Junior Project Prize - 2021

JUNIOR PROJECT PRIZE 2021

CONTENTS Battle of Cannae (P)

Tom Payne (Remove)

First Light Piano Composition (P)

Ed Maxwell (Shell)

Are SPACs a bubble? (SM)

Gabriel George Remove)

Scale Model of House (SM)

Freddie Scott (Shell)

New Language Che Melj (SM)

Bernardo Mercado (Remove)

Have things improved? (C)

Mikolaj Rutka (Shell)

Tapas (C)

Will Rosling (Remove)

British Education (P)

Harkirat Malhotra (Shell)

Calculus (SM)

Hyunjo Kim (Remove)

Starting a Business (SM)

Rory van der Grift (Shell)

Red Tsar Poem (C)

Milo Donovan (Remove)

A Revolution in the 21st Century (C)

William Roques (Shell)

Pizza Oven (SM)

Oliver Stanley (Remove)

The Future of Drones (SM)

Rex Singlehurst (Shell)

VTAHD Booster Recovery System (SM)

Max Lian (Remove)

The History of Bosnia and Herzegovina (C)

Max Dawson Paul (Shell)

Supplements (C)

Jo Ashford (Remove)

The Speed of Light (P)

Yiyang Xu (Remove)

Images of Black Holes (SM)

Luca Hargreave (Remove)

Heroes of Telemark (P)

Angus Lowrie (Shell)

Piano Compositions (P)

Kim Chin (Remove)

(C) Commended (P) Prize (SM) Special Mention

INTRODUCTION

During Summer Term 2021 Shell and Remove boys were once again challenged to complete a short project on a subject of their choice. The purpose of the exercise was to celebrate students’ individual interests and passions. It was expected that the work should be scholarly and of use and interest to others. As before, the task was purely voluntary and the mode of submission up to them.

In 2020 the Academic Prefects mentored Junior submissioners and had the job of selecting and judging the best work. Chosen projects were then sent up to the Warden for his appraisal and prize selection. The same process was followed in 2021, but such was the variety and quality of the projects that more contributions were sent up for consideration. Nearly 50 boys entered, and this document celebrates the work not just of the winners and those commended, but also submissions recognised for special mention. Amongst these pieces are exceptional contributions from past winners as well as attractive and original projects that fell just short of the prizes. Where possible, the original formatting has been preserved and work has not been edited.

Ralph Woodling Master in Charge Scholarships

FOREWORD

The Junior Project Prize was a highlight of 2020 and so it was with relish that I received the 2021 selection from the Academic Prefects for my judgement. Once again, submissions spanned an extraordinary breadth of topics and were presented in all formats. Shell prize winners from 2020 featured strongly in the Removes as well as a host of new contributors.

It was a joy to read more original works of fiction and poetry and to experience some astonishingly accomplished musical compositions. As usual, there were some tremendous, traditional, written works on such diverse subjects as The Speed of Light, and the History of Bosnia and Herzegovina. Video submissions were more numerous this year with boys both narrating and starring in their productions, demonstrating technical expertise, initiative and talent that will serve them handsomely after Radley.

Above all, it is very clear to me that academic passion runs deep in our Junior boys. This selection of submissions celebrates outstanding scholarship and cultural richness, and in all cases represents some serious hard work.

In commending this selection of work to you I salute all Shells and Removes who contributed to The Junior Project Prize and have set themselves apart with their fantastic endeavours. My thanks again to Mr. Woodling, Mr. Barlass and to the Academic Prefects for overseeing this great enterprise.

John Moule Warden

TOM PAYNE the battle of Cannae

The History and Significance of The Battle of Cannae by Tom Payne is a very thorough video presentation of the The Battle of Cannae and the lessons is taugh ancient Rome.

Huge amounts of research and industry. Polished and articulate. Lovely pace and enthusiasm.

Click here to watch a video detailing the Battle of Cannae and the lessons it taught Ancient Rome.

ED MAXWELL FIRST LIGHT PIANO COMPOSITION The First Light piano composition by Ed Maxwell is a delightful musical composition influenced by dawn walks during lockdown.

The first section is based on the sun rising and lighting up the sky. The reason this section is the most dramatic is because it demonstrates when light has been completely absent for several hours before it then lights up the sky.

The second section, however, represents the beauty of the morning sunrise and the colour of the clouds and the silence and calmness before any human has got up. Sunrise is often the quietest place in the day and the most peaceful.

Click here to listen.

GABRIEL GEORGE are spacs a bubble?

The rise of SPACs by Gabriel George SPACs have been around for many years, they are ‘Special Purpose Acquisition Companies’, also known as ‘blank cheque companies’ set up, to acquire other companies.

For many years, SPACs were a quiet backwater of the US stock market, however recently they have gained prominence; this has been due to the demand from public stock market investors to access growth companies that do not necessarily fit the criteria to be IPO-ed (typically to be IPO-ed a company needs to have positive earnings, however most companies in their growth phase lose money, and have negative earnings as they grow into their market. This makes them unsuitable to for IPO), and some tweaks in the mechanism in the ‘de-SPAC-ing’ process that made the process easier. De-SPAC-ing refers to the process of actually combining the SPAC with the target acquisition company.

In 2020, there was $83.4b of capital raised on the NYSE and NASDAQ for 248 SPACs (up from $13.6b for 59 in the previous year) and so far in 2021, there has been $100.8b raised to date for 311 SPACs. To put this in context, in the US, there were 494 IPOs in all of 2020 with $174b raised up from $65.4b for the 242 IPOs in the previous year.

It’s little wonder that the new issue equity businesses at large firms (such as Goldman Sachs, or Morgan Stanley) had such strong fee income in 2020.

To understand why SPACs have become so popular, one needs to understand the structure of SPACs and how they can be used to acquire companies; the sort of companies that SPACs target; and, finally, why the owners of these companies would find it attractive to be acquired by a SPAC. Small Company Capital Formation in the US Before the early 2000s, the NASDAQ was the preferred destination of choice for smaller growth companies to raise new equity growth capital. However, during the early 2000s, the governing body of the NASDAQ forced the market makers to decrease their bidoffers through decimalization (previously the bid offer in stocks were quoted in 1/8th of a percentage point, which equals 12.5 cents, after decimalization the bid offer of NASDAQ stocks was required to be 1 cent). This was done ostensibly to help the everyday retail investor decrease their transaction costs; however, it had an unintended consequence. It meant that the smaller and less liquid stocks became less profitable to trade. This resulted in fewer analysts covering these stocks and fewer pools of capital investing in these companies.

With less capital investing in publicly traded small growth companies, these companies had to find alternative sources of capital to fund their growth. They found this capital in the private markets from venture capital firms such as Sequoia and Andreessen Horowtiz, based on Sand Hill Road in San Francisco. These companies, which had traditionally been the providers of seed and early-stage venture capital, were able to extract very good terms for themselves.

GABRIEL GEORGE Therefore, rather than going public, these companies have ended up staying private for much longer periods; and hence the proliferation of private companies valued at $1b+ (‘unicorns’) in the US. Faced with this dearth of publicly traded high growth smaller companies, US stock market investors had a massive appetite when SPACs enabled them to access this risk.

SPACs have typically combined with late-stage venture companies that are backed by venture capital funds. Given the narrative about Silicon Valley VC investors making large profits by investing in these companies, retail investors were keen to invest; unfortunately, retail investors had been ‘price takers’, and have not been able to extract as attractive terms and valuations as the VC funds did when they provided this growth capital; hence the retail investors have paid high valuations via SPACs for these growth companies.

SPAC 2.0 When the money for a SPAC is raised in the stock market through an IPO, the company takes the money and invests it in a trust account for the investors. The capital is held safely in the trust account for two years (24 months) and if a company is not found to combine with, the money is returned to the original IPO investors.

Each new SPAC has a sponsor, which is a group of financial professionals, and/or operating partners in a specific business area who are responsible for finding the acquisition targets.

Once an acquisition target is found, and the deal consummated, the sponsor group is awarded ‘founder’s shares’ in an amount equivalent to 25% of the initial IPO shares. Additionally, as compensation for locking their capital up in the trust account (as mentioned previously) for up to two years, the IPO investors are given options to buy more of the stock at a price typically 15% higher than the IPO price. Therefore, if the stock does well, after the de-SPACing process, the original SPAC shareholders will make additional profits from these options.

Before 2019, if the IPO shareholders wanted their money back, they would have to vote against the combination. This meant that if the company being acquired was not attractive, the business combination would usually not go through, because a majority of the IPO shareholders would vote against the combination in order to get their money back. However, in 2019, SPAC 2.0 presented a new structure whereby the IPO shareholders could vote for the combination, yet still get their money back. This had the effect of making the business combinations more likely to go through; all the sponsors had to do was to find new investors to take the place of the redeeming IPO investors who wanted their money back. These investors are known as PIPE (private investment in public equity) investors, and the entire process is known as de-SPAC-ing.

Due to the fact that the SPAC shareholders can always get their money back, it can be assumed that the combination will always be voted for. However, for the de-SPAC-ing process to be completed the sponsor group must find a sufficient number of PIPE investors to take the place of any of the original SPAC investors who opt to vote for the deal, but to get their money back.

GABRIEL GEORGE Dilution Because the amount free founder shares awarded to the sponsor group is such a large percentage relative to the initial SPAC amount, the shareholders require the acquired company to be significantly larger than the SPAC itself so that the free founder shares do not overly dilute the number of outstanding shares of the combined entity. For example, if a $200m SPAC awarded $50m of free shares to the sponsor group, it would result in a 20% dilution, if the new entity was the same size as the initial SPAC. Whereas, if the target was acquired at a $1b valuation, with the SPAC holders getting 20% of the $1b company and the acquired company shareholders owning 80%, the $50m founder share award would only result in a 5% dilution to the business combination shareholders. This is much more palatable to the shareholders.

Misalignment between the sponsor group and the stock investors In the private equity investment business, sponsors typically acquire a company, work on its operations, and then sell the company at a higher price. The capital used to fund these investments typically comes from third party investors (other people’s money, ‘OPM’). The sponsor group usually takes 20% of the profits generated upon the sale. This is the opposite of how a SPAC works, as in SPACs the sponsor groups are awarded founder shares at the initial acquisition rather than the exit. Many commentators have pointed out that this creates an incentive for the sponsor group ‘just to do a deal’. Additionally, the sponsor group has to fund the cost of doing the initial IPO, the ‘risk capital’, this creates other problems. This risk capital is typically $6m for a $200m SPAC and can be provided either by the sponsor group itself or by a third party.

If the capital is provided by a third party, it will typically have first rights to a preferred return when the founder shares are sold. The founder shares typically cannot be sold until 6 months after the business combination is executed. By way of example, in a $200m SPAC, if the $6m of risk capital were to be provided by a third-party investor, this investor would typically require receiving the first $18m (3x initial investment) when the founder shares were sold. This leaves approximately $32m for the sponsor group. However, this occurs only if the stock of the business combination were to maintain its IPO price at the time the founder shares were sold. If in 6 months’ time, the stock of the business combination had fallen 60%, the risk capital provider would still get their 3x MOIC (multiple on invested capital), yet in this case, the sponsor would only have $2m. This, in theory, should incentivize the sponsor group to combine with a company that they think will hold its valuation. Though, if a business combination had not been executed and time was running out, the party who provided the risk capital might pressure the sponsor group to do a sub-optimal deal, as if a deal is not consummated within two years, they would lose the risk capital.

It’s all about the PIPE Securing investors for the SPAC IPO is relatively easy. This is because these investors really take very little risk because their money is invested in US Treasuries in the trust account (as mentioned previously), and they can always get their money back whether or not the business combination is approved or not. These investors do incur an opportunity cost by not having their capital available while it sits in the trust account invested in low-yielding treasuries for up to two years.

GABRIEL GEORGE To compensate them for this opportunity cost the SPAC IPO investors are also awarded warrants to purchase more SPAC stock. These warrants are typically ‘out of the money’ by 15% (i.e., the strike price = $11.50 if the SPAC IPO price = $10) and have an expiration of up to 2 years after the IPO. There are various options strategies employed by sophisticated hedge fund investors to isolate the value of the SPAC options/warrants that help create demand for the SPAC IPO stock.

Given that many of the SPAC IPO shareholders would be expected to redeem their shares and be left holding only the warrants after the business combination is executed, no matter if they approved of it or not, the sponsor group and its bankers would have to raise capital to replace these redeeming shareholders. On top of this capital, to replace the ‘redeemers’ (potentially 100% of the SPAC IPO amount), there could also be additional amounts needed to be raised if the acquisition target required more cash than the amount that was raised in the SPAC IPO to convince the target’s owners to agree to the combination (e.g. the target’s shareholders might require $300m for 20% stake in their company (for a valuation of $1.5b) leaving them with an 80% stake valued at $1.2b, or perhaps they might require $400m for a 30% stake and a $1.33b valuation; in both cases even if none of the SPAC shareholders redeemed there would still be capital required to be raised in a PIPE).

The target’s shareholders are exchanging their private stakes in the target for publicly traded shares, so they generally aren’t actually investing additional capital into the newly combined business; the only parties concerned about the valuation of the stock of the newly combined business are the PIPE investors and whatever SPAC IPO investors who decided not to redeem.

Therefore, to consummate a successful de-SPAC-ing, the sponsor group and its bankers must be able to access investors in PIPE capital and convince them of the valuation of the new business combination... ‘It’s all about the PIPE’.

PIPE investors can be Private Equity funds, Hedge Funds, or more likely investors in public growth equities, who want to get into the stock at a discount (PIPEs are normally priced at a small discount to the $10 IPO price); investors such as Blackrock, Fidelity, etc. are large public equity investors who might invest in a PIPE. Since finding PIPE investors is so important to the business combination, the PIPE investors have a lot of leverage over the sponsor group and might well be able to negotiate some of the free founder shares that the sponsor is due to receive for themselves. Therefore, while the headline number shows the sponsor receiving $50m worth of founder shares for a $200m SPAC IPO, in actuality, the ‘risk capital’ and PIPE investors will take a significant portion of these shares. The actual amount of the founder’s shares that the acquisition targets owners are able to secure for themselves depends on the valuation that the sponsor group is willing to acquire the company at, and on the strength of the sponsor group itself; a strong sponsor group should be able to secure all the founder shares for themselves however a weaker group may have to give up approximately 50% (of their founder shares).

What private companies would combine with a SPAC? Since 2019, most of the business combinations with SPACs have involved high growth private companies worth $1b+ (unicorns). These companies have not necessarily been suitable for IPO

GABRIEL GEORGE as they do not usually have profits despite having substantial revenues. A combination with a SPAC on the other hand enables the company to achieve a stock market listing, without having to prepare a prospectus and to show projected earnings to prospective stock investors; this is different from an IPO, in that in an IPO projected earnings are not allowed to be taken into account, thus companies that are losing money currently however are projected to make lots of profit in the future can be taken to the stock market through a SPAC instead. A combination with a SPAC should not be thought of as an acquisition, as the target company’s management usually remains in place with the sponsor generally being represented on the board of the new company.

These growth companies are generally consuming large amounts of capital at this stage of their lifecycle, as they burn cash to establish market share. Thus, it has not been uncommon to see private growth equity raises in the 100s of millions of dollars at this stage. There are many large private funds that invest in this ‘growth equity’. These funds can be over several billion dollars in size and make investments larger than $100m into growth companies.

New venture capital backed companies raise capital at the incubation/seed stage, then as the business is proven out and built, there are incremental capital raises called Series A, B, C and D, etc. rounds. These raises take in more and more capital at (hopefully) higher and higher valuations. The key to a successful growth and capitalization process is for these larger later rounds to be done at higher and higher valuations, in order not to dilute the earlier shareholders too greatly.

For example, if a company raised $20m in its Series A at a $100m pre-money valuation, the Series A shareholders would own: = (20/(100+20) * 100 = 16.66% of the company after the raise.

If in one year, say, the company had gone through all this cash and needed another $30m to continue its growth trajectory (paying for sales and marketing to get new clients for example), the company might be able to raise this $30m at a substantially higher valuation than the $120m post-money Series A valuation.

Say it could raise the $30m at a $350m pre-money valuation, this would mean that the Series A’s 16.66% was worth $58.33m before the $30m Series B went in.

After the $30m went in the Series B shareholders would own: (30/ 30+350)) *100 of the company = 7.8%.

The original Series A investors would own: (16.66*(Pre-Money(B) Valuation)/((Pre-Money (B) Valuation) + Amount Raised in B round))*100% = (16.66%*350/(350+30))*100% = 15.35% If the company only needed $15m, and it could be raised at a $450m valuation (say), the new Series B shareholders would own 3.22% after the capital raise (15/(450 + 15))*100% The Series A holders, in this case, would own 16.666%*450/(450+15) = 16.12% If the company needed $75m, but could only raise it at a $200m pre-money valuation the new

GABRIEL GEORGE Series B shareholders would own 27.3% of the company after the raise, while the Series A shareholders would be left with 12.12% of the company (16.66%*200/(200+75)).

The less money required in later rounds, the higher the percentage ownership maintained by the earlier investors. Similarly, the higher the valuation of the company in these later rounds the higher the percentage ownership maintained by the earlier investors.

To the owner of a target company the combination with a SPAC is equivalent to a capital raise with the added benefit of seeing their shares listed on a stock exchange. Note that the owners cannot sell their shares on the stock exchange until some set time period has finished, typically 6 to 12 months, after the business combination has been consummated, this period is referred to as the ‘lock up’. These owners view the cash available on the SPAC’s balance sheet (either from the original SPAC IPO investors or the new cash from the PIPE investors) the same as they would cash from a private growth equity (Series C or D) raise. Additionally, they’d compare the premoney valuation that a SPAC sponsor offers them to that which could be obtained in a private round from private equity or growth equity funds.

Generally speaking, public market investors require lower returns on their public stock market investments than private market investors require on their private investments because the public markets investments can be traded on a stock exchange; thus, giving their owners the ability to sell the investment to other investors at any time. However, private investments can be sold to other investors by their owners. The process doesn’t happen on an exchange, and is cumbersome and not transparent… Consequently, investors require a higher return on their private investment to compensate them for this illiquidity. There are many more public market stock investors than private market investors, with multiple times the capital to invest in public markets. Only large institutions and ultra-high net worth individuals are allowed by the government to invest in the private markets, because they are illiquid and lack the protections and transparency that come with a stock exchange listing. The large amount of additional supply of investment capital and the added benefit of liquidity, results in lower required returns for public market investments.

This implies that the valuation a SPAC might offer a private company to combine with it could be higher than that which a private capital provider would offer. For example, if both private and public market investors thought that once the target company had grown its business to a relatively mature level in 5 years (say) it would be worth $5b, the private fund investor might value the company at $1.5b today as he needs a MOIC* of ((5/1.5) = 3.33X) to satisfy his investors while the public market’s investor might value the company at $2.5b today as he’s happy with a MOIC* in 5 years of ((5/2.5) = 2X) as he can sell this stock holding down the stock exchange any time he wants before the 5 years is up (vs the private investor who doesn’t enjoy this liquidity), and thus doesn’t need to earn as high a return (MOIC*).

Recently, the large demand for high growth smaller companies from public stock investors (as described above) has expanded the valuation premium of public market capital raises over that of private raises. For example, companies that could only have raised at the Series D round (say) privately at a $800m pre-money valuation might be able to obtain a pre-money valuation from a SPAC of $1.5b in 2020 vs the same $800m valuation company could only have garnered a $1.1b valuation from a SPAC in 2018.

GABRIEL GEORGE The question asked that I’ll attempt to answer is whether or not these public market valuations available to private companies to take them to the stock exchange via SPACs are in ‘bubble’ territory.

What is a ‘bubble’ Bubbles are markets that reach extreme levels of overvaluation. Famous past bubbles include the South China Sea bubble, the tulip bubble in the Netherlands in the 1600s, the 1929 Stock market bubble, the pre-2008 US housing bubble, the late 1800s railway stocks bubble, and the late 1990’s/early 2000’s Telecom and internet bubble (commonly known as the ‘dot com’ bubble).

All these bubbles can be characterized as seeing huge run-ups in their prices and valuations followed by equally sharp falls.

The bubbles that are most like today’s situation are the late 1800s railway stocks bubble and the internet/telecom bubble of late 1990s/early 2000s. In these bubbles, the equity of companies reached extreme valuations, in fact, traditional valuation measures such as Price to Earnings ratios were ignored as the companies had no earnings (actually negative), so measures such as Price to Revenues and Price to Book were used instead. While the stocks of all the companies in these sectors declined as the bubble was deflated and many went out of business, there were some that subsequently thrived and reached levels far in excess of their bubble peaks (e.g., Amazon). Similarly, the rail lines and fiber-optic networks that were laid down were used after the bubbles burst, perhaps by successor companies after the original owners went bankrupt.

It may come as a surprise that the current valuations of growth stocks are still a lot lower than the valuations reached by tech stocks in the late 1990s. So theoretically, while I expect some moderation in prices over the short term, the growth stocks could still have some room to run in the intermediate term.

(See reference a.)

Do multiples matter?

A common valuation metric used to evaluate companies is the ‘multiple’. There are various multiples used in corporate finance, such as the price to earnings multiple, price to book multiple, or the price to revenues multiple (as seen in the previous section). In growth stocks, the most common multiple used to evaluate companies on a relative basis is the price to revenues multiple, because these companies usually have no positive earnings (so price to earnings, which is widely used to compare stocks, would be unsuitable).

While it may be instructive to compare multiples as a valuation metric between different bubbles, it should be noted that different sectors have the potential to grow at different rates and target markets also differ in size. Thus, a company that is expected to grow very quickly in a huge market should sport a higher initial valuation than one that is expected to grow at a slower rate in a smaller market. Therefore, we need to take this into account when comparing different sectors and different time periods.

(See reference b.)

GABRIEL GEORGE As growth equity valuations moderate, there will be less combinations with SPACs and less SPAC IPOs With the US Government currently holding interest rates down and engaging in massive stimulus, risk assets have been rallying. This explains the recent rallies in things like Bitcoin, Ethereum, growth stocks etc. However, some are ringing the alarm bells about the ‘frothy’ markets.

(See reference c.)

Furthermore, the US authorities are starting to sound concerned about potential losses amongst retail investors. The main mission of the US SEC (Securities and Exchange Commission) is to protect retail investors; the less burdensome disclosure requirements for companies accessing the public stock exchanges via SPACs relative to the IPO route has raised concerns.

(See references d. and e.)

After the NASDAQ exchange effectively stopped being a destination in their growth phase to seek capital, companies that were consuming capital, but not showing positive earnings have been largely funded until recently by private pools of capitals; pools that small retail investors are banned from participating in. This is simply because private pool investors are assumed to be more sophisticated than the retail investors, can absorb losses and live with volatility and illiquidity. Recently, the SEC has made some companies going to the SPAC market (to raise growth capital), reinstate their earnings projections in order to show that they are losing money today and expect to lose money well into the future.

This extra regulatory oversight and worries that the valuations for growth companies were getting ahead of themselves have slowed down the SPAC IPO market recently. Unless the target companies could be offered a significant premium to where they can raise money in the private markets, they’d prefer to stay private rather than take the public market scrutiny during their growth phase, then IPO at a later date, without a sponsor involved in their company. With fewer targets willing to combine with SPACs, the SPAC sponsors who put up the risk capital to do the SPAC IPO are less willing to risk losing all their money if a deal cannot be done.

Who gets hurt when the SPAC bubble ‘bursts’?

My conclusion that while the valuations of growth stocks are high and will likely pause their upward climb or even moderate, they are not in a bubble; and any moderation will be a slow deflation. However, what, in my opinion are in a bubble, are the high numbers of SPACs being brought to market looking for opportunities to combine with growth companies, and to earn their sponsors founders’ shares.

Indeed, pre-IPO SPACs with their US Treasuries collateral and effectively put options at par together with free call options, are likely a good investment for any fund with the sophistication to hedge out the option premium; however, for post-IPO SPACs, after the de-SPAC-ing process, PIPE investors are exposed to any valuation moderation of growth stocks. Nevertheless, as stated above while they are overvalued and prone to a correction are not in bubble territory.

The investor group most likely to be hurt when the growth equity and post de-SPAC-ed companies bubbles deflate are the ‘risk capital’ investors who sponsored the SPACs and who cannot find deals that PIPE investors will invest in. These deals are either too expensive for the

GABRIEL GEORGE PIPE investors, or the valuation is too low for the target to agree to. In this case, the risk capital investors lose 100% of their capital. Additionally, the Investment Banks that booked record fees from these SPAC IPOs will see their earnings decrease, so the investors in investment bank stocks expecting the large fee stream to continue will also be hurt.

(See reference f.)

This bubble will likely end with the sponsors, promotors, and the investment bank investors hurt; stock investors who have concentrated positions might be hurt if they chose the wrong stock, as with any stock investment. Investors who own a diversified portfolio of growth equity and post de-SPAC-ed companies will likely be fine even if they see their portfolios decline or tread water for a few quarters. *MOIC- multiple on invested capital References: a. https://linkprotect.cudasvc.com/url?a=https%3a%2f%2fblogs.cfainstitute.org%2f investor%2f2020%2f11%2f03%2fdot-com-redux-is-this-tech-bubble-different% 2f&c=E,1,riIGB4W577AwfqqNtryRsYdD5kt5OWSpClcDOPV6emTXswvtfiPlA-RnOKFttLA5yvTmtANcBCug68Y35o_hdPviSZ1kF95mHvPvd0XHCqZPMtKsNd6lTqQ7&typo=1 b. https://a16z.com/2020/08/17/role-of-entry-multiples-in-valuations/ c. Https://on.ft.com/3v4W4Bl d. https://www.ft.com/content/99de2333-e53a-4084-8780-2ba9766c70b7 e. https://www.wsj.com/articles/spac-selloff-bruises-individual-investors-11621396808?st =frvnetgoahc3843&reflink=article_email_share f. https://on.ft.com/3vEU9nf

Used for general reference: https://www.mayerbrown.com/-/media/files/perspectives-events/publications/2020/08/whatsthe-deal--spacs.pdf

scale of a model house

The Abbey model, by Freddie Scott, is a scale model of Creake Abbey, known in the past as St Mary’s Abbey. The abbey was founded in 1206 and in 1217 the owners founded the hospital of St Bartholomew. The abbey took up the Order of St Augustine of Hippo and quickly turned into a priory, by Royal Assent, prompting extensions to both church and priory buildings.

FREDDIE SCOTT In 1225 King Henry III elevated the priory to an abbey which made the monastic operation much bigger and enabled it to offer a market selling local food and medicines. In 1484 there was a large fire which massively reduced the size of the abbey. In 1506 the land was settled on Christ’s college Cambridge. This land is now under protection from English Heritage and is accessible to the public all year round. My family was lucky enough to purchase the farm within which the abbey and its grounds sit, in 2003. We are the onsite guardians of it.

Photos below: an aerial view of the Abbey today and the 1930 Ministry of Works Deed showing former layout.

Bernardo Mercado new language Chay Melj is a new language by Bernardo Mercado is a sholarly and quirky look at the construction of a new language, influenced by Tolkien’s Elvish.

Phonology - Consonants Nasals Plosives Affricate Fricative Approximant

labial m b f, v w

alveolar n (~ɴ) t, d ts, dz s, z l, lʲ

palatal ɲ ͡tɕ, d͡ʑ

velar

uvular

glottal

k, g, k’

q’

ʔ

χ

ɦ

ɕ, ʑ j, ʎ

Some allophonic variation is presented through the nasal assimilation of n before velar and uvular before velar and uvular consonants; also the series ti and di, are palatalised (pronounced close to ch and j, respectively) Vowels High Mid Low

Front i ε a (unstressed: ɐ, nasal: ɐ̃)

Back u ɔ

(All vowels have nasal equivalents, indicated by a tilde above).

Phonotactics (consonant clusters allowed): the syllable structure is largely CCVC - Ejectives cannot cluster and must occur directly before the vowel.

- Most consonants can serve as codas, through final vowel loss. Ejectives cannot occur in the coda of a syllable.

Bernardo Mercado No syllable-final ejectives There are some interesting features in this: There is no p, as it became an f (p>v) – this is an areal feature of North Africa and the Middle East, and is partially motivated by the difficulty of pronouncing it.

Two ejectives – k’ and q’, both common in languages with ejectives; the q’ is common for languages with q, however here this debuccalized into the glottal stop, and so only the ejective remains. This is also generally considered an areal feature of mountainous regions, for example in Southern Quechua, which got a similar series to the nearby Aymara language.

There is a (badly organised) palatal series, which came from the palatalisation of alveolar and velar consonants before the /j/ phoneme, which got deleted in the process. This also resulted in some confusion between lʲ, and ʎ, which are merging, but slightly separated, and also between ʃ, ʒ and ɕ, ʑ, which are merging, the latter coming from s, z and the former from k, g (in this there will be no distinction shown).

- Nasal consonants – these were developed in positions around nasal consonants, which often also got deleted.

Romanisation - Vowels – e for ε, o for ɔ, tilde above for nasal vowel equivalent.

