Thermoregulation by Butterfly Wings by Milad Arkian

Temperature Control Mechanism by Butterfly Wings

3rd Year Mechanical Engineering-Initial Report Author: Milad Arkian Project Supervisor: Professor Hector Iacovides

Acknowledgements

“Αγάλι-αγάλι γίνεται η αγουρίδα μζλι”

“The green fruit becomes ripe slowly” (A Greek proverb about patience)

A big thank you to my mentor and supervisor Professor Hector Iacovides without whom this initial report would have lacked sharpness and direction.

Contents 1

Abstract……………………………………………………………………………………………….

Glossary……………………………………………………………………………………………….

Introduction…………………………………………………………………………………………

Butterfly Anatomy……………………………………………………………………………….

Literary Survey……………………………………………………………………………..........

Conductive and Convective Butterfly Heat Transfer System Modelling..

Thermoregulation and the Determinants of Heat Transfer in Colias Butterflies…………………………………………………………………………………………….

5.1 5.1.1 5.1.2 5.2 5.2.1

Thermoregulation and Flight in Colias Butterflies: Elevational Patterns and Mechanistic Limitations……………………………………………………………….. Radiation Heat Transfer Models………………………………………………………….. Thermoregulation and Spectral Selectivity of the Tropical Butterfly Prepona meander ……………………………………………………………………………….

17 19

Behavioural Thermoregulation…………………………………………………………….

19 20

5.3.1

Thermoregulation, Flight of the Wing Pattern in Pierid Butterflies………

5.3.2

Thermoregulation by the Black Swallowtail Butterfly…………………………..

5.3.3

Thermoregulatory Behaviour of the Butterfly Calisto nubile in a Puerto Rican Forest…………………………………………………………………………………………

General Thermoregulation by Butterflies…………………………………………….

5.3

5.4 5.4.1

Mechanistic Contraints and Optimality Models: Thermoregulatory Strategies in Colias Butterflies………………………………………………………………

5.4.2

Thermoregulation in Unpalatable Danaine Butterflies…………………………

26 27

5.4.3

Thermoregulation and Wing Colour in Pierid Butterflies……………………...

5.4.4

Analysis of Heat Transfer in Vanessa Butterflies: Effects of Wing Position and Orientation to Wind and Light………………………………………...

5.5

Conclusions from the Literary Survey…………………………………………………..

28 29

5.6

Gaps in Knowledge………………………………………………………………………………

Appendix……………………………………………………………………………………………..

6.1

Databank……………………………………………………………………………………………..

6.2

Nomenclature………………………………………………………………………………………

References……………………………………………………………………………………………

Gantt Chart………………………………………………………………………………………….

List of Figures Figure No

Caption

An annotated diagram of the general body parts of the butterfly species……..

Annotated butterfly showing difference between forewing and hindwings…..

3 4

Flight stroke positions…….…………………….…………………….…………………………………

Wing scale structure…………………….…………………….…………………….……………………

5 6

Annotated picture showing the upper body parts of the butterfly………………….

Butterfly proboscis in curled position…………………….…………………….………………...

Uncurled proboscis…………………….…………………….…………………….………………………

Cross-section of proboscis…………………….…………………….………………………………….

9 10

Representation of the yaw angle superimposed over the butterfly body……….

Nusselt number vs. Reynolds number for butterflies at a yaw angle of 45o. The dashed lines represent individual butterflies with the solid line the model cylinder at a yaw angle of y = 90o…………………………………………………………………….

Nusselt number Nu as a function of Reynolds number Re and yaw angle y for one species of Colias Butterfly. …………………….…………………….…………………………

Butterfly body (depicted by the cylinder) and wings (symmetrical lines) are shown in relation to the orientation angle Ψ (normal to the thorax) and wing angle θ (angle between the wings the orientation angle).………………………………

Basking postures: pictorial illustrations of the lateral, dorsal and reflectance basking postures used by butterflies to regulate their temperature.…………………….…………………….…………………….………………………………

Effects of fur thickness on flight time and solar absorptivity: Each line represents a different value for butterfly fur thickness (mm). The research sites are Montrose (elevational height=1.5km) and Skyland (elevational height= 2.8km) …………………….…………………….…………………….…………………………..

Reflectance basking: The black basal absorption areas are responsible for taking in solar radiation and increasing the body temperature through heat conduction. The hatched distal region of the wings was not seen to effect body temperature. The white medial regions reflect solar radiation from the wings onto the thorax or abdomen. …………………….………………………………………………………………………………………………...

Melanisation in Pierid butterfly wings. Where + indicates an increase in temperature when melanisation occurs. O corresponds to no effect and – as a decrease in temperature. …………………….…………………….……………………………….

Difference between the ventral and dorsal side of the wings ………………………..

Relationship between body and ambient temperature of perched male black swallowtails in the field. Solid lines indicate points where body temperatures equal ambient. Dotted lines represent pattern of thoracic temperature. Black spots represent thoracic temperature; white spots are the abdominal

11 12

Page No

temperatures. …………………….…………………….…………………………………………………..

A graph comparing the various postures taken up by the Swallowtail butterfly for given ambient temperatures and levels of solar radiation………….

Close-up of butterfly fur…………………….…………………….…………………….………........

21 & 22

Aposematic colours of the unpalatable Birdwing butterfly.…………………………….

Aposematic colours of the white Pierid butterflies…………………….…………………..

Wind shielding of the thorax by the abdomen…………………….………………………….

Effects of fur thickness on flight time and solar absorptivity: Each line represents a different value for fur thickness (mm) at Mesa Seco (h=3.33.6km) …………………….…………………….…………………….………………………………………..

A2 A3 A4 A5

A6 A7 A8

Body temperatures of Swallowtails in field studies ( C). Mean ± sd above, range below.…………………….…………………….…………………….…………………….…………

Various parameters in relation to different wing and abdominal positions Mean ± sd. (Sample size) ………………….…………………….…………………….……………….

Critical thoracic temperatures for various activities of black Swallowtails in the flight cage. Mean (N = sample size) above, range below (oC)……………………

Identification, sex, means and standard deviations (SD) of body mass m [mg], wing length R [mm], wing loading pw [N m-2], thoracic temperature Tth [oC], ambient temperature Ta [oC], thoracic excess ΔT=Tth-Ta [oC] and solar irradiance I [W m-2] for two species of Danaine butterfly………………………………..

Solar absorptivity, thoracic fur thickness and thoracic diameter of four butterfly species in central Colorado…………………………………………………………......

Cumulative daily flight activity time (KFAT) in hours for the three sites of different elevational heights…………………….…………………….………………………………

Sensitivity analysis of the energy balance model, where Td is body temperature excess (labelled as Tex in the nomenclature), Tex = Tbody-Ta. This graph relates how each parameter may affect the butterfly’s body temperature…………………….…………………….…………………….………………………………... Table of results for experiments carried out at high elevations……………………….

