Temperature Control Mechanism by Butterfly Wings

1

Temperature Control

Mechanism by

3rd

Year Mechanical Engineering

Author:

Project Supervisor: Professor Hector Iacovides

Temperature Control

echanism by Butterfly

Wings

Year Mechanical Engineering - Final

Author: Milad Arkian

upervisor: Professor Hector Iacovides

Temperature Control

utterfly

Final Report

upervisor: Professor Hector Iacovides

2

Acknowledgements

My sincerest and deepest gratitude is due to my personal tutor Professor H.

Iacovides, without whom this report would have lost its heart and its eyes. His

guidance and direction has been essential and have increased my desire and

passion for the world of science.

“Αιέν αριστεύειν”

“Forever improving”

3

Contents

Abstract………………………………………………………………………………………………. 6

Glossary………………………………………………………………………………………………. 7

1 Introduction………………………………………………………………………………………… 10

2 Butterfly Anatomy………………………………………………………………………………. 11

2.1 General body……..……………………………………………………………………….......... 11

2.2 Wings……………………………………………………………………………………………….... 13

2.3 Head & Thorax……………………………………………………………………………..…….. 13

2.4 Proboscis…………………………………………………………………………………………….. 14

3 Literature Survey…………………………………………………………………………………. 15

3.1 Butterfly Heat Transfer Models ………………………………………………………….. 15

3.2 Behavioural Habits & Body Traits in Effecting Thermoregulation ……….. 22

3.2.1 Posture………………………………………………………………………………………………… 22

3.2.2 Shivering…………………………………………….……………………………………………….. 24

3.2.3 Wing Level..………………………………………………………………………………………… 25

3.2.4 Abdominal Pumping……………………………………………………………………………. 26

3.2.5 Tilting…………………………………………………………………………………………………. 27

3.2.6 Fur Thickness………………………………………………………………………………………. 27

3.2.7 Aposematic Colours……………………………………………………………………….…... 28

3.2.8 Wind Shielding………………………………………….………………………………………... 29

3.3 Conclusions of the Literature Survey………………………………..…………………. 30

4 Heat Balance……………………………………………………………………………………….. 31

4.1 General Analysis and Key Assumptions……………………………..………………… 31

4.2 Wing Angle: 90o……………………………..……………..……………………………..…….. 34

4.3 Wing Angle: 45o……………………………..……………..……………………………..…….. 39

4.4 Wing Angles: 46-89o……………………………..……………..…………………………….. 40

4.5 Wing Angles: 10-44o……………………………..……………..…………………………….. 41

4.6 Results & Conclusions……………………………..……………………………..…………… 42

4.7 Summary of Conclusions……………………………………………………………………… 43

5 Future Work………………………………………………………………………………………… 44

5.1 Solidworks Simulations……………………………..……………..…………………………. 45

6 Appendix………………………………………………………………………………….………….. 47

4

6.1 Databank…………………………………………………………………………………………….. 47

6.2 Nomenclature……………………………………………………………………………………… 50

7 References…………………………………………………………………………………………… 52

8 Gantt Chart………………………………………………………………………………………….. 54

List of Figures

Figure

No

Caption Page

No

1 An annotated diagram of the general body parts of the butterfly species…….. 11

2 Annotated butterfly showing difference between fore-wing and hind-

wing………………………………………………………………………………………………………………... 12

3 Difference between the ventral and dorsal side of the wings ……………………….. 12

4 Flight stroke positions…….…………………….…………………….…………………………………. 12

5 Wing scale structure…………………….…………………….…………………….……………………. 12

6 Annotated picture showing the upper body parts of the butterfly…………………. 13

7 Uncurled proboscis…………………….…………………….…………………….……………………… 14

8 Proboscis…………………….…………………….…………………….…………………………………….. 14

9 Representation of the yaw angle superimposed over the butterfly body………. 16

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…………………………………………………………………….

18

11 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) …………………….…………………….…………………….……………………..…….

19

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).………………………………

22

13 Basking postures: pictorial illustrations of the lateral, dorsal and reflectance

basking postures used by butterflies to regulate their

temperature.…………………….…………………….…………………….………………………………..

23

14 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.

…………………….………………………………………………………………………………………………...