-

Glottal stop represented with ’ Ts represented with c Uvular fricative with ch Palatals – ñ, č, dž, š, ž, y and lh from top down The rest are pretty self-explanatory.

Bernardo Mercado Grammar Word order The general sentence order is VSO, or verb-subject-object; however, the English order SVO, is also just as acceptable (the important part is the verb-object order).

As a result of this head-initial order, it has prepositions, and most modifiers following the noun.

Nouns These are quite simple, with no grammatical gender or case, however the indefinite article (meaning a/an), -kach, is suffixed onto the noun. A particle, melj, also after the noun, indicates plural number; paucal number, indicating ‘a few of’ something, uses the particle q’u.

Pronouns Person/Number First Second Third

Singular Eu, Vã (incl.) ‘ab Sa

The other numbers use the particles used for nouns (note: it is considered ungrammatical to have first person paucal number, and is assumed to indicate a non-first person object, usually third person). There is also no case distinction in pronouns, as in noun. They can also be used as possessives with an optional particle ‘ža’ between possessed and possessor.

However, these are incorporated into the noun complex as suffixes, and also fuse with themselves to create polypersonal agreement: Object/Subject-> 1st excl.

1st incl.

2nd 3rd

1st excl.

1st incl.

2nd

3rd

Eu

Vão Ãf Vã’ã Vã

‘ave ‘ava ‘aba ‘ab

São Sava Sab Sa

Ẽ

Esa

Note: there is no number indicated morphologically on the verb, it is again indicated by the particle afterwards, and is understood from context. This poly-personal agreement also allows for some redundancy, and the pronoun can be used for emphasis.

Bernardo Mercado The pronouns also demonstrate clusivity, which is a feature normally used to distinguish between we, including the addressee, and we, excluding addressee; however, I added this to the singular forms, becoming I, the exclusive form, and I and you, the inclusive form. I believe this is present in Aymara, although they also have plural pronouns, whilst this language does not (yet).

-

Deixis & demonstratives

There is a relatively complex system regarding how to refer to something, i.e. demonstratives, like this or that.

Extended Close to speaker More accessible (near speaker) Ach Less accessible (near listener) Ãuch Away from speaker (and level) More accessible (over) Che (across barrier) Aljche Up from speaker More accessible Fei Less accessible Feizo Down from speaker More accessible Una Less accessible Ola General Mão

Restricted Xe Ti Chu Chite ‘ẽl Q’ẽle Da Date Mãte

The indicability distinction (extended vs. restricted) was made on how the object is perceived, as a moving object it largely falls under extended, whilst if static, it would be restricted. The distinction of accessibility largely factors on whether the speaker can (quickly) reach the object being referred to. The other factor, directivity, is largely based on in which the speaker’s head has to look to, up, straight for a distance, down – and general, references general concepts and also can be used for objects obscured from the speaker.

Why did this arise (other than personal interest)? To answer, you can also go into the speakers’ culture, as this can explain a lot about and help in developing further their language, and vice versa. For this, we can say that this language is around North Africa to the Middle East, since it lost /p/, which is common in that part of the world. As a result, it could be important generally to know and concisely communicate the relative direction, distance and state of an object, e.g. for travel through the desert, or navigation around the Mediterranean.

Bernardo Mercado Verbs As shown above, verbs display poly-personal agreement, indicating both the subject and object of the verb in a fusional suffix. It also allows noun incorporation, incorporating the direct object into the verb complex before the verb stem (and in the process, lowering the valency of the verb e.g. from transitive to intransitive, or ditransitive to transitive). An example in English could be the change from ‘I am picking berries’ to ‘I am berry-picking;’ the second sentence cannot really take another object. In this noun incorporation, the stem of the noun is incorporated into the verb, without any indefinite article suffix – this feature is one found often in ‘polysynthetic languages,’ especially in North America and Siberia.

There are also tense codings in the verb: There are three ‘tenses,’ or times considered: past, and the nonpast – although a prospective meaning (‘I am about to -’) can be created through the affix -be. However, these tenses are combined with aspect markings which combine to make different meanings, and there is only one other mood, the conditional.

Past -yõ -ayki -ali -ẽy -yata

Habitual Continuous Inchoative Perfective Conditional

Non-past -sõ -lha -ve -ta

As a result the verb is quite complex. Here is a breakdown of its structure: -1 Incorporated Noun

0 Stem

1 2 Tense-Aspect-Mood Subject-(Direct)Object

For example, the sentence ‘I gave him a rock,’ could be both: xeriẽyesa eu sa ahkela (here, sa as a separate word is used for the indirect object, him) ahkelaxeriẽyesa (in this case, the direct object slot could also be used for the indirect object as the verb can take two objects).

However, the preferred form would likely be the second, and it could be manipulated to give emphasis to parts of the sentence.

Bernardo Mercado Evidentiality A copula verb (to be) arose from the verb ‘to stay’ and is now sẽ, and is used largely for predicative expressions, although it does not co-occur with the participles, which themselves are formed by adding -chaž to the verb stem, or -lhaž if in the past tense.

This created some redundancy, and so participles were largely repurposed, together with the copular verb, to indicate evidentiality, or the source of the information. There is a 3-way distinction between witness, inferred, and reported evidence: the witness, or visual sensory evidence, is indicated with the normal form of the verb; inferred evidence by the copula plus the participle, the participle taking on the inflection for tense, and the copula for the rest; and finally, reported evidence is indicated with just the participle. As a result, this is about the only use for the participle, in evidentiality. This is also shown below: Witness

Va’osa ñu ahkela

Inferred

Va’ochaž ñu ahkela

Reported

Sẽsa va’ochaž ñu ahkela.

I saw that the cat ate the rock.

The cat must have eaten the rock.

I’ve been told the cat ate the rock.

Adjectives Adjectives do not need to agree with nouns, and only demonstratives (as seen under demonstrative pronouns) and numerals above 1 go before the noun. However, possessive adjectives, like most other adjectives, go after the noun – this also applies also to genitive phrases, with order possessed-possessor, and any relative clauses too.

Bernardo Mercado A very short vocabulary There is not much within this vocabulary yet, as this has not been developed largely. However, these are about all the root words used and created as of yet: Va’o - to eat Ñu – cat Ahkela – rock Vefcuwã – water Down – ce Up – dzu Word - chay Eu – I Vã – I and you ‘ab – you Sa – he/she/it/they -kach – I/an Q’u – paucal particle, a few Melj – plural particle Lewvo – person

Kĩlec – house Alhs’a – apricot Vefcuwã – water Down – ce Up – dzu Word - chay

Bernardo Mercado

Mikolaj Rutka HAve things improved?

Nowadays, several global issues have made people question the quality of life and whether the various changes that have taken place have made it deteriorate. In this essay, I will argue that things have improved. To answer this question, I will consider a range of criteria that determine the quality of life- technology; inequality; overpopulation; climate change and economic systems.

Technology can be split into a couple of areas. I will focus on medical science and artificial intelligence as they are most crucial parts of our lives. This is because medical science affects your overall long term health and artificial intelligence enhances the speed, precision and effectiveness of human efforts.

Over the last couple of centuries, humanity has encountered many life-threatening diseases and the improvement of medical technology has proven to be crucial in their defeat. In the 18th century, humanity became a victim of tuberculosis (otherwise known as consumption). Tuberculosis was a deadly disease that tackled the lungs; it made it very difficult for the person to breathe, forcing him to cough up blood. Statistics (Family History) show that it killed one in seven people in the US and Europe in 1882. The development of medicine proved to be important in fighting the disease as it could only be defeated when the vaccine was produced on March 24th, 1882. A different pandemic struck in the 20th century, right after World War 1- Spanish Influenza. This disease destroyed the bronchial tubes that go into your lungs, allowing the bacteria from your nose to invade the lungs. It is estimated that around 50 million out of the 500 million infected died (www.cdc.gov.uk) before the vaccine was released in 1946- this is more than two times faster than the TB vaccine which took 71 years to be produced since its discovery by Robert Koch in 1882. Furthermore, one year ago, another pandemic (Covid-19) took place. From the 138 million people infected, less than 3 million people have died at the time of writing this essay. Moreover, the Covid-19 vaccine came out just 1 year after the discovery of the virus which is more than 28 times faster than the Spanish Flu vaccine and 71 times faster than the TB vaccine. From these statistics, one can clearly see a pattern that, due to the improvement of medical technology, fewer people die from pandemics. Furthermore, as a result of this improved medical technology, average life expectancy has increased from 41 in the 19th century to 73 years nowadays.

Secondly, Artificial Intelligence is becoming an increasingly important part of our lives. In 2018, LawGeex did an experiment where they tested the accuracy of top lawyers against their new contract system. This experiment was performed by both, the AI system and the lawyers, having to analyse an NDA review. The experiment showed that the average accuracy of decisions made by AI is 94%, whereas that of humans is only 85%. Furthermore, the review showed that the maximum accuracy that can be achieved by AI is 100% whereas that of humans is only 94%. This is very useful for the government as well as companies as it increases the country’s GDP. This is because AI drives greater product variety, with increased personalisation, attractiveness and affordability over time. For these reasons, PWC predicts that China’s GDP will rise by 26.1% and that North America’s GDP will rise by 14.5% by 2030. These are an equivalent of $10.7 trillion. Therefore, AI is massively improving the quality of people’s life, and will continue to do so in the future, as increased GDP increases the typical person’s material standard of living. In addition, the NDA review performed a test to see how quickly AI works in comparison to humans. The task was to analyse a lot of documents- this took lawyers 92 minutes, compared to the 26 seconds it took Artificial Intelligence. At this pace, AI is able to complete jobs much faster than humans which also increases the quality of life.

Mikolaj Rutka For example, AI will allow doctors and hospitals to better analyse data and therefore customise healthcare to the genes, environment and lifestyle of each patient. On the other hand, some people think this will create massive unemployment in the long run therefore increasing poverty. However, statistics (PWC) show that, although AI will displace 7 million jobs, its management will create 7.2 million jobs therefore producing a net gain of 200,000. This is and will continue improving the quality of people’s lives.

Gender inequality is another issue that has made people question the quality of this generation.

However, it has grown massively over the past two centuries. From 1840’s, women’s role in society was staying at home and taking care of the children. Statistics (History.com) show that female employment at that time was less than 15%. However, since then, many milestones have taken place. In 1882, the Women Property Act was passed. This allowed women to own separate property from their husband.

Moreover, in 1892, women were allowed to vote in elections. However, there were still age restrictions and it was only by 1928 that women received the same rights as men in this sector (Representation of the People Act 1928). This included voting at 21 as well as being a candidate. When World War 2 broke out, women had to fill in for the men at work and, when it ended, they did not want to leave.

By that time, female employment had risen to 34% in the UK and it has risen much more since; nowadays female employment is more than 72%. In addition, perhaps the most important milestone, was when rape in marriage was made illegal in 1994 in England. All of these things show that life for women has definitely improved a lot over the past two centuries as they have received many more rights. On the other hand, many people think there is a large wage gap between men and women. For example, a lot of people in America state that women make 77 cents for a every dollar a man makes, despite doing the same job (www.politifact.com). This is calculated by taking the median earnings of all women working full time against the median earnings of all men working full time. However, this calculation does not reveal a gender wage injustice as it does not take into account occupation, education, position or hours worked per week. Once this is taken into consideration, statistics (AAUW) state that the pay gap shrinks to 6.6 cents. Even this gap does not show a wage inequality; according to a study by the US department of Labour in 2009, it is purely because of different individual career choices. To give an example from the study, George Town University analysed the percentage of men and women in top five best-paying college majors (perhaps state majors). According to the study, women out-represented men in only one of these jobs by 2%; men out-represented women in the four other jobs by 7- 38%. In terms of the least-paying jobs in the university, men out-represented women only once. On the other hand, some women might argue that another problem is that women earn less in the exact same job. This is also true; according to the study male nurses earn 18% more, on average, than female nurses. However, almost all of these male nurses work at higher-paid nurse institutions and work longer hours. Therefore, all of this data shows that the lives of women have gotten better and that the wage gap is not caused by gender inequality.

Mikolaj Rutka

Another issue that makes people question whether life has improved is overpopulation. This is because overpopulation leads to overconsumption, which is the main driver of biodiversity loss.

Thomas Robert Malthus, a British economist in the 18th century, proposed a theory that, at one point, the population will rise beyond the limit of our resources (An Essay on the Principle of Population).

This was the case in the past. For example, in 1150-1300 UK (Rational Optimist). The courts were richly furnished, monasteries flourished and cathedrals rose towards the sky. This great period was mostly a result of the woollen trade. As Flemish merchants desired more wool, ship owners (who transported the wool), fullers (who cleaned the wool) and above all the sheep owners all got richer.

They would then spend money on bread in the bakery thereby making the baker, the miller (who provided flour) and the grain planter richer. This cycle continued in the industry. As people had more money, this enabled them to have more children. However, as the food demands grew higher and higher and more difficult to supply (because the land could not keep up with them), the prices increased thereby causing the poor to starve. Since the population doubled (2-4 million) in UK from 1150 to 1250, it came back to where it was as a result of famine and Black Death by 1450. However, things have changed over time. For example, Britain avoided the Malthusian Trap in 1830 despite an increase in population. This was due to trade. At that time, Britain had seventeen million acres of arable land, 25 million acres of pastureland and 2 million acres of forests. However, due to trade, Britain managed to produce sugar from West Indies equivalent to (in calories) another two million acres of wheat. Furthermore, another example is Germany. In the 19th century, it experienced a massive increase in population and it avoided the Malthusian Trap by a flood of immigrants to the United States. Therefore, overpopulation used to be a problem but it has been stopped as a result of international trade and emigration. This therefore means that things have improved as people are better fed, have better living quality and fewer people live in poverty.

Mikolaj Rutka

Another thing that has made people question today’s standard of living is air pollution. Many think this has gotten worse over the past 100 years. However, this could be due to an increase in the public eye. For example, from the graph above, we can see that London has decreased its pollution massively over the past three hundred years- from 250 SPM (suspended particulate matter) per cubic meter in 1700, to 10 SPM nowadays. The graph shows that countries who are just starting their industrial development, such as India, are experiencing a massive increase in air pollution. This data therefore shows that things have improved for more developed countries because the air is cleaner and less harmful to the environment. On the other hand, some people can ask the question about air pollution around the world- if developed countries are replaced with developing countries in terms of pollution, how has it changed around the world? Ironically, the Coronavirus pandemic has improved air pollution massively (CNBC) as a result of decreased flights and cars on the roads over the past two years.

Graphs show that areas affected the most by the pandemic, such as Italy and America, have decreased air pollution by almost a half. WHO predicts that 4.2 million people die of pollution every year (1.1 million in China) but, as a result of the Coronavirus pandemic, countries (for example China) have saved an estimated 50,000 lives. This therefore shows that life has improved as many lives have been saved.

Over the past ten years, the world has taken many steps to decrease climate change as much as possible. For example, more than a third of the FTSE 100 companies have promised to be carbon neutral by 2030 (www.gov.uk). Furthermore, 197 countries signed the Paris Act in 2015. This act aims to keep annual temperature increase to 2 degrees Celsius. According to Climate Action Tracker, before this act was signed the world was going towards a 3.5 degree increase by 2100 but, since the act, the prediction has decreased to 2.9 degrees Celsius. This is also going to continue decreasing massively due to, for example, the growth of electric cars. For example, Tesla’s stock prices have increased by 3600% since 2010 when it first sold stocks. Even during the pandemic, electric car numbers have gone up by 43%. In 2015, electric cars made up 1.1% of the global car market and nowadays it is 4.2% (The Guardian). Moreover, according to Deloitte, electric cars have a compound annual growth of 29%. The growth of electric cars has made things improve as it is more effective in stopping climate change.

Research by the European Energy Agency found that carbon emissions of an electric car are 17-30% lower than that of a petrol/diesel car. Decreasing the effect of climate change has been extremely important in improving quality of life. This is because climate change causes many things- for instance, more serious wildfires or flooding.

Mikolaj Rutka

The final thing that I will discuss is economic systems. History has seen many economic systems and, to decide if they have improved, we need to take a look at their positives and negatives. Nowadays, capitalism is the leading economic system. It is a system where private entities own the factors of production. These include entreupeneurship, capital goods, natural resources and labour (balance. com). Capitalism has a lot of positives. These include the fact that owners can operate their companies efficiently and therefore maximise profit. Furthermore, incentives to be rich encourage innovation and therefore profit too. However, capitalism has a couple of negatives. Although it thrives to bring maximum profit, one could argue that it ignores external costs such as climate change and pollution in the process. For example, a recently published report found that 100 energy companies are responsible for 71% of all industrial emissions (nrdc.org). However, this is improving nowadays as many companies have promised to become carbon neutral (as mentioned in previous paragraphs).

In addition, one could argue that companies have too much ability to evade tax. For example, it was found that Amazon had paid just 9.4% in federal tax in 2020 with the statutory corporate tax being 21% (itep.org.uk).This is because, if the American government forces the company to pay tax, Amazon will threaten to move to a different country where the taxes are smaller. This would have a negative impact on America’s economy so they will allow Amazon not to pay tax. In the past, other economic systems have also been present- communism is an example of it. Communism was a system where everything was owned by the government and its aim was to give every person a basic living standard.

However, communism had many flaws. First of all, since the government had absolute power, there was no freedom of speech as well as massive corruption. An example of this is Stalin’s Russia where 20 million people died as a result of famine, execution and labour camps (nytimes.com). Furthermore, receiving the same salary notwithstanding the amount of work you have done discouraged hard work along with difficult jobs. Both of these things damaged the economy. Another economic system that one must take a look at is socialism. This is the system where the government oversees the factors of production. In theory, socialism has the greatest commonwealth goal from all of the systems. However, when it comes to practice, it becomes a less severe form of communism. As a result of the government overseeing the factors of production, there are smaller rewards which decreases motivation and slows down economic growth. This is due to diminishing returns that later led to the collapse of most socialist economies in the 1980’s. Altogether, I think all of the examined economic systems are flawed.

However, capitalism is the best option. This is because it provides the fastest economic growth and ensures the highest average living standard.

Both the past and the present are not perfect and each have their significant flaws. However, without the development of medical technology, artificial intelligence and our escape from overpopulation, life would still be lacking in stability, safety and quality. Therefore, I think things have improved.

Mikolaj Rutka

Bibliography: https://www.familyhistory.co.uk/the-tuberculosis-epidemic/ https://www.cdc.gov/flu/pandemic-resources/1918-pandemic-h1n1.html https://www.worldometers.info/coronavirus/ https://en.wikipedia.org/wiki/COVID-19_pandemic#:~:text=The%20earliest%20known%20person%20 with,patient%20zero)%20originated https://www.google.co.uk/l?sa=t&rct=j&q=&esrc=s&source=web&cd=&ved=2ahUKEwjSyNGehdbvAh WPa8AKHRkFCBEQFjAIegQIEhAD&url=https%3A%2F%2Fourworldindata.org%2Flife-expectancy&usg =AOvVaw0MsNsocHOAU4I90aPQWHXI https://towardsdatascience.com/advantages-and-disadvantages-of-artificial-intelligence182a5ef6588c https://www.pwc.com/gx/en/issues/data-and-analytics/publications/artificial-intelligence-study.html https://www.history.com/topics/womens-history/womens-history-us-timeline https://www.google.co.uk/url?sa=t&rct=j&q=&esrc=s&source=web&cd=&ved=2ahUKEwjEq6WiOzvAhXv_rsIHdJZBs4QFjABegQIBBAD&url=https%3A%2F%2Fresearchbriefings.files.parliament. uk%2Fdocuments%2FSN06838%2FSN06838.pdf&usg=AOvVaw0yw5m1V0pwS4ZHo5zftEOV https://ourworldindata.org/london-air-pollution https://www.gov.uk/government/news/third-of-uks-biggest-companies-commit-to-net-zero https://www.thebalance.com/capitalism-characteristics-examples-pros-cons-3305588 https://realbusiness.co.uk/six-companies-that-avoid-paying-their-taxes/ https://www.nytimes.com/1989/02/04/world/major-soviet-paper-says-20-million-died-as-victims-ofstalin.html https://www.nrdc.org/experts/josh-axelrod/corporate-honesty-and-climate-change-time-own-and-act https://itep.org/amazon-has-record-breaking-profits-in-2020-avoids-2-3-billion-in-federal-incometaxes/

Will Rosling The history and preparation of tapas

Video available here.

Harkirat Malhorta The educational divide Introduction For as long as I can remember, I have been fascinated by the importance of education and the different forms of education which there are in the United Kingdom. Undoubtedly, education plays a vital part in all of our upbringing and is a commodity that helps us to make decisions throughout our lives. The importance of education varies from community to community but for me, it is one of the most important things which we are lucky enough to have and we must never stop learning. This journey of learning will continue for the rest of our lives. Furthermore, education gives us the power to be able to think with more clarity. To have a productive nation I would say that education is one of the most important factors; to have a successful country, having an educated nation would play a vital role.

As someone who has spent their life going through the state system and is now at one of the most prestigious private schools, Radley college, I feel that I have some experience of the two main systems that we have in this country. The divide has been there for as long as I can remember but having gone through both systems the differences are much more apparent to me. I hope to achieve a clear understanding of the two sides of the argument and obtain a firm grasp of the main differences between state and private education. I strongly believe a poor education has a correlation on the levels of productivity as a nation and I hope to prove this.

Education There has always been a divide between state and private education and society. Private education is something which some parties have proposed to abolish but this has never happened. However, the UK is very proud of its private schools and even some of its state and grammar schools. There is a very clear difference between the state and private sector of education; this is seen in society and some children feel that they are a lot more disadvantaged because of the school they go to and the environment which is in place to facilitate their learning.

Productivity This has been one of the biggest problems for Britain since the financial crisis of 2008. Productivity is how a nation is compared to other nations. The work rate on a nation is measured through how productive a nation is. What productivity means is being able to do more work per hour than someone else doing the same job somewhere else. Effectively, what is trying to be achieved is producing a higher output for every person working. To achieve this; people, technology, education, and strategies are vital. Education plays an essential role in how productive an individual can be, so it is necessary to have good education to have a productive nation.

The divide There do exist some differences which are a lot more visible than others: private schools are known for producing excellent members of society, they are able to become prominent members of society as they have had confidence drilled into them from a young age. The qualities of leaders are taught from a young age and this then in later life helps them become the leaders, CEOs or other productive members of society.

However, this is not saying that state education is not able to produce members of society who are equally productive or sometimes even more so than their private educated counterparts. This can be seen when the same job is being held by someone who is state educated and someone who is privately educated. State educated pupils have a greater understanding of what life is like for the average person, thus allowing them to share a sense of familiarity with a larger demographic. Only 7% of children in the UK go to a private school compared to the 93% who are educated in state schools. When a state educated pupil becomes a leader, they are more likely to be able to understand what the people at the bottom of the pile go through and how to support them. This is unlikely for people educated privately because, of no fault of their own, they were not exposed to enough societal experiences at a young age.

Harkirat Malhorta The wealth of your parents determines so many factors, whether it be the opportunities which are available to someone or simply being able to go to school having had something to eat. One third of people from a poor background are unable to read, write and do basic numeracy by the time they leave primary school, as there is not enough support for each child due to larger class size, a staggering statistic. It follows from this that 36% of students are not able to get a grade 4 in English or mathematics at GCSE. In addition, if someone comes from a poor background, they are four times more likely to be permanently excluded from school compared to their wealthier counterpart. Furthermore, coming from a poorer background means you are 2.5x less likely to be admitted into a selective university. Hence it is clear that children from less fortunate families are at an incredible disadvantage. This divide affects the national economy.

Grammar schools When talking abut the divide, most people will think of a huge gap between the two sectors of education, but this is not entirely true. In reality there is only half a grade difference between what private and state education students. The divide academically is not as large as is thought to be.

[Fig 1:graph taken from BBC] It comes down to the up bringing of the child, the behaviour, the confidence and one of the most important factors for later life, the networking helping them in their future. These things really separate the privately educated and the state educated. Grammar schools were a great way to keep the divide as minimal as possible as these were institutions which produced great academic excellence as well as productive members of society.

In this graph it is clear that there were a substantial amount of grammar schools, not as many as private schools (there are around 2600 private schools currently) but still a substantial amount. This number dramatically reduced in the 1950s and 60s. With this cut, students who where selected and given great academic opportunities where now in schools which sometimes struggle to provide the best education.

How productive a classroom is down to the environment created within the classroom. In some state schools, the environment is not one which is the most productive. There are a lot of distractions in state schools such as pupils who don’t want to learn creating distractions and a lot of the lesson is spent dealing with behaviour.

This then leads to students who want to do well very little time to learn at school. Whereas at private schools most of the time the behaviour is not so bad and lessons flow a lot smoother. As the lessons don’t have many disruptions, a lot more is achieved in a lot less time.

This being said, it does not mean that behaviour at private schools is perfect. There are still many incidences but these are dealt with thoroughly and not only do the teachers tell the children off but they also reach out to their parents. One of the biggest differences is the parents and their input in the child’s education. Students who come to private schools are normally have parents who are extremely involved in the education of their child. The child at home is surrounded with books and parents who are more likely to be high achievers themselves. All these play a factor in how well the child will do in their own education.

In state schools some parents are involved and keep track of their child but most of the time this is not the case Why?. Children at home do not have the motivation to do well in school or feel the need that they have to

Harkirat Malhorta do well academically. The child then does not see the importance of education hence them causing disturbance in the classroom. To go to a private school which people are paying for, makes those attending value it more and hence why private schools are seen as better institutions for education than state.

Tests Grammar schools test at 11+ and are selective schools which are state funded most of the time. The fact that an 11-year-old has one opportunity to secure great free education or will have to wait at least 5 years before another chance is not right. I believe that students should be given more than one opportunity and should also be tested at an older age to get into a grammar school. Grammar schools should also test at 13 allowing more students to join them at age 13 rather than at such a young age of 11.

Some private schools do not test their students before they come to the school. The ones which do test, often don’t make the tests particularly arduous or it is not necessary to have the highest grades. On the other hand, the scholarships are extremely difficult and for someone who is coming from state education to private they have to be extremely clever to get a scholarship in most cases. This is unfair to these pupils as the ones coming from private schools are solely preparing for the 11+ or 13+ at school whereas state school children have to work outside of school hours to be able to secure a place.

A study done by Durham university found that someone educated privately is most likely to have had two more years of education by the age of sixteen compared to their state educated counterpart. This means that private schools are able to educate their students two more years worth of education. This gives them an unfair advantage, but nevertheless private schools create that environment in which the students are able to flourish.

This something state schools sometimes lacks in. Private schools have a test which has to be sat and are not fully selective as the tests are not extremely hard. There should be a lot more scholarships for students who can excel in academics, music, drams and sports. Students who can pay the fee should pay but others who can’t should be given a reduction to what they have to pay.

Private schools who have a huge name and can do this should try to give a lot more scholarships and a lot more bursaries. A lot of the students who go to private schools now are not there because they are gifted in any way but simply because they are able to pay the expensive school fees. Only 1% of all private school students are on a 100% bursary. A third of the people who attend private education are on some sort of bursary or scholarship but this can be anything from 5% up. This could be improve with more scholarships offered to less privileged people.

Housing prices It is a known fact that if there is a good school in the area then the housing prices go through the roof. Instead of buying a house near a good state school they would rather send their children to private schools.

However, if all the state schools in the country are almost as good as each other than this should not affect the housing prices. To make each and every school just as good as each other, many things needs to be done but if this is achieved then the effect it has on housing prices should be minimal. There could also be laws in place to stop this from happening. Creating easy transport for travel to school may also be a way to help keep the housing prices down around the school. Nonetheless, going to a local school is beneficial for all and the best way to keep house prices low is to raise the standards for all schools.

Debating Debating is done by everyone. It takes many different forms and is a skill which is extremely important to excel in life. A huge distinction made between someone privately educated and someone state educated is how confident they are. Privately educated students have confidence drilled into them. They feel like leaders from a young age. However, this is not the same for the state sector. State school students do not always have the same amount of confidence because of social factors. Debating is a great way to boost confidence in pupils; it helps to build character. The extra energy that young children have can be channelised into something positive, creative and disciplined. A lot of young people do not read as much as they should: debating gives them the

Harkirat Malhorta opportunity to read and keep up to date with current affairs. Furthermore, debating can be something that some students may look forward to each week, helping them stay out of societal problems. This also builds critical thinking skills to analyse problems. In the future, these skills will have a positive impact on them in all aspects of their life. Arguing for the other side of the argument will help them empathise for the other side.

This teaches them to look at the wider picture and when it comes to making big decisions, they are able to make better choices. It also helps them understand why someone might make a certain decision. This gives them a better understanding of society and can help them become better leaders and workers in society.

Not only debating but things like sports, drama and music can also help students discover there potential and find something that they are passionate about. These skills will help narrow the gap but all require investment from the government. Doing something productive and beneficial will help make better leaders and workers.