32 33

1 Abstract Biomimicry is nature inspired technology, mimicking natural processes, systems and models in order to solve human related problems. Butterflies are known to survive in environments with transitory weather changes. They use their wings effectively when regulating body temperature. This trait may have potential uses in the energy sector, with innovative ways of using solar radiation from the sun. As butterflies are cold blooded they require a heat control mechanism to prevent over-heating from wing flapping, yet the body temperature must be sufficiently high to be able to aid flight. The aim of this project is to investigate the biomimetic process by which butterflies regulate and maintain their body temperatures by modelling and understanding the heat energy balance equations. Appropriate simulation software will be used to solve the heat equations. Three main postures are responsible for the basking practice butterflies use to regulate temperature behaviourally: dorsal, lateral and reflectance basking. Cooling (during soaring) or heating (caused by excessive wing flapping) occur depending on the flying style and requirement of the butterfly. Thermoregulation in the wings occurs through a combined effect of colour pigmentation and skeletal structure supplemented with behavioural heat regulation habits. Detailed research will be carried out from the onset of this initial report with a more thorough look at the wing structure and wing material properties and how they can affect heat transfer rates.

2 Glossary Abdominal Pumping: Contraction of the abdominal muscles that results in the expansion of the air sacs. This forces greater active ventilation, as opposed to passive ventilation that occurs by normal breathing. Aposematic coloration: In biology, the technical name for warning coloration markings that make a dangerous, poisonous, or foul-tasting animal particularly conspicuous and recognizable to a predator. Examples include the yellow and black stripes of bees and wasps, and the bright red or yellow colours of many poisonous frogs and snake, ref Cooling curve: A curve obtained by plotting time against temperature for a solid-liquid mixture cooling under constant conditions. DFW, Dorsal Fore Wing: top side (posterior) of the butterfly wings located at the larger fore wings. DHW, Dorsal Hind Wing: top side of the butterfly wings located at the smaller hind wings. Diffuse Radiation: radiation that has been scattered by atmospheric constituents (e.g. clouds, particulates, aerosols). Delineate: To represent pictorially. Dimorphism: Are the systematic differences acquired in form that occurs due to a difference in gender amongst the same species. Common examples include colour, size or the absence of certain body organs such as antlers or tusks. Direct Radiation: Portion of radiation emitted by a radiation source which reaches the observed receiving point via the shortest distance, possibly weakened by existing shielding walls. The direct radiation is distinguished from scattered (diffuse) radiation which may reach the receiving point indirectly due to scattering on other media. Electromagnetic spectrum: The complete range of frequencies of electromagnetic waves including, in order of lowest to highest: radio, infrared, visible light, ultraviolet, X-ray, and gamma ray waves. Emissivity: defined as the ratio of the energies emitted radiated by the material and by a black body at the same temperatures. Heat Flux: Heat flux is the rate of heat energy transfer through a given surface. Hemolymph: The circulatory fluid found in invertebrates. It is a freely flowing fluid that moves on an open plane around the invertebrate’s body. Hydrophobic: A substance/molecule/object that repels water or is incapable of dissolving in water. Irradiance: Irradiance is the term for used in radiometry for the power of electromagnetic radiation at a surface, per unit area. Irradiance is used when the electromagnetic radiation is incident on the surface. The SI units for all of these quantities are watts per square metre (W·m−2). Melanisation: Melanin is a substance known to darken the appearance of the object it is concentrated on. Melanisation is the process by which butterflies have darker pigments on their bodies due to a local concentration of melanin. Mesothorax: The middle of three segments of the thorax on an insect’s body. The mesothorax houses the second pair of legs. 7

Monochromatic: Pertaining to radiation composed of only one wavelength. Monochromatic Absorptivity: Defined as the ratio of the absorbed radiation at a specific wavelength and temperature to the absorbed radiation by a black body at the same wavelength and temperature. Perching: The butterfly rests or perches at a position or spot for roosting. Photoperiod: The duration of the organism’s daily exposure to light, especially in regards to the effect of its growth and development. Quiescent: Still, inactive or at rest. Radiance: Radiance or spectral radiance are radiometric measures that describe the amount of light that passes through or is emitted from a particular area, and falls within a given solid angle in a specified direction. They are used to characterize both emission from diffuse sources and reflection from diffuse surfaces. The SI unit of radiance is watts per steradian per square metre (W·sr-1·m-2). Radiant energy: The energy transported by electromagnetic radiation Radiant flux: Radiant energy per unit time. Irradiance: Total amount of radiative flux incident upon a point on a surface from all directions above the surface hemisphere. Roosting: The butterfly settles down for rest or sleep. Specular radiation: The incident radiation rays are reflected according to the law of reflection. The law of reflection states that should a construction line normal to the flat reflective surface, the incident and reflected rays will exhibit equal angles. Solar spectrum: The spectrum of the sun's electromagnetic radiation extending over the whole electromagnetic spectrum. Solid angle: An angle formed by three or more planes intersecting at a common point. Simple examples of objects that do this are a cone or a pyramid. The SI unit of solid angle is the steradian (symbol sr), which is equal to radian squared. Thermocouple: A junction between two different metals that produces a voltage based on temperature difference. VFW, Ventral Fore Wing: underneath surface (anterior) of the butterfly wing located at the larger fore wings VHW, Ventral Hind Wing: underneath surface of the butterfly wing located at the smaller hind wings. Yaw Angle: The angle between a butterfly’s longitudinal body axis and its line of travel, as seen from above. Zenith angle: The angle at the earth's surface measured between the Sun and an observer's or an object’s zenith (a point directly above the observed object.

3 Introduction The study of biomimicry has exposed many solutions to human related problems. For example, spiderâ&#x20AC;&#x2122;s silk is known to be 5 times stronger than steel for a given length. Furthermore the sonar system that bats use to navigate blindly around caves is now being mimicked for radar systems. As butterflies have to survive through the daily challenges of varying temperature conditions, there is sufficient purpose to research and understand the structure of the wings and the heat regulation process. Butterflies are known to live and survive under delicate environmental conditions. They are biologically cold blooded and some form of basking (reclining under solar radiation to increase body temperature) is required in order to raise their body temperatures for flight. This basking and its link with thermoregulatory practices of the butterflies will be under investigation. If possible, an accurate representation of the physical heat transfer mechanism between the butterfly and its surroundings will be made. As the behaviour of butterflies is key to their thermoregulation, additional research will be done on the perching, roosting, mating and flight activity and how each of these parameters can affect the thoracic and abdominal temperatures. Links will be made between the difference of habitat elevation and the change it makes to body temperature as well as ambient temperature. Furthermore an investigation of the butterfly fur and its relationship to thermoregulation will be made. As well as the behavioural aspects of thermoregulation, an enquiry will be made of the physical size and wing colour of the butterflies and whether body size can reduce heat loss. Wing colour is based on the reflective tendency of each wing scale. The wavelength of light that is not absorbed is reflected and this gives the iridescently powerful colour of the wings. A short study will be made on whether the pigment of colour of a butterflyâ&#x20AC;&#x2122;s wing can help it absorb heat efficiently. From a better understanding of the mechanisms of butterfly thermoregulation gained from the literary survey the rest of the report will focus on modelling the heat energy equations. The butterfly heat regulation process comprises of conduction, convection and radiation and each of these modes of heat transfer will be developed in terms of their respective equations. The databank in the appendix will provide a useful source of experimental values for the key parameters in the heat balance equations. After simulating the heat transfer processes it will become clear whether these thermoregulation processes are useful for human related problems. Can the structure of the butterfly wings or their pigments provide useful clues to efficient thermoregulation? This question will be explored.

