavage. lasped together, up the buttons f her dress and up her seductively exposed cleavage. Her cleavage marks the central point the ph ortrait, which is eaxposed hint to chleavage. er relationship with Gm rant. this dress oaf nd up er seductively Her cleavage arks Htowever, he central point of the portrait, which is a hint to her relationship with Grant. However, this line of osf ymmetry is dw isrupted Vanessa’s ilted head aw nd distant point the portrait, hich is ab y hint to her rtelationship ith Grant. gHaze. owever, this line of symmetry is disrupted by Vanessa’s tilted head and distant gaze. line of symmetry is disrupted by Vanessa’s tilted head and distant gaze. Vanessa’s facial expression becomes the main focal point of the portrait. Vanessa’s facial expression becomes the main focal point of the portrait. Although tfhey occupy less obf ecomes the picture han phoint er body, her striking facial Vanessa’s acial expression the p mlane ain ftocal of the portrait. Candidate N ame: Freya Sackville-‐West Although they occupy less of the picture plane than her body, her striking facial features ctaptivate the vl(ess iewer. Vanessa’s are mirrored by hthe lue beads of Candidate No.: ofph561 000102 -‐0159) Although hey ccupy of the picture epyes lane than her body, er sbtriking facial features captivate the viewer. Vanessa’s eyes are mirrored by the blue beads of her necklace, and hter is irrored the most element features captivate he svlightly iewer. dVetached anessa’s setare yes tahat re m by etntrancing he blue beads of of the portrait; she looks lost in thought.

Light and tone

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12 12 12

Vanessa is looking towards the light source and although the light is manipulated

Candidate Name: Freya Sackville-‐West Candidate No.: fph561 (000102 -‐0159)

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her necklace, and her slightly detached stare that is the most entrancing element of the portrait; she looks lost in thought.

Light and tone Vanessa is looking towards the light source and although the light is manipulated subtly (there are no striking contrasts between light and dark), her nose, eyes and lips are all highlighted in order to draw attention to these features.

Although outlines are used to frame Vanessa’s figure (as well as smaller details

in her hands), within these outlines Grant contours her body. These contours are distinctly post-‐impressionist in style; Grant substitutes light and tonal changes with alterations of the colour51 – particularly on her left forearm, around her

chest, collar bones, neck and face. This accentuates Vanessa’s features, giving her the ‘blotchy’ look as well as giving her body a sense of volume.

Colour Perhaps, the most striking element of this portrait is Grant’s use of vibrant,

fauvist colours. The contrast between the cool blue background and the warm

red dress pushes Vanessa towards the viewer. These saturated colours enhance the intensity of the portrait and Grant’s bold expression of love.

The pink rose that Vanessa clutches could be seen as a symbol of love,

particularly as a similar colour is echoed around her cleavage and the centre of her chest: where her heart is. However, this pale pink colour is also used to

enrich Vanessa’s eyes. A ring of the rose-‐coloured pink encircles her deep blue eyes drawing the viewer into her intense contemplation.

51 Spalding, The Bloomsbury Group, p. 46.

13 126

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Context

Duncan Grant’s portrait of Vanessa Bell52 was exhibited in his first solo

exhibition at the Paterson-‐Carfax Gallery in London in February 1920,53 which

marked a breakthrough in his career.54 Although the exhibition received mixed reviews, twenty-‐four of the thirty-‐one pictures were sold.55 Clive Bell, the art critic and husband of Vanessa, gave Grant his most favorable review:

…Duncan Grant is, in my opinion, the best English painter alive…[his] ancestors are Piero della Francesca, Gainsborough and the Elizabethan poets…In Duncan Grant there is…something that reminds one unmistakably of the Elizabethan poets, something fantastic and whimsical and at the same time intensely lyrical.56

Grant’s interest in the Elizabethan poets suggests he may have also been

attracted to Tudor history; and the flower that Vanessa holds in her hands could

be a reference to the symbol of the Tudor dynasty: a rose. Grant had a traditional artistic training in which the history of art was respected 57 and in 1901 Grant

was being taught by the French artist, Simon Bussy.58 Bussy instructed Grant to use the Old Masters in the National Gallery as inspiration for his own work.59 Although Grant was a leading light in the modernisation of English art, he

understood that in order to do this, he must not forget the art of the past, but rather embrace and incorporate it into his work. Bussy was also friends with

Matisse,60 one of the French artists whose work was exhibited61 in Roger Fry’s

innovative Post-‐Impressionist Exhibitions of 1910 and 1912.62 When comparing Grant’s 1908 portrait of John Maynard Keynes63 with his 1918 portrait of

52 Grant, Vanessa Bell, 1918.

53 Shone, The Art of Bloomsbury, p. 192.

54 S. Watney, The Art of Duncan Grant (London: John Murray, 1990), p. 48. 55 F. Spalding, Duncan Grant (London: Chatto & Windus, 1997), p. 224.

56 C. Bell, ‘Duncan Grant’, Athenaeum, 6 February 1920, cited in F. Spalding, Duncan

Grant (London: Chatto & Windus, 1997), p. 225. 57 Watney, The Art of Duncan Grant, p. 10. 58 Spalding, Duncan Grant, p. 25. 59 Watney, The Art of Duncan Grant, p. 21. 60 Ibid. 61 Spalding, Duncan Grant, pp. 98-‐101. 62 Shone, The Art of Bloomsbury, p. 7. 63 D. Grant, John Maynard Keynes, 1908, oil on canvas, 80 × 59.5 cm., The Provost and Scholars of King’s College, Cambridge (see Appendix Fig. 7). 127

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Vanessa,64 one can see how influential these exhibitions were for Grant. Not only are the colours brighter and used in the Post-‐Impressionistic way (substituting

tonal changes with contrasting colours) but also the paint has been applied much more freely. In addition, both the subject and the environment in which they are sitting are less formal in the latter portrait. The contrast of these two portraits highlights how Grant’s art led the way for modernism in England.

Vanessa Bell (née Stephen) was not only an admirer of Grant’s work (an artist herself), but also his lover for many years.65 As a young girl, Vanessa felt

restricted by her responsibilities as the eldest daughter in a Victorian family, as

described by her sister, Virginia Woolf, in her novel Night and Day.66 Determined

to free herself from these conventions, Vanessa prompted the move to 46

Gordon Square, Bloomsbury with her siblings in 1904.67 In 1907, Vanessa

married Clive Bell.68 Although their friendship continued, they lived apart for

most of their lives.69 In 1913, Vanessa ended her affair with the art critic, Roger

Fry, and Grant became her new lover.70 Although Vanessa was Grant’s only

female lover (he was homosexual), their daughter, Angelica, was born in 1918.71

Perhaps the love Grant expresses in his portrait of Vanessa 72 may not be that of a

sexual attraction, he is depicting the mother of his daughter, a woman he adored – an idea reinforced by Vanessa’s intense facial features. Grant and Vanessa had

worked together closely since around 1910 and this ‘creative union’73 lasted for almost fifty years.74

Both Duncan Grant and Vanessa Bell were part of The Bloomsbury Group, a group of upper-‐middle-‐class intellectual friends who wanted to detach

64 Grant, Vanessa Bell, 1917-‐1918.

65 R. Shone, Bloomsbury Portraits: Vanessa Bell, Duncan Grant, and their circle (Oxford:

Phaidon, 1976), p. 16. 66 Ibid., p. 20. 67 Spalding, The Bloomsbury Group, p. 45. 68 Shone, Bloomsbury Portraits, p. 27. 69 Spalding, The Bloomsbury Group, p. 46. 70 Shone, Bloomsbury Portraits, p. 87. 71 Spalding, The Bloomsbury Group, p. 57. 72 Grant, Vanessa Bell, 1917-‐1918. 73 Spalding, The Bloomsbury Group p. 46. 74 Q. Bell, ‘Vanessa Bell and Duncan Grant’, Crafts, January/February 1980, p. 26. 128

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themselves from Victorian conventions.75 They met once a week at the Stephens’ house in Bloomsbury76 and had a significant impact on British culture.77 In 1910

when Clive Bell met Roger Fry, Bloomsbury became the focus of modernist art in Britain – a result of Fry’s Post-‐Impressionist exhibition.78 In Fry’s ‘An Essay in

Aesthetics’79 he suggests that the artist’s role is to interpret the world around him in order to express an emotion. Similarly, in Clive Bell’s book, Art, 80 he

suggests that for art to be classified as art, it must have ‘significant form’ which produced an ‘aesthetic emotion’ for the viewer81 (although he offers no

definition of these terms). These writings had an incredible impact on

contemporary art82 as they encouraged artists, including Grant, to feel less

inclined to merely imitate objects and encouraged them to experiment with

more abstract forms. Another of Fry’s significant contributions to Bloomsbury art was the opening of the Omega Workshop in 1913.83 Fry made Grant and Vanessa Omega’s co-‐directors84 and they shared Fry’s vision of creating

aesthetically beautiful objects for pleasure.85 Although Omega didn’t survive the

war, it significantly influenced Grant and Vanessa; Vanessa may have designed the dress she wears in her portrait. The decorative interiors at Charleston, in

Sussex also show the impact of Omega.86 The rather secluded farmhouse, where Grant’s portrait of Vanessa87 was painted,88 provided them with an escape from the social constraints in London.89 This freedom encouraged both Grant and

Vanessa to experiment more, not only with the decorative arts, but also with their own painting.

75 Spalding, The Bloomsbury Group, p. 9.

76 Shone, Bloomsbury Portraits, pp. 25-‐26. 77 Spalding, The Bloomsbury Group, p. 5. 78 Ibid., pp.12-‐16.

79 R. Fry, ‘An Essay in Aesthetics’, New Quarterly, 1909, collected in Vision and Design ed.

by R. Fry (London: Chatto and Windus, 1923), pp. 15-‐38. 80 C. Bell, Art (London: Chatto & Windus, 1914; repr. London: Chatto & Windus, 1949) 81 Ibid., pp. 3-‐37. 82 Shone, The Art of Bloomsbury, p. 7. 83 Spalding, The Bloomsbury Group, p. 19. 84 Spalding, Duncan Grant, pp. 135-‐136. 85 Spalding, The Bloomsbury Group, p. 21. 86 Ibid., p. 21. 87 Grant, Vanessa Bell, 1917-‐1918. 88 Shone, The Art of Bloomsbury, p. 192. 89 F. Spalding, Vanessa Bell, (London: Weidenfeld & Nicholson, 1983), p. 164. 129

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Grant’s portrait of Vanessa Bell90, which was not a commission, was up for sale at his exhibition in 1920.91 In the summer of 1919, he worked hard completing

paintings for his exhibition,92 which may have motivated him to perfect the

portrait (although the portrait is similar to Grant’s style in 1918, it is listed as complete by October 1919).93 This portrait of Vanessa is one of three Grant

painted of her in the same dress: a 1915 full-‐length portrait94 with Vanessa’s

similar, distant gaze shows her right dress strap slightly slipping down her shoulder, exposing her cleavage (qualities which are echoed in the 1918

portrait); and a 1916 three-‐quarter length portrait95 which is almost identical to the 1918 portrait, although fabric of Vanessa’s dress is collaged onto the

canvas.96 Perhaps, the two earlier portraits were completed as studies for Grant’s

final outcome, however, the familiarity Grant shared with Vanessa suggests that these portraits were a symbol of their intimate relationship. And although

Grant’s imminent exhibition and the accompanying commercial pressures may have somewhat subverted the purpose of the portrait, ultimately, it was a product of love.

90 Grant, Vanessa Bell, 1917-‐1918.

91 Shone, The Art of Bloomsbury, p. 192. 92 Spalding, Duncan Grant, p. 219.

93 Shone, The Art of Bloomsbury, p. 192.

94 D. Grant, Portrait of Vanessa Bell, 1915, oil and collage on wood, 152 × 61 cm., private

collection (see Appendix Fig. 8).

95 D. Grant, Vanessa Bell, 1916, oil and fabric collage, 91.5 × 61 cm., Mark Lancaster. (see

Appendix Fig. 9)

96 Shone, The Art of Bloomsbury, p. 192.

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Conclusion

Speculating on Master John’s intentions proves challenging as so little is known about him. However, research into Tudor culture and society suggests that the

intention of the sitter, and/or the commissioner were more important than the intentions of the artist. Master John would have wanted to please his

benefactors. Perhaps he was trying to become a prolific court painter, taking the

place of Hans Holbein and therefore he would have wanted to genuinely impress the King and his daughter. As this may have been a marriage portrait, Henry would have wanted his daughter to be presented as beautiful and elegant,

wealthy and of high status – all of which are qualities that are captured by

Master John. An underlying (perhaps also the most significant and touching) intention may be that the portrait97 was a symbol of Henry’s reconciled

relationship with his daughter, which Master John achieves with the lettering in the background.

Duncan Grant’s portrait of Vanessa Bell98 is, too, a symbol of a relationship. The

striking similarities between the two portraits (size, composition, colours) along with Grant’s more subtle hints (the rose in Vanessa’s hand and the detail in her dress), revealed in this investigation, suggests that Grant had the portrait of Mary in mind whilst he painted Vanessa.

Perhaps his most noticeable intention was to celebrate a private, more intimate relationship – an idea that the Bloomsbury Group embraced. Although much more is written about Duncan Grant and his relationship with Vanessa, the

writing provides no true insight into their relationship, and therefore into his precise intentions when painting Vanessa.

What is clear, however, is that by looking back to earlier artistic movements,

Grant acknowledges that in order for art to modernise one cannot simply reject

the art of the past. This idea is represented by the distinct change in technique between the two portraits in question: Grant’s freer brushstrokes contrasted

97 Master John, Queen Mary I, 1544. 98 Grant, Vanessa Bell, 1918.

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with Master John’s controlled brushwork, for example. These stylistic changes, perhaps, draw attention to Grant’s deeper, more understated intention: rather

than dismissing the art of the past, Grant disagrees with artistic conventions of the past – he challenged the submissive role of Master John as the artist. However, further investigation would be needed to confirm this.

To what extent is it possible to speculate on the intentions of Master John and Duncan Grant in their depictions of Mary I and Vanessa Bell? On a

superficial level, the intention of both artists is to convey a relationship. The

respective relationships they portray, however, are different: Master John is

passive in his depiction of Mary’s reconciliation with her father, whereas Grant, as Vanessa’s lover, is a protagonist. It is these, intimate relationships – Mary’s with her father and Grant’s with his lover – that are more challenging to

examine, adding another layer of complexity to the artists’ exact intentions. 132

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Appendix

Fig. 1 Master John, Queen Mary I, 1544, oil on panel, 71.1 × 50.8 cm., National Portrait Gallery, London

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Fig. 2 Duncan Grant, Vanessa Bell, 1918, oil on canvas, 94 × 60.6 cm., National Portrait Gallery, London. 134

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Fig. 3 Paul Emsley, HRH The Duchess of Cambridge, 2012, oil on canvas, 115.2 × 96.5 cm., National Portrait Gallery, London.

Fig. 4 Paula Rego, Germaine Greer, 1995, pastel on paper laid on aluminium, 120 × 111.1 cm., National Portrait Gallery, London.

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Fig. 5 Master John, Katherine Parr, 1545, oil on panel, 180.3 × 94 cm., National Portrait Gallery, London. 136

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Fig. 6 Unknown Artist, Family of Henry VIII, 1545, oil on canvas, 144.5 × 355.9 cm., The Queen’s Gallery, Buckingham Palace, London.

137

Fig. 6 Unknown Artist, Family of Henry VIII, 1545, oil on canvas, 144.5 × 355.9 cm., The Queen’s Gallery, Buckingham Palace, London.

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Fig. 7 Duncan Grant, John Maynard Keynes, 1908, oil on canvas, 80 × 59.5 cm., The Provost and Scholars of King’s College, Cambridge.

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Fig. 8 Duncan Grant, Portrait of Vanessa Bell, 1915, oil and collage on wood, 152 × 61 cm., private collection. 139

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Fig. 9 Duncan Grant, Vanessa Bell, 1916, oil and fabric collage, 91.5 × 61 cm., Mark Lancaster.

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Bibliography

Bell, Clive, Art (London: Chatto & Windus, 1914; repr. London: Chatto & Windus, 1949).

Bolland, Charlotte and Cooper, Tarnya, The Real Tudors: Kings and Queens Rediscovered (London: National Portrait Gallery Publications, 2014).

Cooper, Tarnya, A Guide to Tudor & Jacobean Portraits (London: National Portrait Gallery Publications, 2008).

Correspondance Politique de MM. de Castillon et de Marillac, ed. by Kaulek, M. Jean (Geneva: Slatkine Reprints, 1971).

Fry, Roger, ‘An Essay in Aesthetics’, New Quarterly, 1909, collected in Vision and Design ed. by R. Fry (London: Chatto and Windus, 1923).

Howard, Maurice, The Tudor Image (London: Tate Publishing, 1995).

MacLeod, Catherine, Tudor Portraits in the National Portrait Gallery collection (London: National Portrait Gallery Publications, 1996).

Madden, F. Privy Purse Expenses of the Princess Mary (London: William Pickering, 1831).

Shone, Richard, Bloomsbury Portraits: Vanessa Bell, Duncan Grant, and their circle (Oxford: Phaidon, 1976).

Shone, Richard, The Art of Bloomsbury: Roger Fry, Vanessa Bell and Duncan Grant (London: Tate Gallery Publishing, 1999).

Spalding, Frances, Duncan Grant (London: Chatto & Windus, 1997).

Spalding, Frances, The Bloomsbury Group (London: National Portrait Gallery Publications, 1997; repr. London: National Portrait Gallery Publications, 2013).

Spalding, Frances, Vanessa Bell, (London: Weidenfeld & Nicolson, 1983).

Watney, Simon, The Art of Duncan Grant (London: John Murray, 1990).

Whitelock, Anna, Mary Tudor: England’s First Queen (London: Bloomsbury, 2009).

Articles

Bell, Clive, ‘Duncan Grant’, Athenaeum, 6 February 1920, cited in F. Spalding, Duncan Grant (London: Chatto & Windus, 1997), p. 225.

Bell, Quentin, ‘Vanessa Bell and Duncan Grant’, Crafts, January/February 1980, pp. 26-‐33.

Foister, Susan, ‘Holbein as a Court Painter’, in Henry VIII: A European Court in England, ed. by D. Starkey (London: Collins & Brown, 1991).

141

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Candidate Name: Freya Sackville-‐West Candidate No.: fph561 (000102 -‐0159)

Websites

‘Queen Mary I’, Tudor and Jacobean Portraits Database (London: National Portrait Gallery, 2015 (copyright date)), <http://www.npg.org.uk/collections/search/portraitConservation/mw04264/Q ueen-‐Mary-‐I?> [accessed 19 August 2015].

Plender, Sophie and Cooper, Tarnya, ‘English Workshops: work in progress on 'Master John' & other 1540s native painters’, Making Art in Tudor Britain (London: National Portrait Gallery, 2015 (copyright date)), <http://www.npg.org.uk/research/programmes/making-‐art-‐in-‐tudor-‐ britain/workshops/workshop-‐2-‐abstract-‐3.php> [accessed 19 August 2015].

Works of Art

Emsley, Paul, HRH The Duchess of Cambridge, 2012, oil on canvas, 115.2 × 96.5 cm., National Portrait Gallery, London. (Image from the National Portrait Gallery website <http://www.npg.org.uk/whatson/display/2015/hrh-‐the-‐duchess-‐of-‐ cambridge.php.> [accessed 14 September 2015]).