Alongside all these activities, having the opportunity to get involved with people all across the country will be a great way to get Britain together. The confidence which a debater, sportsperson, actor or musician will get after winning a competition against a great school will push them on even further.

Getting members of the local community involved with schools is also vital so that young people have positive role models to look up to. Local members could help out and guide schools for free to make their community a better place. Having someone from outside of your school to run an activity gives you a different experience rather than it just being a teacher someone sees a few times a week anyway.

Finland Finland have one of the most successful and efficient education systems in the world therefore it would be reasonable to see their take on private schools. In the 1970s Finland abolished private education and made all education state. The local state school became one of the best schools and they were all just as good as each other. Investing only 5% of their GDP in education they are getting a lot out of it. The respect which teachers get in Finland is phenomenal. Teachers are seen as an important member of society which should be the case in the UK but sadly it isn’t. This is partially cultural as in some places education is not very well respected.

State schoolteachers in the UK do not get the respect they deserve. Roughly 25% of newly qualified teachers leave the field each year as it is so difficult and stressful. The culture built around teachers is not the most positive and this is something that needs to be changed.

University Going to university is important to help develop the way you think. This is a vital skill to have a country with an extremely productive nation. Only 49% of adults by the age of 35 have a degree. This is because a lot of teenagers start work after finishing their A levels or GCSEs. It is becoming increasingly popular to do an apprenticeship instead of going to university and this is something which helps provide experience for future employment. Establishments like Oxbridge are now giving a bit more priority to students who come from state schools compared to private schools like they used to. This is because they think that eager state school students will be a lot more active in participating in all that Oxbridge has to offer and make the most of their time at university. However only 13% of state school pupils with the grades make it into Oxbridge. This is not a lot at all. The top universities maybe need to expand or other universities need to become as good as Oxbridge to give more keen learners the opportunity to excel at university.

Vocational degrees Spending three years at university and then not using what you have done may be considered a waste of time.

Almost 50% of degrees achieved are not used after they leave university. Vocational degrees on the other hand have a job waiting for you once you graduate. Young adults in the UK should be taught about the different jobs and what degrees they need rather than someone getting a degree then deciding what to do with their life.

This would in turn create a much more productive society if people know what they want to do and are able to get a job in that field. This enables people to like their job hence wanting to do well in it. The lack of work experience in state schools may be because of the lack of networking. At private schools they tend to have a society in where the ex students help the current ones. Being aware of the many jobs that are out there is very important to help make the decision to what someone is going to dedicate their life to.

Harkirat Malhorta

The government Investment is vital for schools to function. The more money that is invested in a school, the more facilities they can provide for their pupils. Private institutions get there funding through the pupils that attend. The average cost for a day boarding pupil is around £18000 and for boarding it is £41000. This is partially why private schools are able to provide more facilities as they have the means to do so.

[Fig 2: taken from the guardian]

[fig 3: also taken from the guardian]

State schools are funded by the government and this is what the school then has to invest into their pupils.

The average secondary pupil gets £4900 in funding; there is a clear difference between the amount that they have to invest in each pupil. Private schools have over three times more to invest per pupil hence why private schools are able to provide amazing facilities and smaller class sizes for the students.

This diagram shows us that the amount that is being invested into state education is currently on a rise but not very long ago it had taken a downwards turn in the late 1970s and 80s. The amount that government is investing into education is still not enough. The government claims to be giving more to state schools which might be true but the amount of pupils is also rising. The amount the government is giving should rise but the amount spent on each pupil is decreasing due to the number of young children there are in this country.

In fig 3 once again we can see that the investment into state schools is increasing and the government claims to be investing enough in education. Yet the increase is very small. The government are not tackling the issue properly as they are investing every so slightly more and claim that it is enough.

[Fig 4: this graph is from the guardian]

[Fig 5: graph taken from the guardian]

If any government wants to get rid of private schools they ought to improve the state schooling system. It is a reasonable argument that you can not blame the failure of state schools on the success of private ones. But the only way that I see for state schools to do better is if they are funded with a sufficient amount. If state schools

Harkirat Malhorta are to be improved and brought up to the standards of private schools they need the extra funding to close this gap. Academically speaking it is only half a grade but the social gap is a lot worse and one which affects the poor the worst.

From these graphs we can observe that the number of pupils has increased by 700,000 but the funding has not increased as rapid as the amount of pupils has increased but the amount that is spent on each pupil has gone down by 8%. If there is a school of 1000 pupils and each pupil is now getting 8% less than they originally were, it puts a huge strain on the schools. The state schools have had to cut down on staff hence the student to teacher ratio has increased. State schools are sometimes not able to afford the correct science equipment hence having to cut he more creative subjects like art, drama, music and physical education. However private schools have great drama, music, art and sports facilities.

This is where the private sector is doing much better. In private schools they play sports which most state school pupils may have never heard of and have a great variety of activities for the pupils to engage themselves with. The opportunities at some private schools are endless. This means that pupils from state schools are not exposed to the same amount of facilities and experiences. This would mean if a student is not thriving academically at a riveted school they may be able to find what they are good at but in state school the opportunity is limited. The lack of government funding has had a detrimental effect on state schools.The teachers are just as qualified but because the class sizes are so huge there are a lot more problems. Some state schools don’t have cleaners, the teachers have to do it themselves as there is not enough funding. Not only is the teacher a teacher but also multiple other things. A lot of admin is done by the teachers themselves as they don’t have the support of a huge admin team.

The government is also wasting a lot of money in the name of education. Prime minister Boris Johnson has given £700 million to help the education sector recover from COVID 19. A lot of this money has gone to private companies like Pearson the exam board company. They received around £350 million from the government.

This money is not having the same benefits it would have if it had been given directly to schools to see what they need to invest in to help their students. Going through the private sector to is not really helping the state schools. Each school has different needs and it should be based on a student to student bases to help after such a large pandemic.

[Fig 6,7,8 and 9 are taken from the guardian as evidence of the frustration of state schools] State school pupils who are capable of doing well can not as they are not provided with the same opportunities as private school pupils. All the pictures above show us that state schools are under funded.

Students, teachers and headmasters all go on protests together to create awareness of this national crisis. The fact that all these members of a school have to spend time out on the streets instead in the classroom learning for the future holds them back from success with ease.

I think that a share of the failure of state schools should be put on the government as they are just not able to provide the same facilities for the students. The government does not need to give £18000 per pupil but something like £6000 or £7000 will make such a huge difference. Money that is being spent else where that is to very important or not giving the best output should be spent on the important things such as education, healthcare. The government should invest correctly in schools to provide the young citizens of this country the education they deserve.

Harkirat Malhorta Affects it has on productivity

[Fig 10: graphs taken from the financial times.]

Referring to these graphs, it is evident to see that the UK is not as productive as it should be due to the reasons covered above. If Britain does not improve their productivity rates, then they may become unattractive trading partners. Britain had a step back in 2008 as there is a clear dip but as a nation have been falling behind countries from before the 1970’s. In the pre-recession year of 2008, output per hour was only 0.4% higher than in 2014. If this problem is not tackled, Britain will eventually fall behind so much that it will not be able to compete with the world.

This can be tackled by improving the British education system. In 2019, 36% of pupils were unable to achieve a grade 4 or above in their Mathematics and English GCSE. As they do not meet basic requirements for most jobs, unemployment increases, and they become an obligation on society. Because of the lack of basic skills such as numeracy and literacy, workforce of Britain is unable to work as productively as their counterparts across the world. People with better education can carry out tasks more efficiently as their problem solving and critical thinking skills are more developed. Education is an investment in human capital which is something Britain ought to strive for.

Although we need people in this country to do jobs which include manual labour to keep the country running, the rise of technology will soon reduce this need massively. In the future, the need of manual labour will be taken away by machines. This does not mean that there will be less jobs but the jobs available will be a lot more skilled and require more mental strengths not physical.

From recent studies, in the next twenty years, roughly 7 million will lose their jobs because of technology.

However, as companies do not need to employ people to do manual labour at such a high cost, they will be able to hire more personnel. Therefore, robots will also generate around 7.3 million jobs. This means to secure a job in the future certain soft skills will be required and well-educated people will still be employed but those who are not able to do anything but manual labour will suffer greatly.

Conclusion The best way, I think as a nation we can get the most productive nation is through having a very well-educated nation. That said, this is not something that can be achieved easily.

In my opinion, the government should invest more in education and should provide the necessary funding for state schools. The government should also invest properly and not waste money in the name of education by giving it to private companies. This is not about trying to bring private schools down but trying to increase the standards of state schools and this needs to be aided by financial packages from the government More grammar schools should be opened and there should be tests at the age of 11 and 13 so there is more opportunity to get into them. The standard of state schools should hopefully increase if class sizes are decreased and this can only be done through funding.

Private schools that exist and are well established should offer a lot more bursaries and scholarships letting students in based on their academic, drama, music and sports abilities. This would mean that the schools would have to offer a larger amount of bursaries. Some school are already giving out a to of bursaries to support families. However private schools should also help those who struggle to learn and have any learning disability.

Harkirat Malhorta Not only people who are capable but anyone who has potential to do well and is keen to thrive should be provided with the education they deserve.

The opportunity to network should be improved in state schools, opportunities to try out for jobs in the future.

These are all vital to build a nation which is productive. Having extra curriculum activities which involve anyone who wants to take part should be encouraged. Activities such as debating should be done in every school. There should even potentially be a national debating competition in which all schools take part as a learning opportunity.

Getting rid of private schools may not be the solution but using them to benefit society could be. The facilities private schools have states schools will struggle to afford but sharing the facilities may benefit everyone. For example, playing fields are something which not every school will be able to invest in but private schools and sports clubs should offer state schools access to their facilities.

This will not only create a more productive nation but also a nation which is a lot fairer. Having an educated nation will help in lowering crime rates and many other issues we face in society today.

To solve our national productivity crisis, the country ought to step up their education system. The best way to do this is close the gap between state and private education. This gap can only be closed if the government invests properly and if there is more support in primary school for those children who are struggling. Upon children doing well in primary school, they will be more suited to pass their GCSEs and may even go onto doing A levels. Working as a community to support one another is also vital to narrow the social gap being created.

More scholarships and bursaries by existing private schools to more people is also another way the private sector could help.

The key difference is in the confidence that privately educated children have and the networking they are able to do. To give this opportunity to students from those schools they need to have a strong bond with the community and have other speakers coming to the school to help and encourage the pupils and also give them an opportunity to see what is out there.

Essentially the investment in state education is not only a way to create a more productive nation but also a nation which is fair. Investment in education is an investment in a better community, society and nation.

Harkirat Malhorta References https://academic.oup.com/ej/article/114/499/F499/5089322?login=true https://www.investopedia.com/articles/economics/09/education-training-advantages.asp https://www.britishcouncil.hk/en/stateschools_priavteschools https://www.investopedia.com/articles/economics/09/education-training-advantages.asp https://www.ifs.org.uk/publications/15025 https://commonslibrary.parliament.uk/proposed-changes-to-minimum-school-funding-schools-affected-byconstituency/ https://actiontutoring.org.uk/independent-schools-deserve-charity-status/ https://successatschool.org/advicedetails/545/What-are-vocational-qualifications%3F https://commonslibrary.parliament.uk/research-briefings/cbp-7972/ https://commonslibrary.parliament.uk/proposed-changes-to-minimum-school-funding-schools-affected-byconstituency/ https://www.gov.uk/government/news/new-education-recovery-package-for-children-and-young-people https://www.theguardian.com/higher-education-network/blog/2013/jun/04/higher-education-participationdata-analysis https://student-activity.binus.ac.id/bssc/2020/10/will-robots-reduce-human-employment/ https://youtu.be/AaApoIQ9tG8 https://youtu.be/uY-irwEiPHc https://youtu.be/887CJ53UCDE https://youtu.be/2b9wR98Hha0 https://youtu.be/MCzqywM5-H0 https://youtu.be/3bD_p1KloQg https://youtu.be/rjckE2HvnI4 https://youtu.be/Aa5zbnl3ZQI https://youtu.be/4YwFbZ7SR0E

Hyunjo Kim Problems in Calculus of Variations Hyunjo Kim

Radley College

Calculus of variations is an essential technique in many areas of sciences and mathematics. It allows us to calculate a function that minimises (or maximises) a given functional. In this paper, I explore the basic ideas of calculus of variations, using the geodesic problem as an example. I then derive the Euler-Lagrange equation, which is a key equation in solving variational problems. Solutions to selected problems in physics: Brachistochrone, Tautochrone problem, Optics, and Minimal resistance are discussed. Finally, I verify these solutions using computer simulations (independent of variational methods) to illustrate the power of variational calculus in solving physical problems.

1. Introduction

Calculus of variations is an extremely complex topic in mathematics and requires mathematical preliminaries. Before digging in, I suggest you take a look at the mathematical preliminaries section, which includes: integration by parts, differentiation, and partial derivatives.

The concept of partial differential equations (PDEs) proves to be very important as in complex physical systems, there will be more than one variable. We are normally accustomed to seeing a function, f (x).

However, it is more likely that we will be dealing with functions such as this one, f (y, y , x). dy When I write, f (x) note that it is equal to dx . Without the loss of generality, we assume that all the functions we deal with are continuous and smooth, thus differentiable. As I go through the proof of the EulerLagrange Equation, it will get clearer how to utilise it on problems that I have mentioned above.

2. The Euler-Lagrange Equation

Throughout the paper, I will write the Euler-Lagrange equation as the E-L equation for brevity. Before applying it, I will show the proof of the E-L equation.

Hyunjo Kim 2

Figure 1. Possible paths for the integral below. The solid line is a representa-

tion of the curve y(x) which makes I stationary. The dotted curves represent some possible variations.

2.1 Proof of the Euler-Lagrange Equation

We need to first consider this integral: I=

b

F (y, y , x)dx,

a

a and b denote the start and end. The integral, I represents the physics; we often see such functionals when solving problems in calculus of variations. A functional, unlike a function, is a real-valued function that takes a function as its input. That function, F (y, y , x) is dependent on curve y(x). There will be a certain curve such as y(x) that minimises (or maximises) the functional I. The exact form of this function is unknown, thus we can say that it can take the form of: Y (x) = y(x) + αη(x)

(1)

where Y (x) represents all possible functions that can take place and α represents the variation. So if we were to find the minimum of the functional I we would see: dI =0

dY (x) Y (x)=y(x)

(2)

But, essentially, what we are interested in is the variation α. So we can write it like this: dI =0

dα α=0

(3)

Hyunjo Kim 3

This is the condition we are interested in and we will use this to prove the E-L equation.

I=

b

F (Y (x), Y (x), x)dx

a

b ∂ dI = F (Y, Y , x)dx dα ∂α a b ∂F = dx a ∂α Where the I is at some value of α. The reason we use partial differentiation is because we have a function with more than one variable. Now, to show the last expression in a different way, we can use the chain rule:

b a

∂F dx = ∂α

b ∂F dY ∂F dY + dx ∂Y dα ∂Y dα a

Before we move on, we recall that the condition for our minimum was when our variation was equal to zero (α = 0, Y = y, Y = y ) and to simplify the expression above, we can use this: dY dY = η, = η dα dα Therefore, we have dI =

dα α=0

b ∂F ∂F η + η dx = 0 ∂y ∂y a

We can express the second part by Integration by Parts

where u =

∂F ∂y

b a

∂F b ∂F η − η dx = ∂y ∂y a

b a

d ∂F ηdx dx ∂y

and v = η . But we know that

∂F ∂y

η

b

a

= 0 because η(a)

and η(b) are equal to zero. Hence we have the following equation: dI =

dα α=0

b

( a

d ∂F ∂F − ( ))ηdx = 0 ∂y dx ∂y

and in order for the integral to equate to zero without the loss of generality, regardless of what the function η could be, it must follow that d ∂F ∂F − ( )=0 ∂y dx ∂y

Hyunjo Kim 4

,so we have this equation: d ∂F ∂F = ( ). ∂y dx ∂y

(4)

This is the Euler-Lagrange equation and it is a differential equation for function y(x). I will show you one way we can use this equation.

2.2 Straight line

It is a given that the shortest path between two points is a straight line. We can prove this using the E-L equation. We can first consider the figure below:

Figure 2. This is a random path between two fixed points. dx and dy denote

the horizontal variation and the vertical variation, respectively

We know that once we form a right-angled triangle, we can write 1

ds = [(dx)2 + (dy)2 ]1 /2 = (1 + y 2 ) 2 dx The total path from A to B is given by this integral: L=

b

1

(1 + y 2 ) 2 dx

(5)

a

One thing to note is that this equation does not include y (or x) ex∂F plicitly, so ∂F ∂y = 0 hence ∂y = some constant k by the E-L equation.

Now to find the path that makes L stationary, we can do this: 2y y ∂F = k= 1 = 1 ∂y 2(1 + y 2 ) 2 (1 + y 2 ) 2

Hyunjo Kim 5

if we rearrange and integrate it, we can find an expression for y: y=

k 1

(1 − k 2 ) 2

x+C

as you may have noticed, this is the form of a straight line y = mx + c k We can find the exact values if we know the where m = 1 .

2 (1−k ) 2

points. The function that minimises the functional is a line and we can prove this using the E-L equation. In the next sections, we will see how we can use the E-L equation to tackle more complex problems.

3. Brachistochrone Problem

The Brachistochrone curve, or the curve of ’shortest time’, is the curve of fastest descent where a particle slides frictionlessly from a higher point A to a lower point B under the influence of only gravity as shown in the figure below. You may assume that the fastest descent would be a straight line; however, calculus of variations tells us otherwise.

Calculus of variations is not the only way we can solve this problem.

When Bernoulli first proposed this problem in 1696, he used a geometric proof. But, for the sake of this paper, I will be using calculus of variations.

Figure 3. These are some of the possible paths for the brachistochrone problem

We know by the law of conservation of energy that the change of

Hyunjo Kim

6

potential energy is equal to the change of kinetic energy ∆GP E = mgy 1 ∆KE = mv 2 2 1 mgy = mv 2 2

v = 2gy

where g is the acceleration due to gravity and y is the vertical position. √ds . If we are to We know from classical mechanics that dt = ds v = 2gy integrate this to find the time with the limit from the start of the curve to the end, 0 to L, we can write it like this: L ds √ T = 2gy 0

But since we know that we can express ds as ds = dx 1 + y 2 , a 1 + y 2 dx T = 2gy 0 Note that the limit for the integral changes as we are now integrating with respect to x. For now, we can ignore the constant √12g .

T =

0

a

1 + y 2 dx y

As you may have noticed, the functional looks a lot like the one we 2 encountered when applying the E-L equation. Hence if F = 1+y y , 1 ∂F =− ∂y 2

1 + y 2 y3

y ∂F

=√ ∂y y 1 + y 2

By Eq.(4), we need to find

y d

√ dx y 1 + y 2

which through some rigorous calculations can be said to be equal to: 2yy − y 4 − y 2 3

2(y(y 2 + 1)) 2

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So the full E-L equation will look like this:

1 1 + y 2 2yy − y 4 − y 2 − = 3 2 y3 2(y(y 2 + 1)) 2

(6)

Once rearranged and simplified, it will look like this (assuming y > 0): y 2 + 2yy + 1 = 0 Before we do manipulate this equation, I will multiply y on both sides: y 3 + 2yy y + y = 0 We can work out the antiderivative of this:

d 3

2 =0 y + yy y + 2yy y + y = dx Hence, we can say that:

y + yy 2 = C

where C is some constant. By rearranging this equation, we can get:

dy C −y = y = dx y which can be written as an integral:

dx = x=

y dy C −y

y dy C −y

In order to integrate the RHS, I will use Integration by Substitution where y = C sin2 t, dy dt = 2C sin t cos t, hence dy = 2C sin t cos tdt.

C sin2 t 2C sin t cos tdt x= C − C sin2 t

= 2C sin2 tdt

1 1 = 2C − cos 2tdt 2 2 1

1 = 2C t − sin 2t 2 4 using the trigonemetric identity, cos 2t = 1 − 2 sin2 t we know that sin2 t = 12 − 12 cos 2t, so we have two parametric equations: x(t) = Ct −

C sin 2t + D 2

(7)

Hyunjo Kim 8

C C − cos 2t (8) 2 2 You might notice that these parametric equations form a cycloid (inverted): x(t) = c(t − sin t) y(t) =

y(t) = c(1 − cos t) So, after all, the descent of shortest time is not a straight line. In fact, it will look like a cycloid (bottom path in Figure 3). Now, I will prove the tautochrone property of the brachistochrone curve.

3.1 Tautochrone Property

The tautochrone property is the property of ’equal time’. This means that if you put the bead at different positions on an inverted cycloid, both of the beads will reach the bottom at the same time. In order to prove this property we know that from the parametric equation for y that the value of t that gives the maximum is π. Also, we can find out that from the law of conservation of energy and our definition of time that:

t=π dy 2 2 ( dx 1 1 ds dt ) + ( dt ) T =√ =√ dt y − y0 y − y0 2g 2g t=t0 Now, we can substitute our values

(

also, √

dx dt

= c(1 − cos t) and

dy dt

= c sin t

dx 2 dy t ) + ( )2 = (c − cos t)2 + (c sin t)2 = 2c sin dt dt 2

y − y0 =

(9)

√ c(1 − cos t) − c(1 − cos t0 ) = 2c cos2 t0 − cos2 t (10)

Therefore, our integral looks like this once we substitute our values, π π 2c sin 2t sin 2t 1 c √ √ √ √ dt = T = g t0 cos2 t0 − cos2 t 2g t0 2c cos2 t0 − cos2 t Now, we will be using Integration by Substitution, where u = du dt

=

− 12 sin t cos 20

t 2

cos 2t t cos 20

. Hence, sin 2t dt = −2 cos t20 du,

0 −2 cos t20 c

g 1 cos2 t20 − cos2

1 2 cos t20 c

du = g 0 t0 2 u cos2 t20 − cos2 2

t0 2 2u

du

,

Hyunjo Kim 9

For now, we will ignore the constant in front. The limit changes from 0 to 1 as at t0 Then, the integral simplifies to: 1 1 √ du 2 1 − u2 0 this becomes: 2[arcsin u]10 = π bringing back the constant, T =

c π g

as c, g, and π are all constants, we can say that no matter where they start, the time to reach the bottom will always be the same. This is the tautochrone property of the brachistochrone curve.

3.2 Python Simulation

To additionally confirm our result from the brachistochrone curve, I will show you how we can adopt this problem on Python. Instead of using our mathematical techniques, the programme will use more computational methods such as numerical integration. Here is the code: https://replit.com/@hjk922/RandomCode#main.py The result is shown below:

Figure 4. Computational results for the brachistochrone curve

4. Optics

In this section, we will look how we can use calculus of variations when trying to find out more about the behaviour of light.

Hyunjo Kim 10

4.1 Behaviour of Light

You may have seen that on a hot day, the space on top of the road would look like a fluid like the figure below.

Figure 5. Refraction of light in hot air

This, in fact is because the speed of light is different due to the refractive index of the air above the road. As it is hotter, the air is less dense, which is why it has a different refractive index. We know that the speed of light in the medium will be v = nc where n is the refractive index. Consider this integral,

1 1 T = dt = ds = nds v c

1 y2 = f (y) 1 + x2 dy. c y1 Note that our refractive index is function of y as our refractive index changes as we go up or down. So, we have a function 1

F (x, x , y) = f (y)(1 + x 2 ) 2 Now, the E-L equation we will use in this case will be But, as it does not explicitly contain x, we have:

d x √ f (y) · =0 dy 1 + x 2 hence, f (y) · √

x =C 1 + x 2

which then can be rearranged as x =

C dx = dy dy f (y)2 − C 2

∂F ∂x

=

d dy

∂F ∂x

.

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and once we integrate, x(y) =

C f (y)2 − C 2

dy

Before finding a simpler expression, you can write n = f (y) = n0 (1 + αy) as the refractive index increases linearly with height (NB α is an arbitrary constant). So, we can write function x(y) as:

C

x(y) = dy n20 (1 + αy)2 − C 2

C 1

= du n0 α u2 − C 2 /n20 α2

where u = y + 1/α, so du = dy follows. Now, we can substitute u = C C n0 α cosh θ. So, du = n0 α sinh θdθ. After substituting and integrating, we will get: C x= θ+D n0 α

but since u = y + 1/α, θ = cosh

−1

n α(y + 1 ) 0 α +D C

which gives us our final equation for x x=

n α(y + 1 ) C 0 α cosh−1 +D n0 α C

and making y our subject, y=

αn 1 C 0 cosh (x − D) − n0 α C α

Once you put in some arbitrary constants (slide appropriate values), you will get a graph of a curve. In fact, that is the very behaviour of light. The reason we see the phenomenon portrayed in Figure 5., is because light is bending, giving a wavy effect.

5. Minimal Surfaces

Consider a surface of rotation. Our problem for Minimal Surfaces is: what is the function y(x) that minimses the surface area? When

Hyunjo Kim 12

looking at the small change of the surface area dA, the surface area will look like: dA = 2πx · ds where x is to be the radius and ds is to be the rise so x2 x 1 + y 2 dx A = 2π x1

so our function F (which does not explicitly contain y) is equal to: x 1 + y 2 , hence by the E-L equation: y x · =k 2 1 + y 2

where k is some constant. After squaring this expression and rearranging we get the equation: y = √

2k − 4k 2

x2

and by substituting a = 2k, y = √

a x2 − a2

by integrating we have: y=

x2 x1

√

a dx x2 − a2

now we substitute x = a cosh t and dx = a sinh tdt,

a

y= a2 cosh2 t − a2

1

= dx cosh2 t − 1

1 dx = sinh t

1 = a sinh tdt sinh t

= adt = at + C

= a[cosh−1

x a

]+b

This, in fact, gives the curve called the catenary curve. Interestingly, this shape is exhibited in soap films as the stable shape of a soap

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film is the one that minimises energy, which will then be the one that minimises the surface area.

6. Mathematical Preliminaries

In this section, I will introduce some mathematical preliminaries required to fully understand the paper.

6.1 Partial Differentiation

I believe that everyone reading this paper will be familiar to the rules of usual differentiation of one-variable functions (functions of x only etc.) The definition of the derivative of f (x) is: f (x + ∆x) − f (x) . ∆x→0 ∆x

f (x) = lim

For example, if there is a function: f (x) = 3(x2 + 1)2 ,

(11)

the derivative of this function f (x) is: f (x) = 3(2(x2 + 1)2 )(2x) = 12x(x2 + 1).

(12)

I will assume the working knowledge of the usual rules - chain rule, product rule, quotient rule etc. Differentiating an one-variable function is easy. However, in mathematics and sciences, we often encounter functions that are functions of more than one variable. As an example, the pressure p of a gas will depend on its temperature T , volume V , and the number of gas particles measured by the number of moles n.

Thus, we can say the pressure is a function of (T, V, n) such that: p(T, V, n) = ...

(13)

Now consider a function, f (x, y). The partial derivative is denoted by these definitions: f (x + ∆x, y) − f (x, y) ∂f = lim ∂x ∆x→0 ∆x

(14)

f (x, y + ∆y) − f (x, y) ∂f = lim ∆y→0 ∂y ∆y

(15)

If we were to find the first partial derivatives of function, f (x, y) = 2x3 y 2 + y 3 . It would look like this: ∂f = 6x2 y 2 , ∂x

∂f = 4x3 y + 3y 2 ∂y

Hyunjo Kim 14

As you can see, when we compute the partial derivative of f with respect to x, we consider the other variable (y) is considered to just be a constant and the same applies when we find the partial derivative of f with respect to y. Another important thing to note are the second partial derivatives. For a two-variable function f (x, y) they are ∂2f ∂ ∂f ( )= , ∂x ∂x ∂x2 ∂ ∂f ∂2f ( )= , ∂x ∂y ∂x∂y

∂2f ∂ ∂f ( )= , ∂y ∂y ∂y 2 ∂ ∂f ∂2f ( )= . ∂y ∂x ∂y∂x

Thus, using our example from above, our second partial derivatives would be: ∂2f ∂2f 2 = 12xy , = 4x3 + 6y, ∂x2 ∂y 2 ∂2f = 12x2 y, ∂x∂y

∂2f = 12x2 y ∂y∂x

Before introducing the total derivative, I will show you what the chain rule in partial derivatives looks like. Normally, the chain rule will look like this: (f (g(x)) = f (g(x))g (x). Now, what will the chain rule for partial differentiation? Consider the function f (x, y), where x and y themselves are a function of another variable, u. If you wish to differentiate the function f , we could imagine two paths. Path 1: f to x(u) to u, Path 2: f to y(u) to u. ∂f dx ∂f dy df = + du ∂x du ∂y du This will prove to be very useful when we solve problems and can be used to provide a direct method for calculating the total derivative of f.

6.2 Total Derivative

Although we can directly calculate the total derivative using our result from above, it will be clearer to use an alternative method. First, df ∆x consider a one-variable function f (x). We know that ∆f ≈ dx through linear approximation.