4 Butterfly Anatomy Prior to proceeding with the investigation it is useful to understand some of the organs of the butterfly species that may relate to its method of temperature regulation.

Figure 1, An annotated diagram of the general body parts of the butterfly species, (Wilson, 2010)

General body The butterfly anatomy can be broadly labelled into three main sections: the head, thorax and abdomen (figure 1). 6 legs and 4 wings are attached to the thorax, with the wing appearance being the mode of identifying and naming a butterfly. Butterflies are cold blooded and instead of having a method of internal heat production they rely on external heat sources to generate the temperatures required for flight and other energy intensive activities. A butterfly’s skeleton is hard case on the outside and on the inside there is only blood nerves and organs (Thinkquest, n.d). Butterflies have an open blood circulation i.e. they have no veins and the whole of the inside of the body is covered or flooded with blood (Thinkquest, n.d). In vertebrate species the blood circulatory system is closed. The blood flow provides two functions: gas exchange and nutrient/waste exchange. The heart pumps blood to the tissues allowing the cells to exchange material with the blood stream. In invertebrates or insects the gas and nutrient/waste exchange are exclusive. Gas is exchanged with the surroundings via the trachea or ‘windpipe’ opening directly into the air. The process of gas exchange is by simple diffusion through the trachea branches. Butterflies and other invertebrates have a different liquid for circulatory purposes, called hemolymph that carries nutrients and waste. Due to the open circulation system in butterflies the hemolymph isn’t constrained to arteries and veins. A dorsal tube (rudimentary butterfly heart) 10

pumps hemolymph over all its organs, circulating freely throughout the abdomen. The hemolymph is collected back into the heart via simple diffusion.

Forewings

Hindwings

Figure 2, Annotated butterfly showing difference between forewing and hindwings (Wong, n.d)

Flight stroke begins, wings held together Completed stroke Mid-stroke

Figure 3, Flight stroke positions (Smetacek, 2000)

Figure 4, Wing scale structure (Horton, 2010)

Wings Butterflies have 4 wings (2 forewings and 2 hindwings), with the forewings being the top surface layer and the hindwings the smaller, underside set (figure 2). The forewings and hindwings are symmetrical. The colours of the wings are determined from the reflectance of light frequencies by the scale structure. The entire body of the butterfly (including the wings) is covered with a hydrophobic wax layer to protect the species from water related damage. (Thinkquest, n.d). Butterfly flight occurs (figure 3) by the beating of the wings from 0o (above their thorax) and swing through an arch of almost 180o at which the stroke is completed. The structure of the butterfly wing consists of thousands of microscopic scales split into two to three layers (Horton, 2010). Each of these scales is further split into multiple layers separated by air (Horton, 2010). These multiple scale layers provide numerous instances of constructive interference. In constructive interference two waves meet with the resulting wave being the sum of the preceding amplitudes. Consequently, when light beams interact and reflect off these layers, the intense 11

butterfly wing colours are produced (Horton, 2010). A simplified overview of the butterfly wing structure is demonstrated in figure 4.

Compound eyes

Head

Proboscis Thorax Figure 5, Annotated picture showing the upper body parts of the butterfly (Anonymous 3, n.d).

Head & Thorax The thorax is the middle of the three main parts of a butterflyâ&#x20AC;&#x2122;s body, between the head and the abdomen. The thorax houses all the legs and wings of the butterfly therefore it is the crucial organ of the body when it comes to thermoregulation. Should the thorax be at a temperature below or above that of the acceptable flight range the butterfly would suffer from reduced flight capabilities. This could affect territorial defence behaviour, mating and escape from a predator.

Proboscis

Figure 6, Butterfly proboscis in curled position (Kunkel, n.d)

Muscles

Nerve

Trachea Central canal Figure 7, uncurled proboscis, (Knew, 2008)

Figure 8, Cross section of proboscis, (Wilson, 2010)

Proboscis The butterfly proboscis (figures 6 & 7) or ‘tongue’ provides the vehicle through which butterflies feed (predominately nectar) but also sweet fruit occasionally. After a butterfly lands on a source of food there is a reaction that causes the proboscis to uncurl and extend to the source of the food. This high surface area curl allows the butterfly to keep its long proboscis compact until required for use. The proboscis is shaped like a straw (figure 8) when uncurled and provides the vehicle through which the butterflies suck up nectar or other viable food products such as water or tree sap.

5 Literary Survey A compilation of the most relevant data on the subject was collected and reviewed in light of the subject title. The subject headings of the literary survey were labelled according to analogous research papers rather than separate subject titles. This made it simpler to elaborate on each paper in more detail as each individual research paper dealt with one main source of butterfly thermoregulation. As each sub-section of the literary survey is based on one research paper, all the corresponding diagrams and figures that are used are from the respective papers and so superfluous references weren’t used. Where there are differences in notation between the different research papers, a master label has been used in the nomenclature for ease of use. For example Td as well as Tex have been used in the research papers for body temperature excess (Tbody - Ta). Here the label Tex has been chosen as the principal identity for the expression of body temperature excess. Similarly where there is a difference in units between researchers, SI units have been used as the universal set of units. Any data from previous papers will be converted into SI units for calculations and data handling during the simulation of the heat balance. All of the terms are tabulated under Nomenclature in the Appendices.