Grant, Duncan Portrait of Vanessa Bell, 1915, oil and collage on wood, 152 × 61 cm., private collection. (Image reproduced from S. Watney, The Art of Duncan Grant (London: John Murray, 1990) colour plate no. 23)

Grant, Duncan, John Maynard Keynes, 1908, oil on canvas, 80 × 59.5 cm., The Provost and Scholars of King’s College, Cambridge. (Image reproduced from R. Shone, The Art of Bloomsbury: Roger Fry, Vanessa Bell and Duncan Grant (London: Tate Gallery Publishing, 1999) p. 63).

Grant, Duncan, Vanessa Bell, 1916, oil and fabric collage, 91.5 × 61 cm., Mark Lancaster. (Image reproduced from Shone, The Art of Bloomsbury, p. 193).

Grant, Duncan, Vanessa Bell, 1918, oil on canvas, 94 × 60.6 cm., National Portrait Gallery, London. (Image reproduced from Shone, The Art of Bloomsbury, p. 192).

Master John, Katherine Parr, 1545, oil on panel, 180.3 × 94 cm., National Portrait Gallery, London. (Image from the National Portrait Gallery website <http://www.npg.org.uk/collections/search/portraitLarge/mw01957/Katherin e-‐Parr?LinkID=mp00803&search=sas&sText=katherine+parr&role=sit&rNo=0> [accessed 20 August 2015]).

Master John, Queen Mary I, 1544, oil on panel, 71.1 × 50.8 cm., National Portrait Gallery, London. (Image reproduced from C. Bolland and T. Cooper, The Real Tudors: Kings and Queens Rediscovered (London: National Portrait Gallery Publications, 2014) p. 108.)

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Rego, Paula, Germaine Greer, 1995, pastel on paper laid on aluminium, 120 × 111.1 cm., National Portrait Gallery, London. (Image from the National Portrait Gallery website < http://www.npg.org.uk/collections/search/portrait/mw09597/Germaine-‐ Greer> [accessed 14 September 2015]).

Unknown Artist, Family of Henry VIII, 1545, oil on canvas, 144.5 × 355.9 cm., The Queen’s Gallery, Buckingham Palace, London. (Image from the Royal Collection Trust website <https://www.royalcollection.org.uk/collection/405796/the-‐family-‐of-‐henry-‐ viii> [accessed 20 August 2015]).

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What is the Effect of Ingestion of Tea on the Rate at which Heart Rate and Blood Pressure Return to their Resting Levels after their Excitation by a Mental Stressor?

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Miranda Stevens - Biology When I started the daunting task of the extended essay, I was unsure of what exactly I wished to write on. I had narrowed it down to biology and no further. Eventually I decided to look at tea as I felt it had been overlooked as many people had already done EEs on coffee. However I decided to be more specific by looking in particular at tea’s effect on those under mental stress as I thought it to be very relevant to the issues of stress and mindfulness that have gained awareness in the recent years. It was very time consuming to collect all of my data and I ended up using both the EE days and enrichment week to collect data from my thirty test subjects. It was an even more onerous task to process all of this data but by the end of it I managed to get a clear pattern of results that could be attributed to tea, a very satisfying feeling.

Supervisor: Amanda Turner Miranda approached her extended essay with a desire to study an aspect of human physiology and her commitment to her investigation was evident from the outset. This led to a novel investigation where she studied the ‘calming’ physiological effects of drinking tea after a stressful experience. She chose to focus on the more immediate effects of tea on heart rate and blood pressure as this has received relatively little attention in published literature. Throughout the extended essay process she showed an impressive depth of understanding of her chosen subject area and confidently discussed her contribution to the wider scientific community. In reading the essay, I was especially impressed with the clarity and concision in her writing style. She was thorough in her approach to her method and data collection and can take pride in the results she obtained. It was a pleasure to see Miranda’s scientific skills develop through this process and to see her implement meaningful, ethical techniques that one would expect of a successful scientist.

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Contents Introduction 148 Scientific Background

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Methodology 151 Data Processing

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Data Analysis

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Evaluation 162 Conclusion 163 Bibliography 164 Appendix 167

Abstract Tea is anecdotally recommended as useful for counteracting the effects of stress. This experiment investigated the validity of this claim by researching the effect of ingesting tea after a mental stressor elevates heart rate, systolic blood pressure, and diastolic blood pressure. Two major components of tea that effect heart rate and blood pressure are caffeine and L-theanine. Caffeine elevates heart rate and blood pressure while L-theanine counteracts the effect mental stress has on the sympathetic nervous system. The experiment was carried out on human test subjects who would complete a set of questions under time pressure. Then they would be given different concentrations of black tea to drink, their heart rate and blood pressure were measured every minute from them finishing the set of questions for four minutes until the end of the experiment. The experiment concluded that the rate at which blood pressure returns to a basal rate is increased at higher tea concentrations. This is likely to be due to tea containing the chemical L-theanine and it affecting the sympathetic nervous system once ingested. However increasing tea concentrations appeared to have no significant effect on the rate at which heart rate returns to the normal rate.

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Introduction: Tea is a common beverage throughout much of the world and has become an important part of many cultures. Tea drinking is extensive in the United Kingdom with it having the fifth highest tea consumption per capita per annum of 2.74kg (FAOSTAT [2015]) and with this high consumption the effects of upon the physical and mental health of the population should be researched. Tea is also an important part of the British culture with its rapid growth in the days of the British Empire to its use as a stereotype currently. I am personally very fond of tea and was therefore curious whether there could be any biological basis behinds the belief of teaâ&#x20AC;&#x2122;s calming influence. Also, since stress has become a more topical subject due to its connection with mental and physical illnesses, ways of reducing stress and aiding mindfulness are becoming more acknowledged for their possible impact. While researching stress, I found that it can cause fluctuations in many physical aspects of human biology including sleep patterns (Hall et al [2004], p.56-62), blood pressure (Hjortskov, N. et al [2004], p.84-89), and heart rate (Schubert, C. et al [2009, p.325-332]). I decided to investigate the latter two aspects while looking at the short-term as the majority of research looked at the effect of long-term, regular consumption of tea. Therefore this experiment focuses on the short-term effect of ingestion of tea on heart rate and blood pressure. Due to time pressures and restrictions upon equipment that I had access to, it was simplest to look at heart rate and blood pressure in the short-term.

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Scientific Background: Heart rate and blood pressure are two physiological indicators of stress and are easy to measure without complex equipment. Heart rate can be measured in beats per minute and a basal or resting rate can be used to compare the fluctuations in the heart rate. Heart rate is measured by a pulse monitor which can measure the pulse rate at many different arteries. Resting heart rate should be between 60bpm and 100bpm (American Heart Association [2015]). Blood pressure is in two parts, systolic and diastolic with systolic being the maximum blood pressure and diastolic being the minimum blood pressure reached within the cardiac cycle. Systolic blood pressure for adolescents aged 13-18 should be 95-140 and diastolic should be 60-90 (UCLA Health System [2010]). A stressor is a stimulus that causes stress to an organism, there are many different types including chemical stressors, environmental stressors, and social stressors and these stressors cause physical, chemical and mental responses in a human. Normal homeostasis is maintained by the body’s autonomic nervous system (Abrahams, P. [2007] p. 472) which is made up of the sympathetic and parasympathetic nervous systems. These two systems work antagonistically to each other to form a balance within the body. The parasympathetic normally slows down heart rate when required and the sympathetic increases heart rate when required. A stressor such as fear or anger causes the activation of the entire sympathetic nervous system as part of the ‘fight or flight’ response. The mental stressor of a set of ten verbal reasoning questions used in this experiment helped create a slight response by using time pressure of only eight minutes to exacerbate the response of undergoing an examination. However the response was only slight as this stressor was still not particular intense so as not to cause excessive stress on the test subjects. When the sympathetic nervous system is activated there are many different responses, the most significant for this experiment being increased heart rate, vasodilation in skeletal muscles and brain, vasoconstriction in the gastrointestinal organs (Silverthorn, D. et al [2009] p. 379–386), and an increase in blood pressure. These physical responses are caused by three main hormones: epinephrine, norepinephrine, and cortisol. The release of cortisol increases the blood pressure (Fraser, R. et al [1999]). The release of epinephrine increases heart rate through the sinoatrial node (Allott, A. and Mindorff, D. [2014] p.304). The release of epinephrine also increases blood pressure but its effect on blood pressure is less strong than that on heart rate. (Klabunde, R. [2015]). Norepinphrine release increases heart rate and blood pressure but its effect on heart rate is very short-lived (Klabunde, R. [2015]). Black tea is made by infusing the dried leaves of the plant Camellia sinensis (Martin, L. [2007] p.8) in boiling water so that all soluble ingredients come into solution while the tea is brewed. Tea contains many substances such as polyphenols and aluminiums ions however these do not have any effect on heart rate, systolic blood pressure, or diastolic blood pressure as they are only present in small quantities (Street, R. et al [2007] p.1662–1669). Tea also contains caffeince, which acts as a stimulant and increases blood pressure (Green, P. and Suls, J. [1996] p.111-128). Caffeine starts to effect within five minutes of its ingestion and its effect is greatest thirty minutes after ingestion. This should mean that while blood pressure will decrease, the rate at which it decreases will be less, later in the experiment (Centre for Addiction and Mental Health [2011]). 149

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Another component of tea is L-theanine which is an amino acid, while it is higher in green tea, there is still a significant amount in black tea that its effect must be considered. Ltheanine naturally occurs in camellia sinensis, the plant tea comes from (Vuong, Q. et al [2011] p.1931-1939). Existing data from an investigation by Kimura, K. et al found that Ltheanine also helps create a relaxed but alert mental state and can help reduce heart rate (Kimura, K. et al [2007] p.39-45). Also Kato et al found that the intake of L-theanine reduced the blood pressure of hypertensive rats (Kato et al [1994] p.615-618). Yoto, A. et al found that L-theanine â&#x20AC;&#x153;can attenuate the blood pressure elevation induced by mental tasksâ&#x20AC;? while they were conducting a similar experiment considering different types of stressors over a slightly longer timescale and using direct doses of L-theanine (Yoto, A. et al [2012] p.28). It can be concluded from these experiments that L-theanine is capable of reducing the effect that mental stress has on blood pressure.

Figure 1: The Chemical Structures of L-theanine and Glutamine.

This effect on blood pressure is attributed to L-theanine being structurally similar to the amino acid glutamate. Glutamate is a neurotransmitter and the most abundant one in the nervous system (Meldrum [2000]). L-theanine can act as a competitive inhibitor for glutamate and while the effects of glutamate inhibition are varied, most significantly the serotonin levels are increased (Nathan, PJ. [2006]). This results in the various serotonin receptors being activated, including the 5-hydroxytryptamine 1A (5-HT1A) receptors. This will cause the suppression of cardiac and vasomotor response of the dorsomedial hypothalamus to acute psychological stress (Horiuchi, J. et al [2008]).

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Methodology: The independent variable in this experiment was the concentration of black Twinnings English Breakfast tea that the subject was given to ingest while the dependent variables were the heart rate, systolic blood pressure, and diastolic blood pressure. The heart rate was measured by a heart rate monitor and measured in beat per minute (bpm). The two blood pressures were measured by a blood pressure monitor and measured in millimetres of mercury (mm Hg). A preliminary investigation was conducted where different concentrations and types of tea were considered to determine which could be suitable for exploration within the limits of the experiment. The heart rate, systolic blood pressure, and diastolic blood pressure were measured before the stressor and then at 0, 60, 120, 180 and 240 seconds after it. There was a control of a group of five subjects who were not given anything to drink after the stressor but still had their heart rate, systolic blood pressure, diastolic blood pressure measured. The mental stress was created by giving the subject a set of ten questions a practice question paper from the Thinking Skills Assessment (TSA) taken from the Cambridge website (Cambridge Assessment [2006]) as these questions are aimed at a similar age group as that of the test subjects. However while those taking the set of fifty TSA questions usually have ninety minutes to complete the questions (1.8 minutes per question) in this experiment the subjects were only give eight minutes to complete ten questions (0.8 minutes per question) and by adding a time pressure the mental stress level of the subjects is thought to be elevated as shown in figure 2. The questions the subjects were given to complete were practise questions for a university entry exam that many of the subjects would be take in the future and therefore they would be of suitable difficulty. The ten questions were chosen randomly from the set of fifty using a random number generator to remove any bias. An example of one set of questions can be found in Appendix E. 120

Heart Rate /bmp ±0.5

100 80

Systolic Blood Pressure /mm Hg ±0.5

60 40

Diastolic Blood Pressure /mm Hg ±0.5

20 0

Resting

120

180

240

Time during the experiment Figure 2: A Line Graph showing how the Heart Rate, Systolic Blood Pressure and Diastolic Blood Pressure changed during the experiment for Participant 21 (a control)

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The concentration of tea was controlled by brewing 250ml of tea, with one tea bag (2.5g) for the 250ml of boiling water; this would then be diluted with boiling water to create the mixture that would be given to the subject. The concentrations of tea were 0, 0.25, 0.5, 0.75 and 1 (units) which were created using the ratios of boiling water (millilitres) to brewed tea (millilitres) as follows: 200:0, 150:50, 100:100, 50:150 and 0:200 respectively. This meant that all test subjects drank 200ml of tea except the control group. The procedure of the experiment was as follows: 1. Subject was given the consent and medical forms (see Appendices A and B) to complete and had the experiment explained to them. 2. The resting heart rate, systolic blood pressure, and diastolic blood pressure were measured and recorded. 3. The subject was given a series of ten verbal reasoning questions to complete within eight minutes. 4. 250ml of tea was brewed using one tea bag for 250ml of boiling water with the tea bag in the mixture for 3 minutes. 5. The correct ratio of tea to boiling water was used to create the correct concentration tea for the subject and the final volume was 200ml. 6. The temperature of the tea was measured. 7. Once the eight minutes that the subject had to complete the questions are over, the subjectâ&#x20AC;&#x2122;s heart rate, systolic blood pressure, and diastolic blood pressure were measured. 8. The subject drank 50ml of the tea in one minute and then had their heart rate, systolic blood pressure, and diastolic blood pressure measured again. 9. This was repeated until at four minutes all the tea has been drunk, a final heart rate, systolic blood pressure, and diastolic blood pressure was measured.

The brand and type of tea should be controlled in this experiment so that the composition of the tea is the same. Ideally every tea bag should be from the same box so that the chance that they are grown in the same area or are from the same plant is increased. This will reduce any variation in the concentrations of the various chemicals differing. The volume of boiling water and number of tea bags used to create the original tea must be kept the same so the concentration of the final mixture is controlled. The age of the subjects should be kept the same as this could affect the original heart rate, systolic blood pressure, and diastolic blood pressure and the rate of recovery; therefore all subjects were aged 16-17 as this was the most abundant age of subjects, allowing more repeats to be done. The general health of the subjects should be controlled to prevent any medical issues from affecting their heart rate, systolic blood pressure, and diastolic blood pressure and their rate of recovery and therefore subjects were asked to complete a medical form (see Appendix A). The brewing time of three minutes shown in the procedure should be kept the same to prevent it effecting the concentration of the final mixture.

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There are many ethical and safety issues that must be considered in this experiment due to the involvement of human test subjects. There is a safety risk involved with using boiling water to brew the tea and therefore the boiling water should be handled with care. The brewing time for the tea is three minutes to allow time for the tea to cool down so there is no danger of the subject scolding themselves. There are many ethical and safety concerns with using human subjects and applying stress to them; the IB ethical guidelines say that experiments should not cause anxiety, stress, pain or discomfort for participants however in the case of this experiment the stress is required. Additionally the stress created in this experiment does not exceed the everyday stress the participants would experience. It is important that participants are fully aware of the procedure of this experiment, given the option to quit the experiment at any point. Also the nature of the stress should be considered as the mental stress is very temporary with it having no lasting effects upon the participant. To ensure that the participant is fully aware of the experiment and their rights regarding it they are asked to complete a consent form as shown in the Appendix A. There is an issue with making sure that there is no medical risk to the participant when human test subjects are used; despite the effects of the experiment being temporary the medical form that the participant is asked to complete checks whether the participant has any medical issues that would mean it would advisable for them not to complete the experiment. The medical form can be seen in Appendix B. It is also important that the participantsâ&#x20AC;&#x2122; confidentiality is maintained and therefore they will remain unnamed in this essay and are simply have numbers corresponding to their data. They are also given the opportunity to be given a copy of this essay so they can see the results of the experiment they took part in.

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Data Processing: The raw data collected can be found in Appendix C. The data was processed using the following formula: Heart rate (%) = ((heart rate â&#x20AC;&#x201C; resting heart rate)/(heart rate at 0 â&#x20AC;&#x201C; resting heart rate))*100 For example ((83-64)/(85-64))*100 = 90.48% This calculates the percentage of the difference in heart rate when compared to the original difference caused by the stressor. The same method was used to calculate the processed data for systolic and diastolic blood pressure. The mean value for each concentration of tea would then be calculated as is shown in figures 3 to 5. This method of processing was used because it meant that the difference that the heart rate or blood pressure changes by between the resting and the stressor does not affect the results. This would mean that the results for one test subject where the heart rate increased by 40 and then decreased by 10 would have the same results as a test subject where the heart rate increased by 4 and then decreased by 1 as it is the rate at which the heart rate decreases by when compared to the original change that is considered for this investigation. Once the mean change in percentage is plotted on a graph against time, the rate can be determined by the gradient of the line of regression on the graph. The gradients for the lines for each tea concentration can then be compared and the direct correlation between tea concentration and rate can be determined.

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Data Analysis: Time /seconds ±0.5 0 60 120 180 240

Heart Rate % ±1 0 0.25 100.00 100.00 81.08 84.90 73.83 99.60 68.10 66.63 90.77 85.10

Time /seconds ±0.5 0 60 120 180 240

Systolic Blood Pressure % ±1 0 0.25 0.5 100.00 100.00 100.00 94.11 88.30 78.04 78.48 79.19 58.56 56.72 70.10 39.91 46.77 55.02 24.05

0.5 100.00 60.83 39.33 52.87 22.17

0.75 100.00 99.10 70.72 31.91 20.23

1 100.00 82.17 47.89 38.20 34.46

Control 100.00 88.57 69.05 66.67 59.52

0.75 100.00 85.84 63.62 41.41 12.18

1 100.00 77.10 54.00 32.42 4.91

Control 100.00 92.18 76.53 67.54 54.11

1 100.00 72.68 46.31 20.15 6.19

Control 100.00 87.49 73.68 56.28 48.45

Figure 3: A Table showing the Mean Heart Rate for each of the Concentrations

Figure 4: A Table showing the Mean Systolic Blood Pressure for each of the Concentrations

Time /seconds ±0.5 0 60 120 180 240

Diastolic Blood Pressure % ±1 0 100.00 94.33 85.33 72.33 48.00

0.25 100.00 86.08 68.85 56.80 46.03

0.5 100.00 85.94 74.81 52.45 33.06

0.75 100.00 88.41 70.25 41.62 8.13

Figure 5: A Table showing the Mean Diastolic Blood Pressure for each of the Concentrations

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120

MEan Change in Heart Rate (%)

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120

180

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Time (seconds) Figure 6: A graph to the show the variation in the mean percentage change in heart rate over time. Legend: Dark blue – Tea concentration 0, Red – Tea concentration 0.25, Green – Tea concentration 0.5, Purple – tea concentration 0.75, Light blue – Tea concentration 1, Orange – Control

The data for the mean percentage change in heart rate shows that at low concentrations (0 and 0.25) there is very little decrease in the heart rate from its original rate at 0 seconds. However at higher concentrations of tea there is a more significant decrease in heart rate. However the control that would be expected to have the lowest rate of decrease actual has the third highest. However the strengths of the correlations vary with them having the following Pearson correlation coefficients: Tea concentration 0 R = -0.387 Tea concentration 0.25 R = -0.555 Tea concentration 0.5 R = -0.889 Tea concentration 0.75 R = -0.965 Tea concentration 1 R = -0.954 Control R = -0.964

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These R values show that the correlation is always negative and it is strongest for high concentrations of tea and the control. Therefore it can be concluded that at high concentrations tea does increase the rate at which heart rate returns to a basal rate after its elevation by a mental stressor. However at low concentrations, tea appears to decrease the rate at which heart rate returns to a basal rate when compared to the control.