For a two-variable function f (x, y), we can understand the total derivative by thinking of a plane. Let’s say we have point A that is on the plane, which is vertically lower than point B. We can equate this rise from A to B, the total rise to be equal to the rise due to x + the rise due to y: ∂f ∂f ∆f = ∆x + ∆y (16) ∂x ∂y

Hyunjo Kim 15

this is where partial derivatives become useful as we are looking at the rise from both of the variables separately. And as ∆x and ∆y become very small (tend to 0), we have our definition of the total derivative: df =

∂f ∂f dx + dy ∂x ∂y

6.3 Integration by Parts

The substitution rule for integration corresponds to the chain rule for differentiation. The product rule corresponds to something called the rule for integration by parts. This is the product rule: d [f (x)g(x)] = f (x)g (x) + f (x)g(x) dx This can be integrated,

f (x)g (x)dx + f (x)g(x)dx = f (x)g(x) If we rearrange the equation,

f (x)g (x)dx = f (x)g(x) − f (x)g(x)dx This is the common formula for integration by parts. You may have seen different versions, but they are all the same. I will show how we can use this to answer a question like this:

x sin xdx = f (x)g(x) − f (x)g(x)dx

= x(− cos x) − (− cos x)dx

= −x cos x + cos xdx = −x cos x + sin x + C

7. References References [1] Riley, K. F., et al. Mathematical Methods for Physics and Engineering. Mathematical Methods for Physics and Engineering. Cambridge University Press, 2006.

[2] Boas, Mary L. Mathematical Methods in the Physical Sciences. Third ed., Wiley, 2006.

Hyunjo Kim 16

[3] Grasmair, Markus. BASICS OF CALCULUS OF VARIATIONS, Department of Mathematics, Norwegian University of Science and Technology, 7491 Trondheim, Norway, 2015, wiki.math.ntnu.no/media/tma4180/2015v/calcvar.pdf.

[4] Freire, Alex. THE BRACHISTOCHRONE PROBLEM, Department of Mathematics University of Tennessee Knoxville, TN 37996-1300, www.math.utk.edu/ freire/teaching/m231f08/m231f08brachistochrone.pdf.

[5] Takeuchi, Tatsu. The Tautochrone/Brachistochrone Problems: How to Make the Period of a Pendulum Independent of Its Amplitude, Department of Physics, Virginia Tech, Blacksburg VA 24061, USA, 12 Oct. 2019, www1.phys.vt.edu/ takeuchi/Tools/CSAAPT-Fall2019takeuchi.pdf.

[6] Zheng, Siqi Clover.

CALCULUS OF VARIATIONS: MINIMAL SURFACE OF REVOLUTION, 2019, math.uchicago.edu/ may/REU2019/REUPapers/Zheng,SiqiClover.pdf.

[7] “The Calculus of Variations.” Principles of Optics: Electromagnetic Theory of Propagation, Interference and Diffraction of Light, by Max Born et al., 7th ed., Cambridge University Press, Cambridge, 1999, pp.

853–872.

[8] Nearing, James. Calculus of Variations, Physics 315, University of Miami, www.physics.miami.edu/ nearing/mathmethods/variational.pdf.

Rory van der Grift

How to start a business when you are young

Rory van der Grift

Contents 1. Initial concept (i) Idea/design (ii) Name, logo and strapline

2. Company setup (i) What type of company you want to be e.g. self employed or Ltd etc (ii) Trademarking and copyrighting (iii) ESG or not

3. Marketing (i) Website (ii) Social media platforms (iii) Market research

Rory van der Grift

4. Manufacturing (i) Research materials (ii) Find manufacturer (iii) Sampling

5. Packaging and delivery (i) Design packaging (ii) Source delivery options

6. Launch!

Rory van der Grift

1. Initial Concept

Idea/design This is the first stage to starting a business. You need a good solid idea and you need to know what you are looking to achieve with this product or service.

Whether you want to gain wealth or fame or whether it’s something which you want to enjoy. An effective way to form a good idea is to think about your interests in life and some problems in the world at the moment. Then see if you can find a way to link them both together, such as a clothing brand made of recycled plastic etc. (This has been done already so it’s just an example).

Rory van der Grift

Name, Logo and Strapline The Name, Logo and Strapline are some of the most essential parts of a business. These are how customers will remember your company. They need to be memorable, catchy and fun.

The Logo must be aesthetic and pleasing to the eye and could contain the name and strapline if you want, as shown above.

There are many logo makers online, some might cost money, but some are free.

There are also companies called website builders who can build your website and logo, but the strapline and name are completely up to you.

Rory van der Grift

2. Company setup

What type of company you want to be There are three basic types of company. There are private companies limited by shares, (LTD). Public companies, (PLC) and there are one person companies.

Private companies allow you to hold more of the shares of your company and therefore you have more control because they are not open to the public.

Public companies' shares are open to the public. To become a public limited company, your company must float on the stock market and your shares will become available for investors to purchase. Going public increases prestige and helps a company raise capital for future investment.

Single person or sole trader companies are self employed and often are smaller companies .

It is very important that you take advice from an accountant before you make your decision.

Rory van der Grift

Trademarking, Copyrighting and Registering The three abovesaid words are legal ways to protect original ideas from being stolen and used by someone else .

Copyright is for drama, music, literature or intellectual property.

Once something is finished it receives copyright protection.

Trademarks are used for words, symbols, devices or names that are used for recognizing a company or manufacturer.

Registered, or Registered Trademark means that if the trademark has registration, it is illegal for another company to use whatever has been trademarked.

Rory van der Grift

ESG or not?

ESG stands for Environmental, Social and Governance. This is really becoming an important factor for whether investors invest in your company. ESG are the three main factors in measuring the sustainability and societal impact of a company or business.

It would be very wise to consider ESG as an integral part of your business because you are more likely to gain popularity with investors and the general public, and it also helps the planet.

Rory van der Grift

3. Marketing Website and Social Media platforms.

Marketing is very important because it can make or break a business. Getting your business out there is essential to success because you need a website which is attractive and easy to use.

Also, you need to have accounts on social medias such as Instagram, Twitter and Facebook. The rest such as Reddit, Snapchat, TikTok etc aren’t as essential as the others for advertising and marketing because of the way they function at the moment, but things could change in the future.

There are companies known as website builders who you can pay to build a website for you if you give them the right specifications, although they can be quite costly. There are alternatives such as Wix or Godaddy, these let you build your own website with a small monthly fee.

Another thing to consider is payment methods on your website, many people use PayPal, which can be an expensive option as they charge you for each transaction, but new options are being introduced all the time.

Rory van der Grift

Market research Market research provides critical information about the market you will operate in. Market research is where you research who else is making similar products to you, so in other words, you are finding out who your rivals are.

You do this to see what you can do to be better than them. You should research the approval rating of your rivals from the general public to see if you can improve from their mistakes and you must try to learn who your customers really are so you can tailor your products to that type of person.

Rory van der Grift

Researching materials and finding a manufacturer When you research materials, you decide what materials you are going to use for your product, if you are supplying a service then this doesn’t apply to you. Good materials to use would be recycled plastic or recyclable plastic or fabrics made of plastic bottles etc. These materials are all better for the planet and therefore may also have the added benefit of making your product more sellable.

When finding a manufacturer, you should research on the internet and choose a country you would like to manufacture in.

Do some research and send some emails to the ones which attract you. Once decided on a manufacturer, always take in the work conditions in the factory, how often they check the machines and how they treat their employees. A good way to do this is visit the factory in person.

Rory van der Grift

Continued...

Sampling

Once you’ve found a couple of manufacturers, you ask them to make up a sample to your design using the materials that you have chosen. After it is produced, you can then begin to discuss pricing and minimum order quantities (MOQ). Minimum order quantities fluctuate between each manufacturer, they are the minimum amount you can order at any one time.

Rory van der Grift

5. Packaging and delivery

Design your packaging Packaging must have your brand on, it should advertise to anyone that looks at it. It must have your logo and name plus maybe your strapline. You should aim to make your packaging as sustainable as possible, and don’t over pack.

What I mean by this is don’t waste lots of packaging on one tiny package, be sparing with your packaging. This helps the planet and you because you don’t have to produce as much packaging, and you don’t have to spend as much on packaging.

Rory van der Grift

Source delivery options To start off with, you may want to package and send out your product yourself, but as your company grows, it would be more convenient to use a company that provides a service where they keep the stock at a warehouse and package and send the product out for you. They will also order new stock as its needed. This will free you up to work on other aspects of the business.

Rory van der Grift

Launch!

You have only got one thing left to do, and that is launch your business! You need to publish your website and then you are finished. All you need now is to launch. A good way to announce your launch is to have a party with a big banner and invite all your friends. Other ways are announcing it on all of your social media platforms. Send invitations out to people who you think might help your business such as people that inspire you or influencers.

You could also offer a discount code for anyone that attends your party or anyone who visits the website for the first time.

Well done and good luck!

Milo Donovan The Red Tsar From the balcony he gives his address, a revolutionary reactor.

A catalyst from a mount on high to the mounds of heads.

The world listens with intent, with vigour, For from those wise eyes and iron boots treads A drive for gain, and act, and rigour.

A new dynasty reels from the past dreads.

And as the new god shows His trajectory, A Generalissimo - of the reds, Propelling men to their true destiny; Custom is torn to shreds.

For mere men exposed to Him blind, They feel the full weight of earth’s compression.

For He knows man’s ills much as the crystalline structure of their mind.

They learn to show themselves no mercy, a bodily repression.

And as Russia’s prominence ticked up, he would wind.

The first, second, third five year plan etched by, The glory of the budding plant drawn silently to light.

And by His name, His liberation they did provide; Here incarnate a Lord of binding might.

Whilst a key to locked Orthodoxy clicks and swings wide.

As collectivisation and reformation did show Russia’s gilding, With new tactics and His plan guiding forth to new heights.

While peasants ploughed and workers cut, He was building Up from dawn on the new empire rising, our true delights.

A new era beckons one so hilding.

The utmost devotion is mandatory to God’s memoir, A master who is no preacher, no, a Messiah; All graciously give way to the white Jaguar, Lord of empire, industry and Gaya.

Even time, the reaper of most, falls by to Koba.

Edifices and institutions grow like shoots From the ground under Russia’s fertile soil, Roots grasping the initiative, branches bearing their fruits.

His single minded drive to achieve a destiny less toil, Reshaping education, law and culture for greater attributes.

Milo Donovan

The cost of success is always a heavy toll, Always to try and make the kingdom lusher, Taxing on morale, the people’s soul, But none so much as The Red Tsar’s Russia.

A republic growing beyond control.

Yet, unbeknownst to the world, waiting to unfold, A gulag looms in the frost bitten underbelly of Siberia, Enslaving those who dare oppose the beast, left in death’s mould.

A screaming tormenter to those who reject The Cause, dealt manic hysteria.

Just a backwards glance will sentence a man to hell tenfold.

For a few though, the prospect is rather grimmer, Gunpowder and smoke echo in their ears, The blast of oppression and light growing dimmer, In launching men to terror beyond any tears, Waking to some forgotten, purgatory blur.

In face of facts, searching for an ulterior motive’s location, Utter butchery, complete dominion; The power to grasp a nation’s formation; In its way stands peace, a quivering minion.

Society’s right to suffer liquidation.

And as the Red boils up, the blood flag shrill, On does He watch, His divine mission soars along.

The perfection of power, a lord of skill, Ever pristine, with eagles to pick Him clean of wrong Watches on, to the beauty of evil.

WILL ROQUES THE RUSSIAN REVOLUTION The Russian Revolution- how did it happen and could it happen again.

Revolutions. A thing of the past we may think. But is it? Are these things that we see as something of the past or are they something that could potentially be looming right round the corner. You could say that the conditions outlined by Marx for the demise of capitalism are more in place now than ever.

Perhaps the brand of capitalism that is being showcased across the world today is very similar to the brand of capitalism that Marx sought to destroy. Or for example the February revolution, the ‘dress rehearsal’ for the infamous ‘October Revolution’, this was started (or at least the start of the strikes, protests and eventual overthrowing of the tsarist regime that was marked as the February revolution, this was by no means a cause of it, merely a match to an ever- growing bonfire). But these protests on international women’s day were started by the peaceful protests for international women’s daypeaceful turned violent. Can you think of any legitimate, good protests that have gone violent on a large scale recently? Exactly. Is the revolution that Marx foretold over 100 years ago starting to gain footing today? We shall see.

First we must ask why the revolution happened in the first place? Was it the release of pent up anger from the Bloody Sunday massacre in 1905, when tsarist soldiers fired on innocent civilians. Or perhaps the influence of the industrialisation of Russia on the people. Perhaps the new expansions on the technology front made the Russians realise that their government was the thing that was really out of date.

The government in Russia was at that time, run by the tsars- absolute monarchs. Virtually all over Europe the idea of ‘absolute monarchy’ had become very alien. The tsarist regime was, as one can imagine, not too much in favour of the proletariat. It was not good for the working class. The aggravation caused by this way of government would eventually culminate in the October revolution of 1917 and the complete transformation of Russia into what we know it as today.

At the beginning of the 20th century Russia was seen by the rest of Europe as very backward- absolute monarchy. One of the last times a monarch had a belief in the divine right of kings it did not end too well. A form of the feudal system that had disappeared from Europe over 300 years ago was still in place. At the time Russia was one of the most impoverished countries in Europe, with serfdom only being abolished around 40 years ago. Russia was also very unindustrialised at the time whereas the rest of Europe was undergoing very heavy industrialisation or had already gone through the the process. When it finally did this was about to cause massive changes. The affects of this we can still feel today. In the 19th century Russia experienced a massive population boom. This would then mean more people would be in jobs and pay would have to be lowered so that the government could afford it. Furthermore after a series of very costly wars beginning with the Crimean war in the 1850’s and a massive empire to feed meant food shortages became commonplace in Russia.

Low pay, lack of food- of course this had to go somewhere, and it did. It would start out peacefully with protests against the monarchy which subsequently would lead to the Bloody Sunday massacre of 1905. This would evidently not be taken too kindly by the public and it lead to to a series of workers strikes that would prove to be temporarily crippling for Russia. The next scrap of meat that was to be thrown to the great bear was Russia’s entry to World War One in August 1914. A war, even when you completely disregard the outcomes, can be socially, economically and politically crippling for a country. And in the case of Russia it did just that. The ways in which the Great War crippled Russia number many but here are just a few: the economic impact is fairly obvious- the enormous cost of the front was due to the constant destruction of the Russian forces at the front. The soldiers needed food and this would be another cost. They needed ammo. They were ill supplied. Very badly undersupplied. The morale of the Russian people would drop every week. Every week more soldiers would be sent back to Russia either in the bleached white coffins of WW1 or severely injured whether this be mentally or physically. And eventually the casualties, in fact very soon, would become far too

WILL ROQUES

much for the Russian force to handle. This was also despite the fact that one of Russia’s supposed only advantages was that of its seemingly endless supply of men. But as I said its ‘seemingly’ endless supply of men. Most of these men were already the sole male worker in their family and therefore could not go to war. Another large portion of these men were too young to be mobilised. Further disadvantages came in the fact that the Russian army at the time was in a system where when the first levy of men was exhausted the second would come in to take their place. Yet the men of the second levy were poorly trained and therefore were simply outclassed by their German opponents on the eastern front. Whether or not there was a situation of revolution before the war is a question still mostly shrouded in mist but there is not doubt that the war was a very significant cause of the revolution. The military defeats turned the Russian people against the so called German government (the tsarina was of German descent thus leading to rumours circulating that the court was working against the people). On the back of this it was then seen patriotic to remove the treasonous and incompetent government form power. The February revolution would become a peoples uprising against the monarchy and its autocratical ways. It brought to the front of the people’s minds a view of ‘new’ Russia. A new country with ‘bread, peace and land’. Yet at the time of war- not before it and not after but during the war none of this mindset was present. As in many other European countries the spirit of the war would unite the country and in Russia this was also the case. The storm was calmed for a moment but this moment would prove to be fleeting. Yet in this short time things did change; the constant workers strikes were paused for a moment and there were mass arrests of Bolsheviks. Whilst this may not have been too good for the revolution and its progress, it provided a moment of political peace in Russia. More of this was provided when the Duma (an elected body of politicians that unlike Russian politics at the time provided a very early, yet important role in moving Russia over to parliamentary government. But this was only a moment of peace that the nationwide sense of unity provided. The war was to strengthen the already anti-German views in Russia. Yet the view of patriotism that the war aroused was only for the few. The pensant soldiers did not even know t ].he extent of the empire that they were fighting for, and they only had the slightest notion of what the war had to do with them. But there was hope for the Russians, for a bit. When the war really did start to become the so called war of attrition the weaknesses of the Russian military really began to show.

Due to the political and social disruption caused before the war, the country was in no way ready for a long term war. The country itself was not ready, let alone the governing system who were managing it. The war became a crippling blow to Russia with the highest casualties of the war at 9,150,000 and the second highest deaths of the war at approximately 1,700,000 with Germany just in front at approximately 1,773,700 deaths. The war put the country in a situation for a revolution perhaps not starting the revolution itself but it put the country into the social, political and economic situation that it would need to be in for a revolution.

Another way in which Russia was changing at the time- and eventually changing to the brink of revolution was the movement towards a parliamentary government. At the time Russia was almost completely void of a democratic system. Yet once power, albeit little power was given to the people things would start to change. With the proletariat seeing that some of their own could start to get some position of power, again although it was a small one, this gave a sense of confidence to the people- there was a chance that they could be heard- the power was coming to the people in a way. It was from here that the people started to think that they could seize control. This along with the ideals of Bolshevism and Marxism gave the proletariat just what they needed to begin the revolutionary ‘process’. The ideas of the people after the war became those of the fact that the government- who was supposedly responsible for their wellbeing had made them fight a war they had no hope of winning. The transport system was too weak, the soldiers were supplied poorly. There were stories of the second line of men relying on the rifles of their first line comrades shot dead in front of them- they had no weapon so they just had to find one. The soldiers were trained without rifles. Something similar to the broomstick and potato training that was given to the young men in

WILL ROQUES

World War Two. The war was arguably a huge disaster for the Russians and the country’s political social and economic state and the anger of the great bear was finally released.

February 1917. The first of two acts. It began with bread. Quite literally. But it was not quite the problem that we would automatically think of. There was enough grain in the storehouses to feed the people. The problem was the Russian transport system. The rail system in particular. The freezing winters of Russia in 1917 destroyed the transport system to a degree. The economic damage caused by the war meant the Russia government simply did not have enough money to upgrade its rail system to the more modern systems that were in place and being put into place across Europe.

Thousands of workers were laid off who worked in the bread industry. Women queued outside bakeries all night just to be told at the break of day that there would be no bread on sale that day. And from here the people were people and rumours began to circulate that the capitalists were holding all the supplies for themselves and driving up the prices. The word capitalists was at the time synonymous with the German or Jewish merchants. This was not the fault of the people however. It was a combination of lack of information and clarity from the government along with a slight tinge of xenophobia. (After the war Russia had become a bit more ethnically diverse than it once had been).

On the 19th of February 1917 the authorities in Petrograd would announce that rationing would begin on the 1st of March.

With food man is happy. Without it he is not. This then followed with panic buying, not unlike the panic buying that we saw less than a year ago with the introduction of the first lockdown.

Fights also broke out along with minor rioting, seeing several shops vandalised. Then on the 23rd of February 1917 it all began. It was a relatively warm day for the capital with temperatures rising to an almost spring like minus 5 degrees. The 23rd was international women’s day, this being a relatively important day in the Bolshevik calendar. At midday the protests- largely consisting of female office and shop workers began as the group marched towards the city centre and began to protest (relatively peacefully) for equal rights. The slightly warmer weather increased the turnout to the protests by a considerable amount and spirits were high. Yet the tide was about to turn. The female workers, specifically those of the Vyborg factory district had come out to the protests not to be for women’s rights, but for bread. Along with the men of the metalworking districts they came with the chants such as ‘down with the Tsar’. Every day the crowds would get bigger. Fights broke out with the police and the protesters tried at one point to the soldiers onto their side. One thing that really stood out to the people was the lack of policing of the event. They were expecting the protests to be heavily controlled, such was the nature of the government. There was a few policemen and Cossack soldiers at the occasion but very little, if any action was taken against the protesters- a stark comparison to the protests 12 years ago and the events of ‘bloody Sunday’. Perhaps the thought was that if the people were free and left alone then perhaps they would not become so angry with the government and the momentary spirt of protest would die down and nothing further would happen but this peace would only last until the 26th, after three, arguably successful, days of protesting the tsar ordered the chief of the Petrograd military district to ‘put down the disorders tomorrow’ and put down they would be. Overnight the city became a militarised camp and the following day the events of bloody Sunday were to be repeated. At noon the protesters came out once again from their factory districts and marched to the city centre but this time they were not to make it to the city centre. As the crowds came towards the Nevsky Prospekt, police soldiers fired one the protesters from many angles- virtually making escape impossible. the next morning however, when the soldiers were ordered again to fire upon the protesters who came out again unperturbed, yet this time they would not fire on the people but their own commanding officers.

The soldiers then proceeded to join the crowd. And the side of the people in general. The other

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regiments deployed in Petrograd would soon follow suit. This mutiny advanced the protests into a full-blown revolution. The tsarist authorities became almost without power and were afraid to send in troops from the northern front in fears that Russia would start to lose their already weak foothold in the war. Yet this did not grow fast. The military presence in the city meant that despite the mutinies there was some form of control over the revolutionary crowds. As well as this there was no proper support of leadership of the people as many of the socialist parties were caught off guard with many of their prominent leaders in jail. But eventually the revolution would disband until October when the real revolution began. With the tsarist autocracy being overthrown as a result of the February revolution the October revolution was more of a killing stroke that would put the country through the change into what we know as the USSR. Russia had been run by a ‘provisional government for the interlude between the two revolutions.

The provisional government was thought that it would subdue the revolutionary spirit as the tsarist influence was now removed from the Russian government. The first scene of the October revolution would start as the socialist revolutionary party ( left SR’s) held power in the provisional government. This angered the Bolsheviks greatly and subsequently began to call for a military uprising. With aid of the military would be much needed in order to gain power over government to ensure that they (the Bolsheviks) did not instantly loose power. The Petrograd soviet, let by Trotsky also supported this uprising. In an attempt to control the rumours of uprising spreading further, he provisional government shut down all the newspaper shops and restricted the printing of newspapers in the capital (at that time the capital was Petrograd not Moscow). As a result of this a few small armed skirmishes broke out but this would be a mere scratch compared to what was going to happen the following day. The next morning the revolution came into full swing. This began as thousands of soviet soldiers sailed into the Petrograd harbour and came to please the wants of Trotsky with the Petrograd soviet and the wishes of the Bolsheviks in general. The parties, along with the help of the soldiers began to control various government buildings and taking some of the government’s power with them. However, they were still to take the centre of power, the winter palace. Here resided the provisional government. This was to be taken from them the following day and with this power was taken from the SR’s. with power now in the hands of the Bolsheviks, Trotsky dismissed all opposing parties from the assembly of the provisional government (this being the Mensheviks and SR’s). the provisional government was not destroyed however. Russia would then descent into a partial civil war ending in late 1922 with the formation of the Soviet Union. The end of the civil war would be labelled by the Bolsheviks as a completion of their ideology- the victory of the worker over capitalism.

I think that across the world a revolution is far closer to happening than we actually think. The arrival of a political ideology that we shun almost across the entire world could be about to creep back into our society and we completely unawares could be thrown into a full scale revolution just like that of Russia’s in 1917. The circumstances are there but not all in one place. Yet they are still there and that is where the issue lies. The main three circumstances that one can find in Russia at the time are in three categories those of political situation, economic situation and lastly the social situation in a country. I think that a revolution relies on these three things. Yet the case of Russia was relatively unique and the ideals of the revolution were based on the opinions of Friedrich Engels and Karl Marx laid out in one document- the communist manifesto. The manifesto itself was published as a platform for the then called communist league.

One belief stated is that of the fact that as long as man has existed they have been in a struggle of class- the bourgeois and the proletariat. This is the struggle that we see every day in societies across the world. For example in south Africa- one of the largest wealth gaps in the world.

The top 20% of the population holds nearly 70% of the income compared to the average of 47%

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around the world. This figure is not one dissimilar to that of Russia in 1917. The similarities are there.

They are waiting.

One of the main factors that influenced the Russian revolution, or was rather the catalyst to the Russian revolution was that of the economic situation at the time. Although the circumstances are there they need something to trigger them- the match to an ever growing bonfire. The economic situation in Russia at the time was catastrophic. The war was still raging across Europe and in an effort to help that much of Russia’s money was going to the eastern front. This along with considerable amounts of supplies that were needed on the front would go on to completely cripple Russia I an economic way. Prices for even the simplest things skyrocketed. This would add to the content of the February revolution as they became more like riots for food and economic stability than the international women’s day marches that they started out as. Across the world we see many examples of inflation on massive scales. For example in Venezuela, although it is not as large of a country as say Russia it is still one of relative significance. Over the year 2018-19 there was an inflation rate of 300,000%. Comparatively to the inflation rate of Russia at the time of the revolution this is an enormous change. The precautions that are and have been put in is again not dissimilar to what happened in Russia. The constant introduction of new currency and many other things were both commonplace in both situations. The situation is there for a revolution to happen. Basic foodstuffs are scarce. In fact, it does not need to be as specific as just one country. Any nation with any major inflation problems would be at risk from this. I think that one of the main criteria for a revolution is that of an inflation problem, or more generally a bad economic situation, this subsequently throwing the country into a situation that only gets worse. Prices go up, the people become angrier. Yet this factor of the economic situation is just one of the elements that is needed for the fire of revolution.

The next factor is that of the social situation and to what degree the people are behind any given revolution. Without the support of the people one will end up with a situation like that of Myanmar as of a few months ago. The people and the military are divided and the situation becomes that of a revolution that has gone hideously wrong. One will end up with a constant struggle for power between the people and whatever party has initiated the revolution- the military often or otherwise (for example the Bolshevik party). The peace and change of power that the revolutionaries seek can never be maintained and will fall apart very quickly. However there is still a spark of what some will call hope, others hell. The Russian revolution did not change Russia instantly.

The events of October and February 1917 sent Russia into a civil war that would last until 1923 with the formation of the USSR. But here another element of the social situation must kick in. The people must understand the revolution. If it is to become a so-called peoples revolution like that of Russia then not only must it have the support of the people but the understanding of the people. The consequences of a lack of understanding will be the people fighting for something that they do not have adequate knowledge of. Otherwise they will just turn back on their morals starting perhaps another revolution. The people must support a revolution and they must understand what they are undertaking. Without this the revolution is very unlikely to happen or rather be successful.

The third main factor that I believe must be in place is the correct political situation.

People will be unlikely to revolt against a government that is strong. This will either be hardly in their (the people) favour or be impossible due to the strength of the government. The first part of the political situation that must be right is that of the stability of a government. A weak government is

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first easy to topple and secondly it is normally in the favour of the people to take over. Of course the rule of the powers that take over may be no better, but in the eyes of the powers that are trying to take control it is, and that is what I am focussing on in this circumstance. The people will want to take over if there is a revolutionary desire and with a weak governing system they are likely to do so. Many would say that this makes the political situation a sort of sub-circumstance but this takes me onto my next point. The political situation is oftentimes what leads people to revolt. Their own unhappiness with the way they are being governed leads them to revolt. Another political factor that leads the people to revolution is the form of how the government works. The most basic form of this is how benevolent the the government is. In summary the causes of the political situation that is needed for a revolution to occur are that of a poor government and this will then be compounded by how the government treats the people along with the opinion they create..

A country has to be in the following situation to reach a revolutionary state on a large scale, meaning a complete overturning of how we as outsiders and onlookers see the country. The country must first have a governing body that is not in favour of the people or the proletariat. Examples of this would be ab autocratic government and virtually any dictatorship. Whilst governments like these can be needed in some situations, in order to temporarily keep things under control, these forms of government are normally carried on past the point of which they are needed and this can further grow anger against the government. The second political factor is the government needs to be relatively weak. Poor decision making resulting in a financial crash and or inflation is an example of this.

Secondly the economic situation must be right. This is simple. Any form or financial crash or any major financial problems in a nation will almost always result in the angering of the people. Thirdly the people must support and understand the revolution. I am looking at the Russian revolution which was a revolution for the people. So for the re-creation of the Russian revolution it must be a people’s revolution and therefore they must support and understand it.

All this considered, there are definitely specific circumstances for a revolution like that of Russia in 1917 to happen again. But we cannot have them separately. Whilst there clear examples of places with massive inflation rates, economic crises, poor governing system and some groups wanting a revolution and understating it, they are not all in one country. They are scattered all over the world.

Yet this does not quite destroy the argument. In some places we see two of three, that being the economic situation normally coming with a weak or badly managed government. This is definitely something that is a potential threat to this crazy world of the 21st century. And although at the moment we see the circumstances only in fragments, we can see they can happen and I think that it is likely that they will occur all together in the near future.