5.1 Butterfly Heat Transfer Models 5.1.1 Thermoregulation and the Determinants of Heat Transfer in Colias Butterflies Research paper reference: (Kingsolver, 1982) The foremost purpose of Kingsolver’s thesis is to determine the convective heat transfer hf for real and model butterflies. A significant section of the research is carried out on a set of model and real butterflies in an open circuit wind tunnel under Reynolds numbers Re of around 0 to 3,000. A graph (figure 10) of the Nusselt number Nu (Nu = hfDeff/k) against Re is made, with 0, 45 and 90 degrees of yaw angle (rotation about the vertical axis (figure 9)). These yaw angles will compare the real and model butterflies and whether their orientation to the wind makes a change to the convective heat coefficient. The Nusselt number is the ratio of convective to conductive heat transfer normal to the boundary surface of a body. Further tests from the author attempted to explore the effects of fur on the coefficient of convective heat transfer. The tests concluded that fur acts as an insulation layer to reduce convective heat loss. Wing geometry was seen to have little effect on heat loss.

y â&#x20AC;&#x201C; Yaw angle: rotation about the vertical a axis

Figure 9, Representation of the yaw angle superimposed over the butterfly body (Hicker, n.d) The yaw angle (figure 9) is the angle between a butterflyâ&#x20AC;&#x2122;s longitudinal body axis and its line of travel, as seen from above the butterfly. Kingsolver begins the mathematical modelling of the heat transfer by stating the most important equations in the study. The mathematical derivation is described below: Reynolds Re number was defined as (1.0) Where (1.1) V, the volume and L, the longitudinal length of the butterfly model were measured experimentally. Deff is the characteristic dimension of the butterfly model (taken to be the maximum width of the mesothorax including the fur). The thorax has three sections, the mesothorax being the middle segment. To study the convective heat transfer coefficient the author defines its equation as: (1.2) Equation (1.2) states that the rate of convective heat transfer is obtained from the product of hf, A and (Tbody-Ta). In his experiments, Kingsolver used a combination of steady state and transient methods for estimation of heat transfer coefficients. For the transient model, the butterfly model is heated and time constant Ď&#x201E; estimated from the resulting cooling curve: (1.3)

The total heat transfer coefficient hT is then calculated from: (1.4) Where the area of the model: A=πDeffL The forced convective coefficient, correction factors for radiation and conduction heat transfer are required. When free convection is negligible the forced convective coefficient may be written as: (1.5) The radiation correction factor hR may be estimated by: (1.6) The correction factor for conductive heat transfer of thermocouple wires and support structures: (1.7) For the transient derivation, the criterion used for experimental conditions (where free convection is negligible) is stated below: (1.8) Gr is the Grashof number = (gβ(Tbody-Ta)D3eff/ν2), a dimensionless measure of the free convective heat transfer. The ratio (Archimedes number Ar) indicates the relative magnitude of free vs. forced convection. In the steady-state analysis, the butterfly model is heated internally with a resistance wire. The power input to the heater and steady-state model temperature and ambient air temperature are being measured here. From the steady-state energy balance, the convective heat transfer coefficient is estimated to be: (1.9) Kingsolver writes that the free convective heat transfer coefficient is a function of the temperature difference ΔT between the model and the air, whereas the forced convection coefficient hf is not. For the state-state method, a plot of hf against ΔT at low values of Re confirmed that free convection was negligible for the experimental conditions used. The verification of the experiment procedure was based on a standard cylinder at a reference wind velocity, where the results from the author’s experiment agreed within ±10% for all data. 15

Figure 10: Nusselt number vs. Reynolds number for butterflies at a yaw angle of 45o. The dashed lines represent individual butterflies with the solid line the model cylinder at a yaw angle of y = 90o.

A Nusselt number of order of around unity would indicate sluggish motion, only slightly more effective than a pure fluid conduction case, e.g. Laminar flow in a long pipe (White, n.d). A large Nusselt number would indicate efficient convection, e.g. values of order 100 to 1000 occur for turbulent flow in a pipe (White, n.d). An example of the delineated experiment results are shown in figure 10. The results show that for a given Reynolds number the Nusselt value for Colias butterflies are consistently below that of the model cylinder. This indicates greater laminar flow around the real butterflies as opposed to the cylinder models.

Figure 11: Nusselt number Nu as a function of Reynolds number Re and yaw angle y for one species of Colias Butterfly.

Figure 11 shows that the Nusselt number is essentially independent of the yaw angle for a given Reynolds number (common Reynolds numbers experienced by the butterflies in external fields are 25-1200). For a given yaw angle, as the Reynolds number increases so does the Nusselt number. Yaw angle y at 45o gave the largest increase of Nu with 90o giving the lowest and intermediate angles such as 30o to 60o fitting in in-between. Further work by the author based on fur and non-fur models show that fur has a distinctive effect on the heat transfer process, especially as an insulation barrier against convective heat loss.

5.1.2: Thermoregulation and Flight in Colias Butterflies: Elevational Patterns and Mechanistic Limitations Research paper reference: (Kingsolver, 1983): A prominent section of this report deals with elevational effects on flight activity times for butterflies. This is split into three separate regions of low, mid and high elevational regions measured from the ground. These regions are represented by Montrose at height h=1.5km, Skyland at h=2.8km and Mesa Seco at h=3.3-3.6km. The author touches on the diverse meteorological conditions placed on the respective butterfly populations living in the low to high regions. Some of the conditions include wind velocity, butterfly wing absorptivity, fur thickness and cloud coverage. To develop a model of the heat transfer processes Kingsolver begins by stating a general set of conditions, widely applicable for the Colias butterflies. Firstly their body temperatures are assumed to be isothermal and the ideal position of rest is at the top of a vegetational layer. For these set of conditions the steady-state energy balance is: (2.0) Where Qs is total solar radiative heat flux, Qt is thermal radiative heat flux and Qc is convective heat flux. Furthermore Kingsolver defines an equation for a resting butterfly and the corresponding solar radiative energy flux: (2.1)

(2.2) Qs.dir, Qs.dif and Qs.ref are the direct, diffuse and reflected solar radiative heat fluxes respectively (equation 2.3). Hs.dir, Hs.dif and Hs.ttl are the direct, diffuse and total solar radiative horizontal flux densities. As.dir, As.ref and As.ttl are the direct, reflected and total solar radiative heat transfer surface areas. Îą is the solar wing absorptivity, rg is substrate solar reflectivity and z is the zenith angle. For basking Colias butterflies orientated perpendicularly to solar beams Kingsolver has assumed that As.dir = As.ref = 0.5As.ttl. Values of the total solar horizontal flux density were measured in the field. For sunny conditions the relative proportion of direct to diffuse sunlight was taken to be a function of the elevation, location, date and time of day. For z < 80o, Hs.dir and Hs.ttl are given to be nearly constant (0.92). In cloudy conditions the solar radiation is taken to be completely diffuse. Substrate reflectivity rg is assumed to be 0.3 (a typical value for grassland vegetation). The thermal radiative flux is given to by: (2.3) At is the thermal radiative heat transfer surface area, Tg is ground surface temperature and Tsky is equivalent black body sky temperature. Thermal emissivity is proposed to be 1 (in the thermal 17

infra-red spectrum at about 5 Âľm. As the angle of view of a butterfly is close to the normal, it is appropriate to give a value of 1 for the emissivity. If the emissivity was given a value less than 1, the temperature and temperature differences would have been underestimated (Clark et al, 1973). Moreover the equivalent black body temperature is estimated from the Brunt equation (Sutton, 1965): (2.4) Where m and n are constants, e is vapour pressure in the lower levels of the atmosphere, Stefanâ&#x20AC;&#x2122;s constant and T is the absolute temperature. The convective heat flux is given by:

is the

(2.5) It was assumed by Kingsolver that Ac = At = As.ttl. The total convective heat transfer coefficient ht may be split into two conductances in series: a boundary layer conductance hb and a fur layer conductance hfur. For simplicity the process was modelled as a cylindrical body covered with a thin layer. ht is given by:

(2.6)

is the thoracic fur thickness and ke thermal conductivity of the fur. The body radius is assumed to be 0.15cm (a typical value for these species). The Reynolds and Nusselt numbers (equation 2.7) may be used to obtain values for the boundary layer conductance hb as well as the characteristic dimension of the butterfly (taken to be the maximum width of mesothorax including the fur). (2.7) For high wind speed and low intensity radiation conditions there is negligible free convection therefore from one of his previous thesisâ&#x20AC;&#x2122;, Kingsolver uses the relation between the Reynolds and Nusselt numbers for a bare cylinder, similar to butterfly models without fur. Due to the potential of a mixed flow comprising of free and forced convection, Archimedes number is used to relate the two: (2.8) If Ar is >> 1 then natural convection is dominant in the flow field and conversely should the forced convection be dominant then Ar << 1.

5.2 Radiation Heat Transfer Model 5.2.1 Thermoregulation and Spectral Selectivity of the Tropical Butterfly Prepona meander Research paper reference: (Berthier, 2005) This thesis (5.2.1) begins by building up understanding of the basic components of radiation heat transfer. The research carried out is specifically for the basal region of the butterfly wings, known to absorb the most solar radiation due to its dark colouration. The author Berthier states that for a solar collector such as a butterfly the thermal balance equation depends on solar absorptivity α and the total emissivity εT. The radiation properties are also a function of the direction and wavelength. The author thus states the equations detailing directional absorptivity: (2.9)

(3.0) Equations 2.9 and 3.0 represent the directional and total absorptivity respectively. The directional absorptivity is a function of the monochromatic absorptivity α’λ and the monochromatic irradiance of the incident flux Lλ which in this case is the solar spectrum. Similarly the emissivity has been given in terms of directional and total values: (3.1)

(3.2) Equations 3.1 and 3.2 represent the directional and total emissivity. Mλ is the monochromatic emittance of the black body temperature T. According to Kirchhoff’s second law, for a given direction and wavelength the absorptivity and emissivity are equal: (3.3) Moreover absorptivity is further related to the transmittivity τmis and reflectivity ρ according to the law of energy conversation: (3.4) The author states that butterflies have outer scales referred to as cover scales and ground scales underneath the top layer. A combination of these scales over the basal region of the wing provides 4 absorbing layers for solar radiation. A segment of the report deals with experimental data resulting in the average value for the absorptivity being stated as α = 0.95. This will aid in using accurate values in the energy balance model to be carried out.

5.3 Behavioural Thermoregulation 5.3.1 Thermoregulation, Flight of the Wing Pattern in Pierid Butterflies Research paper reference: (Kingsolver, 1988) This research paper is about the basking techniques applied by butterflies to either increase or reduce body temperature depending on the required action.

Ψ α α

Figure 12, Butterfly body (depicted by the cylinder) and wings (symmetrical lines) are shown in relation to the orientation angle Ψ (normal to the thorax) and wing angle θ (angle between the wings the orientation angle). An example as shown in figure 12, the circle and two slanted lines are a simplification of the butterfly body and wings with two key parameters being highlighted by the author, wing angle denoted by θ and orientation angle denoted by Ψ. Three main postures are outlined by the author as the typical butterfly postures for thermoregulation; they are lateral, dorsal and reflectance (figure 13 below). Lateral basking is when the wings are closed over the body and orientated perpendicularly towards the sun’s solar beam. This posture is mainly used to avoid temperature increases in the body. In dorsal basking the butterfly opens its wings normal to the solar rays thereby directly heating the wings, thorax and abdomen. Finally, in reflectance basking the butterfly will open its wings in such a way as to reflect solar rays off the medial region of its wings onto the thorax and abdomen (figure 15).

Figure 13, Basking postures: pictorial illustrations of the lateral, dorsal and reflectance basking postures used by butterflies to regulate their temperature. The basal regions of the butterfly wing due to their melanisation (influenced by photoperiod during the larval stage) are responsible for the majority of the heat absorption of the wings. Melanisation is the process by which butterflies have darker pigments on their wings and bodies due to a local concentration of substance known as melanin. For this reason the author asserts that butterflies living in cooler habitats tend to be darker in colour, aiding the tougher heat regulation conditions as opposed to butterflies living in more favourable mild climates. The radiation taking place is a function of the wing colour and is labelled as solar absorptivity and this parameter is defined as the fraction of absorbed solar radiation when it strikes a surface. Furthermore the author argues that there are primarily four parameters that help to quantify the link between butterfly thermoregulation characteristics and flight activity time: body size (thoracic diameter), thermoregulatory posture (figure 13), solar absorptivity of the VHW (Ventral Hind Wing) and fur thickness. Three sites in Colorado USA are used to compare the relative differences that an elevational gradient will bring to the rate of flight activity. They are Montrose (height h=1.5km), Skyland h=2.8km and Mesa Seco h=3.3-3.6km. At each site, flight activity is given to be a function of VHW absorptivity and fur thickness. An example of the relevant data collected is shown in figure 14 below.

Figure 14, Effects of fur thickness on flight time and solar absorptivity: Each line represents a different value for butterfly fur thickness (mm). The research sites are Montrose (elevational height=1.5km) and Skyland (elevational height= 2.8km).

The various line numbers for each respective site are different fur thicknesses ranging from 0 to 1.5mm, which are the possible useful ranges of fur thickness for thermal regulation. There are clear indications that for a given % solar absorptivity and fur thickness there is a much longer flight time for the butterflies habituating at lower altitudes. This is further supported by figure A1 (Appendix). According to the author, all Coliadine butterflies utilised the lateral basking posture for thermoregulation, this is a key parameter between the VHW colour and flight time. However nearly all Pierines use the reflectance posture for thermoregulatory practise.

Figure 15, Reflectance basking: The black basal absorption areas are responsible for taking in solar radiation and increasing the body temperature through heat conduction. The hatched distal region of the wings was not seen to effect body temperature. The white medial regions reflect solar radiation from the wings onto the thorax or abdomen.

The author asserts that there is a link between basking angle and body temperature based on figure 15. He states that the greater the melanisation % on the wings the larger the wing angle required to maximise body temperature.