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Mean Change in Systolic Blood Pressure ( %)

100

120

180

240

Time (seconds) Figure 7: A graph to the show the variation in the mean percentage change in systolic blood pressure over time. Legend: Dark blue – Tea concentration 0, Red – Tea concentration 0.25, Green – Tea concentration 0.5, Purple – tea concentration 0.75, Light blue – Tea concentration 1, Orange – Control

The graph shows that as tea concentration increases, the rate at which systolic blood pressure decreases also increases, this positive correlations also appears to be quite strong as which the exception of tea concentration 0.25, the gradients of the trend lines on the graph become steeper as the tea concentration increases. The tea concentration 0.25 is an anomaly as it would be expected to lie between the trend lines of tea concentration 0 and tea concentration 0.5. This anomaly could be caused by the caffeine in the tea at that concentration increasing blood pressure more than the L-theanine decreases it. It is expected that the trend line of tea concentration 0 to have a steeper gradient than that of the control. All of the Pearson correlation coefficients for this data set are high with them varying from -0.985 (tea concentration 0) to -0.999 (tea concentration 1). 13 157

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120

Mean Change in Diastolic Blood Pressure (%)

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120

180

240

Time (seconds) Figure 8: A graph to the show the variation in the mean percentage change in diastolic blood pressure over time. Legend: Dark blue – Tea concentration 0, Red – Tea concentration 0.25, Green – Tea concentration 0.5, Purple – tea concentration 0.75, Light blue – Tea concentration 1, Orange – Control

The graph shows that as tea concentration increases, the rate at which diastolic blood pressure decreases also increases, this positive correlations also appears to be quite strong as which the exception of tea concentration 0, the gradients of the trend lines on the graph become steeper as the tea concentration increases. The gradient for tea concentration 0 is less steep that expected but the correlation for the trend line is strong with an R value of 0.950 therefore the reason for this anomaly is unknown as by doing multiple trials and taking a mean there should be little room for error.

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Concentration of Tea 0 0.25 0.5 0.75 1

Gradient of Trendline Systolic Blood Heart Rate (Figure 6) Pressure (Figure 7) -0.2397 -0.0524 -0.1802 -0.0801 -0.3167 -0.3779 -0.3668 -0.02727 -0.3914 -0.2917

Diastolic Blood Pressure (Figure 8) -0.21 -0.2287 -0.2789 -0.3842 -0.4002

Figure 9: A Table showing the Gradient of each of the Trendlines for Heart Rate, Systolic Blood Pressure, and Diastolic Blood Pressure

0 -0.05

Gradient of trendline

-0.1 -0.15 -0.2 -0.25

RÂ˛ = 0.1809

-0.3 -0.35 -0.4

0.25

0.5

0.75

Tea concentration Figure 10: A graph to show the effect of increasing tea concentration on the rate at which heart rate increases by using the gradient of each trend line in figure 6.

Figure 10 uses the gradient of each of the trend lines in figure 6 (except the control) to show how this compares to the concentration of tea for that trend line. This therefore shows the direct relationship between the rate at which heart rate increases as tea concentration increases. The graph shows that there is a general negative correlation between the rate at which heart rate increases and tea concentration but this correlations is weak with the Pearson correlation coefficient being only -0.425. The gradients of the trendlines show the rate at which the heart rate returns to the resting rate and by graphing them against the tea concentration, the direct correlation between tea concentration and rate can be determined.

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0 -0.05

Gradient of trend line

-0.1 -0.15 -0.2 -0.25 -0.3

RÂ˛ = 0.7726

-0.35 -0.4 -0.45

0.25

0.5

0.75

Tea concentration Figure 11: A graph to show the effect of increasing tea concentration on the rate at which systolic blood pressure increases by using the gradient of each trend line in figure 7.

Similarly to figure 10, figure 11 uses the gradient of each of the trend lines in figure 7 (except the control) to show how this compares to the concentration of tea for that trend line. This therefore shows the direct relationship between the rate at which systolic blood pressure increases as tea concentration increases. The figure shows that the correlation between tea concentration and rate at which systolic blood pressure increases is a strong negative correlation with a Pearson correlation coefficient of -0.879. This means that as tea concentration increases the rate at which systolic blood pressure decreases also increases.

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0 -0.05

Gradient of trend line

-0.1 -0.15 -0.2 -0.25 RÂ˛ = 0.9337

-0.3 -0.35 -0.4 -0.45

0.25

0.5

0.75

Tea concentration Figure 12: A graph to show the effect of increasing tea concentration on the rate at which diastolic blood pressure increases by using the gradient of each trend line in figure 8.

Similarly to figure 10 and figure 11, figure 12 uses the gradient of each of the trend lines in figure 8 (except the control) to show how this compares to the concentration of tea for that trend line. This therefore shows the direct relationship between the rate at which diastolic blood pressure increases as tea concentration increases. The figure shows that the correlation between tea concentration and rate at which diastolic blood pressure increases is a very strong negative correlation with a Pearson correlation coefficient of -0.966. This means that as tea concentration increases the rate at which diastolic blood pressure decreases also increases.

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Evaluation: The one strength of this experiment is that there are many repeats that help make the results more reliable and the experiment could be made more reliable by increasing the number of repeats for each concentration and increasing the range of concentrations. However the experiment could benefit from doing more repeats in a wider sample base. Also the raw data collected is objective and has a small error of only Âą0.5 for all of the raw data. However, one issue is that the amount of stress the mental stressor exerted on each subject varies meaning that some may barely be affected and therefore could affect the results. This could be improved by measuring the stress the subject is under by measuring the levels of epinephrine, norepinephrine, and cortisol in their blood. The effectiveness of the stressor could be increased by using a different stressor such as the trier social stress test. The experiment could be expanded by looking at other varieties of tea such as green tea which is meant to have higher levels of L-theanine or by using a supplement. However, despite the strengths of this investigation there was still some irregularities in the data that may be due to various different reasons such as temperature or caffeine content. The correlation between tea and heart rate at low concentrations of tea is weak and this may be due to any effect the L-theanine has being counteracted by the ingesting of a hot beverage so that the increase in core body temperature would increase the heart rate more than the L-theanine decreases it. Similarly the tea concentration 0 would increase the bodyâ&#x20AC;&#x2122;s core temperature slightly and while this increases the heart rate, it has the opposite effect on blood pressure as it causes vasodilation which lowers blood pressure. It is possible that at low tea concentrations, the L-theanine concentration is too low to have any major effect as it could be counteracted by the caffeine in the tea that would disrupt the heart rate and blood pressure. In spite of these unexpected results, the strength of the conclusion indicates that the conclusion can be considered valid.

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Conclusion: This experiment shows that tea appears to have a strong effect on the rate at which systolic and diastolic blood pressure decreases after their elevation by a stressor. This is likely due to the effect of L-theanine inhibiting the effect of glutamate. However the effect of tea on heart rate is less clear, possibly due to other factors like caffeine and temperature affecting heart rate as well as caffeine acts as a stimulant and increasing core body temperature will increase heart rate. It is possible that the effect of L-theanine is less on heart rate as it is on blood pressure because the increased serotonin levels may supress the vasomotor response to a greater extent than it does the cardiac response. These results are useful at looking at the short time effect of tea which has not been as widely researched as its long term effects. The long term effects suggest that tea can be useful in prevent issues with blood pressure such as hypertension (Yang, Y. et al [2004]) and itâ&#x20AC;&#x2122;s possible that its short term effects can be linked to this. The effect of L-theanine needs to be researched further, especially since Ltheanine supplements are now put into food in Japan as it helps add taste to green tea flavoured foods and while it is generally recognised as safe (PubChem [2015]), itâ&#x20AC;&#x2122;s possible effects should be further investigated to assess the effect, positive or negative, that this will have on the Japanese population.

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Bibliography: Abrahams, P. [2007], How the Body words, Amber Books Ltd Allot, A. and Mindorff, D. [2014], Biology Course Companion, Oxford University Press American Heart Association [2015], All About Heart Rate (Pulse) [Online]. Available from: http://www.heart.org/HEARTORG/Conditions/More/MyHeartandStrokeNews/All-AboutHeart-Rate-Pulse_UCM_438850_Article.jsp [Accessed 25 August 2015] Bowen, R. [1998], Adrenocorticotropic Hormone (ACTH, corticotropin) [Online]. Available from: http://www.vivo.colostate.edu/hbooks/pathphys/endocrine/hypopit/acth.html [Accessed 25 August 2015] Cambridge Assessment [2006], Thinking Skills Assessment Demonstration Test [Online] Available from: http://www.admissionstestingservice.org/images/24890-tsa-cambridgespecimen-test.pdf [Accessed 12 June 2015] Centre for Addiction and Mental Health [2011], Caffeine [Online. Available from: http://www.camh.ca/en/hospital/health_information/a_z_mental_health_and_addiction_i nformation/Caffeine/Pages/default.aspx [Accessed 14 June 2015] FAOSTAT [2015], Trade / Crops and livestock products [Online]. Available from: http://faostat3.fao.org/browse/T/TP/E [Accessed 25 August 2015] Green, P. and Suls, J. [1996], The effects of caffeine on ambulatory blood pressure, heart rate, and mood in coffee drinkers, Journal of Behavioral Medicine [Online], 19, 111-128. Available from: http://link.springer.com/article/10.1007/BF01857602 [Accessed 14 June 2015] Hall et al [2004], Acute Stress Affects Heart Rate Variability During Sleep, Psychosomatic Medicine [Online], 66, 56-62. Available from: http://journals.lww.com/psychosomaticmedicine/Abstract/2004/01000/Acute_Stress_Affec ts_Heart_Rate_Variability_During.9.aspx [Accessed 12 June 2015] Horiuchi, J. et al [2008]. Role of 5-HT1A receptors in the lower brainstem on the cardiovascular response to dorsomedial hypothalamus activation, Autonomic Neuroscience: Basic and Clinical [Online], 142, 71-76. Available from: http://www.autonomicneuroscience.com/article/S1566-0702(08)00104-5/abstract [Accessed 21 September 2015] Hjortskov, N. et al [2004], The effect of mental stress on heart rate variability and blood pressure during computer work, European Journal of Applied Physiology [Online], 92, 94-89. Available from: http://link.springer.com/article/10.1007/s00421-004-1055-z [Accessed 12 June 2015] Kato, Y. et al [1994], Reduction Effect of Theanine on Blood Pressure and Brain 5Hydroxyindoles in Spontaneously Hypertensive Rats, Bioscience, Biotechnology, and 20 164

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Biochemistry [Online], 59, 615-618. Available from: http://www.tandfonline.com/doi/abs/10.1271/bbb.59.615#.VeG80_lViko [Accessed 28 August 2015] Kimura et al [2007], l-Theanine reduces psychological and physiological stress responses, Biological Psychology [Online], 74, 39-45. Available from: http://www.sciencedirect.com/science/article/pii/S0301051106001451 [Accessed 28 August 2015] Klabunde, R. [2015], Circulating Catecholamines [Online]. Available from: http://cvphysiology.com/Blood%20Pressure/BP018.htm [Accessed 28 August 2015] Lowry, N. [2014], Tea and theophylline [Online]. Available from: http://helios.hampshire.edu/~nlNS/mompdfs/TeaTheoph.pdf [Accessed 25 August 2015] Łuczaj, W. and Skrzydlewska, E. [2005], Antioxidative properties of black tea, Preventive Medicine [Online], 40, 910-918. Available from: http://www.sciencedirect.com/science/article/pii/S0091743504005456 [Accessed 27 August 2015] Martin, L. [2007], Tea: The Drink that Changed the World, Tuttle Publishing Meldrum [2000], Glutamate as a neurotransmitter in the brain: review of physiology and pathology, Journal of Nutrition [Online]. Available from: https://www.ncbi.nlm.nih.gov/pubmed/10736372 [Accessed 28 August 2015] Nathan, PJ. et al [2006]. The neuropharmacology of L-theanine(N-ethyl-L-glutamine): a possible neuroprotective and cognitive enhancing agent, Journal of Herbal Pharmacotherapy [Online], 6, 21-30. Available from: http://www.ncbi.nlm.nih.gov/pubmed/17182482?dopt=Abstract [Accessed 21 September 2015] PubChem [2015], L-theanine [Online]. Available from: https://pubchem.ncbi.nlm.nih.gov/compound/439378?from=summary#section=Top [Accessed 29 August 2015] Schubert, C. et al [2009], Effects of stress on heart rate complexity—A comparison between short-term and chronic stress, Biological Psychology [Online], 80, 325-332. Available from: http://www.sciencedirect.com/science/article/pii/S0301051108002317 [Accessed 14 June 2015] Silverthorn, D. et al [2009], Human Physiology: An Integrated Approach, Pearson/Benjamin Cummings Street, R. et al [2007], Total content and speciation of aluminium in tea leaves and tea infusions, Food Chemistry [Online], 104, 1662–1669. Available from:

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http://www.sciencedirect.com/science/article/pii/S0308814607002464 [Accessed 28 August 2015] UCLA Health Systems [2010], Paediatric Age Specific Self Learning Module [Online]. Available from: http://hr.uclahealth.org/workfiles/AgeSpecificSLM-Peds.pdf [Accessed 25 August 2015] Vuong, Q. et al [2011], L-Theanine: properties, synthesis and isolation from tea, Journal of the Science of Food and Agriculture [Online], 91, 1931â&#x20AC;&#x201C;1939. Available from: http://onlinelibrary.wiley.com/doi/10.1002/jsfa.4373/abstract?userIsAuthenticated=false& deniedAccessCustomisedMessage= [Accessed 28 August 2015] Yang, Y. et al [2004], The Protective Effect of Habitual Tea Consumption on Hypertension, JAMA Internal Medicine [Online], 164. Available from: http://archinte.jamanetwork.com/article.aspx?articleid=217219 [Accessed 29 August 2015] Yoto, A. et al [2012], Effects of L-theanine or caffeine intake on changes in blood pressure under physical and psychological stresses, Journal of Physiological Anthropology [Online], 31, 28. Available from: http://www.biomedcentral.com/content/pdf/1880-6805-31-28.pdf [Accessed 28 August 2015]

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Appendix A:

Research information [To be kept by the participant] This sheet provides you with information about the study you are participating in. You will be asked to fill in a short form with some medical information, this will be anomalous but may be used to show controlled variables and explain anomalies.  You will be asked to complete a set of 10 problem-solving and critical thinking questions within a set time.  You heart rate and blood pressure will be taken before the questions and repetitively after completing them.  The aim of this experiment is to put you under a mental stressor of doing questions under time pressure.  Should you wish to withdraw at any moment you may without any issue.  Some of the participants will be asked to drink some tea after doing the questions; if this causes any issue you may withdraw or drink hot water (control) instead.  Participants’ names will not be disclosed in the essay.  Please do not hesitate to ask any questions about the study. ------------------------------------------------------------------------------------------------------------------------------------- 

Consent form [To be returned to Miranda Stevens] Have you read the ‘research information’ section?

Please delete as appropriate: Yes No

Have you had an opportunity to ask questions and discuss the study?

Yes

If yes, have you received satisfactory answers to all of your questions? Yes

Have you received enough information about the study?

Yes

Who have you spoken to? Do you understand that you are free to withdraw from the study:  At any time.  Without having to give a reason for withdrawing. Participant’s signature

Date

Name (Block capitals) [This will only be used for administration purposes and will not be disclosed in the research writeup.] If you would like a copy of the final results to be made available to you, please provide your e-mail address. This will only be used to send you information concerning the results of the study. E-mail address:

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Appendix B: Medical Form [To be returned to Miranda Stevens] Name _______________________________________________ Age ________________ Sex ________________ Do you have any medical conditions that may affect your heart rate or blood pressure? If so, please give details. ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ _________________________________________________ Do you like tea and if so how do you like it? ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ _____________________

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Appendix C: Participant 4 Time /seconds Heart Rate Systolic Blood Pressure ±0.5 /bmp ±0.5 /mm Hg ±0.5 Resting 64 102 0 85 125 60 83 124 120 80 121 180 76 117 240 73 115 Concentration of tea 0 Temperature of tea /degrees Celsius 64 Participant 14 Time /seconds Heart Rate Systolic Blood Pressure ±0.5 /bmp ±0.5 /mm Hg ±0.5 Resting 63 101 0 73 117 60 74 117 120 74 114 180 78 108 240 75 103 Concentration of tea 0 Temperature of tea /degrees Celsius 67 Participant 15 Time /seconds

Heart Rate Systolic Blood Pressure ± /bmp ±0.5 /mm Hg ±0.5 0 . 5 Resting 64 109 0 74 124 60 71 123 120 70 120 180 67 116 240 82 118 Concentration of tea 0 Temperature of tea /degrees Celsius 66

169

Diastolic Blood Pressure /mm Hg ±0.5 72 82 83 80 76 76

Diastolic Blood Pressure /mm Hg ±0.5 67 73 73 75 75 71

Diastolic Blood Pressure /mm Hg ±0.5

64 79 76 74 73 73

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Participant 19 Time /seconds Heart Rate Systolic Blood Pressure ±0.5 /bmp ±0.5 /mm Hg ±0.5 Resting 54 114 0 73 132 60 71 131 120 67 128 180 65 126 240 63 123 Concentration of tea 0 Temperature of tea /degrees Celsius 67 Participant 20 Time /seconds Heart Rate Systolic Blood Pressure ±0.5 /bmp ±0.5 /mm Hg ±0.5 Resting 63 102 0 74 133 60 68 129 120 69 126 180 68 121 240 70 119 Concentration of tea 0 Temperature of tea /degrees Celsius 68 Participant 1 Time /seconds Heart Rate Systolic Blood Pressure ±0.5 /bmp ±0.5 /mm Hg ±0.5 Resting 60 128 0 75 135 60 73 132 120 70 131 180 68 131 240 72 130 Concentration of tea 0.25 Temperature of tea /degrees Celsius 67

170

Diastolic Blood Pressure /mm Hg ±0.5 72 84 83 80 79 76

Diastolic Blood Pressure /mm Hg ±0.5 80 90 89 88 87 84

Diastolic Blood Pressure /mm Hg ±0.5 78 88 85 83 81 81

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Participant 10 Time /seconds Heart Rate Systolic Blood Pressure ±0.5 /bmp ±0.5 /mm Hg ±0.5 Resting 89 107 0 93 117 60 90 114 120 92 117 180 89 116 240 92 113 Concentration of tea 0.25 Temperature of tea /degrees Celsius 63 Participant 13 Time /seconds Heart Rate Systolic Blood Pressure ±0.5 /bmp ±0.5 /mm Hg ±0.5 Resting 54 110 0 63 121 60 66 125 120 73 120 180 68 118 240 69 117 Concentration of tea 0.25 Temperature of tea /degrees Celsius 65 Participant 26 Time /seconds Heart Rate Systolic Blood Pressure ±0.5 /bmp ±0.5 /mm Hg ±0.5 Resting 63 103 0 78 119 60 76 117 120 73 116 180 72 114 240 70 112 Concentration of tea 0.25 Temperature of tea /degrees Celsius 63