Oliver Stanley

Oliver Stanley

Oliver Stanley

The pizza oven has come into great use all throughout the last year. I pizza's we have had from it are delicious along with the pulled pork we have cooked in it. It has also created a sociable courtyard in the garden.

Oliver Stanley

Rex Singlehurst the future of drones What is the future of drones?

A nano drone compared to an adults finger.

An American UAV (Unmanned Aerial Vehicle). The people that control this are 1000s of miles away.

Popular perception is to think of unmanned aerial vehicles (UAVs) as being recent technological developments of the last decade, however the origins of drones date from the first quarter of the twentieth century. A drone is an aerial vehicle that does not require an onboard pilot too operate. A drone can be anything from a plane that weighs multiple tons too a quadcopter that weighs 250 grams or a Nano drone that ways 25g.

In fact the first drone was a military “drone” and was created by the British it was first tested in March 1917 and then in 1918 the Americans followed with the Kettering Bug which first flew in October 1918. However neither was used in the First World War. The military drone was first used (on a large scale) in the Vietnam War. However the use of drones is not just military. In the future drones are predicted to help with agriculture, photography, delivery but although drones may seem useful, they there are countless things wrong with them, because of this restrictions are starting to arise that may bring the future of drones to a halt.

In this project I want to find out what the general public think about the use of drones as well as the views of the people who work with drones on a daily basis. Then, using this information is want to work out what the future might hold for drones. However, to do this I have split the drone industry into 4 parts: Military, the use of weaponised drones in wars; agriculture-the use of drones to plant crops; photography and leisure-the use of drones to take aerial photos; personal drones for entertainment; and, finally, delivery, the use of drones for companies such as Amazon to deliver their products. Personally, my hypothesis is that I think that the use of drones for leisure and delivery will be heavily regulated because these drones would fly in suburban areas where restrictions are tightening. However I think that the use of drones in agriculture and the military will carry on unaffected by the rules that are being set in place. This is because in agriculture these drones will be flying over private land and then in the military, they are an effective weapon that does not require the loss of the pilot if it is shot down.

Rex Singlehurst To discover the future of drones I think that you have to know what most peoples opinions on drones are. So I set up a questionnaire and sent it around to people. The questions that I expect too learn the most from are: 1.Would you be worried if you saw a drone flying around your neighbourhood?

2.What is your opinion on military drones?

3.What do you think about the use of drones by farmers to plant crops?

4.What do you think about drones to deliver packages?

5.What do you think about the UK spending the 2 billion pounds on military drones by 2025 (part of this money is going towards Tempest Fighter Jets)?

6.Do you approve of drone strikes?

Out of the 47 people that answered this questionnaire only a third said that they wouldn’t be worried about a drone flying around their neighbourhood. I think that this shows that tensions around drones are higher than you might expect because of the fact that currently anyone has access to drones and that drones could be used to do anything with minimal risk to the owner.

Then, I asked whether or not the responders approved of military drones. I think that it is very interesting that the majority agreed with the use of military drones. Then I asked why they thought this. Some responses that thought were interesting were “Lower risk for pilots, Less risk of casualty on our side” as well as “I don’t think we should detach ourselves from the enormity of death”. The first two were very typical answers however the third portrayed very well what I think the 13 people thought when they voted that military drones are bad. They see these drones as an easier way to escape from the guilt of taking another humans life but to test whether the people who voted yes understood the extent of the damage of drones I asked this next question!

Rex Singlehurst

For reference the different sectors are: Blue: My view has changed and is now yes Orange: My view has changed and is now no Green: I still think they are good Red: I still think they are bad I believe that this shows that although some people clearly don’t understand the damage caused by military drones and so changed their mind after I told them the full extent to the “collateral damage” the majority do understand and their opinions have already made about military drones.

So if a vote was given to the general public about the future of military drones we could be very confident that most of the answers would be from people that new what military drones did and were very confident with their answers.

This graph is very clear in what most peoples views on agricultural drones are. I believe that the majority said it was good because they would only fly on private land, they would have a fundamental use and finally they would be very efficient. This is backed up by the fact that when asked why they voted what they voted people said “Efficiency, saves money” ,but also interestingly “the job losses would be quite substantial” I think they said this because it takes a lot of people to do the work that one drone could do in a day.

Rex Singlehurst

Instead of asking whether people approved of recreational (personal) drones or not I instead asked this question because I wanted to know whether people thought drones where too untraceable. However I found something even more interesting the amount of people that think drones should all need a licence was the exact same amount of people that would be worried if they saw a drone flying around on their street (look at first pie chart). This shows that the next step in restricting drones as far as most people are concerned should be too make everyone who owns one have a licence.

This is the last bit of my questionnaire that I want to talk about because personally the use of drones to deliver packages is what I find most interesting. Then when asked why they voted what they voted people said “speed, efficiency and reliability” as well as “it will clutter the skies” and “I don’t like the idea of drones flying around urban areas”.

Having done this questionnaire I decided to interview Alan Proto who works with drones on a day to day basis. He set up Phantom flight school which teaches people how to properly fly a drone as well as more specialised things such as how too take incredible pictures with them. During the call the internet was very bad because he was driving through the Pennines.

What is it you do with drones? What is your job?

So basically, I founded a company called Phantom flight school six years ago, because I thought that the technology could be, you know, monumental in terms of creating an entirely new form of transport, an entirely new form of communications, etc, etc, I thought it could be transformational anD the business that I founded Phantom flight school is basically a one stop shop for consumer uses of drones and commercial uses of drones of the type that are widely available to purchase, you know, kind of sub 10,000 pounds per unit.

So we will come around to the other elements of it in a minute. But basically, our job is to advise people on the drone that will suit their purposes, sell them the drone, teach them how to use it, in the past, teach them how to use it commercially, and then advise customers on what to buy because I think a lot of customers can look at a drone and go, this is an amazing idea but not understand it’s true potential and so we’ve worked with companies like Weetabix, British Aerospace, Mercedes Benz, the Jeep investments, Tottenham Hotspur Football Club, to help them to kind of meet the need that they have for data using a drone.

Would you say you’re kind of one of the pioneers of using drones in this unique way?

I do not claim to be a pioneer, I think a pioneer is two grand a word for what I do. I think what I have been able to do is pull together different aspects of drones in order to make them useful to more people, you’ve probably trained more people how to fly drones than anybody else in the United Kingdom. That would be my claim to fame. I’m not a trailblazer. You know, the value of my company is about 34 pounds, the value of frame-lines company DJI is about 34 billion. I think he gets to be the pioneer. And I just get to be a nice guy who’s taught a lot of people to fly drones.

Rex Singlehurst What was your first experience with drones?

So that was seven years ago, which was the same time that a company called DJI founded, released sorry, drone called the Phantom three and it was the first consumer facing drone that you didn’t need to spend every night of your life with the internet in one hand and a soldering iron in the other to make it work. You could you can buy it at an electronics shop, you can take it home. And if you read the instruction manual carefully enough, you can have fun with it safely time and time again, I bought one of these and it’s quite funny how these things happen. I bought one of these Drones. I had read about it in the Financial Times and you don’t normally read about children’s toys in the Financial Times. So I bought one and I immediately thought, Oh my God, this thing is amazing.

And then I thought that I could kill someone with it. I need somebody to teach me how to use it and I went looking for somebody to teach me and there was literally no, not anyone. I went to people who claimed they can teach me and they were terrible. And so I thought okay, this is a an innovative, radical technology. There’s gonna be a lot of demand for this product. I know how to teach people things. I will become a drone instructor. And I was probably the first person. I suppose if you want to tag me with pioneer, I was probably the first person to start teaching people the practicalities of how to fly drones seven years ago. I’ll be completely honest, I was making enough as I went along.You know, the first few people that came for lessons, they probably didn’t know that I was only barely more knowledgeable than they were.

Do you think everyone that owns a drone should have special training?

Well, it’s funny, one of the places that we teach, it’s quite near a busy dual carriageway and many, many times in the last five years when someone has got out of their car, and I’ve started to set up the drone, they have said, goodness, I’m not sure I would fly this close to the roads. To which my reply is always I know, do you realise how dangerous those things are! You know, cars killed 25 people a day on the roads of Great Britain? Yet, drones haven’t killed anyone.

What is your opinion on then the increasing restriction restrictions on drones and how has it affected you with your business?

So I take a slightly contrary view on this and that’s because I live in the sector. And I’m not trying to create sound bites that will create media headlines that will create clickbait because the simple truth is that the drone regulations are not becoming more restrictive. Quite the quite the opposite is and anybody who actually looks at what has been happening will agree with me that basically.

So when I set up seven years ago, there were some basic rules, but the rules in every country in Europe were different and the EU looked at drones, and they looked at working at height, ladders, and a terrifying number of people die falling off ladders, every single year 1000s 1000s of people.

Yeah, so they looked at ladders. So they looked at drones and they went, wait a minute, why are we making it hard for people to fly drones? And so over the last four years, the EU now regrettably, we have left the EU and that is a source of desperate regret for me. But happily, the CAA follows the EU’s rules for Drones, because otherwise, Ryanair wouldn’t be able to land in Brussels. Yes. And so even though we’re not on the EU, we have the EU rules. And the US rules from the first of January of this year, to make it much easier for people to fly drones in many, many more places.

Yeah. So the media headlines which talk about increased regulation. And if you look across the globe, you now have regulation in the EU, in Japan, in China, and in the USA, that looks very similar. So it’s not even that the EU is an outlier. Basically, all of the large countries of the OECD have looked at drones, and they’ve gone Yeah, okay. You could hurt somebody with this. But you can hurt someone with a lawnmower, or a hedge trimmer, or a kitchen knife or a car. And, you

Rex Singlehurst know, you can buy a yacht without any kind of qualifications. So in the bigger scheme of things, yes, drones carry a risk. but so does everything in life, the frying pan that you use to cook an egg for you. And it’s been uploaded. So the rules aren’t getting more restrictive. They’re getting more open. Yeah. And so I don’t see the use of drones suddenly disappearing. What I do think is that the first wave, if you like, has largely been tech geeks. A bit like me, you know, I have to have the latest Apple products. I love tech. I love new love fast. I love, love cool. And drones were all of those things. And it’s true that you can take a great photograph with a drone. Yes, but where I see and I maybe I’m coming on to answer the question, so the answer on regulation is it’s not getting tougher. It won’t get in the way. It has been carefully considered. The rules are even reasonably well balanced. And no, that hasn’t impacted on my business.

What is your opinion on military strikes and military drones?

Well, and this is I was your age, I have been worrying about and telling other people that I was worried about artificial intelligence, essentially becoming a higher life form and taking over the world. Yes. Now maybe that’s, that’s an extreme abbreviation. But it’s interesting that people as intelligent as Ilan Musk, Peter teen, and Bill Gates have put 10s of millions of their own money into Founding Fathers COVID as the Centre for existential threats. Yeah. rates, artificial intelligence as the most likely cause of the end of humanity. So we’re talking about quite big things here. So maybe we have jumped topic a little bit. Yeah. But I see military drones as a stepping stone to a world in which most military vehicles will be unmanned. Yeah, at which point it will be drones fighting drones. And unfortunately, you know, it’s terribly sad if you have a soldier in a war and they get shot. That’s a terrible source of sadness to the family of that person. But it means that people are quite careful about where they put soldiers. Once. Once drones of every type replaced soldiers, yeah, then then the risk is that someone sitting 5000 miles away, pressing the buttons and release a bomb, or laser or whatever, doesn’t have quite the same personal on that with that decision. So I think, I think military drones are inevitable, every technology in history has been turned to military use, if it can be. So there’s no point wishing that it wobbles. Wow, I’m driving through the canines at the moment up in the north of England. rainstorm is coming. Like I said, I’m sorry. It might affect the radio policy. Okay, thank you. Thank you. So my view is military drones perform a function killing bad people. Bad people sometimes needs to be killed in my view. And I think it’s just the start of this. I do think there will be armies of drones. Yeah, it will be Star Wars.

That’s my view.

What do you think about the use of drones in agriculture?

It’s already happening. Yeah. And I think it’s just one of the powerful ways that drones will change.

Whole industrial sectors. And I think it’s, I think it’s much larger than just agriculture. And I mean, I was very privileged to be invited to give a talk to 300 of the senior managers at Airbus, which is, actually they have their offices in Chester, which is where I live. But preparing for that talk. My kind of observation was that the media headlines of the type that you’ve described, you know, encroaching regulation and negativity around drones will change once everyone has had a positive experience in drones. Yeah, so so there’s an amazing company and if you haven’t looked them up before look them up. After this conversation, a company called zip line who We invented a winged drone that could carry a pound and a half of blood or other important medical supplies more than 100 miles. And they started using them in Rwanda seven years ago. And in those seven years, life expectancy in Rwanda has gone up by seven years. And I think it’s principally because of this ability to get important medical supplies out to outlying villages that in the past might have been a two or three day drive, fly a drone in half an hour. brought the blood save the life. Yeah, that’s Yeah, they’re using they’re using them to drop defibrillators in New York City. They’re using them on an industrial scale to improve agricultural yields in Taiwan and in China. They are using them. You know, part of China’s success with dealing with the pandemic was that they had 1000s

Rex Singlehurst of drones deployed in a surveillance capacity to identify people leaving their homes that have been told not to. Yeah, you know, you have Amazon, who are still working day and night to bring drone delivery to the globe as a reality. So I think the example I gave was that it took 30 years between the invention of the railway and people in England deciding that they didn’t need a man with a red flag walking in front of the train. So looked at in that context. We are so much of the birth of drone technology, that it’s just kind of its little ripples in the water at the moment, I think we will see.

Another one is a company called ehang, which are opening drone hotels in China. Wow. Where, where there will be no room in the hotel at all. And so you’ll be collected from the airport and flown to the hotel in an unmanned drone. And then each morning, you’ll take off from the roof of the hotel and visit spec to fly over spectacular natural wonders and landscapes. Again, in a completely unmanned vehicle flight over and have your lunch been full. That’s so cool. There are so many ways in which drones are coming. It’s just that it’s it always takes longer than anybody expects, doesn’t it but two years ago, I was reading about how Elon Musk’s Tesla was going to go bust. And now it’s the most valuable company on Earth. I guess which company had the biggest stand and created the most excitement at the Shanghai Motor Show last week. It was DJI because they have such advanced collision avoidance built into their drones. Yeah, they realised that they collision avoidance is probably just the thing that cars need to become self priming. Yeah. That’s so DJI could be the next car company.

What do you think about delivery drones now?

Well, so what is happening is that in a few places, and this is always the way with edgy innovation.

So DHL parcel delivery company, have been flying medical supplies to a remote German islands, using drones for the last two years. And Reykjavik in the capital of Iceland. I’ve not been selected, but apparently, the city is on both sides of quite a large River. Yeah. And there’s only one bridge and the traffic across that bridge in Russia areas appalling. And for the last two years, our company has been delivering pizza over the river with a drone. Wow. Do you then go on Amazon, you’ve got deplaning lander, and they’ve now signed deals with Ghana with Nigeria. Yeah, and you’ve got a you’ve got Amazon. And it was a $4 package to deliver by courier Yeah, they recommended me the drone.

Thank you. Well, we have we’ve covered all of the topics

Rex Singlehurst So unlike my hypothesis Delivery drones do and will have a future. When talking to George Blonsky ,who is a photographer that works with drones, he said that the problem with how people think delivery drones will work is mainly incorrect. Most people think that they will be flying maybe 20 metres off the ground. When actually they will be much higher than this. They will actually fly between 400-500 ft and the amazon drones come directly down to the place where they drop the parcel off. Not only this but currently amazon is working with drone flying professionals to train the drones to deal with any scenario. Whether that be kids running around in the garden or a washing line these drone experts are flying these drones in these situations so that the drones system will be able to land anywhere. So I think it is very obvious that drones in the future will deliver packages because not only will it be faster but also cheaper for amazon. However it isn’t the only thing drones deliver. As we speak drones in countries are using zip-line to deliver medical supplies to places where normally it would take days to get there. So delivery drones do have a future.

My hypothesis for photography and recreational drones was also wrong. I had thought that they would start to shut down because of increasing restrictions. However, this is not true, first of all whenever the more the technology progresses, the cheaper and easier it is to get a drone. So governments have to put restrictions up for things such as flying over an airport because of the increase in people that own a drone and so therefore the increase in the chance of someone using drones for illegal activities. The average drone pilot won’t be affected by most of these rules. As long as you restrict your flying to a park and stay away from residential areas, then you should be fine. However, I think that in the future anyone who owns a drone will have to own a licence.

Unmanned Aerial Vehicle’s, the most controversial of all types of drones because these are used in war and have caused around 1000 civilian deaths. These are the original drone and in recent they have come under fire. Due to their politically controversial nature used to kill terrorists in the middle east and because of this have caused hundreds of civilian casualties. My hypothesis was that they would carry on unaffected. This was almost right. Clearly the majority of people think that military drones are good when given no background information. However when told about the “collateral damage” it turned out that the majority of people where against military drones. So we can tell that if a vote was done the result would very much depend on how much research those who vote do. However it will probably never come to this because those in the government who control these drones have decided that being able to kill terrorists is better than the civilian casualties are worse. Also as this technology progresses it is likely that the way that the targets are killed will become even more accurate.

Rex Singlehurst

Finally my hypothesis for the use of drones in agriculture was also largely correct. These drone’s would fly on privately owned land far away from any towns or citys. In fact, this type of drone are already being used. A company called ‘Drone-seed’ uses drones to plant trees as part of rapid reforestation. In 2019, this company was used as part of a fundraiser to plant 20 million trees and it worked impeccably. The drone would fly across a pre prepared area and drop “seed bombs” of the trees that needed planting.The only downside of this is that many people would lose their jobs if this became commonplace.This technology is always improving and is expected to become even more accurate in the future.

Rex Singlehurst In conclusion I think that drones do have a future. Right now we are at the forefront of drone technology, in twenty years time I am sure that people will laugh at how primitive our current drone technology is. In the future the drones will probably be nearly unrecognisable from what they are now. A lot of the uses we will have for drones would be impossible to think of looking at the drone technology we have know but will have soon. However as the technology increases more and more people will have access to it so I think that I. The future everyone who owns a drone will have to pass a test to get a “drones pilot licence”. Before DJI and the pre-made drone you had to create your own drone “with the internet in one hand and a soldering iron in the other”. Over the past few months I have been trying to make a drone the “old fashioned way” and it’s very hard. I have poured 24+ hours into it I’m not yet done. I think this improvement from make it your self to pre-made drones is massive so I am very excited to see what happens in the future with drones.

References: BBC drone and bees- https://www.bbc.co.uk/news/business-56344609 Civil aviation authority- https://www.caa.co.uk/home/ Drone seed- https://droneseed.com/ Guardian military drones- https://www.theguardian.com/news/2019/nov/18/killer-drones-howmany-uav-predator-reaper Geo pictorial (George Blonsky)- https://www.geopictorial.com/index Interview with Alan Proto- https://radleycollege-my.sharepoint.com/:u:/g/personal/rex_ singlehurst2020_radley_org_uk/EexUCRfJ7BxGrHzYjwZLjZwBWD6i559rtwz4CEYrr78LA?e=cJE2a1 Phantom flight school youtube- https://youtu.be/ER6JzbEoIm4 Phantom flight school- https://phantomflightschool.co.uk/flight-school/ Youtube history of drones- https://youtu.be/QyKH93hKLwQ Youtube consumer drones- https://youtu.be/s35HIK_OGtY Zipline- https://flyzipline.com/

Rex Singlehurst

Max Lian EXPLORING THE POSSIBILITY OF REUSABLE SPACE LAUNCH VEHICLES Introduction During space race in the 20th century, the rocket engineers started to realise that they need a launch vehicle not necessarily as powerful as super-heavy expendable rockets like Saturn V, but can be reused and frequently launched at low cost. To meet this demand the American Engineers developed one of the most iconic space launch vehicle in history – the space shuttle, which can put more than 27 tons of cargo to LEOI or 16 tons of cargo to the international space station while carrying 7 crews onboard. The shuttle program was highly successful at the start, as the orbiters could be relaunched very shortly after recovery and simple refurbishments. However, the 2 shuttle disasters II, which was more likely to be caused by human error of the ground staff rather than a critical problem of the shuttle system itself, forced NASA to carry out more refurbishment which inevitably raised the launch cost and eventually to retire all the space shuttles.

However, the legend of reusable space launch vehicles did not end there.

In fact, it has just begun as the rise of new-generation reusable launch vehicles like the Space X’s Falcon 9 and the Starship. So, or my junior prize project, I will be exploring the possibility of future reusable Space launch vehicles and designing the ultimate solution for reusability in my theory. Some of my ideas are very new and original, which were not introduced for space launch industries ever in the past.

I – LEO: Low Earth Orbit II – There were 2 shuttles lost in mission. Shuttle Challenger was destroyed in an explosion during one of it launch, mostly because NASA managers insists to launch it although it is known that the weather condition at the time might lead to an O-ring failure in the booster. Shuttle Colombia was lost during re-entry because the heat tile was damaged by piece of insulator layer that fell from the external tank during launch. This was observed by the NASA engineers, but the NASA managers again insists to take the risk dur to multiple reasons. Both disasters led to the loss of 7 astronauts and mission specialists, and in total 14 people were killed in action during shuttle launches.

Chapter 1 – Design philosophy of space launch vehicles At the end of and after the space race, engineers came up with many unique launch vehicles with very different design philosophies. Many of them are reusable spaceplanes such as space shuttles or even SSTO I vehicles such as Skylon proposed by Britain engineers. Others are usually crazy super heavy rockets like the Sea dragon, the proposed replacement of the legendary Saturn V moon rocket or even Boeing’s proposed LMLV rocket, which is designed to be capable of delivering 200 million tons to orbit! All these ideas were designed to meet the increasing demand of better space launch vehicles to fulfil the goal of building large infrastructures or mega-constellations in orbit, carrying out further human exploration in space, or whatever else. People have been arguing about which one is the best space launch vehicle ever designed.

In fact, there are no best space launch vehicles, in theory. Different types of mission require different types of rocket. For example, China’s Longmarch 5 rocket is one of the mightiest heavy lift rocket in the world

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(by 2020), but it is only specialised for deep space mission or transferring payload to the GTOII, while Longmarch 5B with the upper stage removed and longer fairing is specialised to launch payloads to LEO despite being “weaker”. This is because different rocket configuration can have different abilities in launching payloads to different trejactory. Let’s explain this by taking the example of Longmarch 5. Longmarch 5 have a Cryogenic upper stage, which enable it to boost heavy payloads further to the GTO, Moon, Mars and beyond, while “in theory” also to LEO. However, a cryogenic upper stage has volume, which means that there is less space in the payload fairing, limiting the size of the payload, which does not help increasing the payload capacity at all. On the other hand, Longmarch 5b can hold more cargo because it has got a larger fairing. The U.S.’s Atlas V rocket is a more modular rocket, and it also have different launch configurations to deliver the payload into different trajectories.

One of the most important thing about a rocket is its payload capacity. Space launch vehicles are classified into 4 classes. Those which can deliver under 2000 kg to LEO are called Small-lift launch vehicles, and those which can deliver above 2000 kg and below 20000kg are called Medium-lift launch vehicles. Those which can deliver between 20000kg to 50000kg to LEO are called Heavy-lift launch vehicles and anything that is able to deliver above 50000kg to LEO is called a Superheavy-lift launch vehicle.

Besides the payload capacity the cost is also important. There are two ways of looking at the cost, which are the overall launch cost and cost per kilogram. Cost per kilogram is a new concept and is important when it comes to considering ride-share services while there is margin in payload capacity of a rocket. However, small-lift launch vehicle still exists even though reusable medium-lift launch vehicles like Falcon 9 might have a lower cost per kilogram. This is because small-lift launch vehicles have a lower launch cost and are more dedicated for small payloads, so the costumers don’t have to wait for months or even years for a ride share service on Medium-toheavy-lift launch vehicles. Let’s understand this with a simple analogy: would you want your pizza to be delivered with a semitruck while a scooter suffices?

While different rockets are designed to deliver payloads of different mass to different orbits or trajectories, they are Falcon 9 Electron also designed to deliver different types of payload. These classification can be simplified into 2 classes, which are cargo or human. Those rocket designed to have human onboard must be man-rated, which means that they are designed to be ultra-safe and must ensure the safety of the crews onboard at anytime during flight. This does not mean that cargo launchers do not require reliability, but simply boils down to the fact that there is a need to separate human-launch vehicles and cargo launch vehicles. Even with the rockets that are capable of launch both types of payload, details on the rocket must be modified to carry out the mission better. Space shuttles can carry crew and cargo at the same time, but it should be regarded as a crew launch vehicle with capability of carrying cargo.

Max Lian Space launch vehicles can also be simply divided into 2 groups: reusable and expendable. As this is very related to the main topic of this project, in the next chapter I am going to talk about the reusable launch vehicles nowadays and how do they compare to the expendable ones.

Chapter 2: Current reusable launch vehicles - Parachutes, or propulsive landing?

Reusable Launch vehicles are the ones which can be recovered, or partially recovered after each launch and be reused again in another mission. The earliest example of these is the space shuttles, the reusable orbiters with expendable lower stages, and in the recent decade, rockets like falcon 9 with a reusable 1st stage and expendable 2nd stage start to appear. Both are designed to cut down the launch cost by reusing parts, and in the next few decades many fully reusable rockets will appear, furthermore cutting down the launch cost and the period between each launch.

Comparing to expendable rockets, reusable rockets can achieve more affordable prices and more frequent launches, but it also need a more complicated ground system to support its reusability, and most importantly, extra hardware and fuel onboard to enable it to be recovered and then to be reused, instead of smashing into the ocean or land surface like the non-reusable rockets. This will inevitably contribute to the rocket’s dry mass. The recovery hardware can take different forms according to the design, and this will be discussed below.

Parachuting the boosters is the earliest way of recovering them that the engineers thought of. It was considered in the very early age of space exploration, much earlier than most of the people think. In fact, it was explored in the Mercury-Atlas program, the one of very first few manned spaceflight program. The SRBs I of the space shuttles were recovered with parachutes, and some are even refurbished and used in later missions. However, these plans were all abandoned, and this is because the limited capabilities that parachutes have. Firstly, the heavier the object is, the bigger the parachute need to be, and a giant parachute is inefficient and heavy due to its smaller surface area to volume ratio comparing to smaller ratio. Secondly, parachute cannot slow most of the heavy rockets to a ‘safe velocity’ because rockets are in fact very fragile because to increase the performance of the rocket engineers must not spend too much weight on structural support. Thirdly, the deployment for a large parachute can be a very complicated and risky process, especially for high-speed objects like falling rocket boosters. A large parachute can also be structurally impractical. A cluster of smaller parachutes is also unrealistic for medium to heavy rockets, since they have a great chance to tangle with each other, resulting in a failed deployment.

Let’s take the examples of the rockets that are launched form the Kennedy space centre. If a rocket is launched from there, the drop-area of the lower stage boosters must be in the Atlantic Ocean, and since boosters that are recovered with parachutes are unable to change their overall ballistic trajectories, they cannot escape the fate of dropping into the corrosive salt water of the sea. According to NASA’s official financial documents, it is more expensive to refurbish and reuse a SRB than building a new one, mainly due to the corrosion from the sea water. In the SLS II Program, NASA no longer have the plans to recover the extended SRBs deprived from the Space Shuttles’ SRBs. There is an interesting way that can give parachutes a chance to play a role in rocket recovery, however.

That is called mid-air retrieval. The name is rather self-explanatory. It means to capture and retrieve an

Max Lian object mid-air with an aircraft. The process was first used to retrieve military drones without landing gears. The capturing was achieved by hooking onto the parachute of the target object with a long hook attached below an aircraft, usually helicopters for their ability of landing on ships after the mid-air retrieval is completed. This process effectively avoids the contact of the target object with the surface. However, because the target object must be hanged underneath an aircraft, its weight is limited to the maximum lifting capabilities of the aircraft. A medium-lift rocket has the dry mass that exceed most of the helicopter’s payload capacities, and a fixed-wing aircraft strong enough such as the C-17 is simply unable to adapt to this task due to many limitations. A solution to this is to simply reduce the weight of the target object, either to only use mid-air retrieval for small rocket boosters, or only partially recover a booster. On ULA’s Vulcan rocket III only the engines will parachute down and be captured by a helicopter and the rest of the rocket is expended. Of course, this limits the possibility of furthermore down cutting down the launch cost.

Mid-air retrieval is also a risky process. Just like other means of recovery by parachutes the process can be greatly affected by the weather condition and the wind, and to catch the booster mid-air the pilot must carry out some manoeuvres that are usually considered as stunts. With these limitations there are many few organisations which still insists to research on mid-air retrieval for rockets. In fact, it seems like the majority is looking towards an alternative plan – propulsive landing.