Figure 16, Melanisation in Pierid butterfly wings. Where + indicates an increase in temperature when melanisation occurs. O corresponds to no effect and â&#x20AC;&#x201C; as a decrease in temperature.

As shown in figure 16 the author uses a functional map to show the effects of melanisation in Pierid butterflies. There is a striking difference between the dorsal and ventral areas of the wing. The dorsal or posterior side of the wing has an increase in solar absorption when the basal region consists of a black pigment, increasing the wings absorption rate. The medial and distal regions of the dorsal wing bear little effect on direct absorptive thermoregulation.

Dorsal top side of the wings Ventral underneath surface of the wings

Figure 17, Difference between the ventral and dorsal side of the wings (Anonymous 1, 2010)

5.3.2 Thermoregulation by the Black Swallowtail Butterfly Research paper reference: (Rawlins 1980) The major objective of this paper is to identify the links between physical and behavioural changes that the Swallowtail butterfly exhibits in regulating their body temperatures. Physically the abdomen, thorax and wing positions of the Swallowtail butterfly and their relation to heating and cooling are discussed with qualitative data to back the theories made. Attempts are made to associate thermoregulation to behavioural characteristics of the butterflies, which include shivering, perching, roosting as well as a change in flight patterns that consist of soaring and flapping (vigorously and quiescently). Shivering occurs when the muscles contract allowing for a quick increase in body temperature. A very expensive process in terms of energy dissipation, it is only used 23

in situations of absolute need, i.e. avoiding predators by sufficiently raising their body temperature for required flight. Rawlins also considers minimum and maximum temperature ranges that the butterflies can withstand without procuring fatal injuries.

Figure 18, Relationship between body and ambient temperature of perched male black swallowtails in the field. Solid lines indicate points where body temperatures equal ambient. Dotted lines represent pattern of thoracic temperature. Black spots represent thoracic temperature; white spots are the abdominal temperatures.

Based on figure 18, for a given ambient temperature, thoracic and abdominal temperatures are higher than the ambient temperature. In terms of thermoregulatory practise the author states that for low ambient temperature conditions the Swallowtail would usually raise its abdomen above the wings, exposing them to direct solar radiation and raising the abdominal temperature Tab. Conversely for hotter weather conditions the Swallowtail often levelled itâ&#x20AC;&#x2122;s abdomen to wing height or just below thereby shading it from direct sunlight. Similarly the Swallowtail exhibited a raised abdominal position at lower perching heights and longer perching durations. This is shown by the data collected and shown below in figure 19.

Figure 19: A graph comparing the various postures taken up by the Swallowtail butterfly for given ambient temperatures and levels of solar radiation.

The author Rawlins states that at thoracic temperatures Tth of 37.1 Âą 1.5 sd (oC), the butterfly began struggling, pumping its abdomen. Abdominal pumping is the contraction of the abdominal muscles that results in the expansion of the air sacs. This occurs mainly when insects are active and require cooling through greater respiratory exchange. During abdominal pumping there is a decrease between the thoracic and abdominal temperatures. This is due to a zero net increase in thoracic temperature, where the abdominal temperatures are seen to increase in temperature, indicating heat transfer from the butterflyâ&#x20AC;&#x2122;s thorax into the abdomen. This practise is mainly evident when the thorax is exposed to solar radiation and the abdomen is shaded. The transfer of heat from the thorax to the abdomen reduces the likelihood of thorax over-heating. After investigating shivering behaviour of the butterflies, Rawlins asserts that shivering may be used by the butterflies to improve basking sites under low solar radiation, select suitable roosting sites in the evening or to regain a roosting spot after being dislodged. It may also be a good spontaneous tactic to avoid predation (a fatal attack on the butterfly from a predator) when ambient temperatures are below those required for flight. Moreover Rawlins says that conditions under which heat exchange is carried out between the thorax and abdomen may depend solely on whether the butterfly exhibits abdominal pumping. During abdomen-shade posture, pumping occurs and heating exchange via the hemolymph is maximised. In cases where the thorax is overheated and the abdomen shaded, a useful cooling procedure (heat transferred from thorax to abdomen) occurs to reduce stress from excessive temperatures.

5.3.3 Thermoregulatory Behaviour of the Butterfly Calisto nubile in a Puerto Rican Forest Research paper reference: (Shelly and Ludwig, 1985): This report was interested in understanding the behaviour of Calisto butterflies under a forest location as opposed to the more common open land habitats from previous reporters. Tilting behaviour was analysed and found to elevate the rate of heat intake in the thorax and so reduce the time required for thoracic temperature Tth to rise. Titling behaviour occurs in lateral baskers (figure 13), where the butterfly positions its body for the most effective angle for increased rate of heat intake from solar radiation. It is especially used for short duration basking where it is a useful way of heating the body more quickly.

Figure 20, Close-up of butterfly fur, (Anonymous 2, n.d)

5.4 General Thermoregulation by Butterflies An additional chapter of the literary survey has been assigned to general features that the butterflies have, that aids thermoregulation. These include fur thickness, aposematic colouring of the wings and other heat regulation techniques. These do not directly link in with the proposed heat balance that is to be carried out but provide useful background information that may be called upon when required.

5.4.1 Mechanistic Contraints and Optimality Models: Thermoregulatory Strategies in Colias Butterflies Research paper reference: (Kingsolver and Watt, 1984): The fundamental reason for this paper by Kingsolver lies with two important constraints that can be used as effective parameters in varying optimal conditions for maximum flight activity. Namely fur thickness and solar absorptivity and they are tested with three different habitats of butterflies ranging from low to mid and high elevations (Montrose h=1.5km, Skyland height=2.8km and Mesa Seco h=3.3-3.6km. The main article of importance sprung from a better understanding of the effects of pubescence (fur) on butterfly thermoregulation. According to Watt & Kingsolver, fur decreases the butterfly bodyâ&#x20AC;&#x2122;s sensitivity to temperature changes. This is advantageous for high elevation butterflies (that have more fur) controlling their body temperatures at higher wind speeds. Conversely butterflies dwelling in lower elevations have less fur but this allows them to fly for extended periods when there is little wind 26

Figures 21 & 22, Aposematic colours of the unpalatable Birdwing butterfly. Left (Wong, 2010), right (Mun, 2010)

5.4.2 Thermoregulation in Unpalatable Danaine Butterflies Research paper reference: (Dudley 1991): The author attempts to link relations between palatability (figures 21 & 22) in butterflies and the difference between the thoracic and ambient temperature labelled as thoracic excess. As it is a short thesis there is only one principle experiment with tangible data for use (see appendix figure A5). Palatable butterflies according to Dudley fly in arbitrary flight patterns at the cost of expensive energy consumption expended due to the increased wing beat count and metabolism rates. In contrast unpalatable Danaine butterflies fly more slowly and soar for longer as they have less need of avoiding predators and as there is a connection between predation rates and flying speeds. This thesis didnâ&#x20AC;&#x2122;t bring to light direct heat transfer information for the Danaine butterfly species but rather highlighted a reason for elevated or reduced body temperatures for butterflies depending on their predatory desirability.