171

Diastolic Blood Pressure /mm Hg ±0.5 73 82 81 79 79 78

Diastolic Blood Pressure /mm Hg ±0.5 78 90 89 86 85 83

Diastolic Blood Pressure /mm Hg ±0.5 81 98 97 95 92 90

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Participant 30 Time /seconds Heart Rate Systolic Blood Pressure ±0.5 /bmp ±0.5 /mm Hg ±0.5 Resting 54 109 0 68 130 60 67 128 120 65 126 180 63 125 240 62 123 Concentration of tea 0.25 Temperature of tea /degrees Celsius 69 Participant 2 Time /seconds Heart Rate Systolic Blood Pressure ±0.5 /bmp ±1 /mm Hg ±0.5 Resting 76 115 0 91 126 60 79 125 120 77 122 180 81 119 240 69 117 Concentration of tea 0.5 Temperature of tea /degrees Celsius 69 Participant 8 Time /seconds Heart Rate Systolic Blood Pressure ±0.5 /bmp ±0.5 /mm Hg ±0.5 Resting 67 115 0 77 123 60 75 122 120 74 120 180 73 117 240 71 116 Concentration of tea 0.5 Temperature of tea /degrees Celsius 64

172

Diastolic Blood Pressure /mm Hg ±0.5 71 85 83 82 80 78

Diastolic Blood Pressure /mm Hg ±0.5 72 79 77 79 76 74

Distolic Blood Pressure /mm Hg ±0.5 75 92 90 86 84 81

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Participant 9 Time /seconds Heart Rate Systolic Blood Pressure ±0.5 /bmp ±0.5 /mm Hg ±0.5 Resting 72 102 0 86 114 60 80 110 120 73 108 180 82 108 240 79 105 Concentration of tea 0.5 Temperature of tea /degrees Celsius 65 Participant 16 Time /seconds Heart Rate Systolic Blood Pressure ±0.5 /bmp ±0.5 /mm Hg ±0.5 Resting 52 78 0 70 94 60 66 87 120 64 86 180 63 85 240 60 83 Concentration of tea 0.5 Temperature of tea /degrees Celsius 65 Participant 17 Time /seconds Heart Rate Systolic Blood Pressure ±0.5 /bmp ±0.5 /mm Hg ±0.5 Resting 68 116 0 81 125 60 77 124 120 74 122 180 73 120 240 71 119 Concentration of tea 0.5 Temperature of tea /degrees Celsius 67

173

Diastolic Blood Pressure /mm Hg ±0.5 73 83 81 79 76 75

Diastolic Blood Pressure /mm Hg ±0.5 51 64 65 62 60 57

Diastolic Blood Pressure /mm Hg ±0.5 73 90 87 84 82 79

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Participant 3 Time /seconds Heart Rate Systolic Blood Pressure ±0.5 /bmp ±0.5 /mm Hg ±0.5 Resting 80 103 0 103 119 60 97 118 120 95 114 180 89 111 240 82 107 Concentration of tea 0.75 Temperature of tea /degrees Celsius 63 Participant 7 Time /seconds Heart Rate Systolic Blood Pressure ±0.5 /bmp ±0.5 /mm Hg ±0.5 Resting 67 90 0 81 99 60 78 97 120 77 94 180 73 92 240 69 89 Concentration of tea 0.75 Temperature of tea /degrees Celsius 63 Participant 12 Time /seconds Heart Rate Systolic Blood Pressure ±0.5 /bmp ±0.5 /mm Hg ±0.5 Resting 46 102 0 52 110 60 56 110 120 51 108 180 47 106 240 49 103 Concentration of tea 0.75 Temperature of tea /degrees Celsius 67

174

Diastolic Blood Pressure /mm Hg ±0.5 69 75 73 74 71 68

Diastolic Blood Pressure /mm Hg ±0.5 70 81 78 76 74 71

Diastolic Blood Pressure /mm Hg ±0.5 52 59 61 58 56 53

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Participant 25 Time /seconds Heart Rate Systolic Blood Pressure ±0.5 /bmp ±0.5 /mm Hg ±0.5 Resting 93 103 0 103 122 60 102 117 120 100 114 180 95 110 240 94 105 Concentration of tea 0.75 Temperature of tea /degrees Celsius 69 Participant 29 Time /seconds Heart Rate Systolic Blood Pressure ±0.5 /bmp ±0.5 /mm Hg ±0.5 Resting 76 113 0 98 138 60 95 134 120 90 131 180 85 125 240 80 119 Concentration of tea 0.75 Temperature of tea /degrees Celsius 69 Participant 5 Time /seconds Heart Rate Systolic Blood Pressure ±0.5 /bmp ±1 /mm Hg ±0.5 Resting 55 113 0 76 130 60 65 128 120 64 123 180 59 119 240 56 114 Concentration of tea 1 Temperature of tea /degrees Celsius 64

175

Diastolic Blood Pressure /mm Hg ±0.5 65 79 78 75 72 68

Diastolic Blood Pressure /mm Hg ±0.5 70 86 83 79 75 72

Diastolic Blood Pressure /mm Hg ±0.5 79 94 90 87 83 81

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Participant 6 Time /seconds Heart Rate Systolic Blood Pressure ±0.5 /bmp ±1 /mm Hg ±0.5 Resting 60 116 0 73 131 60 73 128 120 66 125 180 67 121 240 68 118 Concentration of tea 1 Temperature of tea /degrees Celsius 62 Participant 11 Time /seconds Heart Rate Systolic Blood Pressure ±0.5 /bmp ±0.5 /mm Hg ±0.5 Resting 59 98 0 79 106 60 77 103 120 62 102 180 65 101 240 73 99 Concentration of tea 1 Temperature of tea /degrees Celsius 66 Participant 18 Time /seconds Heart Rate Systolic Blood Pressure ±0.5 /bmp ±0.5 /mm Hg ±0.5 Resting 59 118 0 75 130 60 73 128 120 70 125 180 67 123 240 64 118 Concentration of tea 1 Temperature of tea /degrees Celsius 64

176

Diastolic Blood Pressure /mm Hg ±0.5 74 83 78 76 75 73

Diastolic Blood Pressure /mm Hg ±0.5 68 76 77 73 68 69

Diastolic Blood Pressure /mm Hg ±0.5 72 83 78 76 75 73

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Participant 22 Time /seconds Heart Rate Systolic Blood Pressure ±0.5 /bmp ±0.5 /mm Hg ±0.5 Resting 63 120 0 84 134 60 81 130 120 77 126 180 71 122 240 64 119 Concentration of tea 1 Temperature of tea /degrees Celsius 65

Diastolic Blood Pressure /mm Hg ±0.5 71 85 82 79 76 72

Participant 21 Control 1 Time /seconds Heart Rate ±0.5 /bmp ±0.5 Resting 49 0 63 60 61 120 58 180 57 240 56

Systolic Blood Pressure /mm Hg ±0.5 102 113 112 110 109 107

Diastolic Blood Pressure /mm Hg ±0.5 73 86 86 84 81 80

Participant 23 Control 2 Time /seconds Heart Rate ±0.5 /bmp ±0.5 Resting 63 0 70 60 71 120 68 180 69 240 69

Systolic Blood Pressure /mm Hg ±0.5 103 117 116 114 113 111

Diastolic Blood Pressure /mm Hg ±0.5 78 85 84 83 81 81

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Participant 24 Control 3 Time /seconds Heart Rate ±0.5 /bmp ±0.5 Resting 75 0 81 60 79 120 78 180 78 240 77

Systolic Blood Pressure /mm Hg ±0.5 94 111 111 108 107 104

Diastolic Blood Pressure /mm Hg ±0.5 74 84 81 80 79 78

Participant 27 Control 4 Time /seconds Heart Rate ±0.5 /bmp ±0.5 Resting 75 0 89 60 87 120 86 180 84 240 83

Systolic Blood Pressure /mm Hg ±0.5 104 113 112 110 109 108

Diastolic Blood Pressure /mm Hg ±0.5 76 85 84 82 81 81

Participant 28 Control 5 Time /seconds Heart Rate ±0.5 /bmp ±0.5 Resting 73 0 94 60 92 120 90 180 89 240 88

Systolic Blood Pressure /mm Hg ±0.5 106 123 121 120 118 117

Diastolic Blood Pressure /mm Hg ±0.5 68 82 81 80 78 75

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Appendix D: Processed Data for Heart Rate of Tea Concentration 0 Time Participant Participant Participant Participant /seconds 4 % ±1 14 % ±1 15 % ±1 19 % ±1 ±0.5 0 100 100 100 100 60 90 110 70 89 120 76 110 60 68 180 57 150 30 58 240 43 120 180 47

Participant Mean 20 % ±1 % ±1

Standard Deviation

100 45 55 45 64

100 81 74 68 91

0 24 22 47 59

Mean % ±1

Standard Deviation

100 94 78 57 47

0 5 4 11 19

Mean % ±1

Standard Deviation

100 94 85 72 48

0 11 28 36 14

Processed Data for Systolic Blood Pressure of Tea Concentration 0 Time Participant Participant Participant Participant Participant /seconds 4 % ±1 14 % ±1 15 % ±1 19 % ±1 20 % ±1 ±0.5 0 100 100 100 100 100 60 96 100 93 94 87 120 83 81 73 78 77 180 65 44 47 67 61 240 57 13 60 50 55 Processed Data for Diastolic Blood Pressure of Tea Concentration 0 Time Participant Participant Participant Participant Participant /seconds 4 % ±1 14 % ±1 15 % ±1 19 % ±1 20 % ±1 ±0.5 0 100 100 100 100 100 60 110 100 80 92 90 120 80 133 67 67 80 180 40 133 60 58 70 240 40 67 60 33 40 Processed Data for Heart Rate of Tea Concentration 0.25 Time Participant Participant Participant Participant /seconds 1 % ±1 10 % ±1 13 % ±1 26 % ±1 ±0.5 0 100 100 100 100 60 87 25 133 87 120 67 75 211 67 180 53 0 156 60 240 80 75 167 47

179

Participant Mean 30 % ±1 % ±1

Standard Deviation

100 93 79 64 57

0 39 59 56 48

100 85 100 67 85

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Processed Data for Systolic Blood Pressure of Tea Concentration 0.25 Time Participant Participant Participant Participant Participant /seconds 1 % ±1 10 % ±1 13 % ±1 26 % ±1 30 % ±1 ±0.5 0 100 100 100 100 100 60 57 70 136 88 90 120 43 100 91 81 81 180 43 90 73 69 76 240 29 60 64 56 67 Processed Data for Diastolic Blood Pressure of Tea Concentration 0.25 Time Participant Participant Participant Participant Participant /seconds 1 % ±1 10 % ±1 13 % ±1 26 % ±1 30 % ±1 ±0.5 0 100 100 100 100 100 60 70 89 92 94 86 120 50 67 67 82 79 180 30 67 58 65 64 240 30 56 42 53 50 Processed Data for Heart Rate of Tea Concentration 0.5 Time Participant Participant Participant Participant /seconds 2 % ±1 8 % ±1 9 % ±1 16 % ±1 ±0.5 0 100 100 100 100 60 20 80 57 78 120 7 70 7 67 180 33 60 71 61 240 -47 40 50 44

180

Standard Deviation

100 88 79 70 55

0 30 22 17 15

Mean % ±1

Standard Deviation

100 86 69 57 46

0 10 13 15 10

Participant Mean 17 % ±1 % ±1

Standard Deviation

100 69 46 38 23

100 61 39 53 22

0 25 31 16 40

Mean % ±1

Standard Deviation

100 78 59 40 24

0 16 8 10 9

Processed Data for Systolic Blood Pressure of Tea Concentration 0.5 Time Participant Participant Participant Participant Participant /seconds 2 % ±1 8 % ±1 9 % ±1 16 % ±1 17 % ±1 ±0.5 0 100 100 100 100 100 60 91 88 67 56 89 120 64 63 50 50 67 180 36 25 50 44 44 240 18 13 25 31 33

Mean % ±1

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Processed Data for Diastolic Blood Pressure of Tea Concentration 0.5 Time Participant Participant Participant Participant Participant /seconds 2 % ±1 8 % ±1 9 % ±1 16 % ±1 17 % ±1 ±0.5 0 100 100 100 100 100 60 71 88 80 108 82 120 100 65 60 85 65 180 57 53 30 69 53 240 29 35 20 46 35 Processed Data for Heart Rate of Tea Concentration 0.75 Time Participant Participant Participant Participant /seconds 3 % ±1 7 % ±1 12 % ±1 25 % ±1 ±0.5 0 100 100 100 100 60 74 79 167 90 120 65 71 83 70 180 39 43 17 20 240 9 14 50 10

100 86 75 52 33

0 14 17 14 10

Standard Deviation

100 86 64 41 18

100 99 71 32 20

0 38 8 13 17

Mean % ±1

Standard Deviation

100 86 64 41 12

0 11 13 12 15

Mean % ±1

Standard Deviation

100 88 70 42 8

0 25 15 11 15

Processed Data for Diastolic Blood Pressure of Tea Concentration 0.75 Time Participant Participant Participant Participant Participant /seconds 3 % ±1 7 % ±1 12 % ±1 25 % ±1 29 % ±1 ±0.5 0 100 100 100 100 100 60 67 73 129 93 81 120 83 55 86 71 56 180 33 36 57 50 31 240 -17 9 14 21 13

181

Standard Deviation

Participant Mean 29 % ±1 % ±1

Processed Data for Systolic Blood Pressure of Tea Concentration 0.75 Time Participant Participant Participant Participant Participant /seconds 3 % ±1 7 % ±1 12 % ±1 25 % ±1 29 % ±1 ±0.5 0 100 100 100 100 100 60 94 78 100 74 84 120 69 44 75 58 72 180 50 22 50 37 48 240 25 -11 13 11 24

Mean % ±1

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Processed Data for Heart Rate of Tea Concentration 1 Time Participant Participant Participant Participant /seconds 5 % ±1 6 % ±1 11 % ±1 18 % ±1 ±0.5 0 100 100 100 100 60 48 100 90 88 120 43 46 15 69 180 19 54 30 50 240 5 62 70 31

Participant Mean 22 % ±1 % ±1

Standard Deviation

100 86 67 38 5

100 82 48 38 34

0 20 22 14 31

Mean % ±1

Standard Deviation

100 77 54 32 5

0 10 7 11 9

Mean % ±1

Standard Deviation

100 73 46 20 6

0 26 17 14 10

Processed Data for Systolic Blood Pressure of Tea Concentration 1 Time Participant Participant Participant Participant Participant /seconds 5 % ±1 6 % ±1 11 % ±1 18 % ±1 22 % ±1 ±0.5 0 100 100 100 100 100 60 88 80 63 83 71 120 59 60 50 58 43 180 35 33 38 42 14 240 6 13 13 0 -7 Processed Data for Diastolic Blood Pressure of Tea Concentration 1 Time Participant Participant Participant Participant Participant /seconds 5 % ±1 6 % ±1 11 % ±1 18 % ±1 22 % ±1 ±0.5 0 100 100 100 100 100 60 73 44 113 55 79 120 53 22 63 36 57 180 27 11 0 27 36 240 13 -11 13 9 7 Processed Data for Heart Rate of Control Time Participant Participant Participant /seconds 21 % ±1 23 % ±1 24 % ±1 ±0.5 0 100 100 100 60 86 114 67 120 64 71 50 180 57 86 50 240 50 86 33

182

Participant Participant Mean 27 % ±1 28 % ±1 % ±1

Standard Deviation

100 86 79 64 57

0 17 12 14 20

100 90 81 76 71

100 89 69 67 60

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Processed Data for Systolic Blood Pressure of Control Time Participant Participant Participant Participant /seconds 21 % ±1 23 % ±1 24 % ±1 27 % ±1 ±0.5 0 100 100 100 100 60 91 93 100 89 120 73 79 82 67 180 64 71 76 56 240 45 57 59 44 Processed Data for Diastolic Blood Pressure of Control Time Participant Participant Participant Participant /seconds 21 % ±1 23 % ±1 24 % ±1 27 % ±1 ±0.5 0 100 100 100 100 60 100 86 70 89 120 85 71 60 67 180 62 43 50 56 240 54 43 40 56

183

Participant Mean 28 % ±1 % ±1

Standard Deviation

100 88 82 71 65

0 5 7 8 9

100 92 77 68 54

Participant Mean 28 % ±1 % ±1

Standard Deviation

100 93 86 71 50

0 11 11 11 7

100 87 74 56 48

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Appendix E:

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Hugo Sunnucks - Philosophy

To what extent does Wittgensteinâ&#x20AC;&#x2122;s Private Language Argument refute Solipsism?

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Hugo Sunnucks – Philosophy When choosing my extended essay topic I knew I wanted to use Wittgenstein as I had recently been reading some of his work. I wanted to not simply analyse his work, but see how it could be applied to other areas that had perhaps not been examined before. Therefore I took a part of Wittgenstein’s philosophy, his private language argument, and looked to see what its implications were for other theories. I thought that it quite nicely addressed Cartesian philosophy and having found some literature and supporting material I decided that it would be a worthy topic to analyse solipsism. At first I did have some issues in trying to visualise how the two theories interacted but having thought through it in some depth I decided to impress my own opinion on Wittgenstein’s work in order to bring forth the salient points. I derived great value from trying to make my interpretation one and felt like I was (perhaps presumptuously) actually participating in philosophy rather than simply learning about it.

Supervisor: Andy Waldron Hugo’s essay is an investigation of a notoriously complex and intricate issue in Philosophy (Wittgenstein’s ‘Private Language Argument’), and its implications for the sceptical problem of other minds. This required him firstly to grasp the argument and be able to present it as coherently as possible; and secondly, to apply the argument as construed to another area of philosophical enquiry. That he accomplished both of these tasks with such mastery and facility is remarkable: this is very difficult philosophy and his presentation, exploration and evaluation demonstrate superb analytical rigour.

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Contents Introduction 194 Solipsism 194 Private Language Argument and rule-following

195

Critique of Solipsism

198

Conclusion

200

Bibliography 201

Abstract The title: “To what extent does Wittgenstein’s Private Language Argument refute Solipsism?” gives a focused evaluation of the theory of Solipsism. Solipsism itself is not a widely-held theory; however, it comes from Cartesian notions that have influenced the last 400 years of philosophical thought. The scope then, which at first seems narrow, can actually have much larger applications. If there are links between Solipsism and other theories, especially Dualism, then the ramifications of the refutation of Solipsism could be great. Wittgenstein mainly deals with metaphysics and logic, and these large areas of philosophy are the concern of this essay. When Descartes originally created doubt about everything around him he used God and arguments we now see as wrong to reason his way out. Without God he may have had to consign himself to Solipsism, as he could not have rid himself of many doubts. Wittgenstein though, argues that the original doubting is what creates the problem. Asking questions where there is no reasonable argument to be had is essentially futile. Utilising what Wittgenstein argues is a necessarily public language to doubt the existence of the public is nonsensical. The language is public according to Wittgenstein because language, he says, works as a communal entity, and not as a stringent logical system that corresponds and ‘pictures’ reality. The conclusion is then that Wittgenstein’s Private Language Argument does refute solipsism, because it shows that the private language that the Solipsist assumes is impossible. The links between this and larger theories would need to be argued in further essays. Furthermore, the nature of the Private Language Argument and other formulations of it may also have to be researched to see if the entire argument is coherent.