Propulsive landing was the idea of landing a rocket booster at a landing platform vertically with the power of its own engines – a very comic idea it is. In 1990s NASA tested a prototype for McDonnell Douglas DC-X, a reusable SSTO vehicle that can make propulsive landings at target sites. Progress was made but the project was soon abandoned due to setbacks and lack of fund, and the two prototypes were both functionally destroyed during tests. In the next decade most of the NASA officials considered propulsive landing impractical due to the failures in the DC-X project. However, DC-X project influenced the future of propulsive landing, and some of the engineers involved in the DC-X project were employed by Blue Origin, and helped Blue Origin to build New Shepard, the first rocket that flew over the Karmen Line to make a successful propulsive landing at the target site.

The Falcon 9, one of the most famous rocket today made its first successful propulsive landing in 2015. It is the first orbital-class rocket with the 1st stage that can be recovered by propulsive landing. Soon, Space X mastered how to land their rocket on drone ships placed in advance on the sea surface. This started a revolution in space industry, as the low launch cost achieved by reusing the 1st stage challenged the place of most traditional expendable rockets, and its LEO payload capability of 15.6 tons as a medium-lift launch vehicle exceeds most of the rockets today. The utilisation of ASDSIV removes most of limitations on the launch trajectories as it can be placed anywhere on the sea. Space X later assembled 3 falcon 9 boosters together to build Falcon Heavy, the most powerful rocket in the world until 2021. Falcon 9, together with the New Shepard rocket proved propulsive landing practical, and now many new companies are trying to replicate their success by researching on propulsive landing.

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However, although it seems to be an ultimate solution for recovering and reusing the booster, propulsive landing still has few problems that must be taken into consideration. Firstly, because the booster must re-enter the atmosphere while being oriented engines-first, which subjects them to few thousand Celsius degrees depending on the speed it is travelling at, and without a heat shield available the engines must ignite during re-entry to slow down faster to prevent melting. This manoeuvre is called re-entry burn by Space X. This worked quite well for Falcon 9s, but for the core stage of Falcon heavy, a modified falcon 9, the re-entry speed is too fast that even re-entry burn cannot save the hydraulic systems from melting. In the first 2 missions of Falcon Heavy so far both core stages suffered from mechanical failure caused by the re-entry heat and resulted in a failed recovery, and it is not sure whether this problem can be solved or not in Falcon Heavy’s next few missions. From this we can learn that it is important to reduce the separation speed of the boosters that are meant to be recovered by preforming propulsive landings. This adds more work to do for the 2nd stage of the rocket, and on Falcon 9 it resulted in a larger G-force load on the payload and the crew onboard. Limiting the G-Force is important to delivering delicate payloads.

Propulsive landing requires a big volume of extra fuel to perform the deceleration manoeuvres during landing. Grid fin or control surfaces and RCS thrusters V are needed to make minor adjustments during decent to finetune the trajectory. Landing legs are of course also needed to absorb the shock of landing. These together are considered as deadweight during ascent, as they are not needed on traditional, expendable rocket boosters, and reduce the rocket’s dry mass ratio, thus compromise payload capacity by around 32%. However, Falcon 9 has one of the most impressive dry mass ratio in the world, despite having to carry these extra hardware! This is because the clever engineering inside the Falcon 9, which not only reduce the weight of these hardware, and the fuse large and the engines! This showed us that it is acceptable to add all these extra hardware onto rocket if we use other methods to cancel out the negative effect of them, but this also comes with disadvantages. Because the weight spent on structural support is minimised on Falcon 9, its ability to bear both weight and thrust is not impressive. An upper stage and payload that is too heavy can easily ‘break its neck’ and cause the rocket to snap in half either on the ground or in mid-air. Vertical assembly, an important manufacturing process in rocket industry is also not available for Falcon 9 because of its lack of structural support, and because lots of the important payloads today requires vertical assembly the range of mission of Falcon 9 is limited. The was a proposal of using Falcon Heavy to deliver the Orion spacecraft, but the proposal is rejected because the Orion requires vertical assembly. Nevertheless, Falcon 9 is a very excellent rocket among all of them today for its reusability and decent payload capacity. For designing reusable medium-lift launch vehicles, propulsive landing is definitely an admirable solution.

Space X is now researching their next-generation fully reusable superheavy-lift class launch vehicle, the Starship. It consists of a massive 1 stage called the Superheavy, and the reusable upper stage known as the

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Starship itself. The Space X team want the Superheavy to be able to land back at the launch tower, which need the Superheavy to make a boost-back burn once it separates with the Starship. This cost lots of fuel and to reduce the fuel used the gravity turn must be carried out slower to reduce the horizontal speed when separation happens, leading to a steeper accent profile. To fully understand this more advanced understanding of orbital mechanics is needed but to be simple I will just tell you that it is not a very efficient way of going into orbit. However, this compromise must be made to meet Space X’s ambitious plan to carry out more frequent launches.

Since Starship’s development has not yet been completed, it will be interesting for us to see how they deal with these things, and it is almost definite that these disadvantages can be cancelled out by the design capability of the Starship, but these really make me rethink about the design of the reusable launch vehicles: Is there a better solution, or we must stick with these limitations until we develop something like the alien technology?

Chapter 3: Introduction to VTAHD system - inspirations and first thoughts It is not until I decide to dive into the small hill of ‘ash heap of history’ of rocketry remained from the work of the Soviet Union engineers on a casual day that I realised that I could improve their design into a potential, whole-new system. All these crazy thought remained from the 1980’s hope of establishing an inter-planetary travel system, and many of them are ignored in the shine of others. That day I was researching on the Energia-Buran program, the almost forgotten Soviet shuttle program, and accidentally saw one of its proposed variants, Uragan, or better known as ‘Energia II’, although it is not known by a lot anyway. It is a fully reusable superheavy-class launch vehicle designed in the 1980s – around 30 years earlier than Space X’s Starship!

In this proposal, propulsive landing is not used to recover the boosters and instead they decide to intergrade rocket boosters with planes and space shuttles elements to give it ability to glide to a landing at an airfield. The rocket has 4 side boosters with extendable wings deprived from the Zenit boosters of the original Energia rocket, and a massive core stage with a diameter of 7.75 metres and wings like the ones of space shuttles. What really interested me is that in this method no burns during descent is needed as the booster make more uses of aerodynamic forces to slow down than rockets like Falcon 9, potentially decreasing the mass of the booster as no extra fuel for main engines are needed. Also, because the engines are not re-lit during descent the time of engines’ operation during each flight is reduced, potentially decreasing their need for refurbishment. However, the details I can know about this method from Soviet Union’s document is limited as it collapsed not long after the program started.

Surprisingly the Europe had also done some work on fly-back boosters. In 1999 the German Aerospace Centre started to research on an alternative option for side boosters of the Ariane 5 rocket to replace the SRBs (different to space shuttle’s SRBs), and they decide to work on a fly-back booster which they call the LFBB. LFBB is liquid fuelled and smaller comparing to the Zenit boosters of the Energia rocket and has fixed wings and canards. The LFBB project was cancelled because of the limited fund comparing to its complexity and size, and ESA officials decide to stop its development because they think Space Shuttles and SSTO launchers like the Venture Star are better alternatives in terms of economic savings. I consider this as a mistake and a serious decision failure because the Space Shuttle later became very not affordable for NASA and even more expensive than expendable rockets, and Venture Star project ended up getting cancelled

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due to the technical problems and concerns in development cost. A cryogenic tank failure in 2001 caused the government to withdraw the federal support for this project. There were too many new technologies that are on Venture Star to be developed, while on another hand according to all the new technologies for LFBB would have been developed within 10 years according to the documents. I learned from the available information and documents about LFBB project that according to the engineers’ approximation, hardware on LFBB would cost around 30% of the payload capacity, like reusable boosters such as Falcon 9.

The data from the LFBB program disappointed me. I thought fly-back boosters might achieve lower loss in payload capacity comparing to Falcon 9 which loses 32% of its payload capacity when recovered, as discussed above. Although I hoped this to be the case, I was not surprised when I saw that. A fly backbooster, just like the boosters that use propulsive landing, need to carry extra hardware (deadweight) during launch. A fly-back booster obviously needs wings and control surfaces, also a set of landing gears which consists of even more complex hydraulics than landing legs. These are the primary elements of deadweight on a fly-back booster. The requirement for extra fuel depends on the specific design. Some fly-back booster designs like LFBB have turbofan engines which consumes fuel for in-atmospheric flight during decent, and some hand scripts I later found on website of NPO Molniya showed that most of the Soviet engineers planned not to put turbofan or turbojet engines on their fly-back boosters, although people later argued that there would be a jet engine integrated into the booster. If there is one, I would say it is likely an AL-31 jet engine that was also integrated into OK-GLI prototype in Energia-Buran project. For those fly-back boosters designed with a jet engine, the weight of its jet engine also contributes to its deadweight because they do not operate during ascent.

NPO Molniya was the company that was responsible for Buran-Energia program and development of Energia II. I did not enjoy browsing through documents written in Russian, but I found lots of useful information there with the help of machine translator.

Now, let’s get back to the main topic. If you have read and understood the things we have already discussed, you probably understand that reusability equals compromises on payload capacity, which is a cruel rule of physics stipulated by the Tsiolkovsky rocket equation. It is just the matter of how much or less, so we should focus on reducing the weight of the recovery hardware and the rocket itself to maximize the capability of a reusable rocket, and the main way to achieve this is to get rid of any form of weight that can be taken off the rocket, while maintaining its basic structural strength and functionality. I have got a solution for this based on the fly-back booster design ideas in the past, but firstly I want to talk about how I solve another limitation on fly-back boosters, which then led the possibility of cutting down their weight.

There is one limitation of fly-back boosters that I did not mention above, and it is about the location of landing. As the fly-back boosters need a runway to land like a normal plane, they need runways.

Considering the engineers probably want to save weight on breaks of the landing gears, they probably need a very long runway as well. This means that they must land on a specific site instead of landing anywhere in

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the Atlantic Ocean on an ASDS like Falcon 9. This heavily restricts the trajectory of the rocket during the very beginning phrase of ascent to make sure that the boosters can reach the runway in atmospheric flight during descent and limits the range of the missions the rocket can perform. No mobile landing platforms like ASDS for Falcon 9 were proposed ever in history for fly-back boosters. The reason is obvious. The only mobile runways for planes known to human are aircraft carriers, and they are designed for aircrafts with small landing distance and a tailhook to catch the arresting gear on the runway. Flyback boosters are obviously not in the list. It is also not very realistic to frequently deploy even 1 aircraft carrier for recovery missions, as they are too busy going around the world to maintain the strategic deterrence of the country they belong to, not talking about deploying multiple ones of them for recovering more than 1 of fly-back boosters used in a mission. It is almost impossible to build a mega-aircraft carrier, as it costs too many funds to build. This is the main factor which forced most of the engineers add an extra jet engine in their design to increase its range of in-atmospheric flight by compromising its payload capacity, as their boosters cannot reach the appropriate airfield by just gliding.

However, this limitation only exists because no one came up with a solution for them. I present to you the Vertical-Takeoff & Aerial-Horizontal-Docking solution, which is I named VTAHD for short. Vertical-takeoff simply refers to the way of the booster take off from the pad, and Aerial-horizontal-docking is the key element of it. Different to the VTOL (Vertical-Takeoff & Landing) boosters which use propulsive landing such as Falcon 9, and VTHL (Vertical-Takeoff & Horizontal Landing) boosters such as Energia II side boosters and LFBB, VTAHD is a semi-passive recovering system, in which the rocket is recovered with the help of another vehicle while still adjusting its position, velocities and altitude actively. The key to this idea is relative speed, much like how space docking and aerial refueling work. Instead of having a runway which allow the booster to slow down within its length, I designed the booster to land on a platform which is traveling at the same speed as it, so the relative speed between them is 0. This will significantly lower the size of the platform, which creates the chance of mobilizing it and put it in the sea. However, the landing speed for a typical Boeing 737-800 airplane is around 75 m/s and considering the fly-back boosters probably do not have flaps as strong as a passenger plane this figure can be up to 100 m/s for them. This speed goes way beyond the average speed of cruisers, one of the fastest ship types, so I decided to use another type of vehicle as the

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landing platform, and it is the Ground-effect vehicle. Ground-effect vehicle is sometimes considered as a ship, although it works more like a plane. By utilizing the ground-effect it is more efficient than planes while being able to achieve greater speed than ships. Because its wings produce more lift than normal airplanes it has lower stall airspeed, which means that it can carry out operations in a larger speed range – almost perfect for my idea of VTAHD recovery. As you can see below there is a diagram that I drew to demonstrate this concept.

Similarly, this process can also be carried out on land if a ‘landing sled’ is used. It can be a mobile platform built on high-speed a railway. Landing sled will work similar to the ground-effect vehicle in the diagram and can be utilized when the trajectory of the booster is not going into the sea, such as when the rocket is launching the payload into the polar orbit.

The utilization of ground-effect vehicle or landing sled removes the limit of landing location on fly-back boosters because they can be deployed to anywhere on the sea. This removes the need for jet engines as the booster does not need to deliberately reach their landing platform but their landing platform can reach them. Also, this removes the need for landing gear because no breaking is needed in this scenario as the relative velocity of the booster and the ground-effect booster is close to 0. This removes one major component of the rocket’s deadweight, which increases its dry-mass ratio and decreases the loss in payload capacity. Additionally, because ground-effect vehicles are proven to have a top speed of 400 mph, much faster than Space X ASDSs, fly-back boosters retrieved using VTAHD recovery solution can be transported back to the port in a very short time, shortening the period between each launch. Overall, I think VTAHD is a better solution than Space X’s ASDS in many ways.

Chapter 3: Simulation and testing I put my concept into a test in Kerbal Space Program, the most reliable and realistic TM spaceflight simulation software available to the public society, although it is usually considered as a game. To get the most reliable test result I modified the in-game algorism for atmospheric flight with mods available on the internet.

The first prototype I built was named VTAHD-MK1. It is a rocket with a diameter of 2.5 meter, smaller than a lot of the rockets today. It is propelled by a single methane-fuelled full flow stage combustion engine. As you can see on the picture it has a pair of nose stakes, a pair of dihedral tail fins to provide stability, and a deployable main wing which in the picture is retracted. It has some RCS thrusters which I think is needed to dock with the ground-effect vehicle during the final phrase of its descent.

In each test VTAHD MK1 is put into a suborbital trajectory with an apoapsis (highest point) of 75 km above the sea surface to simulate a booster’s trajectory in a real operational flight. In real life this is equivalent to around 85-100 km above the sea surface, but the atmosphere of Kerbin (the home planet in Kerbal space

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Program) is thinner than earth so I choose 75 km to be the maximum altitude in my simulation.

The biggest problems encountered in the test flight of VTAHD MK1 is mainly about dynamic pressure during re-entry. Although the aerodynamic design of VTAHD MK1 showed decent subsonic performance, it seems like its supersonic and hypersonic performance is not very good. During re-entry if the angle of attack (AoA) is too small the booster cannot slow down fast enough and will be subjected to deadly re-entry heat, and if the AoA is too big the nose of the booster tends to rise, and the booster will stall and lose control.

Multiple attempts ended in failure. All the VTAHD-MK1 prototypes which did not melt due to re-entry heating splashed down in Ocean, as the instability during re-entry did not allow a precise rendezvous with the Ground-effect vehicle. As you can see from the flight record on the left, the purple line representing the AoA jumped up and down a lot during re-entry, which marks out the instability of the booster during this Learning from the previous failure, I developed VTAHD MK2 in the picture at the right. It has a bigger diameter of 3.75 metres and is propelled by 3 engines rather than 1. The shape of its fuselage is more adapted to supersonic and hypersonic flight. Other than that, it is very similar to VTAHD MK1. It proved that these adjustments solved the problem very well. During re-entry, I programmed the flight control system so that angle of attack is hold at 10-20 degrees according to the altitude, and this provide enough deceleration while maintaining control of the booster and not letting it be destroyed by aerodynamic forces. This also expose the nosecone of the rocket to the highest temperature. This is important because in this case the engine is protected from most of the re-entry heat, unlike for Falcon 9 engines must be exposed to highest re-entry heat.

At the altitude of around 7000-5000 metres the main wings are deployed, as shown in the picture. The wings are designed to be thin but long since this gives the best gliding ratio according to the law of aerodynamics. The wing might look too small for the rocket, but it is important to remember that the booster is mostly empty of fuel now which means that it is much lighter than you think. During this phrase of the decent the booster will keep its trajectory very inclined to save and possibly gain some kinetic energy, which is important for gliding as they cannot be generated actively on a gliding booster which is like a glider.

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When the booster is at around 1500-1000 metres from the sea surface it will start flying flat, looking for a chance to dock with the ground-effect vehicle, which will be travelling on the sea surface below on the same time trying to match the speed. Approaching the ground-effect vehicle the booster will use RCS thrusters to carry out minor adjustment, and it will execute a landing flare manoeuvre to round out most of its vertical velocity. The ground-effect vehicle will extend its robotic arms to grab the booster and put it on the mounting structure on its back to complete the retrieval.

With the help of modern avionic algorithms, the precision of landing can be down to centimetres. The robotic arms mounted on the ground-effect vehicle allow more margin in precision as they can freely move to catch the booster. The whole process is going to be monitored by high-precision GPS system, aided with optic observation sensor onboard the ground-effect vehicle at the final phrase to track the exact location booster. Note that as discussed above, this process can also be carried out on land with a landing sled in missions to polar orbits.

The ground-effect vehicle itself is powered by 8 turbofan engines and can resist the force from the booster while maintaining levelled flight. This is because at subsonic speed air below the wing is considered as an incompressible fluid, and it was proven that Lun-class ekranoplan, a ground-effect vehicle designed and built by the Soviet Union, was able to maintain levelled flight while launching anti-ship missiles mounted on its back at an angle.

The ground-effect vehicle I designed had 2 sets of wings, which are the main wings at the bottom and the anhedral wings at the rear. Both sets of wings provide lift for the vehicle, and the anhedral wings also provides instability to contribute to the manoeuvrability of the vehicle in the yaw direction. This configuration requires advanced avionics system because of its natural row and yaw instability and the natural instability of ground-effect flight, but I believe that this can be achieved in real life because our computing technology is way more advanced than before.

Max Lian

Chapter 4: Wyverns After designing the VTAHD-MK2, I think it is time to develop it into a fully functional rocket. I decide to name it Wyvern instead, considering the way it flies lands.

To make maintenance and refurbishment easier for the rocket, I decide to make Wyvern booster modular. It will consist of 3 parts, which are the nose cone section, fuselage, and the propulsion unit. After each launch the module which needs refurbishment can be easily taken off the booster and be replaced with a refurbished one. This will make the process of refurbishment much easier comparing to the current one Space X’s have for falcon 9 and the one of space shuttles. Also, because the fuselage and the engines can be replaced freely, I decide to make it able to run on multiple fuel choices. There will be 2 types of fuel that Wyvern boosters use. Wyvern A will be powered by 3-4 full-flow-staged-combustion-cycle engines fuelled with liquid methane and liquid oxygen as oxidiser for a better overall performance, and Wyvern B will have a single engine using oxidiser-rich-staged-combustion-cycle, running on RP-1 Kerosene and liquid oxygen for providing larger thrust at low-altitude, which makes it a perfect choice for boosters for large rockets.

During testing of VTAHD-MK2, although the booster is able to glide fairly well through the lower atmosphere, I noticed that its stall capability at subsonic speed is still not very ideal.

This is because the air foil of the retractable wing is thin and flat in order to be stowed away during launch. To get the ideal low speed performance, the wing needs to have a concave shape and be thicker at its leading edge. However, if the wings are manufactured into that shape, it cannot be stowed away because of the gap between them and cannot be deployed normally. I improved the design of the retractable wings so that they have better low speed capabilities. I designed the leading edge of the plane to be a hollow structure supported by extendable skeletons. The skin of the rear end is designed to be made of sheets of stainless steel which is only 0.3 millimetres thick.

When the wing is deployed the leading edge is inflated with high-pressure gas, which cause the steel sheet and the skeleton to expand, becoming thicker and rounder. The high-pressure gas can be directed from the pre-combustion chamber of the engine mid-flight so that it does not need to be carried deliberately during launch.

Max Lian

The design of Wyvern makes it suitable to be a side booster, but it is hard to make it a core booster because Its nose cone gets in the position of the upper stage. Because of this the configuration of the next 2 rockets I am going to introduce is a little bit weird, but it is definitely feasible.

The first configuration, as you can see, is what I call the Pterosauria. It has got only 1 wyvern A booster as its lower stage, and the upper stage is strapped to the side of the rocket instead of being put on top, much like the space shuttle. This off set in centre of gravity can be cancelled out by the thrust vectoring of the engines. It is designed to a medium-lift launch vehicle capable of lifting around 18-22 tons into LEO and 12 ton into GTO. It can support some moon and interplanetary missions as well. The rocket is only partially reusable, and the upper stage is expendable.

The second configuration of wyvern booster is called the Griffin. It is a three-stages partially reusable superheavy-lift launch vehicle, that can lift more than 60 tons to LEO, and more than 35 tons to the Moon and beyond. Griffin A consists of 2 Wyvern A boosters and will have 1 cryogenic hydrogen 2nd stage in the centre core and another cryogenic 3rd stage on top of it. At lift off only the Wyvern A boosters ignites, and the core stages which actually serve as upper stages will ignite later in the flight when the Wyvern booster separates. The number of Wyvern A boosters can be added to 4 if needed, turning Griffin into an even more powerful rocket. Because of the 3-stage design Griffin will have a very balanced G-force curve through out its flight, making it an ideal choice for launching crewed spaceships to the moon.

The last configuration that I am going to introduce is similar to the Energia II of the USSR. I would like to call it ‘YingLong’, the king of dragons in Chinese Mythology. It consists of 4 Wyvern B boosters and a reusable centre core just like the Energia II. The centre core looks like a large space shuttle and will be recovered in similar way. However, I improved the design of it. First of all, instead of having the core stage running purely on liquid hydrogen, I designed the core stage of YingLong to be running on tri-propellant, which is a mixture of RP-1, liquid hydrogen, and liquid Oxygen. During lift off the engines will mainly be running on RP-1 and liquid oxygen mixed with a little bit of liquid hydrogen to produce maximum thrust, and the ratio of the mixture will change as the rocket goes into the vacuum of space. In the vacuum the rocket will be purely running on liquid hydrogen for maximum efficiency. According to NPO Molniya, having the rocket running on tri-propellant will reduce the weight of the rocket for at least 30%, and according to the data from Robert Salkeld, an engineer in United states, this will double the payload fraction of the rocket.

Another advantage of tri-propellant engines is that cryogenic liquid hydrogen can be run to cool the nozzle, which solves the problem of keeping the engines cool, allowing them to operate at best state. I also designed it to carry a small amount of hydrazine fuel to run the RCS and OMS (Orbital Manoeuvring system) for orbital manoeuvring. YingLong is a 1-stage-and-ahalf rocket, which means that all of its main engines ignite at launch and the centre core will go into LEO. The core stage will release the payload in orbit, and make a small de-orbit burn with the hydrazine-fuelled orbital manoeuvring system and skip through the upper-atmosphere multiple times using Sänger’s trajectory. This way the core stage will land back at the launch site by going around the globe rather than making a boost-back burn like Space X’s Superheavy booster, which means that it saves more fuel and weight than Superheavy. Less heat-protection is needed if Sänger’s trajectory is used because the re-entry heat is distributed in serval contacts with the atmosphere instead of applied to the booster all at once. YingLong core stage does not have landing gears but will land at a landing sled at the launch site, from which it can be taken to the launch pad again in a short time period for the next launch. All the rocket parts are designed to be recovered and re-assembled in 36 hours, and the rocket is designed to be launched again every 48-72 hours or less. The payload is going to be loaded into the rocket horizontally with its cargo bay open, while the boosters are designed

Max Lian

to be attached to the booster by vertical assembly at the launch site.

Also, I plan to replace all the hydraulics on the rocket with electronic actuators, further cutting down the weight and integrating modern technology into the booster. This rocket is specialised for LEO cand can put more than 150 tons into orbit, making it perfect for constructing an interplanetary ship around Earth before sending it to Mars and beyond.

If necessary, this rocket can also carry a cryogenic or even nuclear upper stage to carry out deep space missions. YingLong may have a slightly longer period between each launch than Space X’s Starship but will have a much greater payload capacity than the Starship.

Conclusion I think I should end this article here. I could talk so much more about it, such as the fuelling system, the manufacturing techniques, and materials as well as many other aspects of it, but that will be too complicated to explain without writing a short book (which I might do in future). However, I enjoyed researching on this things that I am interested in and I am absolutely surprised by the information I can find out there on the internet, especially when I discovered the Russian website that provide an astonishing amount of useful information to my project.

I believe that my idea can be potentially better than lots of the solutions that most of the engineers came up with, although it still needs to be improved. However, it depends on many technologies that were supposed to be further developed in abandoned projects, such as ground-effect vehicles. The human society seems went onto another branch on the technology tree. I am not saying that they are not realistic. In fact, they are realistic, but it needs a lot to revive these projects, but I still believe that one day, at least fractions of my idea if not all, will be brought to reality whether by me or other clever engineers in the world because of their unique advantages over others.

Max Dawson Paul The History of bosnia and Herzegovnia

Modern day flag of Bosnia and Herzegovnia

Modern day physical map of Bosnia and Herzegovnia

Max Dawson Paul Bosnia and Herzegovina, also known simply as Bosnia, is a country in Southeastern Europe on the Balkan Peninsula. Its capital is Sarajevo and it is the largest city in the country. The three official languages are Bosnian, Serbian and Croatian. The area of Bosnia is 51,129km2 and 1.4% of that is water. It ranks 135th in the world in terms of population, the 2019 estimate was 3,332,593. The population density is 69/km2. Furthermore, the 2021 estimate for nominal GDP is $21.953 which places it 113th globally. The Convertible mark (BAM) is used as their currency . In this essay, I will write about the history of Bosnia, from the Neolithic times all the way to the present day.

Bosnia has been inhabited since the Neolithic times, from circa 10,000 BCE, during the final period of the Stone Age. During the Neolithic times, there was an interesting mix of Pannonia and Mediterranean cultures, at this stage, people still lived in caves. On the upper part of the Bosnia river and in the northeastern parts of Bosnia, people lived in houses on the river made of wood. The Neolithic times were followed by the Chalcolithic times, which led up to the Bronze and Iron Ages. The Bronze Age settlements in Bosnia were built like citadels and necropolises. The Illyrians begun to form in 800 BCE and had their own culture, art form and ethnicity. They lived in today’s Kosovo, Serbia, Montenegro, northern Greece, Albania, Slovenia, Croatia and Bosnia. Bronze ended up being replaced by iron in the seventh century BCE. Illyrian tribes eventually evolved into kingdoms.

The first recorded one began in around 400 BCE and ends in 167 BCE. A vital factor to the Illyrian people, was the cult of the dead. In the northern part of Bosnia, people were buried in shallow graves or cremated. However, in the south, the dead were buried in large stone or mud tumuli, these are mounds of stone or mud of raised over a grave. These tumuli became so big, that they reached 50m wide and 5m tall. The first invasion of the Illyrians was from the Celts. Their impact on Bosnia was minimal as they only passed on their way to Greece.

The ethnicity of the Balkan Peninsula then becomes very mixed as Illyrians and Celtic tribes mixed, and many languages ended up being spoken in a very small geographical area. This may explain why Bosnia has a large amount of official languages today, with three.

In 229 BCE, conflict broke out between the ancient Romans and the Illyrians. The Illyrian territory became the Roman province of Illyricum in 168 BCE. By 9 A.D, Rome had completely annexed the province and ended a three year rebellion of Illyrians against Romans. In 10 A.D. Illyria was divided and the northern strip along the south side of Sava River on today’s Bosnia became a part of the new province Pannonia while the rest of Bosnia, Montenegro and western Serbia became part of the Roman province of Dalmatia. During its Roman rule, Latin speaking settlers from the Roman Empire lived among the Illyrians and Roman soldiers were actually encouraged to retire in the region. Many Bosnian towns which exist today were founded under Roman rule, an example of this is a town on the Buna River which is built on the former Roman town of Bona and today is called Blagaj. Bosnia under Roman rule was developed hugely, the economy was mainly based on the exploitation of mines. Christianity had arrived in the region by the end of the first century. When the Roman Empire split as a result of various events in 337 and 395, Dalmatia and Pannonia were included in the Western European Empire. This region went on to be conquered by Huns. The Huns were a group of nomadic warriors who primarily terrorised Eastern Europe and the Roman Empire in the 4th and 5th century. Some historians believe that Huns originated from the nomad Xiongnu people in 318 B.C and that they attacked the Qin and Han Dynasties in China. It is also believed that the Great Wall of China was built to protect against the people of Xiongnu. The Huns were known to attack on horseback and had mastered the art of equestrian warfare.

Bosnia was then conquered once again in 455 A.D by the Ostrogoths. Ostrogoths were Germanic people and were one of the two great Gothic kingdoms within the Roman Empire, along with the Visigoths. The Byzantine Empire defeated the Ostrogoth kingdom in the Gothic War between 535-553 A.D. The Byzantine Emperor at the time was called Justinian and he ruled from 527-565 A.D. The Sclaveni were early Slavic people who came in contact with the Byzantine Empire in the sixth century. They invaded, raided and eventually settled in the Balkans, including Bosnia in the early Middle Ages. The Sclaveni are widely regarded as the ethnogenesis of the South Slavs.