Figure 23, Aposematic colours of the white Pierid butterflies, (Jack, 2010)

5.4.3 Thermoregulation and Wing Colour in Pierid Butterflies Research paper reference: (Kingsolver, 1987) The author writes about a special white pigment on the Pierid butterfly wings that deter predators from attacking the butterflies as it’s a sign of unpalatability. Kingsolver justifies a hypothesis that the white wing pigment represents aposematic coloration (figures 21 & 22) that may ward of predators. Aposematic colours specifically warn off predators from poisonous, dangerous or bas tasting animals, i.e. bright yellow colour of golden poison frog. Furthermore from his previous studies Kingsolver relates a second useful function for the white wing pigment-a reflective colour to aid reflectance basking in the Pierid species. Therefore this white pigment assists predation avoidance as well as aiding thermoregulation through basking practise. He also argues that melanisation of the wings can increase the rate of thermoregulation during basking due to increased solar absorption.

The abdomen acts as a ‘shield’ and prevents convective cooling of the thorax from the wind

Wind direction Figure 24, Wind shielding of the thorax by the abdomen, (Toogood, n.d)

5.4.4 Analysis of Heat Transfer in Vanessa Butterflies: Effects of Wing Position and Orientation to Wind and Light Research paper reference: (Polcyn and Chappell, 1986) This is a very thorough and interesting paper that throws some light on thorax temperature when light and wind are applied across a dead butterfly’s body at different angles. The researcher attempts different combinations of wind/light angles and wind velocities and cites the different temperature variations that each parameter has on the butterfly thorax. He also asserts that pubescence (fur) has an effect on temperature. He concludes that closing the wings actually increases Tth (due to a reduction in convective cooling) and that wing angles of 180o (towards the tail of the butterfly) give the maximum increase in temperature due to the wind shielding of the thorax by the abdomen. Wind shielding occurs when the butterfly flies against the wind direction and the abdomen acts as a buffer for the thorax from direct convective cooling from the wind (figure 24). Lastly, pubescence was seen to regulate temperature but to a lesser extent as compared to behavioural actions.

5.5 Conclusions of the Literary Survey 



 

Radiative heat gain occurs at the basal region of the butterfly wing, where the mode of heat transfer is due to thermal conduction. The process is enhanced by the local dark colouration that grants greater thermal absorptivity of solar radiation. The heat conduction process is aided by the close proximity of the basal region of the wings to the thorax and abdomen. The medial region of the wings essentially reflects solar radiation onto the thorax and abdomen of the butterfly. This posture is named as reflectance basking. The butterfly angles its body towards the solar rays thereby heightening its chances of heat gain. Fur helps to reduce convective heat loss and is more apparent on butterflies existing in colder climates. When the butterfly is flying against the wind direction its abdomen is responsible for shielding the thorax from convective heat loss. This reduces the chances of the thorax temperature dropping below an acceptable flight range. Melanisation of the wings is one of the most valuable traits of their wings providing a much increased rate of solar radiation. Under high temperatures the butterflies often shade their abdomens below their wings, allowing the excess heat from the thorax to conductively transfer into the abdomen.

5.6 Gaps in Knowledge  It is desired that a better understanding of the structural aspects of the butterfly wing are understood. This will include a more in depth study of the nano-scale scans of the wing. Moreover a detailed investigation will occur on the full effects of the wing structure and its direct effects on thermoregulation.  An extended understanding of the radiation model of the heat transfer equations. This includes a thorough search on the emissive and absorptive properties of the wings. A better appreciation of the wings absorptivity to transmittivity and reflectivity is required. A question of considerable interest is whether the wings are more efficient than solar panels in absorbing solar radiation.  Does the material/powder coating of the wings enhance/decrease heat transfer rates?

6 Appendix 6.1 DataBank

Figure A1, Effects of fur thickness on flight time and solar absorptivity: Each line represents a different value for fur thickness (mm) at Mesa Seco (h=3.3-3.6km), (Kingsolver, 1988)

Figure A2, Body temperatures of Swallowtails in field studies (oC). Mean Âą sd above, range below, (Rawlins 1980).

Figure A3, Various parameters in relation to different wing and abdominal positions Mean Âą sd. (Sample size), (Rawlins 1980).

Figure A4, Critical thoracic temperatures for various activities of black Swallowtails in the flight cage. Mean (N = sample size) above, range below (oC), (Rawlins 1980).

Figure A5, Identification, sex, means and standard deviations (SD) of body mass m [mg], wing length R [mm], wing loading pw [N m-2], thoracic temperature Tth [oC], ambient temperature Ta [oC], thoracic excess Î&#x201D;T=Tth-Ta [oC] and solar irradiance I [W m-2] for two species of Danaine butterfly, (Dudley 1991).

Figure A6, Solar absorptivity, thoracic fur thickness and thoracic diameter of four butterfly species in central Colorado, (Kingsolver 1983).

Figure A7, Cumulative daily flight activity time (KFAT) in hours for the three sites of different elevational heights, (Kingsolver 1983).

Figure A8, Sensitivity analysis of the energy balance model, where Td is body temperature excess (labelled as Tex in the nomenclature), Tex = Tbody-Ta. This graph relates how each parameter may affect the butterflyâ&#x20AC;&#x2122;s body temperature, (Kingsolver 1983).

Figure A9, Table of results for experiments carried out at high elevations, (Kingsolver & Watt, 1984).

6.2 Nomenclature Symbol

Quantity

Units

A Ar

Effective area of butterfly model Archimedes number: Ar = Gr/Re2 Convective heat transfer surface area Direct solar radiative heat transfer surface area Reflected solar radiative heat transfer surface area Total solar radiative heat transfer surface area Thermal radiative heat transfer surface area Cross-sectional area of wire Specific heat of butterfly model Characteristic dimension of the butterfly model (maximum width of mesothorax including the fur): 1/2 Deff = (4V/πL) Vapour pressure Gravitational constant Grashof number = (gβ(Tbody-Ta)D3eff/ν2) Boundary layer conductance Conductive heat transfer coefficient Convective heat transfer coefficient Fur layer conductance Radiative heat transfer coefficient Total heat transfer coefficient Direct solar radiative horizontal flux densities Diffuse solar radiative horizontal flux densities Total solar radiative horizontal flux densities Solar Irradiance: amount of solar power received over a certain area Thermal conductivity of air Thermal conductivity of fur Thermal conductivity of wire Length of butterfly model Length of wire Mass of model Nusselt number: Nu = hfDeff/k Wing loading: the weight of the butterfly divided by its wing area Heat transfer rate by forced convection Rate of internal heat input Convective heat flux Total Solar radiative heat flux Diffuse solar radiative heat flux Direct solar radiative heat flux Reflected solar radiative heat flux Thermal radiative heat flux Ground solar reflectivity Body radius

cm2 ---

Ac As,dir As.ref As.ttl At Aw cp Deff e g Gr hb hc hf hfur hr ht Hs.dir Hs.dif Hs.ttl I k ke kW L Lw m Nu pw conv in