23

15 Melanisation in Pierid butterfly wings. Where + indicates an increase in

temperature when melanisation occurs. O corresponds to no effect and – as a

5

decrease in temperature. …………………….…………………….………………………………. 24

16 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. …………………….…………………….…………………………………………………..

25

17 A graph comparing the various postures taken up by the Swallowtail butterfly

for given ambient temperatures and levels of solar radiation………………………..

26

18 Close-up of butterfly fur…………………….…………………….…………………….………........ 27

19 & 20 Aposematic colours of the unpalatable Birdwing butterfly.……………………………. 28

21 Aposematic colours of the white Pierid butterflies…………………….………………….. 28

22 Wind shielding of the thorax by the abdomen…………………….…………………………. 29

23 Proportion of solar radiation striking the butterfly body………………………………… 32

24 Butterfly body, wings and interaction with incoming solar radiation……………… 33

25 Forced convection along the butterfly body……………………………………………………. 34

26 View factor to the surroundings ~ 0.5…………………………………………………………….. 38

27 Proportion of body acquiring incident radiation……………………………………………… 39

28 View factor to the surroundings for wing angles of 46-89o…………………………….. 41

29 View factor to the surroundings for wing angles of 10-44o……………………………… 41

30 Solidworks model of the butterfly (view 1)…………………………………………………….. 45

31 Solidworks model of the butterfly (view 2)…………………………………………………….. 45

32 Applying ambient heat conditions on meshed butterfly body………………………… 46

Table 1 Body Dimensions…………………………………………………………………………………………….. 31

Table 2 Equilibrium temperature and proportions of solar radiation from sun and

wings

42

Table 3 Proportions of key experiment parameters 42

A1 Body temperatures of Swallowtails in field studies (oC). Mean ± sd above,

range below.…………………….…………………….…………………….…………………….…………

47

A2 Various parameters in relation to different wing and abdominal positions

Mean ± sd. (Sample size) ………………….…………………….…………………….……………….

47

A3 Critical thoracic temperatures for various activities of black Swallowtails in

the flight cage. Mean (N = sample size) above, range below (oC)……………………

48

A4 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………………………………..

48

A5 Solar absorptivity, thoracic fur thickness and thoracic diameter of four

butterfly species in central Colorado…………………………………………………………......

48

A6 Cumulative daily flight activity time (KFAT) in hours for the three sites of

different elevational heights…………………….…………………….………………………………

49

6

A7 Sensitivity analysis of the energy balance model, where Td is body

temperature excess (labelled as Tex in the nomenclature), Tex = Tb-Ta. This

graph relates how each parameter may affect the butterfly’s body

temperature…………………….…………………….…………………….………………………………...

49

A8 Table of results for experiments carried out at high elevations………………………. 49

7

Abstract

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 for different wing postures. The Swallowtail species of butterfly was taken for the body

dimensions. Three main postures are responsible for the basking practice butterflies use to regulate

temperature behaviourally: dorsal, lateral and reflectance basking. Thermoregulation in the wings

occurs through a combined effect of colour pigmentation and skeletal structure supplemented with

behavioural heat regulation habits. Wing angles between 10-44o provided the largest equilibrium

body temperature (76.2oC) and the radiation reflected onto the body is an order of magnitude above

wing angles of 45 and above. Using a higher wing angle has an advantage of reducing the heat loss

via radiation and convection and may be adopted at low wind speeds where the butterfly is at a

favourable body temperature. The equilibrium body temperature is approximately constant for wing

angles above 45o which indicates that the reduction in convective and radiative heat loss is balanced

by a lower intensity of heat uptake. Radiation in-take is highly dependent on wing melanisation and

heat loss can be reduced by behavioural postures such as tilting the body away from the solar rays

or having thick fur to prevent convective heat loss.

8

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.

9

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

).

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.

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.

10

1 Introduction

The study of biomimicry has exposed many solutions to human related problems. For example,

spider’s silk is known to have five times the tensile strength of steel for a given diameter (Heimbuch,

2010). Furthermore the sonar system that bats use to navigate blindly around caves is now being

mimicked for submarine/air craft 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 their heat regulation behaviour.