However, by the start of the seventh century, the first waves of Slavs had begun to settle in Bosnia. They primarily settled akong the Adriatic coast along the rivers Bosna, Drina and Vrbas. In the last few years of the 620s, the Serbs and Croats arrived. The Serbs and Croats mainly arrived as they had been asked by Emperor Heraclius to battle the invasion of the Pannonian Avars who had settled in western Bosnia at this point.

Emperor Heraclius was the Byzantine emperor at the time and the Pannonian Avars were a nomadic group of

Max Dawson Paul East Asians and Siberians. They were quite relevant in the early Middle Ages. They dominated the Pannonian Basin and dominated a lot of central and Eastern Europe. They began to decline after 780 A.D and the Avar chieftains surrendered and accepted Christianity in 796 A.D. By the ninth century, Bosnia was almost entirely Christian, thanks to Latin priests. The northeastern part of Bosnia was taken by the Carolingian Franks in at the start of the ninth century. The Carolingian Empire was a large Frankish-dominated empire in western-central Europe. It lasted between 800-888 A.D. Bosnia in 838 at the latest was already a political and territorial entity.

In 949 A.D a civil war begled to Časlav, who was Serbian, leading a conquest into Bosnia. After his death in 960 A.D, Bosnia was retaken by Kresimir of Croatia. The Byzantine Emperor Basil II forced the Croat and Serb rulers to accept Byzantine jurisdiction in 1019. In reality though, this meant very little for Bosnia itself. The northeastern part of Bosnia ended up being given to the king of Croatia and Hungary in 1030 by Raška in 1030. The Byzantines compiled a huge coalition. This included the ruler of Bosnia at the time and the prince of Zahumlje. They did this against Stefan Vojislav, ruler of Duklja. Vojislav defeated this coalition and defeated the coalition, he annexed Zahumlje shortly afterwards.

Serbian princes ruled in Zahumlje and in the 1070s, Zahumlje ended up integrating with Raška under Constantine Bodin. In the 1080s, Bodin expanded his empire and conquered the entirety of eastern Bosnia. His kingdom disintegrated after his death in 1102. The Hungarians began their reign of Bosnia in 1102, almost immediately after the death of Bodin. During the 1150s, the Croation Ban Borič, who was the first known Ban of Bosnia as a Hungarian vassal, led Bosnian troops to assist Hungary in Belgrade against the Byzantines.

Bosnia was functionally independent although the kingdom of Hungria and Croatia claimed it. King Kočopar of Duklja attempted to reunite Bosnia and Duklja but it failed with the death of Kočopar. After the Hungarian kingdom entered a personal union with Croatia in 1102, almost all of Bosnia became a vassal to Hungary. A personal union is where two or more countries share the same monarch but different rules. Byzantium defeated Hungary in the Battle of Zemun in 1167 and took over the entirety of Bosnia under its territory. This would remain the case until the death of Manuel I Comnenus in 1180. After the Hungarian Kingdom took Croatia and the Hungarian Kingdom and while Serbia was going though a dormant phase, Bosnia was heavily contested between the Byzantine Empire and the Kingdom of Hungary. The Hungarians tried to use church politics in 1203 to claim sovereignty over Bosnia. The Hungarians kept trying to claim Bosnia, this only ended in 1254 after an unsuccessful invasion. Between 1273-1303, Bosnian nobility threw off the authority of the Bans through several crusades. During this time, most of Europe was heavily influenced by Popes. In the thirteenth and fourteenth century, the Roman Catholic Church took part in many crusades all over Eastern Europe, including Bosnia. In the thirteenth century, Bosnia tried to resist the Roman Catholic papacy from meddling in their governmental affairs. Bosnia refused to accept the theocracy and monolithic religion which papacy depended on. Bogomilism started in the tenth century. A Bogomil is a member of a dualist religious sect that did very well in the Balkans. Based on a dualistic cosmology, the Bogomils’ believd that the Devil created the material and visible world. It spread though Europe and Asia rapidly, including the Byzantine Empire. It was very popular during between the tenth and fifteenth centuries.

Stjepan II Kotromanič became Ban of Bosnia in 1322. He ended up capturing bits of the Dalmatian coast and Croatia during the first five years of his reign. He signed multiple peace treaties, namely with Ragusa in 1334 and Venice in 1335. His nephew succeeded him at the age of fifteen after he died in 1353. His nephew was called Stephen Tvrtko. The state Kotromanič fragmented after his death as the nobles felt no true loyalty to Tvrtko I. Shortly before the death of Kotomanič, he had married Elizabeth, his daughter to Louis, King of Hungary. This meant that Tvrtko I could ask for the lands of Hum. However, as he had no support from his nobles, Hungary kept ist territory in Hum. War broke out in 1363 between the two kings. Louis invaded the northern provinces which were divided in loyalty. In 1366 his nobles expelled Tvrtko I and he strangely fled to Hungary who wierdly accepted him. The nobles then made Tvrtko’s brother, Vuk, king. Tvrtko I went back into Bosnia with Hungarian troops and Vuk was exiled while Tvrtko took back the throne. The Serbian Empire collapsed after the death of Stefan Dušan who was the King of Serbia. This left many competing kingdoms and countries fighting for bits of the Serbian Empire. Tvrtko lent troops to Lazar Hrebljanovič, who was a Serbian ruler at this time. Lazar created the most powerful and biggest kingdom on the land, previously occupied by the broken down Serbian Empire. In return for Tvrtko lending him troops, Lazar gave Tvrtko some land, and in 1337, Tvrtko crowned himself King of Bosnia. After Tvrtko’s death in 1391, the kingdom of Bosnia did not break, the political leadership was severely weakened and the nobles all contended for power. In 1404, King Ostoja

Max Dawson Paul was removed from power by the nobles and the son of Tvrtko I was made king, Tvrtko II. Ostaja then went back to Bosnia, having gone to Hungary to gather an army and he captured part of Bosnia. Over the next decade, he slowly regained authority. The Ottomans declared that the deposed Tvrtko II was the rightful King of Bosnia, and hence invaded. Within a year, the Ottomans won a decisive battle against the Bosnian and Hungarian forces. They agreed to keep Ostaja on the throne, although he was really just a puppet king for the Ottomans.

When Ostaja died in 1418, his son was exiled two years later by Tvrtko II. The Turks took southern parts of Bosnia between 1433-1435 from the the Hungarians. Tvrtko II died in 1443 after the Turks had seized the Srebrenica. The successor of Tvrtko II, Stephen Tomaš then got involved in a three year civil war with Sephen Vulkčic. When Tomaš died and his son Stephan Tomaševič came into power, he immediately asked the Pope at the time, Pius II for help in 1463 against the inevitable Ottoman invasion. He received no assistance. Mehmet the Conqueror then conquered Bosnia and Tomaševič was executed. King Matthias of Hungry then invaded and captured parts of Northern Bosnia. In 1471, Matthias created a Bannate, loyal only to him and he renamed the Ban, King of Bosnia. The Turks destroyed the Hungarians, in a battle called the Battle of Mohács and completely removed the Hungarinas from Bosnia.

The Ottoman conquest of Bosnia began a new era in Bosnian history. The Ottomans made Bosnia its own province of the Ottoman Empire and introduced many new political and cultural concepts, such as a landholding system. Bosnia was also able to keep some Pre-Ottoman rule culture.The Ottomans were also responsible for hugely increasing the Bosnian population of Muslims. Furthermore, a large quantity of Sephardi Jews went to Bosnia, after they were expelled from Spain at the end of the fifteenth century. The Bosnians thrived under the Ottoman Empire, especially as the empire expanded as it then no longer was a frontier province. Cities, such as today’s capital, Sarajevo were founded. Under Ottoman-rule, Bosnians played a vital role and it was not uncommon to see Bosnians in high ranking positions in the military and as city governors.

Bosnians also undoubtedly had a profound impact on Ottoman culture. Towards the end of the seventeenth century, the Ottoman Empire’s military failures began to have unfortunate effects. After the Treaty of Karlowitz as well as other battles and treaties, by 1699, Bosnia became the Ottoman Empire’s westernemost province once again. Further conflicts and battles left Bosnia in a bad way and the Ottoman Empire was certainly in decline. This reached a climax when a revolt by Husain Gradaščevič failed in 1831. Throughout the 1860s the Ottomans did everything they could to keep the Ottoman Empire together. However, in 1875 the Herzegovinian rebellion begun, this was a widespread peasant uprising. This conflict affected many states in the Balkans and Great Powers. This meant that Bosnia had to pass Bosnia to the Austro-Hungarinas under the Treaty of Berlin in 1878.

At the beginning of the Austro-Hungarian military takeover, there were many tensions, particularly in Herzegovina. However, stability was soon reached and the Habsburgs made a particular effort to integrate Muslims into the kingdom and to make Bosnia a ‘model colony’. Overall, the transition between the two empires was almost seamless. The Austro-Hungarians introduced a successful economy to Bosnia, on the other hand, they failed to stop the increase in popularity of Nationalism. The concept of a unified South Slavic state slowly increased in popularity through the 1910s. As a result of the Bosnian Crisis, the Austro Hungarian government annexed Bosnia-Herzegovina in 1908 and on 28 June 1914, Gavrilo Princip, a young Bosnia revolutionary assassinated the heir to the Austro Hungarian throne in Sarajevo. This of course then started a chain of events which kicked off the First World War. After the end of the First World War, Bosnia and Herzegovina were added to the kingdoms of Serbia, Croatia and Slovenia. These nations then became Yugoslavia. The Agarian Reform of 1918-19 caused a plethora of economic and social unrest due to this reform leading to property confiscations, among other things. Unfortunately, the simple ideological differences between the four states were so great. Thankfully for Bosnia, its politicians were able to keep the six oblasts which divided Bosnia and Herzegovina, these have been the same since the Ottoman times, therefore their boundary and quantity of territory was kept the same after Yugoslavia fell apart.

Bosnian entity was completely removed after the government of the Kingdom of Yugoslavia, formed in 1929, deliberately divided the kingdom into banates, completely different to what they had been historically. This only further increased tensions within the kingdom. However, the government had to focus on the threat of Nazi Germany and the increasing likelihood of invasion. Yugoslavia repeatedly attempted appeasements and even joined the Tripartite Pact which was also known as the Berlin Pact. It was an agreement mainly between Germany, Italy and Japan which was signed in Berlin on 27 September 1940. It was signed by Yugoslavia on

Max Dawson Paul 25 March 1941. As a result of this, a coup d’état in Belgrade occurred just two days later when Prince Paul of Yugoslavia, who was pro-Axis was overthrown and King Peter II, who was anti-Axis came into power. Hungary, Germany and Italy repsonded by invading Yugoslavia on 6 April 1941. The Axis powers had taken over the entirety of Yugoslavia by 18 April 1941, in 16 days. The Yugoslavs had been heavily outnumbered in terms of vehicles and equipment. Germany had well over four times the amount of tanks and it was the same with aircraft. The invasion begun with a lot of aircraft use from the Axis powers and the Germans easily pressed through most of Yugoslavia. By the time the Italians arrived and attacked in the direction of Ljubljana, the Axis powers felt little to no resistance at this point. An armistice was signed on 17 April 1941 which stated the complete surrender of the Yugoslav army. This came into effect at noon on 18 April. Soon after the Nazis had conquered Yugoslavia, it was given to the Independent State of Croatia. The Croaitions ruled very harshly over Yugoslavia. They almost entirely destroyed the Jewish population and hundreds of thousands of Serbs were killed bywere killed by Croation Utaša authorities in concentration camps. Many Serbs armed themselves and joined a nationalist Serb movement called the Chetniks. They were responsible for a lot of widespread killing and persecution of non-Serbs and communists. The Chetniks primary massacred the primarily Muslim population of Bosnia and Herzegovina. It is predicted that 8.1% of the Bosnian and Herzegovinan population were killed by the Chetniks and that in total that they killed about 90,000 people. Yugoslav communists created their resistance group ‘the Partisans’ in 1941, they were led by Josip Broz Tito. They fought against the Axis powers, Ustaše and the Chetniks. They were also responsible for numerous atrocities, such as the Kuders of many political opponents. The Anti-Fascist Council of National Liberation of Yugoslavia, led by Tito on 25 November 1943 met in Jajce. It was here that Bosnia and Herzegovina was restored as a republic, inside of Yugoslavia. The Allies backed up the Partisans and on 6 April 1945, Sarajevo was captured by the Partisans.

After the end of the war, the Federal People’s Republic of Yugoslavia was established. Bosnia and Herzegovina was one of the six constituent republics in the new state.

The first elections after the Second World War were on the 11th November 1945. The general population now backed the People’s Front, who were communist. However, the politics soon became radical. The Yugoslav government allied with the Soviet Union unde Stalin. They closely followed the Stalinist model of economic development, which was fo course very communist. There were considerable tensions between the United States and Tito in Yugoslavia as Yugoslavia shot down two American planes flying over Yugoslav airspace on 9 and 19 August 1946. Until 1948, the Yugoslav communist government sided with the Eastern Bloc, the Eastern Bloc was a community of socialist states during the Cold War. However, in 1948, the Tito-Stalin split left Yugoslavia adopting a policy of neutrality. They tried to cover it up as simply an ‘ideological dispute’. However, in reality, the conflict was a result of a geopolitical clash in the Balkans. The Yugoslavs supported a communist insurgency within Greece. The Soviets opposed this. There had also been a territorial dispute in Trieste and Carinthia and steadily deteriorating relations between the two countries. Yugoslavia managed to maintain neutrality thought the Cold War and it also moved to a market-based socialism economy from a command economy. A market-based socialism economy is where a social owner ship of the means of production exists.

Yugoslavia is known to be a a founding member of the United Nations and the World Trade Organization. Tito died on 4 May 1980, following this, the Yugoslav economy began to crumble. Due to this, unemployment and inflation hugely increased. This led to a rise in popularity of ethnic nationalism towards the end of the 1980s and the beginning of the 1990s. After the collapse of communism in Eastern Europe, talks between the six republics of Yugoslavia began, in an attempt to turn the federation into a confederation, a confederation is ‘an organisation consisting of different groups of people working together for business or political reasons’ according to the Cambridge dictionary. This however failed dramatically, and led to the start of the Yugoslav wars and the end of Yugoslavia. The European Union, then the European Community sai dit would handle the disintegration of Yuogolsovia, however this did not work to plan. The Serb dominated Yugoslav army threw the first punch and thousands were killed in Slovenia initially and in Croatia. The conflict ended after the UN imposed a ceasefire. It broke up on 27 April 1992.

Max Dawson Paul As Bosnia had a large quantity of Serbs, Muslims and Croats, it made thing complicated. Bosnia tried for independence, which the Muslims and Croats wanted. Bosnian Serbs disagreed and they were backed up by Serbs elsewhere. Their leader Radovan Karadzic threatened the Bosnian Muslims and Croats, who outnumbered the Serbs, with death if they tried for independence. In a referendum for independence on 1 March 1992, the Serbs boycotted it. The turnout was 64% and 98% of people voted in favour of independence. Therefore, Bosnia became an independent state on 3 March 1992. Following this, a major Serbian offensive occurred and began later that month. The first rounds fired in the conflict were on 7 March 1992 when Serb paramilitary forces attacked Bosniak villages, near Čapljna. The Serbian artillery then attacked Neum on 19 March of the same year. The killing of a female Bosniak civilian on 5 April 1992 who was protesting against the raised barricades of Bosnian Serbs. Open warfare begun in Sarajevo on 6 April 1992. When the conflict was recognised internationally, the Yugoslav People’s Army withdrew their forces from Bosnia and Herzegovina. The Bosnia Serb members of this armies mostly joined the Army of Republika Srpska who were armed form Yugoslav People’s Army weapons had most of the county under its control. Around 70% of the country was unde Serbian control.

The Serbs ran concentration camps and practised ethnic cleansing. The Serbs internally displaced 1.5 million people. Serb snipers would prowl the urban streets and prey upon civilian Muslims. After Bosnia split apart, the Bosniak Muslims were left in a small part of the country, landlocked, with minimal natural resources and next to no allies. The Serbs and Croats also split apart and unfortunately there was nothing the UN, NATO or EU could do about the Serbs. The UN created a ‘no-fly zone’ to prevent bombing. The UN made ‘safe areas’ which did not really work as they hardly put down any soldiers. The UN Protection Force then went int to feed the 1 million starving refugees. The Croat-Bosniak war begun in the summer of 1993 and the Croats struck first on 16 April 1993 when 117 Bosniaks were murdered in a village called Ahmici which was less than a mile from a UN base. Many Mosques were destroyed and so forth. A ceasefire started on 23 February 1994 after American pressure. Many demilitarisation agreements were made. However Pam there was a large massacre in Sarajevo on 28 August 1995 and so NATO went in to finish the job. At the end of this, the Dayton agreement was signed on 21 November 1995 which split the country. Over the three year war around 100,000 people were killed and over two million displaced.

Since then, Bosnia and Herzegovina has become an applicant of NATO and the European Union and has steadily rebuilt itself. It is now bordered by Serbia to the east, Montenegro to the southeast and Croatia to the north and southwest. It has a very narrow suit of land along the Adriatic Sea, approximately 20km long. The climate is continental and Bosnia is also mountainous. Today Bosnia is home to three main ethnicities. The largest of which is Bosniak and the Serbs second and finally Croats. It has a three-member presidency made up of one from each ethnicity. However, the city is mostly decentralised. Bosnia and Herzegovina also consists of 10 cantons. A canton is simply a different name for a county. It also ranks 73rd in human development and is classed as a ‘developing country’.

In conclusion, it can be seen that Bosnia and Herzegovina is a country with one of the richest history’s in the world. It has been inhabited since the Neolithic times and has captured and been under the possession and part of many different kingdoms, countries and empires. The first of these was the Romans and the last of these was Yugoslavia. As well as this, its location in Eastern Europe in the Balkans means that it has a very plentiful mixture of ethnicities and religions. You can find Jews, Turks and Muslims as well as many other races of people in Bosnia and Herzegovina. This wide variety of people have trickled in and settled throughout the centuries.

You could argue that the Turks and Muslims came from the Ottoman times and settled. This means that the culture of Bosnia and Herzegovina is very rich. It can also be seen that many conflicts and battles have occurred in Bosnia and Herzegovina, some of the effects are still being recovered from today. It can also be seen that the people of Bosnia have had a hard time throughout the millennia, they have been continually persecuted, whether it be the Muslims or the Serbs. Furthermore, they have had many economic challenges. Overall, Bosnia and Herzegovina has had a very turbulent history, although things are starting to look up now as the country develops.

Max Dawson Paul

Map of Bosnia and Herzegovina frm the 12th to the 14th century

Map of the Axis invasion of Yugoslavia in 1941

Max Dawson Paul

Coat of arms of the Socialist Republic of Bosni and Herzegovina

A photo of Josip Broz Tito (lived 1892-1980)

Max Dawson Paul

A map showing the distribution of former Yugoslav countries today

Bibliography https://en.wikipedia.org/wiki/History_of_Bosnia_and_Herzegovina https://en.wikipedia.org/wiki/Bosnia_and_Herzegovina https://en.wikipedia.org/wiki/Neolithic https://www.britannica.com/event/Neolithic https://en.wikipedia.org/wiki/Early_history_of_Bosnia_and_Herzegovina https://www.britannica.com/topic/history-of-Bosnia-and-Herzegovina https://en.wikipedia.org/wiki/Tumulus https://www.historyhit.com/divorce-and-decline-the-division-of-east-and-west-roman-empires/ https://en.wikipedia.org/wiki/Western_Roman_Empire https://www.infoplease.com/world/countries/bosnia-and-herzegovina https://www.history.com/topics/ancient-china/huns https://en.wikipedia.org/wiki/Ostrogoths https://en.wikipedia.org/wiki/Bosnia_and_Herzegovina_in_the_Middle_Ages https://www.historyofbosnia.com/2018/07/01/bosnia-1273-1303-the-middle-ages/ https://military.wikia.org/wiki/Sclaveni https://en.wikipedia.org/wiki/Carolingian_Empire https://www.quora.com/Who-are-the-Avars-and-where-did-they-come-from https://en.wikipedia.org/wiki/Ban_Bori%C4%87 https://www.britannica.com/topic/Bogomils http://www.worldwar2facts.org/tripartite-pact.html https://doc-research.org/2018/03/rise-fall-market-socialism-yugoslavia/ https://en.wikipedia.org/wiki/Socialist_Federal_Republic_of_Yugoslavia https://www.bbc.co.uk/news/world-europe-17632399 https://hmh.org/library/research/genocide-in-bosnia-guide/ https://www.history.com/topics/1990s/bosnian-genocide https://en.wikipedia.org/wiki/Josip_Broz_Tito

Also, I used knowledge from a talk I attended from General Peter Williams on the Bosnian War here in Radley on 17 May 2021.

I also read a book on the Bosnian War called ‘The War in Bosnia: how to succeed in genocide’ by Muhamed Borogovac.

Jo Ashford Has supplementing become a new way of life or are we all under the influence of advanced marketing?

Video available here

Yiyang Xu

A Brief History of Lightspeed

Yiyang Xu

A Brief History of Lightspeed A Brief Introduction to Lightspeed

The history of Lightspeed is full of little details and incredibly complex theories, and is much too lengthy for me to cover fully. Thus, I will have to gloss over some details and only focus on the most defining points in its storied history.

Ole Römer (1676)

The story truly starts with Ole Römer, since before this it was generally accepted that light travelled at an infinite speed, and those who did believe it had a finite speed justified it through philosophical means. Römer had been timing the eclipses of Io 1 around Jupiter after Galileo, who was the first to observe it, had suggested that it could be used as a clock. Perhaps surprisingly, the motivation for this was actually navigation. Knowing your longitude and latitude would give you your location on the Planet. The problem of Latitude had been proven to be quite simple- there were many ways. For example, you could measure the angle from Polaris and the horizon with an inclinometer.

As for longitude, they were able to realise that, if you knew the local time and the time in Greenwich, you would be able to deduce how far East/West you were (in the same way as time zones). In the modern day, it would be easy just to use a clock that is tuned to GMT and find out the time at where you were by looking at the Sun’s position in the sky (or to use a GPS). However, the best Clocks during his day were all pendulum clocks- thus, the rolling of the ship and the very slight differences in gravity meant that they were almost useless. But there was another way- if you knew the time of an event that was visible at any point on the Earth at GMT, then by finding the same time where you are, you would be able to know the time difference, and thus where you were relative to Greenwich. Previously people attempted to use Lunar eclipses, however, they were far too rare and difficult to observe. On the contrary, Io was the innermost moon of Jupiter, and was eclipsed roughly every 42.5 hours. That was the idea behind observing Io. Observing it, he found that the time between the eclipses was not constant. In fact, these variations seemed to correspond with different times of the year. Since he had the orbital paths of Earth and Jupiter, and found that when they moved away from each other there was also a longer interval between eclipses, and visa versa, he deduced that this could be explained if light travelled at a finite speed.

Römer explaining what he had found “Now supposing that the Earth when at L (Figure 1), near the second quadrature of Jupiter, has seen the first satellite at the time of its emersion or coming out of the shadow at D; and supposing that about 42.5 hours afterwards, i.e., after a revolution of the satellite, the Earth being at K, the return path at D, it is evident that if light takes time to cross the intervening space LK, the satellite will be seen at D later than it would have been seen if the Earth had remained at L, so that the revolution of the satellite, thus observed by means of its emersions, will be1 retarded by as much time as the light will have taken to pass from L to K. On the other hand in the other quadrature FG, the Earth when approaching goes before the light, and the succession of the immersions will appear shortened by as much as those of the emersions had appeared lengthened.”

1

One of Jupiter’s 4 big moons

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Figure 1- Romer’s diagram He explains that as you head away from L to K, if the speed of light is finite there would be a lengthening of the time periods between each emersion. As you move from F to G, if the speed of light is finite there would be a shortening of the time periods between each emersion. Thus, when he recorded a difference in the time periods at different times of the year (he estimated that it would be 11 minutes early when nearest to Jupiter and 11 minutes late when farthest), he concluded light travelled at finite speed. Unfortunately for Römer, many did not accept thissome blamed it on the unreliability of the instruments used, and some just did not believe in the Copernican idea that the Earth orbited the sun anyways. But he still laid the foundation by finding evidence that light was finite.

The First Measurement of the Speed of Light

Römer also added that if the diameter of the Earth's orbit were known, they would be able to estimate the speed of light relatively accurately using this equation. 𝒄𝒄 =

𝑫𝑫 𝒕𝒕 − 𝒏𝒏𝒏𝒏

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where c is the speed of light, D is the distance between the Earth’s positions where the first and last eclipses had been observed, t is the measured time between the first and last eclipses, n is the total number of eclipses that have happened, and T is the true period of Io’s orbit (42.5 hours). However, Römer himself did not calculate a value for the speed of light.

That was a Dutch scientist by the name of Chiristiaan Huygens, who calculated a speed of 212,400,000 m/s (where the actual value is 299,792,458 m/s).

James Bradley and the Aberration of light

James Bradley, born in 1693, was a student of theology at Balliol College Oxford. He was important in the story of the speed of light because he provided rock-solid evidence that the speed of light was finite, whilst also providing a much more precise measurement for the speed of light. Originally he had intended to measure the parallax of the sun. Parallax is the perceived displacement of an observed object when viewed from two or more different lines of sight, as shown in Figure 2.

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Figures 2&3- a (greatly exaggerated) example of the effects of parallax This was because one of the main arguments for a geocentric universe was the fact that those who believed in the Copernician model had been unable to measure the parallax of the sun.

(This was because the angle was 0.3’’, which was much too small to be seen by the instruments of the day.)

However, whilst they were unable to measure the parallax of the sun, they were able to make another important discovery. Whilst observing a nearby star named Gamma Draconis, which lay directly over their house, which therefore minimised refraction of light rays, they noticed that, whilst the star did appear to move in a circle, it looked a lot more like figure 4.

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Figure 4- an exaggeration of the results of Bradley’s observations It seemed that instead of the star appearing on the opposite side of its orbit, it was always slightly ahead of Earth. Therefore it could not be parallax. He excluded the wobble of the Earth’s axis by comparing its motion with another star. As he continued to observe Gamma Draconis, he noticed that it also seemed to vary throughout the year. As described by Thomas Thomson in his 1812 history of the Royal Society: At least, when he despaired of being able to account for his observations, a satisfactory explanation occurred to him all at once… he accompanied a please party on a sail upon the river Thames. The boat had a mast, to which a vane was attached at the top. Dr Bradley remarked, that every time the boat put about, the vane shifted a little, as if there had been a slight change in the direction of the wind. The sailors told him that the wind had not shifted, but that the apparent change was owing to the change in the direction of the boat… this accidental observation led him to conclude that the phenomenon which had puzzled him so much was owing to the combined motion of light and of the earth.

Gamma Draconis and the Earth had been experiencing the same effect, with the wind being the light and the Earth being the boat. Because the Earth is moving whilst the light is coming, it appears as if the light is coming from ahead of you (this is akin to running in the rain as it is pouring straight down- it appears as if it is coming towards you). And so, the star appears as if it is always ahead of the Earth’s orbit. This also provided some groundwork for Einstein’s theory of relativity.

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Figure 5. Aberration of light: light from a distance source appears to be from a different location for a moving telescope due to the finite speed of light He was able to work out the angle of stellar aberration, and with it, he was able to work out the speed of light- he arrived at 3,001,000 km/s- this was an incredibly accurate measurement.

Fizeau and Foucault

Fizeau and Foucault were two great scientists and friends. They had worked before on many projects. Before in 1834, Charles Wheatstone had developed a method of studying transient phenomena- essentially things that occur in a very short time- using rotating mirrors.

Wheatstone suggested to a scientist named Arago that he could use this same technique to measure light, who would in 1845 pass this idea on to Fizeau and Foucault. However, in 1849, they had a falling out, and so pursued it separately. Fizeau, from 1848 to 1849, instead used a rotating wheel. It is worth mentioning his technician Paul Froment, who was said to be able to split hairs into four pieces lengthwise, and drill a hole down a darning needle. Fizeau first used a 720 toothed wheel (a simplified version is found in figure 6).If you spin the wheel at a speed that by the time the beam, reflected by the mirror, meets the wheel it has rotated ½ (360 degrees/ 720 teeth), to the next gap between the teeth, then the observer (at D) would see the light. So if you had it going through one gap, and increased the speed till it hit the tooth (in reality light was much too fast to consider trying to rotate it any further than this), you could figure out the time it took (by knowing the speed of the rotation) and because you knew the distance you could calculate the speed of light.

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Figure 6- A diagram from the book ‘Lightspeed’ by John C.H. Spence, where T is the rotating toothed wheel, D is the observer, and S is the source.