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Introduction Wittgenstein opens his Philosophical Investigations with this quote from Johann Nestroy: “The trouble about progress is that it always looks much greater than it really is” (Nestroy, 1847). Wittgenstein’s writing is exactly like this; when reading his work one is left with a feeling that something profound has been said, and this makes the task of unpicking his work extremely important. Solipsism itself is not a widely-held philosophical theory; however, it is based on many Cartesian arguments that have been extremely important to the last 400 years of philosophy. The contention that your mind is the most certain thing you can know has led to this view that we cannot know anything else exists. When people think about an area such as the mind and body they often reason to something such as the soul to explain their experience; Wittgenstein attempts to disprove the Dualistic notions that many people hold. Addressing Dualism in the Research question would be too broad to tackle in so few words; Solipsism is a much simpler theory that still has much philosophical importance. The significance of the question “To what extent does Wittgenstein’s Private Language Argument refute Solipsism?” comes from Wittgenstein’s attack on the foundations of Solipsism. Wittgenstein’s reversal of certainty and his conviction in the irrelevance of sensations in language seems to lead to the conclusion that Solipsism is incoherent. His destruction of the correspondence theory of truth is compelling and his thoughts on rule-following also prove to be powerful arguments. The disproval of these assumptions and by extension private language shows that it is impossible for the Solipsist to express his ideas without a public language and thus a community around him.

Solipsism Réne Descartes used a systematic method of doubt to render unknowable all he believed about the world. He started by realising that sometimes he was tricked by his senses, such as in the case of a square tower that looks round from a distance, and he reasoned from this that the shape and colour of things amongst other properties was sometimes doubtful (Descartes, 1641 Pg.53). He then went on through successive layers of doubt until he found the ultimate doubt; perhaps an evil demon was tricking him about all material things around him, and even concepts such as maths. Descartes thought that it was a possibility that the demon could make him add 2+2 to make 5. The only thing he found of which he could be certain was that “I am, I exist” (Descartes, 1641 Pg.17). Even the demon could not trick him about his existence; for there had to be something to trick. From this, Descartes espoused a conception of the soul as an ontologically separate substance, in which experiences and beliefs inhered. He thought that because he could doubt everything apart from his soul there had to be a “real distinction” between his body and mind. This has led to the egocentric view we have of the world, with ideas coming from within us and our private realm, rather than coming from the public space. This is a deeply intuitive idea; it seems correct that only we can know our own sensations. Solipsism arises from the doubt that Descartes created and this assumption that we have private access to our feelings. The 1

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Solipsist position is that “I am the only thing that exists”, as they believe no other reasonable bases for belief can be built to know anything else. The Solipsist’s answer to any arguments attempting to affirm the outside world will be that there are doubts about everything, and that the only thing they can really know that exists is their mind. Existence of other things is then based on my experience; the world and people in it exist in my consciousness. For the solipsist there is no meaning to propositions which posit a world separate from him as he is the source of his own meaning. The outer world only exists insofar as it relates back to the solipsist’s experiences, as he must derive meaning from inner ostensive definition. This is because if the Solipsist doubts the existence of the world a statement such as “That is a leafy tree” can’t be referring to a real thing outside but must refer to some aspect of the Solipsist’s experience. We can imagine that the meaning derives itself from a ‘picture’ of a leafy tree in the Solipsist’s mind. The Solipsist maintains that he gained his language by systematically naming his experiences such feeling pain or seeing red. Solipsism is clearly a theory that strays very far from common sense, and from what can be learnt by the senses. Indeed if a line of enquiry leads to Solipsism it is often thought to prove a corruption in the enquiry. Solipsism as a theory, however, is based on different theories which are more widely held. It is based on the Cartesian conception of the soul and mind as separate entities, the possibility of private language, and the idea that we can only ever know our own mind. Wittgenstein, in his private language argument, attempts to tackle all three of these assertions and in doing so argues against a deeply held intuitive position.

Private Language Argument and rule-following Wittgenstein’s private language argument is a repudiation of the concept of a ‘private language’. A private language in the Wittgensteinian sense is one that cannot in principle be translated; it is inaccessible to anyone but the subject. If I use a secret language with my friend where we code certain words; this is not a private language. This is because it is logically decodable and translatable into a language that other people would understand. A Wittgensteinian private language is one in which a person names a sensation, irreducible into any other words, so that no other person could know what this sensation was. As qualia are traditionally conceived this may at first seem plausible; it would make sense that the ontologically subjective world of our sensations could only be named and recognised by us. Stephen Law uses the analogy of a prisoner and a rat to explain this. He says that just as a prisoner may write down an exclamation mark in his diary every time he sees a rat in his cell (Law, 2004 Pg.2); a person could write down a letter S in his diary every time he has a sensation (Wittgenstein, 1953 §258), and we could imagine this as a primitive language. Here it seems intuitive, Law argues, that both the prisoner and the person are following rules; they are creating their own ‘language’ in which they privately define their own symbols. Wittgenstein agrees that language is a rule-following activity; he argues that language is a web of agreements between people that forms the basis of a ‘game’, but questions whether we can apply the concept of ‘rules’ to the examples above. Wittgenstein thought that rules entailed a certain mode of reputable verification. He also argued that 2

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rules and language only find meaning in a community, as language only has use insofar as other people understand it. Wittgenstein thought that our conception of language and feelings had led us to the false view that a private language is possible. One of Wittgenstein’s main arguments centres on the rule-following aspect of language. In this, Wittgenstein highlights the essential distinction between thinking you are following and following a rule. If an activity doesn’t maintain this distinction, he says, it is no longer a rule-governed activity. For example, if I handle the ball in a football match, and no one tells me not to, the game will quickly collapse into something unrecognisable. This is because the distinction has not been maintained between me thinking I am playing football and actually following the rules. Wittgenstein says: “And that’s why it’s not possible to follow a rule ‘privately’; otherwise, thinking one was following a rule would be the same thing as following it.” (Wittgenstein, 1953 §202). In a private language there is no ‘referee’, and a private language-user is just like the unruly football player; in the case of a private language it is not right to talk about ‘correctness’ or rules. It may be objected that you can ‘self-regulate’ and manage to maintain your rules finding some ‘self-meaning’, however, Wittgenstein says that this would be "as if someone were to buy several copies of the morning paper to assure himself that what it said was true” (Wittgenstein, 1953 §260). This is because the meaning of verification as it is normally conceived does entail some independent-check; for example, an exam marked by the examinee would not be trustworthy, and likewise a language that was managed by a single person would not be the kind of thing that we apply the concept of correctness to. So, because a private language lacks public verification, and it is incoherent to suggest self- verification is possible; the idea of private language is incoherent. Whether rule-following activities need strict public criteria of verification, however, is contested. David Pears said that rules necessitate “a useable criterion of successful performance.” (Pears, 1988 Pg.345), however, this is open to many interpretations. Stephen Law argues that we intuitively want to say the prisoner in the earlier example is following a rule. He has an ability to recognise and apply a course of action in a set of circumstances (Law, 2004 Pg.7). There may not be any public criteria of correctness, or a distinction between thinking you are following and following a rule, but he argues that we can see the prisoner is following a rule. The prisoner is not getting lucky every time he follows the rule correctly; he knows he is following it because he has a faculty of rule following. Law’s central point is that the verificationist stance is too strong, and that it doesn’t allow for certain instances of rule following where there is no public check. By analogy the person who writes S in their diary would fall into this category, and so Law validates the possibility of a private language. This objection fails to grasp the crux of what is being said though; it is not that we can’t imagine a private language-user, but that we must realise the concept of language does not apply to his case. David Pears uses the example of an archer who shoots at a target but cannot go and look to see where his arrows have hit to explain this (Pears, 1988 Pg.333). If the archer is following the rule “hit the bullseye” and doesn’t know whether he is 3

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hitting it; even if he does hit the bullseye he will not be following a rule, but will have accidentally fallen into accord with it. This is because he does not know whether he is succeeding at his practice or failing. The private language-user is in the same situation as the archer. We can imagine that all the time the prisoner thought he was following the rule he was actually looking at mice, and on one particular day there was a rat. On this day he will have followed his rule correctly, but he will have done so by accident; no one would say he had followed the rule. The prisoner is following a rule in a vacant sense, and not really using a language. If I am not intentionally following a rule then it is merely a “ceremony” (Wittgenstein, 1953 §258). This description rings true; the prisoner in his attempt at selfamusement is not really following a rule, but forming a personal habit. If I always get out of bed on the right and on one day I get out of bed on the left no one would say I had broken a rule. This is because we do not think of personal tendencies in the same way as rules. A private language, because of its lack of rules, would be an altogether alien activity. Activities only become rule-bound and meaningful when they have criteria for their success. Wittgenstein also denied the possibility of a private language by saying that meaning in language comes from public use and understanding, not from correspondence with a certain object. The meaning of the symbol S is not directly linked to the sensation in his body; S means nothing unless there is some public understanding of what it means. For example, if I leave a sign on my door when I am grumpy; its meaning to other people does not derive itself from my inner state, but from their understanding of what will happen if they enter my bedroom. So, without a public domain of receivers no language would have any meaning, and so a private language would have no meaning. Wittgenstein uses the example of a community who all hold a box containing what they say is a beetle to further illustrate his point. None of them can look into each other’s boxes, but all of them think they have a beetle. The meaning of the word is not directly referring to what is in the box, as it is completely possible everyone has different items; Wittgenstein says “The thing in the box has no place in the language-game at all; not even as a something: for the box might even be empty.—No, one can ‘divide through’ by the thing in the box: it cancels out, whatever it is..” (Wittgenstein, 1953 §293).The meaning instead comes from use; this is what the people have agreed they mean when they refer to their ‘beetle’. If there was no public understanding of the meaning of “beetle”; the beetle would lose all meaning entirely. In a private language there would only be the sensation or ‘beetle’ to talk about; this, however, has no place in discerning the meaning of a proposition, and so a private language would be meaningless. The example of the beetle, however, seems to bring up certain objections. It is hard to see how the object in the box is irrelevant. If one community-member had nothing in their box and another had a red ball they would surely be able to describe and discern that they didn’t have the same object in their box. Similarly, there could be no greater difference between showing pain behaviour without pain, and genuinely being in pain (Wittgenstein, 1953 §304). It seems that the thing that is in the box does in some way confer meaning to 4

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language. For if it didn’t there would be no difference between knowing that someone else almost certainly had something different to you, and not knowing anything at all. If we realise we have different objects, the word beetle loses its meaning and we must come up with different words. This has relevance to private language because if the correspondent in the real world, S for example, does play a role in the game then the writing of S derives its meaning from it occurring in you; so a private language is possibly meaningful. Wittgenstein agrees that the thing in the box isn’t irrelevant, but he cryptically says “It’s not a Something, but not a Nothing either!”(Wittgenstein, 1953 §304 ); he suggests that of course it is important, but not in the language game. The difference between a faker of pain and a person in genuine pain will never be verified by appeal to their mind, but by appeal to their action. If a person has pretended to injure their leg they will still be able to walk if told to stand; a person with a genuinely painful leg won’t be able to. From this example it is clear that in our judgement the feeling plays a role, but at the same time is not relevant in our investigation.

Critique of Solipsism In expressing any Solipsistic argument the Solipsist makes use of language; this language in the Solipsist’s view will have to be private as only they exist. Private languages necessarily use the correspondence theory of truth. This means that a proposition’s “agreement or disagreement of its sense with reality constitutes its truth or falsity” (Wittgenstein, 1922 2.222). The example of the beetle, however, discredits the theory of correspondence. The language which the community use doesn’t derive its truth or falsity from what is in the box, but from the agreement of the members. A private language would not be meaningful as there would not be any use for language, as use derives itself from a communal understanding. There would be no point in talking about truth or falsity as these concepts only apply to a public activity. Furthermore, if the private language must rely on correspondence it is very hard to imagine what is being ‘pictured’ in a solipsistic proposition. A sentence like “I am the only thing that has certain existence” doesn’t picture an object, but only a concept in the mind of the Solipsist. Wittgenstein says “Skepticism is not irrefutable, but obvious nonsense if it tries to doubt where no question can be asked.” (Wittgenstein, 1969 Pg.44). The Solipsist’s denial that anything exists goes directly against anything in reality, and becomes nonsense. If there is a community which recognises there is doubt about many things which they think they know, then the ideas of Solipsism develop meaning in this context. In the context of a solitary thinker it is hard to conceive how his words will derive meaning from correspondence to his ideas. We cannot even conceive of how the private language-user will create a full and meaningful language. It is clear that rules, especially when being used in regards to larger activities, need some type of verification. Verification, however, is not an applicable concept to a private language. To apply ideas of correctness to a proposition there must be some outside check to verify that one is not just thinking you are following a rule, but actually following it. A language where this is not the case would be relative and personal; this would make the whole language 5

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meaningless to anyone but the subject. The private language argument effectively shows that a community is needed to create use for a language and to confer meaning to words. It also shows that a language without rules, as a private language would be, would be no language we would recognise and would not even be possible. We clearly have a meaningful and rule-governed language, so it necessarily follows that it is communal. This means that the very tools the solipsist uses to doubt other people’s existence are actually given to him by those people. The last assumption that solipsism arises from is that necessarily private experiences constitute what we think is most certain about the world. The position is that we can only ever know for sure that we exist, as we rely on no sense data to perceive that we exist. Wittgenstein, though, in his private language argument discredits this view. The statement “Only I can know when I am in pain” relies on our conception of the phrase “I am in pain” as a meaningful reference to our mind. As correspondence is not what confers meaning to phrases though; “To say "I have pain" is no more a statement about a particular person than moaning is.” (Wittgenstein, 1935 Pg.67). We can never say something meaningful about a private entity about which nothing can be known because statements about it can never be verified. Saul Kripke said “we do not pity others because we attribute pain to them, we attribute pain to others because we pity them” (Kripke, 1982 Pg.142). Kripke is saying that pitying a person is what pain consists of; when I say “That must be painful” I am not making a statement about their inner condition but displaying another piece of pain-behaviour in our language-game. It is because we have a faulty view of what pain is that we think the ‘main’ part of being in pain is the feeling; the feeling is not what matters as in the case of S. The inner sensation plays no role in the use of language, however, it does unintentionally arise from our assessment of public behaviour. In view of this the solipsist’s contentions become confused. It is common to think that only you can know your pain, however, Wittgenstein makes a fundamental reversal with his private language argument. Wittgenstein imagines seeing a person writhing in agony on the floor and saying that he doesn’t really know he is in pain. If we return to a more common sense view of the world it is clear that a Solipsist’s contentions have very little traction. The only meaningful conversations we can have are about the intersubjective; the most certain things we can know of are those things that can be publicly verified and talked about. In fact it is this communal connection that Wittgenstein uses to verify his position. Wittgenstein says “Look at a stone and imagine It having sensations.” (Wittgenstein, 1953 §284) he expects his reader to find the proposition ridiculous. A Solipsist, however, should not find this ridiculous; in a world where only you exist there is no reason why you should find the idea that a stone has a mind any more ridiculous than anything else. Descartes’ ‘real distinction’ here is too strong; he has created a situation in which the physical and mental have no real connection. Wittgenstein’s argument is that we could not have come across the idea that only animate objects have sensations without other people. Hence, because we have these concepts and ideas, and find the concept of a stone with a mind ridiculous, we have got a community around us.

Conclusion

The conclusion to the question “To what extent does Wittgenstein’s Private Language Argument refute Solipsism?” is that199 Wittgenstein’s private language argument does undermine some of the fundamental assumptions that Solipsism is based upon. Because a Solipsist must have language to use his concepts and ideas, and this language

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we have these concepts and ideas, and find the concept of a stone with a mind ridiculous, we have got a community around us.

Conclusion The conclusion to the question “To what extent does Wittgenstein’s Private Language Argument refute Solipsism?” is that Wittgenstein’s private language argument does undermine some of the fundamental assumptions that Solipsism is based upon. Because a Solipsist must have language to use his concepts and ideas, and this language cannot come from him; there must be an outside world, and his position is false. In making appeals to methodical doubt and logical argumentation the Solipsist is using the very tools that public language has conferred on him. The Solipsist, otherwise, would not have any rules on which to base his arguments as rules necessitate some kind of public verification. As “A non-linguistic solipsism is unthinkable and a thinkable solipsism is necessarily linguistic.” (IEP, 2015) the solipsist relies on the necessarily public language to make his case. As discussed language is necessarily public because we see that language does have meaning and meaning has to arise from use. Any appeals the solipsist may make to a correspondence theory of truth are also undermined by Wittgenstein’s arguments. Solipsism is a philosophy that attempts to reason from what is obvious to what is not; it is evident to us that we do have a meaningful language and do apply concepts to the world that are necessarily derived from community. We have been tricked in our use of language into thinking that when we talk about sensations we are talking about a hidden soul, when really we are talking about the things of which we have acquaintance. Wittgenstein turns around our views; we must view what is public as most certain, and not attempt to reason everything from our own case. Solipsism is a philosophical problem which has the form “I don’t know my way about.” (Wittgenstein, 1953 §123) and Wittgenstein shows the way to discredit the theory. This essay has only presented one version of Wittgenstein’s private language argument. In answering the question many new areas of enquiry have arisen. For example, whether it would be worthwhile to look at how different formulations might have affected the possibility of a Private Language. It may also be a worthwhile question to ask whether Dualism leads inevitably to Solipsism. If this link can be made then the disproval of Solipsism will mean, by extension, that Dualism must be false as well. This would be hugely impactful for religion and many doctrines which have based their arguments on a conception of the soul in this way. Whether Wittgenstein was correct in his argument is an unresolved issue, however, it has been shown in this essay that parts of his writing effectively disprove the possibility of Private Language and Solipsism.

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Bibliography Descartes, R., 1996.Meditations on First Philosophy. Cambridge: Cambridge University Press. Kripke, S., 1982.On Rules And Private Language. Cambridge, Massachusetts: Harvard University Press. Law, S., 2004.Five Private Language Arguments, International Journal of Philosophical Studies, 12(2). Nestroy, J., 1847.The ProtĂŠgĂŠ. 4.10. Pears, D., 1988.The False Prison Vol 2. Oxford: Clarendon Press. Thornton, S., 2015.Solipsism And The Problem Of Other Minds, [Internet Encyclopedia of Philosophy]. Available at: http://www.iep.utm.edu/solipsis/ [accessed 3 August 2015] Wittgenstein, L., 1922.Tractatus Logico-Philosophicus. London: Routledge. Wittgenstein, L., 1935.Blue Book and Brown Books. Oxford:Blackwell. Wittgenstein, L., 1953.Philosophical Investigations. Oxford: Blackwell. Wittgenstein, L., 1969.Notebooks 1914-16. Oxford: Blackwell.

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What is the most significant economic impact of an ageing population on the nursing-care industry in Machida-city, Japan?

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Nanako Watanabe - Economics Having had an interest in the contributing factors of the recessionary economy of my home country, Japan, I decided to investigate its super-ageing population, which exemplifies a worldwide challenge that will occur earliest there. I had planned to do an internship over the summer under Mr. Masanobu Ogura, a Japanese politician representing Machida-shi, and hence decided that it would be best for me to centre my research on the economic impacts of the nursing industry in Machida-city, which particularly suffers from its ageing population. The experience of conducting research of my own interest gave me the opportunity me to undergo a range of tasks and gain new skills from extrapolating useful data from government statistics to interviewing professionals. In conclusion, the supporting and opposing evidence for my hypotheses that I gained from my research was fascinating and made this overall experience rewarding!