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. An attempt to

accurately represent the physical heat transfer mechanism between the butterfly and its

surroundings will be made. This will include analysing the proportions of incoming solar radiation to

out-going heat loss via convection and radiation and obtaining the equilibrium body temperature for

the butterfly. The main parameter used to quantify thermoregulation is wing angle and four bands

of wing angles (10-44o, 45

o, 46-89

o and 90

o) will be used to better understand how the butterfly uses

solar radiation to increase its body temperature.

In providing a heat balance for the butterfly, crucial body dimensions will be taken from the

literature survey and any assumptions made will be backed by either previous scientific researchers

or used with supporting reasoning. The databank in the appendix will provide a useful source of

experimental values for the key parameters in the heat balance equations. The final section of the

research consists of a complimentary conclusion section that will attempt to explain the significance

of the results and provide insight into the benefits of thermoregulation for the butterflies.

The industrial relevance of this project lies with better understanding how a natural phenomenon

such as butterfly thermoregulation may benefit current research on solar panel efficiency. Other

potential engineering benefits include using the wing structure to model Nano-scale computer chips

to better dissipate heat. Although not considered in this study, the way in which light interacts with

the wings is becoming increasingly important and may benefit areas of optical research.

11

2 Butterfly Anatomy

Prior to proceeding with the inve

butterfly species that may relate

Figure 1, An annotated diagram

2.1 General body

The butterfly anatomy can be broadly la

abdomen (figure 1). 6 legs and 4 wings are attached to th

shape) being the mode of identifying and naming

instead of having a method of internal heat production

generate the temperatures required

skeleton is hard case on the ou

(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

In vertebrate species the blood circulatory system is closed. The blood flow provides two functions:

gas exchange and nutrient/waste exchange.

to exchange material with the blood stream

exchange are exclusive. Gas is exchanged with the surroundings via the trachea

opening directly into the air. The process of gas exchange is by simple diffusion

branches.

Butterflies and other invertebrates

hemolymph that carries nutrients and waste. Due to the open circulation system in butterflies the

Prior to proceeding with the investigation it is useful to understand some of the organs of the

relate to its method of temperature regulation.

annotated diagram of the general body parts of the butterfly species

The butterfly anatomy can be broadly labelled into three main sections: the

. 6 legs and 4 wings are attached to the thorax, with the wing appearance

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

skeleton is hard case on the outside and on the inside there is only blood nerves and organs

. 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).


gas exchange and nutrient/waste exchange. The heart pumps blood to the tissues

with the blood stream. In invertebrates or insects the gas and nutrient/waste

Gas is exchanged with the surroundings via the trachea

The process of gas exchange is by simple diffusion

and other invertebrates have a different liquid for circulatory purposes, called


some of the organs of the

of the general body parts of the butterfly species, (Wilson, 2010)

the head, thorax and

e thorax, with the wing appearance (colour,

Butterflies are cold blooded and

rely on external heat sources to

for flight and other energy intensive activities. A butterfly’s

tside and on the inside there is only blood nerves and organs

. Butterflies have an open blood circulation i.e. they have no veins and the whole of


The heart pumps blood to the tissues allowing the cells

invertebrates or insects the gas and nutrient/waste

Gas is exchanged with the surroundings via the trachea or ‘windpipe’

through the trachea

for circulatory purposes, called


12

hemolymph isn’t constrained to arteries and veins. A dorsal t

pumps hemolymph over all its organs, circulating freely throughout the abdomen. The hemolymph is

collected back into the heart via simple diffusion.

Figure 2, Annotated butterfly showing difference

Figure 3, Difference between the ventral and dorsal side of the wings (Anonymous 1, 2010)

Figure 4, Flight stroke positions

Hind-wings

Completed

stroke

Ventral,

underside of

the wings

hemolymph isn’t constrained to arteries and veins. A dorsal tube (rudimentary butterfly heart)

its organs, circulating freely throughout the abdomen. The hemolymph is

collected back into the heart via simple diffusion.

showing difference between fore-wing and hind

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

(Smetacek, 2000) Figure 5, Wing scale structure

Mid-stroke

Flight stroke

begins, wings

held together

ube (rudimentary butterfly heart)

its organs, circulating freely throughout the abdomen. The hemolymph is

wing and hind-wing (Wong, n.d)