Fizeau placed his light source in his father’s house, and placed the mirror a distance of 8.66km away. His light source was an ether flame on lime, and his wheel rotated at about 12 revolutions per second. This was driven by clockwork, and was powered by a descending weight. In 1849, he measured a result of 315,000,000 m/s, which was an error of around 5%.

This was special because it was the first terrestrial measurement of the speed of light, and was only slightly less accurate than the astronomical measurements of the time. This would also lead to him winning the Triennial Prize.2 Foucault, in 1850, would instead devise an experiment to determine if the speed of light would be different whilst passing through air and water (the context of this was a ferocious debate over whether light was a wave or a particle). He did, in fact, find that light travels slower in water. One property of a wave was to move slower in denser materials, thus, this benefited the wave theory.

Created by Napoleon III, it was worth 30,000 francs, which was 6 times the annual salary of the physicist position occupied by Foucault at the Paris Observatory 2

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Figure 7- L is the lens, M and M’ are stationary mirrors, and m is a rotating mirror. L’ is a tube filled with water, and ‘Oculaire’ is eyepiece in french. Lumière incidente is the source of light. (Foucault and Measuring the Speed of Light in Water and in Air by Jean-Jacques Sameuli)

Maxwell’s Equations (1865)

Maxwell was trying to find a mathematical expression for Faraday’s finding on electricity and magnetism, from which he developed the famous Maxwell’s equations. Using calculus, Maxwell's equations could be used to show that the electric and magnetic fields obey wave equations. The speed of an electromagnetic wave is determined by the electric constant ε 0 and the magnetic constant μ0 in the equation, 1/(ɛ0μ0)1/2 = 2.998 X 108 m/s. Due to the very similar speed of the measurements of the speed of light then, he concluded that Light was an EM wave, and so, had the same speed.

Michelson-Morley experiment (1881 and 1887) The Michelson-Morley experiment, whilst not exactly being about the speed of light, was the attempt to detect the existence of the luminiferous aether. This was the hypothetical medium that light would be carried through. Whilst it sounds inconceivable now, it did make some sense, and the luminiferous aether was generally accepted at the time. The experiment compared the speed of light in perpendicular directions in an attempt to detect the relative motion of matter through the stationary luminiferous aether ("aether wind").

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Figure 8- a Michelson interferometer Thus, in 1881, he designed this (Figure 8), which would later be known as a Michelson interferometer. The light source would be positioned at a, where it would be split by a halfsilvered mirror3 at g, before being reflected by the mirrors at c and d, before being recombined at b. This would produce an interference pattern4 whose transverse displacement5 depended on the time it took for the light one arm compared to the other arm to reach the eyepiece. His results showed a transverse displacement of 0.018 fringes, far from the expected 0.04.

However, this design was far too erroneous to say anything conclusive.

He would then go on to do this with Edward Morley. This time, they made the light reflect repeatedly in order to increase the path length, and assembled this in a basement, to minimise problems that vibrations and varying temperatures would have caused. However, they still failed to observe their expected results. This result is generally considered to be the first strong evidence against the then-prevalent aether theory.

Einstein’s Theory of Special Relativity (1905)

Albert Einstein, in his theory of special relativity, determined that the laws of physics are the same for all non-accelerating observers, and he showed that the speed of light within a vacuum is the same no matter the speed at which an observer travels. Using this and the principle of relativity as a basis he derived the special theory of relativity, in which the speed of light in vacuum c featured as a fundamental constant, also appearing in contexts unrelated to light. This made the concept of the stationary aether useless.

Other (later) measurements of the speed of light.

The Essen & Gordon-Smith Result (1958) and the Evenson Result (1972)

Another way that you can measure the speed of light and, indeed, any wave’s speed, is to measure its frequency and wavelength. Multiplying these two would give you the value for the speed of light. In 1946, Louis Essen and A.C Gordon-Smith produced a result of 299,792.5 ±3.0 km/s

3

A mirror which lets half the light pass through, and reflects the other half.

4 The 5

interference pattern of two waves is the resulting wave of two waves meeting.

The ‘moving’ of the interference pattern horizontally.

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There would be continued uses of interferometry in later measurements. K.D. Froome would use radio interferometry. Since he knew the frequency of the wave, by knowing the wavelength he would be able to find the speed.

Figure 9- The determination of wavelength.

All he had to do was measure the change in path length between when the waves are in phase, as in the left diagram, and when they are 180° out of phase, resulting in nothing. He would obtain a result of 299,792.50 ±0.10 km/s.

Evenson would then use this with a laser instead, which would grant him greater accuracy, and obtained a result of 299,792.4562 ±0.0011 km/s.

The 17th CGPM (1983)

The story truly ends with the 17 th CGPM- in English, General Conference on Weights and Measures (in French, Conférence générale des poids et mesures). They decided that the metre itself would instead be defined by the speed of light, with the speed of light being exactly 299,792,458 m/s.

A Brief Conclusion

Though I have covered many devious experiments over the span of 300 or so years, there are many more experiments that are mention worthy that I have excluded- hence the ‘brief’.

We have come far from the age-old presumption about light, whether it be its speed, or its nature, or its medium (or lack of it). However, with the shattering of the thinking of an infinite speed of light comes massive implications, some which we are still figuring out today and themselves merit another piece. Perhaps we will forever be bound by the speed limit presented by the speed of light, or perhaps we will never truly get to grips with its strange manipulation of time- but maybe we will. Whilst there may be no more future in the measurement of the speed of light, we can surely immerse ourselves into the challenges its implications present.

Yiyang Xu

Bibliography Lightspeed, by John C.H. Spence https://youtu.be/3JaFVH36WHQ- images also taken from here https://en.wikipedia.org/wiki/Speed_of_light https://en.wikipedia.org/wiki/Michelson–Morley_experiment https://radleycollegemy.sharepoint.com/:b:/g/personal/yiyang_xu2019_radley_org_uk/EdKxdCtBzZJJosRnKoycL rQBS3-xJs8Y8NOP17tiwjegkA?e=LapUy2 https://web.pa.msu.edu/courses/2000fall/phy232/lectures/emwaves/maxwell.html#:~:text=c %20%3D%201%2F https://www.youtube.com/watch?v=xAQrbnXoIug https://en.wikipedia.org/wiki/Ole_Rømer https://linkprotect.cudasvc.com/url?a=https%3a%2f%2fwww.rmg.co.uk%2fstories%2ftopics %2fharrisons-clocks-longitudeproblem&c=E,1,VchdCDq2SrMJArq7XND6rgXqvB_aM1zE6vS09ewJSvfS92lkMUOoZev4Nf P15mCSNVk6i_vu9GKDuWYwPRHnGcmm2_TYHFkfeaK10u4vGgy4YUsA_5kTbQ,,&typo= 1 https://radleycollegemy.sharepoint.com/:b:/g/personal/yiyang_xu2019_radley_org_uk/EWGybxZ4ToJPhKlT9Yglz _EBpTGWMyJdfis2w_dz8ywkSA?e=ISAYG3 https://radleycollegemy.sharepoint.com/:b:/g/personal/yiyang_xu2019_radley_org_uk/EQ_yWoVdNy9PlxkXMEy Hn74B6fqLfnPrCC1xAF1OuKAAZg?e=XXzwhf https://en.wikipedia.org/wiki/Rømer%27s_determination_of_the_speed_of_light https://en.wikipedia.org/wiki/Longitude_rewards https://en.wikipedia.org/wiki/James_Bradley https://en.wikipedia.org/wiki/Aberration_(astronomy) https://en.wikipedia.org/wiki/Fizeau–Foucault_apparatus https://radleycollegemy.sharepoint.com/:b:/g/personal/yiyang_xu2019_radley_org_uk/Ec6S19R2xudLhiW7WK7j NJEBrvs4mQsxgW0s0iqkhneUww?e=FbXKDY https://youtu.be/jUHgIYNEzJQ https://en.wikipedia.org/wiki/Luminiferous_aether https://en.wikipedia.org/wiki/Aether_theories

Luca Hargreave Luca Hargreave

How we took an image of a black hole in m87 How we took an image of a black hole in m87

As someone who enjoys space, I find it fascinating to be able to finally find an image of a black hole as soon as this was taken, I went straight to the NASA website to have a look at the image. The black hole in question is in the constellation of Virgo which is next to the constellation of Leo which holds the supper massive blackhole m87.

Here is a simple large black hole that is in a bath of hot glowing plasma is heated to 10s or even hundreds of billions of degrees and this black hole are an absolute monster okay it is about 7 billion times the mass of the sun. So, we have many ways of ensuring that there might be black holes in the universe you can see how they affect the motion of stars this is one of the biggest black holes by any method anywhere in the universe it is huge. To give you a sense of that if the earth were compressed down to small enough size that it became a black hole all its mass interests small enough region then not even light could escape. It would be about an inch across you could hold it on your finger for comparison the event horizon in m 87 would engulf our entire solar system it would extend beyond the orbit of Pluto. It is so huge but one interesting thing is that bigger black holes are actually less dense the average density within their event horizons so while this earth sitting on your finger would have just unimaginable density the black hole in m87 actually has less density in the area that were breathing it's about the same as the air on the top of Mount Everest so black holes are really quite fascinating. The real game here is that even though this

Luca Hargreave

black hole is enormous because it is so far away it has this tiny angular size on this image which is about the same angular size as if you put a donut and stuck it on the moon it is also about the same angular size as holding an Atom with arms linked. The game is how can we create a telescope, a telescope that can see things that are very small. What the scientists did was to think of a new type of telescope called an interferometer. To understand how an interferometer works it's helpful to draw some inspiration from the ducks they run they jump into a pond and they start kicking their feet wildly .There's this little cluster of ducks they're kicking away and they're stirring up the water and it start up in turbulent but if you look further away from the ducks you will see all these nice outward propagating wave fronts or away from them so close to the docks it's nice and start up far away nice smooth outward propagating wave fronts.

So I'd like to pose a puzzle to you suppose that you're standing on the edge of the pond and you want to tell where the ducks are in the pond but the trick is I will say that you can't see them and you can't hear them your blindfolded and your ears are covered so all you can do is you can stand there and you can feel the water lapping up against your feet and how do you use that information to tell where the ducks are located so let's unpack this little bit here what we will do is use two simple toy models on the left we have ducks that are clustered close together on the right their spread far apart lots of the ones close together start splashing . They're kicking up the water it's nice and turbulent and the wave pattern is regular in the center and far from the center you see these outward propagating wave fronts. Now just imagine that you're sitting there on the edge of the pond feeling the water lapped up and down. So, when you are sitting down the splashes that are further spread apart on the right, we're going to let them start kicking and splashing same thing in the center it's nice and turn turbulent for their part you see these outward propagating wave fronts.

If your standing on the other pond and you see that water lapping up and down just like in the left case you'll notice that there is a pretty big difference between these two cases in that in the start they have very different coherence length so if you were just standing by yourself on the edge of the pond these two cases would look the same to you see the same amplitude of fluctuations of water but let's say that you have a partner who's standing a little ways away from you and you can compare the water that slapping against your 2 feet now we're standing very close to each other what you see is that you experience about the same pattern of sloshing and as you move further and further apart at some point you'll see different patterns of sloshing against your feet and it turns out that if the ducks are very tightly packed together then you and your partner can be very far apart and still see the same sloshing pattern but if you get the

Luca Hargreave

ducks are spread far apart then you and your partner have to be close to each other. What this is telling us is that the correlation structure around the edge of the pond is the thing that contains all the information about where those ducks are located and it's a very beautiful relationship. It is a Fourier relationship between the distribution of the ducks in the center of the pond and splashing pattern that you see on the edge now I know this seems whimsical and probably irrelevant but it's almost a perfect analogy for what we're doing with the event horizon telescope. For black hole we don't have ducks, but we do have electrons when these electrons are gyrating around magnetic fields and as their gravitating around magnetic fields, they are sending out ripples of electromagnetic waves just like the ducks in the pond and of course the distribution of electrons or the image on the Sky that's like the distribution of ducts around the pond. So now we have this black hole that is sending out these electric electromagnetic ripples and so we take telescopes and we spread them apart as wide as possible and then we compare the electromagnetic waves that are being received at each of those telescopes. The correlations of those waves tell us what the distribution of the images is going to look like. for another example, if you just have one telescope all you can tell is how many electrons are gyrating at all you can tell is sort of how much total emission there is from the object but if you piece them all together and act like an interferometer it is like you and your friend are going to be spaced different distances away from each other. With this then you can tell how the emission is distributed on the Sky and this this technique is called aperture synthesis senior.

How we developed the image Synthesizing an aperture was pioneered by Martin Ryle who won the first Nobel Prize in astronomy for his pioneering research in radio astrophysics. Ryle won his Nobel prize for his observations and inventions, of the aperture synthesis technique. As well as Hewish for his decisive role in the discovery of pulsars. If so, why would the scientists go to all this trouble though there is always an advantage. So, for ordinary imaging, it turns out it's easy to tell how fine a detail you want. If there is a problem, you can resolve it just depends on two things the size of your tip your telescope and the wavelength of light you're using. This is something called the diffraction limit you just take the wavelength divided by the side of your telescope so for a human eye observing at visible wavelengths it turns out that the resolution that you can see is about an arcminute. Now radio telescopes (such as NRAO Very Large Array in New Mexico) they can be enormous, they can be hundreds of meters across, but it turns out that the wavelengths of radio telescopes are so much longer than even bigger radio telescopes have about the same angular resolution as your eye not great for angular resolution. However optical telescopes can, of course, be much larger than meters across and observe at the same wavelength as your eye so they can see thousands of times smaller details. Now what about interferometry? So the magic of interferometry is that your resolution doesn't depend on how big you can make any one telescope it just depends on how far apart you can put them so instead of Lamda over the size of the telescope it slammed over the longest space line you have the longest separation between a pair of telescopes, but this comes with a price just spit out an image and instead each base language pair of telescopes is just sampling one spatial frequency of your image so one way to think of this is to imagine. If the image were a song, then each baseline in your interferometer would just hear a singular (note that song). So, you want to see the whole image or hear the whole song what you need as many different baselines as possible both long and short piece all that information together and that's how you get your image.

Luca Hargreave

The

idea of interferometry is maybe we don't have to make a telescope as big as the earth maybe we just sparsely put telescopes all over it and then somehow, we can fill in that missing information with algorithms. That's the idea of the event horizon telescope (EVT) isn't one telescope it's a collection of them spread all over the earth from the South Pole to Greenland and acting together, these telescopes achieve an angular resolution about 20 microseconds, so this is more than 1000 thousand times better than the Hubble Space Telescope. The scientists took existing submillimeter telescopes and then added atomic clocks to them so they could be perfectly synchronized and act together as an interfering metrical array.

The other thing they did is that they added high-speed recording equipment so for if they swallow more data that's like making the instrument more sensitive that's like building bigger telescopes and so they latched on to Moore's law (Moore's law is the observation that the number of transistors in a dense integrated circuit double about every two years.) Currently the EVT is reporting data at about 8 gigabytes per second at every telescope in the array so the scientists can turn these massive amounts of data into an incredibly sensitive telescope and that's how we were able to push into regimes that were never accessible before. When complete you can see that this angular resolution of that is smaller than size of the black hole shadow that we saw in m87. You see this big, blurred puppy image and that's because we're really pushing Aaron strike through its limit, we don't think that it's a blurry image in the Sky that's the fine details of the instrument concede we discussed some of the absurdity of the EVT. I just want to give you one more handle on it and that's that you can imagine suppose that the EVT points at m87 in just recorded continuously for a year the total number generous from m87 would be less than the energy abilities pop a soap bubble it's just stunning that we're able to turn this into a picture of a black holes. So, from start to finish EHT is all these telescopes each of them has these reporters and so they are recording the incoming electric field that is reported onto discs huge banks of discs. These are then taken on airplanes to single centers that then combine all that data and turn it into a digital telescope add delays and that is like unwrapping or even unfolding the earth into a parabolic mirror. So now you can digitally point your telescope we then correlate with calibrating handed off to imaging and then there are many algorithms that try to turn that data into these images extraordinary. The catch here is that the recorded data is vast amounts, petabytes of data so in terms of hard discs they used about half a ton of hard discs to record the campaign however once they had done doing all this processing, they collapse all of that down with no loss of information and so the final data products is as small as something like one MB. One other nice aspect of this is you can online you can download all the data and you can get your hands dirty with it yourself and all the data and imaging algorithms are available online these are available on the ALMA website.

Luca Hargreave

Airplane

Now something you might be wondering is that in 2017 the EHT only had 5 sites that could see only 10 notes (On our pretend music piece,) and even in that simple case of the song most people I think no one would recognize a song with only 10 notes. The question is how could the develops possibly turn only 10 notes into an image. What are we missing is what they asked themselves? It turns out we have one more trick to play and that's how we make the earth part of our instrument. So, let's say that each baseline is joining a pair of telescopes but all we care about is the projected baseline is seen from the source so here on the left we have the earth that's one baseline joining the sites in Chile and in Spain and then that translates from one frequency measurement as the earth rotates thus those fixed pair of sites sampled different frequencies. So how does the earth whilst it is rotating it's sampling lots of different frequencies even for a fixed pair of sites. So, over the course of the night, we can gather lots of information and then we can take all that cumulative information and turn it into just one picture so this is a concept called earth rotation synthesis we use the rotation of the earth to fill in more of this missing information and that's a critical part of the success of EHT. So now we must take this data and the scientists managed to turn it into a picture. Practice this took a spread of year why is it difficult, so I want to take you back a year from a year ago and just try to try to put yourself in the position of what the scientists are doing they are trying to take a picture of something that has never been photographed before using only a handful of measurements that are difficult to calculate with an instrument that has never been used before. The first thing that they want to do is. One starts off and make sure that they are being honest with themselves in all their discoveries and cells rationalizing things after the fact but what they want to do is to eliminate the possibility for that. The second phase started with blinding images which were released but they were forced to cease all communication between each team often analyze it’s image in their own way they got news their own imaging algorithms software and then they were charged with making an image. Now it's not just the imaging that's difficult in this in interferometry often the data have to be discarded so for instance some telescopes have trouble tracking the source that particular elevations so it might be that this sometimes you get data that that's just garbage and you have to throw it away or it might be that sometimes in the morning when the sun comes up thermal deformations on this on the telescope that cause a huge loss of sensitivity from lack of focus and so you have to make these judgments. About what you think you know, maybe one team will say I think this data is garbage I think this whole telescope's data is garbage we're going to throw that away but another team might say no we think that's fine another team might say well we think we can calibrate that and so every team is making their own decisions and there is no communication at all switch team work for seven weeks then they all came together at a workshop and they unveiled for the first time what the images from each set of data revealed.

Luca Hargreave

Most of the groups were confident that they believe what to do next you can't just pick one and say the team like this one best how both groups go from a few images that they think are broadly consistent to say a final image or something that we're ready to interpret for science so for that what they want to do is develop a new objective method for selecting these images. Imaging algorithms were best so they developed suites of synthetic data and a precision procedure were basically the scientists took these different geometric models so here you can see your ring and a Crescent and a disc and a double and these were selected so that when you when you create synthetic data sets from them, they look a lot like them m87 data. So with these models they would create these synthetic data sets were you would sample them as though the EHT was observing these things on the Sky and then we pass them through the imaging algorithms without telling them that these aren't real data they just process them in the same way. In that bottom row of image 1 (below) 1 imaging procedure that's used identically across all four of this the territory's that they were trying to address, it is here that the imaging algorithm works well in rings it produces beautiful rings. Maybe they're so good at making rings that even makes rings when you give the disc right and well likewise maybe something is very good at discs or point sources, but it breaks down it doesn't use rings when there's one in the sky the test training algorithms or are they reliable enough that they can show us things that we weren't even expecting to see. That's what so interesting about this is that because we know the ground truth image here, we can objectively say this algorithm works better than that one or this set of knobs that a person can turn for each algorithm. That is why we use this algorithm to generate hundreds of thousands of imaging parameters and then select spaces among them that produced good images. For all these training sets now, I just want to give you a sense of this process of image formation and kind of how it's using the data to take a picture. For this example the use a team to filter the data which is part of a mini seven data when filtering it, so you just get one baseline. Now when you have just one baseline you basically only know one mode in your image so it's just enough to tell you kind of how big the images.

For the next stage the scientists now have a second baseline, the second baseline now gives them a couple of options because they have two modes along the same direction and so it actually tells us there has to be a little more power there so it breaks that blob when the blob is broken you see this double. Then at the fourth site the scientists now have six baselines and you will start to see this ring structure emerge and you see that the ring has the most structure along the direction of the baseline that you have. Then finally when we had our last station in Spain the resolution along all directions in that range sharpens up and we get to our final image so at this point we have pretty good handle on you know we think the ring is there the think that they understand there data but the thing that really clinched it I think the reason that the were not holding there breath for too long was the fact that they observed over four nights and that means they have four different nights of observations. Each night is a different each night has a different observing cadence ( The term is used as a means of referring to an array of observation times of some astronomical phenomenon.) Some nights had a lot of time observing m 87 some only had a few scans observing m 87. Another big variation is on some nights maybe the telescope performed well others it did less well. Overall, I think that it's a really nice way to cheque and make sure that everything is consistent.

The four images that many centers across the four nights there's just so system you will notice some changes and this is part of the excitement.

Luca Hargreave

Is the image that was taken from the two-day scan in two days April 5th and 6th look very similar and April 10th and 11th look very similar , the different 6 have a little more flux up sitting on the left of the ring. Then on the 10th and 11th there's a little more on the bottom and so this is intrinsic variability of the source and the reason we know this is that we see it in raw data such as closed calibrabration ( I could not find these but thought I may as well add for extra info) . So what we see is that the sources evolving before your eyes it's not just some dormant black hole that sitting in space and what we are seeing is the evolution of the black hole!

Black holes and general relativity So what observers see is broadband admission from m87 what that means is that there's no color information. This means that we just see brightness as a function of position so this is entirely artificial color the teams spent a lot of months iterating on exactly how to visualize it. If you want to develop visualizations that don't draw your eyes particular features that are just the choice of the color the way in which is colored so this is something called a perceptual uniform color map. Near black hole the gravity is so strong that even light is bent so these are photon trajectory's near a black hole and you can see that if protons come close to black hole they can get whipped around they can even get trapped on orbits around the black hole. The net effect of that is if a black hole is sitting in a bath of hot plasma it will cast a shadow on that background and that shadow is almost perfectly circular .So this is what the shadow is coding, it is coding the properties of the space-time near the event horizon of the black hole you can use this to see whether or not general relativity is correct. So, to start imagining that we have a non-spinning blackhole this called the Schwarzschild black hole. The reason it is called this because Einstein published his theory of general relativity in 1915 and Karl Schwarzschild was curious about it and so he derive the

Luca Hargreave

first non-trivial solution to general relativity, he did this during World War One when he was in the trenches. He died less than a year later but it was this incredible achievement.

Less than a year after that David Hilbert a mathematician was the first to calculate the diameter of the Schwarzschild black hole. In a letter that he wrote to Einstein he says as you see the war is kindly disposed toward me allowing me to despite fierce gunfire and decidedly terrestrial distance to take this walk into this your land of ideas. I find it amazing what people can do even amid adversity. In the image below that's the shadow diameter that we expect if there's a hole and if it's not moving at all. It was sort of a long roll until the 60s when Roy curve derived an exact solution for spinning Black hole. Okay it might be that there is a hole but it's got angular momentum and in that case, the shadow becomes just a little bit smaller. This is something that was calculated by Bardeen in the 70s his paper has this nice quote that is conceptually interesting if not Astro physically very important to calculate the precise apparent shape of the black hole unfortunately there seems to be no hope of observing this effect. What this mean is that this is not so long ago that this impossible so you can see the space between a non-spinning black hole in a maximally spending black hole and that's the full space of possibilities if general relativity is correct.

John Bardeen Above is something called the no hair theorem for black holes that black hole is described entirely by its mass and its spin this is very fundamental to general relativity and I love this quote from the famous conversa,” he says in my entire scientific life most shattering experience has been the realization that the exact solution of Einstein's equations of general relativity provides the absolutely exact representation of

Luca Hargreave

untold numbers of massive black holes that populate the universe,” If we want to test this right we want to see are black holes really described entirely by their mass and spin or do they have hair? To test this we have a problem the problem with M87 is that to do this you have to know the mass of the black hole ahead of time the size of the shadow is proportional to its mass so these shadows. The stars that are zipping around M87 are on large scales. You can also estimate the mass of M87 using gas and in that case you estimate that's only about half as big so the gas estimates are maybe seven said that it has about 3.5 billion solar masses the stellar estimates said it had about 6.6 billion solar masses. What the scientists knew is that there is a precise test but it has not been created yet. As it stands all we know is that it's somewhere in this range of 6.6 and 7 billion solar masses. At the moment we actually have a numerical simulations of what black holes look like and we expected to see what is going on to be tremendously dynamic.

So here is a 3 dimensional simulation one of our best simulations and then maybe seven you can see that this thing is not it's not sleeping at all this is a swirling cauldron of fire ( Could copy the spinning version so you will have to use your imagination.) . For one second in this simulation corresponds to two weeks in real time so this is actually an opportunity to watch a blackhole to watch them live and breathe seen material fall through the horizon or be ejected into the jet is an entirely new way to study black holes. The question is we know that there is going to be a little bit of variation for what we see over our five day window or 60 window. The thing is that this variability if we could look at it with sharper resolution would we see this/ To answer my own question I think something really exciting is that we already see hints of this on larger scales so at a slightly longer wavelengths the jet has not become translucent you still see it so this is one of the highest resolution images that was ever made of M 87.

Before the Event Horizon telescope that is at 7 millimeters. Here you're not seeing to the heart of the jet and so you see this big bloom that extends for 10s of thousands of light-years ( Image of jet below.) and what we can do is we take observations of this jet over many months and we can stitch them together and instead of reconstructing an image. This is the jet of M87 and you can see indeed it's alive it's subjecting material and power out to extreme distances. The thing now is that we know that that's being powered by this black hole that's sitting right at the heart of this system this tiny little spot at the heart of the jet. One of the most exciting things mean about the results of this piece is that something that still tentative it's something they have evidenced for but they don't have exclusive evidence for it. It appears that the jet is actually being powered by the black hole and so people often talk about black holes liberating gravitational energy they pull material in and it's hotter and it glows and it releases energy but it's actually possible to extract energy from the black hole itself and this seems incredibly paradoxical. There is a

Luca Hargreave

common misconception and that is once you fall into a black hole you are done but how do you get energy out of that. As it turns out that if a black hole is spinning it's possible to slow it down now spinning black hole with a mass of 87 could have enough energy to power a billion stars for the age of the universe. A spinning black hole can be incredibly efficient and this is how it works you have magnetic fields that come through that Piercy event horizon and as the black hole spins the magnetic fields get dragged along with them just like wires so this is like a motor and spinning up these wires it's generating currents above and below the black hole. So this leads us to think that this could happen in nature. What this means is that these all consist within the jet power we see and X Rays these are all indicating that the black hole is actually powering that jet through its own. So if we can somehow connect this variability all the way down to event horizon telescope scales then we might be able to see this see this living black hole that's actually the source of the power and the jet.

The jet of m87

Angus Lowrie

Angus Lowrie

This is a fictional journal account of Sgt Hans Storhaugs experiences prior to and during Operation Gunnerside in World War Two. Although fictional, care has been taken to follow fact as closely as practicable and anecdotal events have been passed by word of mouth from relatives and close associates as well as the references noted in the bibliography.

Sgt Storhaug was my Great Grandmothers brother, a quiet, tough but unassuming man who participated in one of the most successful commando raids of the 20th Century.

Operation GUNNERSIDE, [which colloquially became known by its Holywood film title ‘The Heroes of Telemark’],

concerns a small team of Norwegians sent from Britain to carry out one of the most daring and important undercover operations of World War II. The aim was to prevent Adolf Hitler building an atomic bomb and the power plant at Vermork in Norway was one of the few places that could provide a key element in the bombs construction - ‘heavy water’. The plant was located on the Hardangervidda, the highest plateau in Northern Europe with some of the harshest winter conditions and treacherous geography.

None of the volunteer saboteurs knew the true reason for the mission nor its import.

I write this in his memory

Angus Lowrie

Angus Lowrie

Angus Lowrie

Angus Lowrie

Angus Lowrie

Angus Lowrie

Angus Lowrie

Angus Lowrie

Angus Lowrie

Mears, Ray.[2004] The Real Heroes Of Telemark: The True Story of the Secret Mission to Stop Hitler's Atomic Bomb, Hodder Paperbacks Lewis, Damien. [2017] Hunting the Nazi Bomb: The Special Forces Mission to Sabotage Hitler's Deadliest Weapon, Quercus Greentree, David. [2018] Heroes of Telemark: Sabotaging Hitler's atomic bomb, Bloomsbury Militaerhistorisk Samling http://www.spycom.org/WW2/ The National Archives https://media.nationalarchives.gov.uk History Net https://www.historynet.com Atomic Heritage Association https://www.atomicheritage.org Traces of War https://www.tracesofwar.com •

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