Supervisor: Alex Smith When Nanako first approached me about her extended essay in the spring of 2015 she appeared a little tentative but very focused on what she wanted to do. She was interested in impact of demographic changes on healthcare with a focus on the economic impact of an ageing population on the nursing care system in Machida-city, Japan. Her research question was, for me, what is so good about the challenge of the extended essay: something that moves beyond the shackles of the syllabus and is a contentious current issue. Nanako planned, researched and wrote her essay in such a thoughtful, measured and intelligent way. Her final submission was beautifully put together and reflected the work of someone who has really engaged with her extended essay. She is an outstanding Economics student who was a pleasure to supervise.

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Contents Introduction 206 Research Method

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Theoretical Hypothesis

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Research Findings

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Conclusion and Evaluation

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Bibliography 218 Appendix

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Abstract Now, in 2015, Japan has come to have the worldâ&#x20AC;&#x2122;s fastest ageing population. Throughout the years, this has negatively impacted the Japanese economy, leading to recession. Much of these negative impacts, particularly on the local citizens and on society, are due to the economic impacts the ageing population has on government expenditures and the nursing-care industry. Machida-city, an ageing city in Tokyo, is now under a new city rebuilding project in order to meet the nursing-care demands of its growing ageing population. Hence, I decided to investigate the economic impacts of an ageing population on the nursing industry and formed the research question â&#x20AC;&#x2DC;What is the most significant economic impact of an ageing population on the nursing-care industry in Machida- city, Japan?â&#x20AC;&#x2122; My investigation was undertaken through the use of primary and secondary sources. Primary sources include interviews with Machida-city and nursing-care experts, and secondary sources include government publications, academic works and financial articles. Exploring and evaluating the significant economic impacts on the nursing-care industry in Machida-city has enabled me to conclude that the lack of monetary resources to fund the nursing industry and collecting such funds from the public is the most significant economic impact of the ageing population on the nursing industry in Machida-city. I came to fully understand the severe significance of the impacts an ageing population has on society. The shortage of caregivers and rise in price made it necessary for Machida-city council and national government to increase their subsidies on the industry, and in turn to increase their revenues. They thus had to raise self-pay for elderlies, insurance premium for all citizens, and reduce subsidies on other industries. The problem with the ageing population has come to the point where citizens who are unrelated to the problem have had to take up the responsibility.

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1. Introduction

1.1 Context The ageing population, people of age 65 and older, is increasing day by day in Japan due to the rise in life expectancy (80.5 men, 86.83 years women)1. Japan is now facing the world’s fastest ageing society in which 26% of its population is above age 652. There are various little areas in Japan like Machida-city where the majority of the population is ageing. The combination of the many ageing cities is a key factor that has led Japan to suffer from a rapid increase in its ageing population. Machida-city is located in the suburb of Tokyo and it holds a total population of 4290253. 25.1% of the population is aged and this percentage, along with the fall in birth rate (1.40 births per woman)4, is predicted to increase to 27.3% by 20255. The rise in ageing population leads to many economic impacts particularly within the nursing-care industry. The nursing-care industry was created to benefit the elderlies in society, hence not to maximize profit. To investigate how the ageing population affects this industry from an economic perspective, I will explore and analyze the impacts on the laws of supply and demand, subsidy theory, idea of opportunity cost, and rising tax theory. 1.2 Goal The ageing population in Machida-city is an important topic for exploration because it has a significant impact on the nursing industry and consequently on society, particularly the Machida-city council, the Machida-city citizens, the other industries, and the Japanese economy. An ageing population is one of the major factors that led Japan to recession6. Discovering the most significant economic impact on the nursing industry and Machida-city can lead to possible solutions that resolve the problem. An ageing population will become one of the most heated problems that the world will face in the future. Examining this problem that is already impacting greatly in Machida-city will help the nation and the world to effectively manage this problem in the future. To evaluate the significant impacts of our ageing population, the question “What is the most significant economic impact of an ageing population on the nursingcare industry in Machida-city, Japan?” was formed.

Japan Today (2015) Life expectancy for men and women in Japan at highest ever. (02/08/2015) The World Bank (2014) Population ages 65 and above (% of total). (Accessed: 30 June 2015). 3 ‘Ishizuka, T. (2015) [Insured Long-term Care Service Plan of Nursing-Care System in Machida-city]. Machida-city Council. (in Japanese) 4 Geoba (2015) Japan - 2015 - Statistics and Rankings. (Accessed: 30 March 2015). 5 Ishizuka, T. (2015) [Insured Long-term Care Service Plan of Nursing-Care System in Machida-city]. Machida-city Council. (in Japanese) 6 Menton, J. (2014) Japan Recession 2014: How A Graying Population Impacts Asian Economies. (Accessed: 30 June 2015). 2

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2. Research Method

2.1 Aim Primary and secondary sources will both be used to gain an in-depth analysis of the significant economic impacts of the ageing population on the nursing-care industry in Machida-city. Primary sources are used to gain first-hand information and opinions about the issue, and secondary sources are used to analyze the economic impacts of the ageing population. 2.2 Sources Primary sources include interviews with experts in order to gain various perspectives on the significant economic impacts. I interviewed Mr. Masanobu Ogura, a Japanese Parliament politician representing Machida-city, regarding his political perspectives on the economic impacts of an ageing society on the nursing-care industry in Machida-city. I also interviewed Mr. Mitsuyasu Watanabe, an entrepreneur who is creating a nursing-care home business in Machida-city, and Mr. Asuka Suzuki, the chief head of social security of the Machida-city council. I enquired about their perspectives on the significant economic impacts on the nursing industry in Machida-city. Despite the outlook from various professional viewpoints, some information may be inaccurate because answers are based on the interviewees’ personal opinions. Secondary sources include textbook, financial articles, academic works and government reports. Economics textbooks were used to understand economic theories for my analysis such as the law of supply and demand. Articles from financial journals including Nikkei, were used to gain insights on the impacts of an ageing population. Academic works by Japan International Cooperation Agency, for example, were studied to expand the analysis of the impacts. Lastly, various reports including those by Machida-city Council, were used to gain statistical data of the past, present, and future of the ageing population and the nursing-care industry in Machidacity.

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3. Theoretical Hypothesis

Predictions of the research question “What is the most significant economic impact of an ageing population on the nursing-care industry in Machida-city, Japan?” will be conducted through economic theories. 3.1 Outline It is hypothesized that a shortage of caregivers and a rise in price will emerge. To fix this problem, the government can increase subsidies on the nursing-care industry by cutting spending on other industries, whilst being aware of the opportunity cost, and by increasing tax. 3.2 Demand & Supply In Machida-city, the increase in ageing population will no doubt lead to an increase in demand, “the quantity of a good or service that consumers are willing and able to purchase at a given price in a given time”7, for nursing-care service. As more people age, more people will be in need of the service and hence demand in the industry will increase. There will also be a shortage of supply, “the willingness and ability of producers to produce a quantity of good or service at a given price in a given time period”8, of nursing-care (ie. caregivers) in Machida-city because of the rapid increase in demand for the service and the insignificant change in supply.

Nursing-care Industry in Machida-city

Figure 1. Graph illustrating a right shift in demand

Figure 1 illustrates the impact of the ageing population on the demand and supply of the nursing-care industry in Machida-city. The increase in demand will lead to a right shift of the demand curve from D to D1. The supply curve S remains at the same position because its change is insignificant compared to the rapid increase in demand. The equilibrium point , the yellow dot, will be at a higher price from P to P1 and a higher quantity from Q to Q1. The price will increase from P to P2 at the same quantity Q. 7 8

Blink, J. and Dorton, I. (2011) Ib Course Companion: Economics Second Edition. p.18 Blink, J. and Dorton, I. (2011) Ib Course Companion: Economics Second Edition. p.27

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3.3 Subsidies on the nursing-care industry in Machida-city The rise in price of nursing-care will make it difficult for elderlies to consume the service; hence to protect the consumers of the nursing-care industry, Machida-city council should intervene in the industry and distribute subsidies from public funds that would reduce the price of nursing-care. A subsidy is “an amount of money paid by the government to a firm per unit of output”9; hence subsidies on the nursing industry will decrease the price of the nursing-care service. Figure 2 illustrates the subsidy on the nursing-care industry, which increases the supply and causes a right shift of the supply curve from S to S-subsidy. This new equilibrium point in yellow will have a lower price from P to P1 and a greater quantity from Q to Q1.

Subsidy on the Nursing-care Industry in Machida-city

Figure 2. Graph illustrating the effects of subsidy on the nursing-care industry. A right shift in the supply curve.

3.4 Solutions for Subsidy In order to subsidize the nursing industry, more revenue of Machida-city council is required because it must be subsidized to other industries as well. There are two possible solutions that enable subsidies on the nursing industry to increase: cut subsidies on other industries and increase tax to gain more revenue. 3.4.1 Cut subsidies on other industries Increasing subsidies for the nursing-care industry will prevent the ageing population from having to have to pay a lot of money because subsidies reduce costs. However, in order to fund more on nursing-care, Machida-city council must make efficient use of its limited revenue by cutting subsidies on other industries. This will negatively affect other consumers and producers who benefit from lower prices of other subsidized goods and services. Examples include education. If ￥10 billion of government revenue is spent on the nursing industry, the government spending on

Blink, J. and Dorton, I. (2011) Ib Course Companion: Economics Second Edition. p.57

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education and other industries will decrease by ￥10 billion10. The opportunity cost, “benefits forgone of the next best alternative”11, in this situation is a greater development of the youth generation and the future society of Machida-city. This 10 education and other industries decrease by ￥10 Thethe opportunity opportunity cost is formed duewill to the reduction of thebillion subsidy. on education cost, 11 , inthethis situation is a greater “benefitsinforgone of the next bestleads alternative” industry Machida-city, which to a fall in quality of education. On the development of the youth generation and the future societyleads of Machida-city. This other hand, subsidizing more on the nursing-care industry to an easing lifestyle opportunity is formed due toand the to reduction the subsidy on the education for a greater cost number of elderlies a greaterofincome for caregivers. In this case, industry in Machida-city, leads a fall in of thethe quality ofpopulation education. and On the Machida-city council will which prioritize thetoproblem ageing will other subsidizing more the nursing-care to an lifestyle focus hand, more on subsidizing theon nursing industry inindustry order to leads increase theeasing number of for a greater number of elderlies and to a greater income for caregivers. In this case, people with a higher quality of living. Machida-city council will prioritize the problem of the ageing population and will focus more on subsidizing the nursing in orderpossibility to increasecurve the number of The opportunity cost is illustrated withindustry the production shown in people with a higher quality of living. Figure 3. Point A is the maximum possible output combinations of nursing-care service and education that Machida-city council can achieve when all resources are in 12 The opportunity cost illustrated the production possibility curve shown full use . Point A willismove downwith to point B which shows that the amount of in Figure 3. Point A isnursing-care the maximum possible combinations of and nursing-care production for the service will output increase from X to X1 consequently, service and education that Machida-city council can when all resources are in the production for education will decrease from Y toachieve Y1. full use12. Point A will move down to point B which shows that the amount of production for the nursing-care service will increase from X to X1 and consequently, the production for education will decrease from Y to Y1.

Production Possibility Curve of nursing-care industry and education Figure 3. Figure illustrating the opportunity cost of nursing-care and education.

3.4.2 Raise Taxes Production Possibility Curve of nursing-care industry and education BecauseFigure the limited revenue of Machida-city produces theand opportunity 3. Figure illustrating the opportunitycouncil cost of nursing-care education. cost that could risk any benefits for the development of the future of Machida-city, it is 3.4.2 RaiseforTaxes important the council to maintain its subsidies on other industries. Hence, in order Because of on Machida-city council produces the opportunity cost to to be ablethe to limited increaserevenue spending the nursing-care industry without having to have that could riskonany benefits for theMachida-city developmentcouncil of the future of Machida-city, it Tax is cut subsidies other industries, must gain more revenue. important for the council to maintain its subsidies other industries. Hence, order increases will enable revenue to rise. Examples of on taxes include indirect taxesin (taxes 13 to be ableon togoods increase thedirect nursing-care industry without having to imposed andspending services)on and taxes (taxes imposed on income) . have to cut subsidies on other industries, Machida-city council must revenue. Machida-city council’s revenue will rise through tax rise andgain will more be enabled to Tax Examples of taxes include indirect taxes (taxes increases subsidy will enable on the revenue nursing-care to rise. industry increase without greatly cutting subsidies on 13 10 imposed on goods and services) and direct taxes (taxes imposed on income) . Riley, G. (2015) Opportunity Cost. Available at: other industries. http://beta.tutor2u.net/economics/reference/opportunity-cost (Accessed: Maybe 2015). Machida-city council’s revenue rise and26will enabled to will rise through tax 11 Anderton, A. G. (2008) Economics. p.5 12 10 Riley, G. (2015) Opportunity Cost. Available at: Riley, G. (2015) Opportunity Cost. Available at: http://beta.tutor2u.net/economics/reference/opportunity-cost (Accessed: 26 May 2015). http://beta.tutor2u.net/economics/reference/opportunity-cost (Accessed: 26 May 2015). 13 11 Blink, J. and Dorton, I. (2011) Ib Course Companion: Economics Second Edition. p.253 Anderton, A. G. (2008) Economics. p.5 12 Riley, G. (2015) Opportunity Cost. Available at: http://beta.tutor2u.net/economics/reference/opportunity-cost (Accessed: 26 May 2015). 13 Blink, J. and Dorton, I. (2011) Ib Course Companion: 8 Economics Second Edition. p.253

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4. Research findings

My hypothesis of the research question “What is the most significant economic impact of an ageing population on the nursing-care industry in Machida-city, Japan?” will be justified or contradicted through primary and secondary investigations. 4.1 Primary Research To gain first-hand information and opinions on the impacts of the ageing society, three interviews were conducted. 4.1.1 Interviews All three interviewees agreed that the great impact of the ageing population on the nursing industry in Machida-city is the shortage of nursing caregivers due to their low wages and the increase in the burden of nursing-care on the Machida-city council. Mr. Ogura stated that there is a shortage of 1 million caregivers at the moment. He explained that because the nursing-care industry is a service given by people, a greater quantity of caregivers is required for the industry, and technology cannot increase its efficiency. As nursing demand increases, the quantity of caregivers must increase as well, yet obtaining a high supply quantity is a serious issue at the moment. In order to reduce supply shortage, Mr. Ogura and Mr. Watanabe agreed that caregivers’ wage needs to be higher in order to build incentive. To increase wage, Mr. Ogura stated that subsidies for the nursing-care industry must rise, and that sufficient government revenue is necessary for this. Thus to increase government revenue to increase subsidy for the nursing industry, Mr. Ogura explained that the government must make a policy with a good balance of three components: increasing taxes, insurance premiums, and self-pay for nursing-care. The government has already made effort by increasing consumption tax, tax on spending on goods and services14, from 5% to 8% and is now planning to increase it to 10%. This may, however, discourage consumers to consume goods and services, which could contract the Japanese economy. Despite Mr. Ogura’s solution of increasing subsidies, Mr. Suzuki emphasized that Machida-city council cannot cut subsidies on other industries any more because it has already been done so. Even after increasing subsidies for the nursing-care industry by cutting subsidies on other industries, the supply shortage still exists, and maintaining the benefits of other industries is necessary for the society. Therefore, cutting subsidies on other industries is no longer a viable solution. Additionally, he mentioned that the government must use its limited revenue to support both growth of its economy and protection for its citizens because Japan is in huge debt and holds a recessionary gap at the moment. This leads to problems of determining the priorities and allocation of the government’s limited revenue. On the other hand, to increase wages, Mr. Watanabe suggested developing mechanical support that replaces physical work of caregivers because fewer workers will be in demand then. 14

Blink, J. and Dorton, I. (2011) Ib Course Companion: Economics Second Edition. p.27

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4.2 Secondary Research Information from government reports, academic works, and financial articles are gathered in the following. 4.2.1 Demand increase and Supply shortage Year Total Population Ageing Population Ageing Percentage

2015 429025

2016 429643

2017 430137

2025 430934

107651

109764

111526

117788

25.1%

25.5%

25.9%

27.3%

Machida-city Ageing Population

Table 1. Table displaying the predicted statistics of ageing population in Machida-city (Ishizuka, 2015).

Year People in need of nursing-care service Percentage of Population

2015 18947

2016 20099

2017 21252

2025 29745

17.6%

18.3%

19.1%

25.3%

Nursing-care demand in Machida-city

Table 2. Table displaying the predicted statistics of demand for nursing-care service in Machidacity (Ishizuka, 2015).

Table 1 and 2 show that the ageing population in Machida-city is just about a quarter, 25.1%, of the total population in 2015 and is predicted to grow larger to 27.3% in 202515. Consequently in correlation to the growing ageing population, statistics predict that the nursing-care demand will increase throughout the years, in which 17.6% is in demand for the service at the moment and 25.3% will be in demand in 202516. This data supports my hypothesis that increase in ageing population leads to increase in nursing-care demand.

Ishizuka, T. (2015) [Insured Long-term Care Service Plan of Nursing-Care System in Machida-city]. Machida-city Council. (in Japanese) 16 Ishizuka, T. (2015) [Insured Long-term Care Service Plan of Nursing-Care System in Machida-city]. Machida-city Council. (in Japanese)

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Quantity of nursing caregivers in Machida-city

Figure 4. Graph displaying the rise in caregivers in Tokyo, including Machida-city, from year 200 to 2011 (Tokyo Bureau of Social Welfare and Public Health, no date).

Insured Long-term Care Service Plan of Nursing-Care system in Machida-city stated that in 2014 in Machida-city, 1854 people avail nursing-care while 1599 people are waiting for nursing-care services to become available17. Hence, a supply shortage exists, just as predicted in my hypothesis. Yet despite the rapid increase in demand and supply shortage (ie. caregivers), the supply quantity is actually rising18. All lines in Figure 4 represent the quantity of caregivers and they show that in general, the quantity of supply is actually rising19. However, the rate of increase in demand is much higher than that of supply, and thus the shortage of nursing caregivers continues to increase. 4.2.2 Price and Self-pay rise The average monthly price of nursing-care for the elderlies is predicted to increase from 5390 yen in 2015 to 8177 yen in 202520. As hypothesized, the nursing-care price increases for the same quantity of service due to the increase in demand for nursing-care. According to Nikkei, this is due to the new Japanese policy that increased self-pay of nursing-care from 10% to 20% of total cost, for those who are able to afford it21. 4.2.3 Long-term Care Insurance System in Machida-city & Japan In 2000, the Japanese government introduced a long-term care insurance system to support the elderlies attaining nursing-care by subsidizing the nursing-care industry22. The cost of nursing-care industry is paid by four basic components: Japan government revenue (22% of total fund), Machida-city council revenue (22% of total fund), self-pay (price of nursing-care) (12% of total fund), and insurance premium (44% of total fund)23. Hence as predicted, the government created a nursing-care subsidy system in order to 17

Ishizuka, T. (2015) [Insured Long-term Care Service Plan of Nursing-Care System in Machida-city]. Machida-city Council. (in Japanese) 18 The Japan Times (2015) Shortage of nursing care workers. (Accessed: 8 July 2015). 19 Tokyo Bureau of Social Welfare and Public Health (no date) [Nursing-care Visits]. (Accessed: 6 May 2015). (in Japanese) 20 Ishizuka, T. (2015) [Insured Long-term Care Service Plan of Nursing-Care System in Machida-city]. Machida-city Council. (in Japanese) 21 Nikkei (2014) Better-off Japanese to pay more for nursing care. (Accessed: 5 June 2015). 22 Ministry of Finance (2014) Japanese Public Finance Fact Sheet. (Accessed: 7 July 2015). 23 Ministry of Finance (2014) Japanese Public Finance Fact Sheet. (Accessed: 7 July 2015).