Qc Qs Qs.dif Qs.dir Qs.ref Qt rg ri 34

cm2 cm2 cm2 cm2 cm2 cm2 J g-1 K-1 cm Pascals cm s-2 --mW cm-2 K-1 mW cm-2 K-1 mW cm-2 K-1 mW cm-2 K-1 mW cm-2 K-1 mW cm-2 K-1 mW/cm2 mW/cm2 mW/cm2 W m-2 mW cm-1 K-1 mW cm-1 K-1 mW cm-1 K-1 cm cm gm --N m-2 mW mW mW mW mW mW mW mW --cm

R Re t T Ta Tab Tba Tbody Tbody*C Tbody*R Tex To Tsky Tt Tth Tw T∞ U V y z α β

ε εT σ τ ν Ψ

Wing length Reynolds number:

Re = UDeff/ν Time Absolute temperature Ambient temperature Abdominal temperature Basking temperature = steady state thoracic temperature of butterfly in basking posture with the wings held at a perpendicular angle to the sun’s beams. Body temperature Transient body temperature (convective heat correction factor) Transient body temperature (radiation heat correction factor) Temperature excess, which equates to the body temperature minus the ambient temperature: Tex = (Tbody - Ta) Initial body temperature Black body sky temperature Body temperature at time t Thoracic temperature Wire temperature Final body temperature Wind velocity Volume of body Yaw angle Zenith angle Solar absorptivity of wing Thermal expansion coefficient Thoracic fur thickness Thermal emissivity of model (=1) Total emissivity Stefan-Boltzmann constant Transient time constant Kinematic viscosity of air Orientation angle

mm --s K K K K K K K K K K K K K K cm s-1 cm3 Degrees Degrees --K-1 cm ----mW cm-2 K-1 s cm2 s-1 o

7 References Anonymous 1, ‘Painted Lady Butterfly’, 2010 Anonymous 2, ‘High Mag Butterfly Focus Stack Tutorial’ http://www.fredmiranda.com/forum/topic/936420/0#8841929, 2010 Anonymous 3, ‘no title’, n.d Berthier S, ‘Thermoregulation and spectral selectivity of the tropical butterfly Prepona meander: a remarkable example of temperature auto-regulation’, 2005 Clark A J, Cena K, Mills. J. N, ‘Radiative Temperatures of Butterfly Wings’, 1973 Dudley R,’ Thermoregulation in unpalatable Danaine Butterflies’, 1991 Heinrich B, ‘Thermoregulation and Flight Activity Satyrine’, 1986 Hicker R, ‘Pink Cattlefish Butterfly’, http://www.hickerphoto.com/pink-cattleheart-butterfly-10295pictures.htm, n.d Horton. J, "Where do butterflies get their striking colors?” http://animals.howstuffworks.com/insects/butterfly-colors.htm, 2008 Kingsolver J, ‘Thermoregulation and Flight in Colias Butterflies: Elevational Patterns and Mechanistic Limitations’, 1983 Kingsolver J,’ Predation, Thermoregulation, and Wing Colour in Pierid Butterflies’, 1987 Kingsolver J, ‘Thermoregulation, Flight, and the Evolution of Wing Pattern in Pierid Butterflies: The Topography of Adaptive Landscapes’, 1988 Kingsolver J and Moffat R, ‘Thermoregulation and the Determinants of Heat Transfer in Colias Butterflies’, 1982 Kingsolver J and Watt W, ‘Mechanistic Constraints and Optimality Models: Thermoregulatory Strategies in Colias Butterflies’, 1984 Kunkel D, Butterfly Proboscis, http://www.astrographics.com/GalleryPrintsIndex/GP2007.html, n.d Miakar P, ‘Boquet’, http://pixdaus.com/single.php?id=268335&f=rs, n.d Mun B, ‘Butterfly of the Month’ http://www.butterflycircle.com/?m=201001&paged=2, 2010 Polcyn D & Chappell M, ‘Analysis of Heat Transfer in Vanessa Butterflies: Effects of Wing Position and Orientation to Wind and Light’, 1986 Rawlins J, ‘Thermoregulation by the Black Swallowtail Butterfly, PapilioPolyxenes’, 1980 Shelly T & Ludwig D, ‘Thermoregulatory Behaviour of the Butterfly Calisto nubile in a Puerto Rican Forest’, 1985 Smetacek P, ‘The Study of Butterflies’, Resonance-The study of Indian Butterflies, No.6,p.8-14, 2000. Sutton O G, ‘Biographical Memoirs of Fellows of the Royal Society’, Vol. 11, pages 41-52, November 1965

Thinkquest, http://library.thinkquest.org/C002251/cgibin/default.cgi?language=english&chapter=3&section=2&mode=chapter&outputmode=0&navmenu =0&javascript=0 , n.d Toogood P, ‘Mission Beach High Resolution Image Gallery’, http://www.missionbeach.me/cairnsbirdwing.jpg, n.d White F, ‘Heat Transfer’, n.d Wong A, ‘Great Mormon’, http://butterflycircle.blogspot.com/2009/08/life-history-of-greatmormon.html, n.d Wong A, ‘Butterfly of the Month’ http://www.butterflycircle.com/?m=201001&paged=2, 2010

8 Gantt Chart

Thermoregulation By Butterfly Wings Project Author Milad Arkian

Research and acquire relevant thesis information Matlab programming practise Background reading on butterfly biology

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Initial Report work Begin write up and organisation of the initial report, including abstract and introduction Select research papers that will provide the main backbone of the project Build up data bank of useful information Research key features of the butterflies anatomy that relates to its thermoregulation Derive the general heat balance equations Sum up the report with a conclusion Check report, organise and label figures, tables, glossary and nomenclature

Poster work Research graphics tools and software that may be required for the poser Research colour designs and effective use of space on the poster organise material that will be used on the poster from the report Design final poster

Final Report work Research the gaps in knowledge from the initial report carry out training of simulation software for the modelling of the heat equations Obtain a better understanding of the butterfly wing structure Refine asbtract, introduction and the literary survey Develop links between biology of the butterfly and possible engineering applications Refine reference list, nomenclature Prepare final report structure Finish final report

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Start Date: 17/06/2010