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

Wing scale structure (Horton, 2010)

Fore-wings

Dorsal, top

side of the

wings

13

2.2 Wings

Butterflies have 4 wings (2 fore

wings and the hind-wings the small

symmetrical. Butterfly wing colour is based on the reflective tendency of each wing scale

wavelength of light that is not absorbed by the wings is reflected and this gives the iridescently

powerful vibrancy of the wings.

a hydrophobic wax layer to protect the

Butterfly flight occurs (figure 4)

swing through an arch of almost 180

The structure of the butterfly wing consists of thousands of microscopic scales split into two to three

layers (Horton, 2010). Each of these scales

(Horton, 2010). These multiple scale layers provide n

In constructive interference two waves meet with the resulting wave being

amplitudes. Consequently, when light beams interact and reflect off these layers, the intense

butterfly wing colours are produced

structure is demonstrated in figure 5

Figure 6, Annotated picture showing the upper body parts of the

2.3 Head & Thorax

The thorax is the middle of the three main parts of a butterfly’s body

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

that of the acceptable flight range the butterfly would suffer fro

could affect territorial defence behavi

Head

Proboscis

(2 fore-wings and 2 hind-wings), with the fore-wings being the

wings the smaller, lower set (figure 2). The fore-wings and

ing colour is based on the reflective tendency of each wing scale


The entire body of the butterfly (including the wings) is

x layer to protect the species from water related damage.

) by the beating of the wings from 5-10o (above their

swing through an arch of almost 180o at which the stroke is completed.


. Each of these scales is further split into multiple layers separated by air

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

, when light beams interact and reflect off these layers, the intense

colours are produced (Horton, 2010). A simplified overview of the butterfly w

figure 5.

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

horax is the middle of the three main parts of a butterfly’s body, between the head and

. The thorax houses all the legs and wings of the butterfly therefore it is the crucial organ of

body when it comes to thermoregulation. Should the thorax be at a temperature below

that of the acceptable flight range the butterfly would suffer from reduced flight capabilities

could affect territorial defence behaviour, mating and escape from a predator.

being the top, larger

s and hind-wings are

ing colour is based on the reflective tendency of each wing scale and the


(including the wings) is covered with

damage. (Thinkquest, n.d).

above their thorax) and


layers separated by air

umerous instances of constructive interference.

sum of the preceding

, when light beams interact and reflect off these layers, the intense

overview of the butterfly wing

(Anonymous 3, n.d).

, between the head and the

. The thorax houses all the legs and wings of the butterfly therefore it is the crucial organ of

body when it comes to thermoregulation. Should the thorax be at a temperature below or above

m reduced flight capabilities. This

Thorax

Compound

eyes

14

Figure 7, uncurled proboscis, (Knew, 2008)

2.4 Proboscis

The butterfly proboscis (figures

feed (predominately nectar) but also sweet

food there is a reaction that causes the proboscis to uncurl and extend to

This high surface area curl allows t

use. The proboscis is shaped like a straw when uncurled and provides the vehicle through which the

butterflies suck up nectar or other viable food products such as water or tree sap.

Uncurled proboscis

Figure 7, uncurled proboscis, (Knew, 2008) Figure 8, Proboscis, (Valentino, 2006)

s 7 & 8) or ‘tongue’ provides the vehicle through

feed (predominately nectar) but also sweet fruit occasionally. After a butterfly lands on a

food there is a reaction that causes the proboscis to uncurl and extend to the source of the food.

allows the butterfly to keep its long proboscis compact until required for

. The proboscis is shaped like a straw when uncurled and provides the vehicle through which the


, Proboscis, (Valentino, 2006)

s the vehicle through which butterflies

fruit occasionally. After a butterfly lands on a source of

the source of the food.

compact until required for

. The proboscis is shaped like a straw when uncurled and provides the vehicle through which the


Proboscis

15

3 Literature Survey

The aim of the literature survey is to compile scientific research previously written on similar aspects

of this study. As the heat balance is at the heart of this study the first section (3.1) of the literature

search will rely on obtaining derivations of the heat balance with accompanying source details. The

heat balances required are the steady state and transient derivations including specifics of

convection and radiation heat loss. Section 3.2 will solely focus on behavioural habits or body traits

that effect thermoregulation of the butterfly such as tilting, fur thickness or wind shielding.