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protect the elderlies. More costs are funded by the local citizens as they pay tax and insurance premiums. Machida-city’s citizens support their local elderlies the most. 4.2.4. Subsidy on nursing-industry in Machida-city

Total Expenditure Percentage

2015 2025 28.1 billion yen 46.3 billion yen 100% 164.8% Machida-city Council Expenditure

Table 3. Table displaying Machida-city council’s expenditure in 2015 and 2025 (Ishizuka, 2015)

Table 3 shows that Machida-city council’s subsidy for its nursing-care industry will increase from 28.1 billion yen in 2015 to 46.3 billion yen in 202524. Clearly, the amount of subsidy on nursing-care will rise, just as hypothesized. The following is an investigation on how the Machida-city council subsidizes its nursingindustry. 4.2.4.1. Spending on other industries

Machida-city council budget distribution

Figure 5. Chart illustrating the distribution of Machida-city council’s expenditure on various industries in 2010 and 2015. The green section of the chart with a label circled in red is the portion of spending on Nursing-care industry (Machida-City Council, 2015).

One method Machida-city council uses to gain revenue to increase subsidy for nursingcare is by cutting subsidies on other industries. Figure 5 shows that Machida-city council’s subsidy on the nursing industry increased from 8.8% in 2010 to 11.1% in 2015, and subsidy on other industries, unrelated to healthcare, including education, debit, sanitation, civil engineering, etc., decreased from 59.0% in 2010 to 55.5% in 201525. A notable decrease was its subsidy on education, which decreased from 6.73% in 2010 to

Ishizuka, T. (2015) [Insured Long-term Care Service Plan of Nursing-Care System in Machida-city]. Machida-city Council. (in Japanese) 25 Machida-City Council (2015) [Budgets in 2007-2016]. (Accessed: 7 July 2015). (in Japanese)

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5.61% in 201526. This clearly depicts that Machida-city council prioritised the nursing industry over the others, and this confirms my hypothesis that subsidies for nursing-care rose by reducing subsidies on other industries. The same can be said for the Japanese government expenditure. On Figure 6, the negative slope on the ‘Education & Science’ curve during year 2000 to 2013 indicates the cut in subsidy on the industry27. On the other hand, the steep, positive slope of ‘Social Security’, which includes nursing-care, during year 2000 to 2013 indicates a great increase in subsidy on the industry. This data proves that the Japanese government also prioritised the benefit of subsidising social security and nursing-care rather than education.

Distribution of Japanese government expenditure

Figure 6. Graph illustrating the distribution of expenditure of the Japanese government from 1960 to 2013 (Ministry of Finance, 2014).

4.2.5. Tax & insurance premium in Machida-city Year Tax paid per citizen (¥)

2010 156176

2015 159764

% Change 2.30%

Machida-city Council Tax Revenue

Table 4. Table displaying the tax revenue gained by Machida-city citizens in 2010 and 2015 (Ishizuka, 2015).

Table 4 shows that tax revenue in Machida-city rose by 2.30% from 2010 to 201528. This is in correlation with the increase in ageing population in Machida-city 2010 to 201529, as displayed along the red line on Figure 7. This data proves that Machida-city council most 26

Machida-City Council (2015) [Budgets in 2007-2016]. (Accessed: 7 July 2015). (in Japanese) Ministry of Finance (2014) Japanese Public Finance Fact Sheet. (Accessed: 7 July 2015). 28 Ishizuka, T. (2015) [Insured Long-term Care Service Plan of Nursing-Care System in Machida-city]. Machida-city Council. (in Japanese) 29 Machida-city Council (2015) [Estimate Outline of Population]. (Accessed: 4 June 2015). (in Japanese) 27

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likely attempted to increase subsidies on the demanding nursing industry by increasing its revenue through tax.

Population in Machida-city

Figure 7. Graph displaying the population of various age groups in Machida-city (Machida-city Council, 2015).

Year Total Cost Monthly Premium

2000 $32.2 Bil. $19

2005 $42.1 Bil. $21

2010 $52.8 Bil. $27

Trend of total costs and monthly premiums of long-term care insurance ($1.00=￥ 130.62)

Table 5. Table displaying the insurance premiums (Ministry of Health, Labour and Welfare, no date).

Nevertheless, tax only increased by 2% in the past 5 years30, hence, the ultimate reason why Machida-city council was able to increase its subsidy on nursing-care was because of the national government’s change in policy of increasing the national insurance premiums31. An insurance premium is a burden for all citizens in Japan, who are part of the labour force, because it is an amount paid for the long-term care system in Japan32. It is obligatory for all citizens, so they are much like taxes. They are devised every three years in order to complement the cost rise of the nursing industry33; hence, citizens who are unrelated to the nursing industry are still forced to pay an increasing amount of insurance premiums. Due to their limited revenue, the national government and Machidacity council are relying on their citizens to pay for the increasing costs of the nursing industry.

Ishizuka, T. (2015) [Insured Long-term Care Service Plan of Nursing-Care System in Machida-city]. Machida-city Council. (in Japanese) 31 Japanese Law Translation (1997) Long-Term Care Insurance Act. 32 Long-term Care Insurance in Japan. Ministry of Health, Labour and Welfare,. 06 June 2015. 33 Tsutsumi, S. (no date) Long-term Care Insurance in Japan. (Accessed: 25 March 2015).

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5. Conclusion and Evaluation

5.1 Conclusion The increasing ageing population in Machida-city has very significant economic impacts on the nursing-care industry. Theoretically, the ageing population leads to an increase in demand for nursing-care service, a shortage of caregivers, and an increase in its price. This price rise leads to subsidy reduction on other industries and tax increase, both done in order to increase the necessary subsidy on the nursing industry. Through primary and secondary research, my hypothesis was proven to be correct. Data from Insured Long-term Care Service Plan of Nursing-care in Machida-city showed that the increasing ageing population leads to a rise in price, a rapid rise in demand for nursing-care service and an increasing shortage of caregivers, despite a slow rate of increase in the quantity of caregivers. Therefore, subsidy for the nursing industry rose. Interviews with experts confirmed my prediction that subsidies for other industries were reduced. Mr. Ogura mentioned that a balance of tax rise, subsidy cuts, and self-pay rise is important to fix the ageing population problem. However, Nikkei stated that insurance premiums were raised more than taxes to gain more revenue for subsidies, which was not predicted in my research investigation. After such deep investigation for my research question “What is the most significant economic impact of an ageing population on the nursing-care industry in Machidacity, Japan?”, I have come to the conclusion that the most significant economic impact is the lack of money to maintain the nursing-care industry in Machida-city and hence the necessity of collecting money from the public. 5.2 Limitations The data gathered in my research is not all collected and based on the same time period. Perhaps the most recently published data, from 2014, would have been ideal for an accurate investigation. However, some statistics, including the insurance premium data, were only updated every three years, and others were just unavailable. Hence, the time period of the data were not controllable and this could have led to fallacies in my research. Additionally, although I concluded that Machida-city’s ageing population and the lack of money is a very significant economic problem, it would have been more ideal if I could have investigated the level of the significance of the ageing population in neighbouring cities. This would have enabled me to compare and contrast and reflect on the real depth and seriousness of the ageing population problem in Machida-city. 5.3 Unanswered Questions After reflecting on this investigation, it has been thought that ethical and political, rather than economical, factors are necessary to understand the value of the nursing-care industry; hence, in order to create practical solutions for the ageing population in Machida-city, the understanding of the three factors are necessary. For instance, the extent of cutting subsidies on other industries touches on the ethical lives of the elderlies and political aspects of society. Such analysis of the ethical and political factors is beyond my economic scope of this research investigation. These are some unanswered questions that will help solve problems emerging from the ageing population.

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6. Bibliography Books: Anderton, A. G. (2008) Economics. 5th edn. United Kingdom: Causeway Press. Blink, J. and Dorton, I. (2011) Ib Course Companion: Economics Second Edition. 2nd edn. New York: Oxford University Press. Reports: Ishizuka, T. (2015) [Insured Long-term Care Service Plan of Nursing-Care System in Machida-city]. Machida-city Council. (in Japanese) Japanese Law Translation (1997) Long-Term Care Insurance Act. Academic Works: Ministry of Finance (2014) Japanese Public Finance Fact Sheet. Available at: https://www.mof.go.jp/english/budget/budget/fy2014/factsheet2014.pdf (Accessed: 7 July 2015). Tsutsumi, S. (no date) Long-term Care Insurance in Japan. Available at: http://gwweb.jica.go.jp/km/FSubject0601.nsf/cfe2928f2c56e150492571c7002a982c/d 8b158cf95c8a1d849257da80004488d/$FILE/Longterm%20Care%20Insurance%20in%20Japan.pdf (Accessed: 25 March 2015). Websites: Geoba (2015) Japan - 2015 - Statistics and Rankings. Available at: http://www.geoba.se/country.php?cc=JP (Accessed: 30 March 2015). Japan Today (2015) Life expectancy for men and women in Japan at highest ever. Available at: http://www.japantoday.com/category/national/view/life-expectancy-formen-and-women-in-japan-at-highest-ever (Accessed: 2 August 2015). Machida-City Council (2015) [Budgets in 2007-2016]. Available at: https://www.city.machida.tokyo.jp/shisei/gyouzaisei/siyosan/index.html (Accessed: 7 July 2015). (in Japanese) Machida-city Council (2015) [Estimate Outline of Population]. Available at: https://www.city.machida.tokyo.jp/smph/shisei/miraidukurikenkyujo/katudounaiyou/s youraijinnkousuikei.html (Accessed: 4 June 2015). (in Japanese) Menton, J. (2014) Japan Recession 2014: How A Graying Population Impacts Asian Economies. Available at: http://www.ibtimes.com/japan-recession-2014-howgraying-population-impacts-asian-economies-1725024 (Accessed: 30 June 2015). Ministry of Health, Labour and Welfare (no date) Long-term Care Insurance in Japan. Available at: http://www.mhlw.go.jp/english/topics/elderly/care/2.html (Accessed: 10 June 2015). Nikkei (2014) Better-off Japanese to pay more for nursing care. Available at:

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http://asia.nikkei.com/Politics-Economy/Policy-Politics/Better-off-Japanese-to-paymore-for-nursing-care (Accessed: 5 June 2015). Riley, G. (2015) Opportunity Cost. Available at: http://beta.tutor2u.net/economics/reference/opportunity-cost (Accessed: 26 May 2015). The Japan Times (2015) Shortage of nursing care workers. Available at: http://www.japantimes.co.jp/opinion/2015/07/07/editorials/shortage-of-nursing-careworkers-2/#.VhNq8BNVikp (Accessed: 8 July 2015). The World Bank (2014) Population ages 65 and above (% of total). Available at: http://data.worldbank.org/indicator/SP.POP.65UP.TO.ZS (Accessed: 30 June 2015). Tokyo Bureau of Social Welfare and Public Health (no date) [Nursing-care Visits]. Available at: http://www.fukushihoken.metro.tokyo.jp/kourei/hoken/kaigo_lib/tuutitou/2_houkai.ht ml (Accessed: 6 May 2015). (in Japanese)

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Appendix Appendix A

Questions asked at Interviews: I. Mr. Masanobu Ogura - Japanese Parliament politician representing Machida-city 1. What do you think is the biggest impact the ageing population has? 2. How do you think it impacts the Japanese government? 3. How should the government manage their money for the ageing population? 4. What do you think are the current problems in the nursing care industry in Japan? 5. How do you think it will impact the nursing industry? 6. In order to prevent the problems from occurring from an ageing population, what must the government do for the nursing industry? II. Mr. Mitsuyasu Watanabe â&#x20AC;&#x201C; Machida-city nursing care-home entrepreneur 1. What do you think is the biggest impact the ageing population has? 2. What impacts does it have on the Japanese economy? 3. What impacts do the economic difficulties of an ageing population have on the nursing care industry in Japan? and in Machida-shi? 4. What do you think are the current economic problems in the nursing care industry in Japan? 5. With a shortage in supply of nursing care workers, how should one improve the nursing care industry and the ageing population? 6. What type of support to the industry is necessary? III. Mr. Asuka Suzuki - chief head of social security of the Machida-city council 1. What do you think is the biggest impact the ageing population has? 2. What impact does this have on the Machida-city council face? 3. How does this impact the nursing-care industry in Machida-city? 4. How does the council manage with a lack of caregivers?

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Can We Accurately Predict the Lift of a Toy Helicopter?

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Felix Wood - Physics In the fall I will begin studying to become and aerospace engineer making it only natural to investigate a related topic for my extended essay. Having recently spent a week with AugustaWestland, a helicopter manufacturer, I decided on an investigation related to helicopters. Initially I planned to use a remote control quadcopter to investigate an equation to calculate lift, however after a few initial tests I landed on the use of a simple helicopter for more accurate data. Formulating my argument from large amounts of data took time yet I was able to organise a solid argument and conclude that the equation was somewhat accurate. Prior to my experiment I had researched multiple theoretical equations for lift so I knew it would be difficult to confirm any one of them however I was able to demonstrate a correlation between variables in equations and my data as proof. The extended essay provided me with useful experience in laying out a complex argument and an entertaining few months flying a toy helicopter around making it very worthwhile.

Supervisor: Dr Steve Sharp Felix is fanatical about all aspects of human flight. He enthusiastically drove this Extended Essay, bringing in 2 toys from home: his quadcopter and the helicopter he finally chose to use after preliminary experiments. Finding the frequency of the rotor blades proved tricky and it was only Felixâ&#x20AC;&#x2122;s perseverance that allowed his data to be accurate and reasonably precise. He does not particularly dwell on this issue in his essay, but he took quite some time to ensure the rotor blade was not a multiple of the frequency measured. This involved marking one with white tape, to eliminate a half-frequency value measurement and comparing the rotor speeds with another rotor with known frequency. The research question gave an interesting angle to this particular investigation. How much of the lift could be determined generically and how much was specific to the particular helicopter toy. Felix worked independently and enjoyed the freedom offered by project work. He has taken much from the experience. This essay has only fuelled Felixâ&#x20AC;&#x2122;s further aeronautical ambitions.

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Contents Introduction 224 Experiment 1

228

Experiment 2

233

Conclusion 235 Evaluation 235 Bibliography 236

Abstract This essay focused on understanding the relationships between factors that affect the lift produced by a toy helicopter, and specifically if it is possible to clearly define an equation for lift. That is, as a research question, “Can we accurately predict the lift of a toy helicopter?” Using Newton’s second laws of motion, plus energy transfer, two equations for the lift of the toy helicopter were generated. One suggesting how the lift depends on the rotational frequency of the helicopter blades and the other predicting the lift is proportional to the square of the airspeed below the blades. To test these predictions my procedure was to carry out two different, but related experiments. One was to measure the frequency of the rotor blades and the corresponding lift values. The second measured the lift at varying airspeeds below the blades. The first experiment involved fixing the helicopter to an electronic balance and altering the frequency to achieve different values of lift. A stroboscope was positioned above the helicopter blades to determine the frequency at which the blades were rotating. The lift was calculated from the change in mass of the balance reading. The second experiment involved measuring the airspeed below the rotor blades whilst also recording values for the frequency. This allowed a graph of airspeed squared against lift to be produced. Due to the need to use airspeed values in the calculation of the lift, my results suggested that knowing the frequency of the blades alone was insufficient to accurately predict the lift of the toy helicopter. However, once the airspeed below the blades had been experimentally determined as a linear function of the blade frequency, we could get close to predicting the lift of the toy helicopter. The discrepancy between the experimental and theoretical lift values was just 6%.

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Physics EE

May 2016

Felix Wood - Physics

Introduction Can We Accurately Calculate the Lift of a Toy Helicopter? Scope: This essay will focus on exploring the relationships between the main factors that affect the lift created by a toy helicopter; the various relationships will revolve around airspeed below the blades, frequency and speed of the blades, the rotor inflow ratio and lift. My emphasis for this essay stemmed from a week of work experience at the UK branch of Augusta Westland. A unique firsthand experience there, along with various lessons on aerodynamics, inspired an interest in rotor craft. Helicopters have become an integrated part of society through their uses in search and rescue, travel and defence; they rely on aerofoils to produce the lift necessary to fly. An aerofoil, simply put, is just a shape (see figure 11); however its ability to produce Figure 1: Shape of an Aerofoil a force in a specific direction, lift, makes it an extremely useful shape. Lift is provided when an airflow is produced over the aerofoil; the faster the air passes over, the more lift is provided. Alternatively, the higher the frequency of rotation, of a helicopter rotor, the faster the speed of the air passing over it meaning more lift; at the same time air is pushed downwards due to the angle of attack of the rotor blades. This model for flight provides the variables that I will be investigating so to determine whether we can accurately predict the lift of a toy helicopter. Approach to the Question: My research lead me to an equation for helicopter flight based around relatively simple physics ideas. I decided to base my investigation around the variables in the equation, looking to prove or disprove the relationships proposed by the equation. To do this I decided on collecting data through two experiments. The first experiment was to find how the lift created by the toy helicopter depended on frequency of the rotor blades. Applying this relationship to the equation derived in the relevant theory section, I was able to conclude on the accuracy of this method for predicting lift. The second experiment was to investigate the airspeed created at different frequencies, and the relationship between airspeed, below the rotor blades, and the lift created. Further comparing the resultant data from the experiment with the theoretical equation I was able to determine a second method for predicting lift. Comparing these methods and results allowed me to conclude on my research question.

https://upload.wikimedia.org/wikipedia/commons/thumb/5/55/Aerofoil.svg/1280px-Aerofoil.svg.png

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Felix Wood

Physics EE

May 2016

Relevant Theory: The aerodynamic design of a helicopter makes it very difficult to develop an accurate equation for the total lift provided. Every helicopter rotor blade follows a similar shape. Towards the central hub the angle of attack of the blade is much steeper due to a lower blade speed; however the further away from the rotor hub you move, the faster the blade travels. This allows a smaller angle of attack to provide the same amount of lift so creating an even lift across the width of the rotor blades. This results in all helicopters having twisting blades instilling potential inaccuracies into any equation for lift. The basis of my experiments was to test the relationships proposed by an equation for the lift produced by a rotor craft. Air, with density ρ, given the value of 1.2 kgm-3 (2), is pushed through the area, A, swept out by the rotor blades, see figure 23, at a velocity, v. Density of air is given by, Density (ρ/kgm-3) = mass (m/kg) / volume (V/m3) m = ρV Where the volume = area x height, where height is the distance through which the air is propelled at velocity, v; therefore height (distance) = velocity x time taken for air to travel through the blade are. Substituting, m = ρAh = ρAvt So that the rate at which air is propelled through the rotor area, dm/dt, is the product of the air density, ρ, the area covered, A, and the velocity of the air directly above the rotor plane, v, measured in ms-1. The force, F exerted by the rotor is equal to the change in momentum of the air over the time that it’s being propelled, (Newton’s second law4) i.e:

Figure 2: Area Swept out by Helicopter Blades

F = dp/dt As momentum = mass x velocity, if the velocity of air is constant, the force: F = (dm/dt)w Where w is the airspeed below the rotor plane, measure in ms-1. The work done by the blades on the air is transformed into kinetic energy. The rate of work done is given by:

https://www.grc.nasa.gov/www/k-12/airplane/airprop.html http://www.aviastar.org/helicopters_eng/mi-54.php 4 http://www.physicsclassroom.com/class/newtlaws/Lesson-3/Newton-s-Second-Law 3

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Felix Wood

Physics EE

May 2016

Fv = (1/2)(dm/dt)w2 Figure 35 distinguishes between v and w. Dividing this by the previous equation we get, w = 2v Substituting this relationship into the equation F = (dm/dt)w, we get the force exerted by rotor blades: F = 2(dm/dt)v Which can then be written as:

Figure 3: Flow of Air Through Helicopter

F = 2ρAv2

Finally, we can define a constant, for each different helicopter, called the rotor inflow ratio, λ, which is defined as the ratio between the speed of the air, v, and the speed of the tip of any rotor blade, ωR, measured in radians per second. Where R is the radius of the circle swept out by the blades, or the length of a blade and ω is the rate of change of the angle, ϴ, over time, also called the angular velocity. λ = v/ωR Experiment 1: Application of Theory How does the frequency of the helicopter blades affect the lift. Varying frequency of blade rotation, recording change in weight, i.e lift produced. Showing the proportional relationship between the lift produced and the frequency, of the rotor blades, squared. Following on from the equation produced on the last page, F = 2ρAv2, we can substitute in for v by rearranging the rotor inflow ratio formula. F = 2ρAλ2ω2R2 We can then substitute for ω, the angular frequency/velocity (Hz): ω = 2𝜋𝜋ƒ and for the area, 𝐴𝐴 = 𝜋𝜋𝑟𝑟 2 F = 2ρ(𝜋𝜋𝑟𝑟 2 )λ2(2𝜋𝜋ƒ) 2R2 Lift = F = 8𝜋𝜋3ρλ2R4ƒ2

Thus providing us with an equation to show the proportional relationship between lift and frequency squared, since all variables before become some constant, k, so that: Lift = F = kƒ2 To calculate k, we need R, the length of a blade, and a value for λ which can be found using value for w, since w = 2v.