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 (Tb - 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.

3.1 Butterfly Heat Transfer Models

Research paper reference: (Kingsolver, 1982)

The purpose of the literature search is to identify research produced by scientists that conform to

similar outcomes required in this report. Additional information in each journal provides a useful

databank from which pools of data may be pulled for the heat balance.

One particular paper (Kingsolver, 1982) provided a strong background model for the heat balance.

Kingsolver provides a derivation of the heat balance equation (steady and transient) whilst providing

additional commentary on the effects of yaw angle and other thermoregulatory parameters in

regards to the heat balance. The foremost purpose of Kingsolver’s (1982) 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.

16

Figure 9, Representation of the y

The yaw angle (figure 9) is the angle

travel, as seen from above the butterfly

The mathematical derivation (Kingsolver 1982)

Reynolds Re number was defined as

Where

V, the volume and L, the longitudinal

Deff is the characteristic dimension of the butterfly model

mesothorax including the fur).

segment. To study the forced convective heat transfe

Kingsolver used a combination of steady state and transient

coefficients. For the transient model, the butterfly model is heated and time constant τ estimated

from the resulting cooling curve:

The total heat transfer coefficient

Representation of the yaw angle superimposed over the butterfly body

is the angle between a butterfly’s longitudinal body axis and its line of

above the butterfly.

(Kingsolver 1982) is described below:

was defined as

��

�� 4��

��

longitudinal length of the butterfly model were measured experimentally.

is the characteristic dimension of the butterfly model (taken to be the maximum width of the

The thorax has three sections, the mesothorax bein

convective heat transfer the author defines its equation as:

��

Kingsolver used a combination of steady state and transient methods for estimation

For the transient model, the butterfly model is heated and time constant τ estimated

from the resulting cooling curve:

ln �# � �$�� $� � �%&

The total heat transfer coefficient hT is then calculated from:

�' � ()*&�

b c

a

superimposed over the butterfly body (Hicker, n.d)

between a butterfly’s longitudinal body axis and its line of

(5-1)

(5-2)

were measured experimentally.

maximum width of the

The thorax has three sections, the mesothorax being the middle

its equation as:

(5-3)

methods for estimation of heat transfer

For the transient model, the butterfly model is heated and time constant τ estimated

(5-4)

(5-5)

y – Yaw angle:

rotation about

the vertical a

axis

17

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:

�� ' � �+ � �� (5-6)

The radiation correction factor hR may be estimated by:

�+ � ,-.��/+0 � ��01��/+ � �� (5-7)

The correction factor for conductive heat transfer of thermocouple wires and support structures:

�� 23�4.��/5 � �41 4�.��/5��1 (5-8)

For the transient derivation, the criterion used for experimental conditions (where free convection is

negligible) is stated below:

�6 � 76�� 8 0.1 (5-9)

Gr is the Grashof number = (gβ(Tb-Ta)D3eff/ν

2), 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 total heat transfer is estimated to

be:

��<� � �� = ,-��0 � ��0 = 23�4�� 4 4 (5-10)

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 experimental 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.

18

Figure 10: Nusselt number Nu

species of

Figure 10 shows that the Nusselt

Reynolds number (common Reynolds numbers experienced by the butterflies in external fields

25-1200). For a given yaw angle, as the Reynolds number increases so does the Nusselt number

angle y at 45o

gave the largest increase

such as 30o to 60

o fitting in in-between.

show that fur has a distinctive effect

against convective heat loss.

In one experiment on regional height experiments, Kingsolver (1988) chose t

USA are used to compare the relative differences that an elevational

flight activity. They are Montrose (height h=1.5km), Skyland h=2.8km and Mesa Seco h=3.3

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 11

Nu as a function of Reynolds number Re and yaw angle

species of Colias Butterfly (Kingsolver 1982).