5 6

http://seniorphysics.com/physics/helicopterEEI.pdf http://seniorphysics.com/physics/helicopterEEI.pdf 226

Felix Wood - Physics

Felix Wood

Physics EE

May 2016

Experiment 2: Application of Theory How does the airspeed below the blades relate to the lift produced? Varying frequency of blade rotation to record airspeed below the helicopter and recording lift at different airspeeds to show the proportional relationship between lift produced and the airspeed, below the rotor blades, squared. Continuing on from the equation presented above, F =��ρ��2�2R2, we can substitute the equation for the rotor inflow ratio, �, to get: F =��ρ�(v/��)2�2R2 Simplifying this we get an equation relating lift and the airspeed above the rotor blade squared; however as we previously showed, w = 2v. Therefore the following can be derived: F =��ρ��2 F = (1/2)ρ��2 F = (1/2)ρ R2w2 ��e final equation shows the proportional relationship between lift and the airspeed squared, since, as previously seen, all other terms become one constant value, M, so that:

Lift = F = Mw2

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Felix Wood - Physics

Felix Wood

Physics EE

May 2016

Experiment 1: Description Showing the proportional relationship between frequency squared and lift produced from the rotor blades. Method: A simple setup was used to both measure frequency and lift at the same time. As seen in figure 2, two lab jack held a stroboscope vertically above the helicopter, which was attached to the electronic top ban balance. Using the remote controller for the helicopter, throttle power was applied to increase the frequency at which the blades rotated, at the same time the stroboscope was adjusted to obtain the actual frequency. Measurement of the frequency was a difficult process, with relatively high errors; to obtain the frequency the stroboscope was adjusted until the light flashes matched the rotation of the blades. The matching frequency would cause the helicopter blades to appear quite still; however it was difficult to achieve a still image. The uncertainty in the bladeâ&#x20AC;&#x2122;s frequency was estimated as Âą 2 Hz. Figure 4: Experiment 1 Setup Lift was calculated by measuring the initial mass of the helicopter, adjusting the throttle, recording the reading given by the balance, and subtracting this value from the initial mass. The throttle was adjusted on the remote controller provided with the helicopter; no value for throttle percentage is provided resulting in a specific throttle level, and frequency, not being reproducible.

Measuring the lift produced was also a challenge as the uneven surface meant the reflected air interfered with the true lift being produced; however the same setup and position of the helicopter was used throughout to keep the error standard across all data points. Further errors were introduced due to the battery life of the helicopter; whilst running, the battery was unable to provide exact constant power meaning the frequency slowly decreased even without making a movement on the remote controller. To counter this issue a few data points were taken at a time, allowing the helicopter to charge fully in between data sets. When recording data I would start the helicopter rotating then quickly adjust the stroboscope to a similar frequency, record the value and subsequently record the mass reading on the electronic balance. To achieve a range of frequency values I would move the throttle from the lowest to the highest position for each set of data points 228

Felix Wood

Physics EE

May 2016

Felix Wood - Physics

and repeat this process after charging the helicopter fully. This resulted in a good range of frequency values from which graphs were created. Results: Frequency, f/Hz ± 2 27 31 33 34 36 38 40 43 46 46 47 49

Frequency squared, f2/ Hz2 729 961 1089 1122 1296 1444 1560 1849 2070 2116 2209 2352

Uncertainty in f2, Δf2/Hz2 110 120 130 130 140 150 160 170 180 180 190 190

Lift, L/N ± 0.02 N 0.12 0.18 0.20 0.20 0.24 0.27 0.29 0.35 0.39 0.41 0.44 0.45

Figure 5: Frequency and Lift Data

Figure 5 shows the data from experiment 1, including the frequency values, and their corresponding lift values. The uncertainty in the frequency, ± 2 was an estimate of the error created by the difficulty using the stroboscope. As explained earlier, matching frequencies cause the rotor blades to appear almost still; however this was never the case meaning an error needed to be introduced. The lift, in newtons, was calculated by taking the difference between the original mass of the helicopter and the mass recorded on the balance, and multiplying by the acceleration due to gravity, g (9.81 Nkg-1). The error in the lift was due to the fluctuations in the mass values as a result of the turbulent air interfering with the helicopter. 0.50

Line of Best Fit: Lift = 0.000205f2 - 0.0273

0.45

Helicopter Lift, L/N

0.40 0.35

Max Gradient: Lift = 0.000252f2 - 0.0898

0.30 0.25

Min Gradient: Lift = 0.000173f2 + 0.0143

0.20 0.15 0.10 0.05 0.00

500

1000

1500

Blade Rotation Frequency

2000

2500

3000

squared, f2/Hz2

Figure 6: Graph of Lift against Frequency Squared

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Felix Wood - Physics

Felix Wood

Physics EE

May 2016

The results of the helicopter lift as a function of blade rotation frequency can be seen in figure 6. The lift is found to be proportional to the blade rotation frequency squared, specifically: Lift = kf2 +c Where k = 8𝜋𝜋3ρλ2R4 and c is representation of the inaccuracy in the data. To confirm the proportional relationship between lift and frequency squared, the value for the constant, k, should be roughly the same as the gradient of the line of best fit shown in figure 4. To determine k, the following was calculated: 8𝜋𝜋3ρλ2R4, the only unknown value here being λ, the rotor inflow ratio. To calculate λ for the toy helicopter the following was done: λ = v / ωR = (1/2)w / 2𝜋𝜋ƒR λ = w / 4𝜋𝜋ƒR However immediately an issues is presented as we cannot confirm a relationship by calculating a constant using collected data. The above equation shows that we would need a value for w, the airspeed below the blades, to calculate λ. This unfortunately means that any calculation involving the rotor inflow ratio, λ, can be used to accurately predict the lift of the helicopter. None the less the value of λ can be calculated and as a result a value for the constant, k, can be found and compared to gradient of the line of best fit shown in figure 6.

Experiment 1: Part II Experimentally determining the unique value of the rotor inflow constant, λ, to calculate a value for the constant k. Setup: Similar to the first experiment, a stand was built above the helicopter to hold the stroboscope in place, just out of view in figure 7. A stand was then used to hold a clamp which held the helicopter in place, elevated above the ground. The anemometer was then clamped 8 centimetres blow the rotor blades, with no objects obscuring the path of air. The distance of 8 cm was chosen as it was far enough below the rotor blades to be within the well-defined air stream. The anemometer was also positioned below the middle of the rotor blades so to make sure it was not in the dead spot of air directly below the helicopter body. Figure 7 proves a full view of the setup. As this was the second experiment, it was carried out further on in the day at which point I’d had the idea 230

Figure 7: Experiment 2 Data Collection Setup

Felix Wood - Physics

Felix Wood

Physics EE

May 2016

to keep the helicopter on charge whilst using it to collect data. This change to the setup meant a somewhat constant level of power was being supplied to the helicopter; however the helicopter still uses battery charge faster than the battery can charge meaning power was still depleting, only at a slower rate. As in experiment 1, the remote control was used to vary the throttle, and directly control the frequency at which the blades rotated. Data was collected by setting the helicopter to function at a frequency, at which point I adjusted the stroboscope to match frequency with the rotor blades, and then the airspeed displayed on the anemometer’s digital screen was recorded. With this experiment there was again error being produced by the inaccuracy of the stroboscope; however the airspeed measurements were quite accurate and little error was involved. The height of the helicopter also meant that turbulent air bouncing off the surface below interfered less with the results. Results: Frequency, f/Hz ± 2 19 22 25 28 31 33 18 20 25 26 42 45

Airspeed, w/ms-1 ± .2 2.0 2.4 2.9 3.4 3.8 4.2 1.9 2.2 2.9 3.2 5.4 5.6

Figure 8: Experiment 1 Part II Data

Figure 8 shows the data collected from experiment 2. As both the frequency and airspeed were noted directly, a fixed uncertainty was considered for both. Error was added to the frequency for difficulty pin pointing the exact frequency, and for having to note the frequency off a visual dial rather than a digital display. A small error was introduced into the airspeed due to small changes presented on the digital display. Graphing the data above and inserting the errors presents us with the graph shown in figure 9.

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Felix Wood - Physics

Felix Wood

Physics EE

May 2016

Airspeed Below Blades, w/ms-1

Line of Best Fit: w = 0.142f - 0.5799

Max Gradient: w = 0.1625x - 1.225

Min Gradient: w = 0.1292f - 0.225

Blade Rotation Frequency, f/Hz Figure 9: Graph of Airspeed against Frequency

The final data point (45, 5.6) was excluded due to it being positioned a small distance away from the line of best fit whilst all other point were located almost directly atop the line. Figure 9 illustrates the relationship between airspeed and frequency. Referring back to page 10 we know: λ = w / 4𝜋𝜋ƒR 4𝜋𝜋R λ = w / ƒ This relationship shows us that the gradient of the line of best fit from figure 9 will be equal to 4𝜋𝜋Rλ; however the value of 4𝜋𝜋R is minimal and can hence be ignored. The value of λ is then the gradient of the line of best fit from figure 6. λ = 0.142 Using this value for λ we can proceed to calculate the constant k to compare with the gradient of the line of best fit from figure 6. Where the radius is 0.08 meters: k = 8𝜋𝜋3ρλ2R4 k = 0.000246 Compared with the value of 0.000205 from figure 6, this leaves us with a percentage error of 16.7%, Felix Wood Physics EE May 2016 a relatively low error. This result is in favour of being able to predict the lift as the theoretical calculation agrees with experimental calculation; however the major flaw in this method is that determining the theoretical value for k relies on data for airspeed and frequency to calculate λ meaning no conclusion can be made based on these results.

Experiment 2

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Showing the proportional relationship between Lift and Airspeed squared

Felix Wood

Physics EE

May 2016

Felix Wood - Physics

determining the theoretical value for k relies on data for airspeed and frequency to calculate λ meaning no conclusion can be made based on these results.

Experiment 2 Showing the proportional relationship between Lift and Airspeed squared Description: Using the airspeed and frequency values recorded earlier, shown in figure 8, we can calibrate a second set of airspeed values which will correspond to the frequency and lift values, from experiment 1, shown in figure 5. This allows for a graph of lift against airspeed squared to be produced and a value for the constant m to be determined from the gradient of the line of best fit. The calibrated values for airspeed can be seen below in figure 10: Frequency, f/Hz ± 2 27 31 33 34 36 38 40 43 46 46 47 49

Airspeed2,w2/m2s-2 10.6 14.6 16.9 17.4 20.5 23.2 25.3 30.5 34.6 35.4 37.1 39.8

Uncertainty in w2 1.6 1.8 2.0 2.0 2.2 2.4 2.6 2.8 3.0 3.0 3.2 3.2

Figure 10: Calibrated Values of Airspeed and Lift Values

Lift, L/N ± 0.02 0.12 0.18 0.20 0.20 0.24 0.27 0.29 0.35 0.39 0.41 0.44 0.45

The frequency values used are from experiment 1. The airspeed was calibrated using the equation of the line of best fit and then squared to get the values shown in the second column. The uncertainty in w2 was calculated by taking the percentage uncertainty in the frequency and multiplying that by the airspeed values. The values for lift are equivalent to those recorded in experiment 1 and so the uncertainty is the same. Using the airspeed squared values and the lift values we can plot the relationship between the two, this can be seen in figure 11.

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Felix Wood

Physics EE

0.50

May 2016

Line of Best Fit: Lift = 0.0114w2 + 0.004

0.45 0.40 0.35

Max Gradient: Lift = 0.0137w2 - 0.0451

Lift, L/N

0.30

Min Gradient: Lift = 0.0098w2 + 0.0333

0.25 0.20 0.15 0.10 0.05 0.00

0.0

5.0

10.0

15.0

20.0

25.0

30.0

35.0

40.0

45.0

50.0

Airspeed2,W2/m2s-2 Figure 11: Graph of Lift against Airspeed Squared

For the proportionality between the airspeed squared and the lift to be true, the proposed constant M (page 7) should be a similar value to the gradient of the line of best fit shown in figure 11. To calculate M the following was used: M = (1/2)Ď đ?&#x153;&#x2039;đ?&#x153;&#x2039;R2 M = 0.0121 This leaves an inaccuracy of 6.1% between the actual value (0.0121) and the experimental value (0.0114). The similarity between the two variables also provides a method for calculating the lift of the helicopter using the equation: Lift = (1/2)Ď đ?&#x153;&#x2039;đ?&#x153;&#x2039;R2w2

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Felix Wood - Physics

Felix Wood

Physics EE

May 2016

Conclusion:

Physics EE

May 2016

Felix Wood

Conclusion: Can we Accurately Predict the Lift of a Toy Helicopter? Experimentally, it has been shown that the relationships between lift and frequency squared, and lift Canthewe Accurately Predict the Lift ofinanature. Toy Helicopter? and airspeed below blades squared, are both proportional This is in agreement with the theoretical predictions. However to compare numerically how the predicted lift depends on the Experimentally, it has been shown that the relationships between lift and frequency squared, and lift frequency of the blades alone, we required values for the airspeed below the blades to determine the and airspeed below the blades squared, are both proportional in nature. This is in agreement with the rotor inflow ratio, λ. Having determined this ratio, the experimental lift values differed by around theoretical predictions. However to compare numerically how the predicted lift depends on the 17% from the theoretical predictions. By experimentally determining the airspeed below the blades frequency of the blades alone, we required values for the airspeed below the blades to determine the as a linear function of the blade frequency though, with just the air density and rotor blade length, we rotor inflow ratio, λ. Having determined this ratio, the experimental lift values differed by around could get close to predicting the lift of the toy helicopter. The discrepancy between the experimental 17% from the theoretical predictions. By experimentally determining the airspeed below the blades and theoretical lift values was then just 6%. as a linear function of the blade frequency though, with just the air density and rotor blade length, we could get close to predicting the lift of the toy helicopter. The discrepancy between the experimental and theoretical lift values was then just 6%.

Evaluation:

Evaluation: My results did agree with the relationships proposed by the formula investigated; however errors throughout both experiments, due to a difficulty in accuracy meant an accurate lift value was not achieved; however results from experiment 2 came quite close. In experiment 1 the need to calculate My results did agree with the relationships proposed by the formula investigated; however errors a value for λ, from experimental data, meant that no conclusion could be made over this experiment. throughout both experiments, due to a difficulty in accuracy meant an accurate lift value was not achieved; however from experiment came quite close.onInpower experiment theaneed to calculate Many of the errorsresults in calculating data were2due to the impact caused1 by depleting abattery. value for experimental data, to meant thathigher no conclusion could be made experiment. As λ, thefrom throttle was increased achieve frequency values, powerover wasthis depleted progressively This issue has a simple solution, using a better and more advanced remote control Many of the errors in calculating data were due to the impact on power caused by a depleting helicopter; however budget issues meant this was not possible. Better equipment, such as a larger battery. As the throttle was increased to achieve higher frequency values, power was depleted more controllable helicopter, would’ve allowed for a stronger and clearer air flow when recording progressively This issue has a simple solution, using a better and more advanced remote control airspeed. helicopter; however budget issues meant this was not possible. Better equipment, such as a larger more controllable forby a stronger and air flowwhich whenwas recording Uncertainties and helicopter, limitations would’ve were also allowed introduced the use of theclearer stroboscope a very airspeed. inaccurate apparatus as it relied highly on my own judgement as to when the blades appeared to match frequency with the stroboscope. The stroboscope also used a small dial with a moderately Uncertainties and limitations were also introduced by the use of the stroboscope which was a very small circumference to change the frequency, this meant the precision of the stroboscope was limited inaccurate apparatus as it relied highly on my own judgement as to when the blades appeared to to ± 2 Hz. match frequency with the stroboscope. The stroboscope also used a small dial with a moderately small circumference to change the frequency, theofprecision of thethe stroboscope limited As seen in figures 2 and 7, the helicopter usedthis hadmeant two sets rotor blades, purpose ofwas which is to to ± 2 Hz. the rotation of the helicopter body by having two equivalent sets of blades spinning in counteract opposite directions. This mechanism could have possibly effected the airspeed data due to the As seen in figures 2 and 7, the helicopter used had two sets of rotor blades, the purpose of which is to opposite paths of airflow. counteract the rotation of the helicopter body by having two equivalent sets of blades spinning in opposite directions. This mechanism could have possibly effected the airspeed data due to the opposite paths of airflow.

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Physics EE

Felix Wood - Physics

May 2016

Bibliography: (n.d.). Retrieved from https://upload.wikimedia.org/wikipedia/commons/thumb/5/55/Aerofoil.svg/1280pxAerofoil.svg.png (n.d.). Retrieved from Aerospace Students: http://aerostudents.com/files/aircraftPerformance2/helicopters.pdf Green Bay West IB. (n.d.). Retrieved from Green Bay Area Public School District: http://www.gbaps.org/hs/West/IB/Documents/Formal_Presentation_of_the_Extended_Essay.pdf Hall, N. (2015, May 5). Air Properties Definitions. Retrieved from National Aeronautics and Space Administration: https://www.grc.nasa.gov/www/k-12/airplane/airprop.html Liebl, M. (2015, May 21). Investigating Flight With a Toy Helicopter. Retrieved from seniorphysics: http://seniorphysics.com/physics/helicopterEEI.pdf Mil Mi-54 Project. (n.d.). Retrieved from aviastar: http://www.aviastar.org/helicopters_eng/mi-54.php Newton's Second Law. (n.d.). Retrieved from the Physics Classroom : http://www.physicsclassroom.com/class/newtlaws/Lesson-3/Newton-s-Second-Law Scott, J. (2001, February 25). Lift Equation. Retrieved from aerospaceweb.org: http://www.aerospaceweb.org/question/aerodynamics/q0015b.shtml

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