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

For a given yaw angle, as the Reynolds number increases so does the Nusselt number

gave the largest increase of Nu with 90o giving the lowest and intermediate angles

between. Further work by the author based on fur and non

effect on the heat transfer process, especially as an insulation barrier

In one experiment on regional height experiments, Kingsolver (1988) chose 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


collected is shown in figure 11 below.

and yaw angle y for one

number is essentially independent of the yaw angle for a given

Reynolds number (common Reynolds numbers experienced by the butterflies in external fields are

For a given yaw angle, as the Reynolds number increases so does the Nusselt number. Yaw

giving the lowest and intermediate angles

based on fur and non-fur models

transfer process, especially as an insulation barrier

hree sites in Colorado,

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.


19

Figure 11, 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 (

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

indications that for a given % solar absorptivity and fur thickness there is a much longer flight time

for the butterflies habituating at lower altitudes.

Conclusions

• This thesis provided a strong background on the steady sta

models taking into any considerations that could have affected the results.

• Fur helps in insulating the butterfly’s body from convective heat loss.

• The Nusselt number is independent of the yaw angle towards the wind direction.

• For a given solar absorptivity and fur thickness, butterflies exhibit longer flying time at lower

altitudes.

Research paper reference: (Kingsolver, 1983):

A second noticeable report (Kingsolver, 1983)

for butterflies. This is split into three separate regions of low, mid and high elevational regions

measured from the ground. The

at h=2.8km and Mesa Seco at

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 c

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 (

height=1.5km) and Skyland (elevational height= 2.8km) (Kingsolver 1988).


1.5mm, which are the possible useful ranges of fur thickness for thermal regulation. There are clear


for the butterflies habituating at lower altitudes.

thesis provided a strong background on the steady state and transient heat balance


Fur helps in insulating the butterfly’s body from convective heat loss.

The Nusselt number is independent of the yaw angle towards the wind direction.

For a given solar absorptivity and fur thickness, butterflies exhibit longer flying time at lower

(Kingsolver, 1983):

(Kingsolver, 1983) deals with elevational effects on flight activity times


These regions are represented by Montrose at height h=1.5km

at h=3.3-3.6km. The author touches on the diverse meteorological


the conditions include wind velocity, butterfly wing absorptivity, fur thickness and cloud c

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


regulation. There are clear


te and transient heat balance


The Nusselt number is independent of the yaw angle towards the wind direction.

For a given solar absorptivity and fur thickness, butterflies exhibit longer flying time at lower

effects on flight activity times


height h=1.5km, Skyland

. The author touches on the diverse meteorological


the conditions include wind velocity, butterfly wing absorptivity, fur thickness and cloud coverage.

20

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:

>? � ># = >� (5-11)

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:

>? � >?.�<@ = >?.�<� = >?.@�� (5-12)

>? � A�?.�<@B?.�<@cos .G1 = A�?.@��B?.@�� = A6H�?.@��B?.##I (5-13)

Qs.dir, Qs.dif and Qs.ref are the direct, diffuse and reflected solar radiative heat fluxes respectively

(equation 2.3). The direct heat flux is the solar radiation, emitted onto the butterfly’s body and

similarly the diffuse heat transfer is the proportion of heat transferred onto the body under cloudy

conditions. The reflected heat flux is the solar radiation reflected off the wings and onto the body

with the units being [W/m2s] for each three. Hs.dir, Hs.dif and Hs.ttl are the direct, diffuse and total solar

radiative horizontal flux densities or irradiance [W/m2]. As.dir, As.ref and As.ttl are the corresponding

direct, reflected and total heat transfer surface areas. α is the solar absorptivity, rg is the substrate

(ground/vegetation) solar reflectivity and z is the zenith angle (defined under glossary).

For basking Colias butterflies orientated perpendicularly to the solar beams Kingsolver has assumed

that As.dir = As.ref = 0.5As.ttl. This assumption is made because at any one time the proportion of solar

radiation reaching the butterfly body is 0.5 as the other half of the butterfly body will be shaded.

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:

># � 0.5�#,-��0 � �?K�0 = 0.5�#,-��0 � �H0 (5-14)

At is the thermal radiative heat transfer surface area, Tg is ground surface temperature and Tsky is the

equivalent black body sky temperature. Thermal emissivity , is proposed to be 1 (in the thermal

infra-red spectrum at about 5 µm. 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):

21

�?K� � .( = L√�1-�0 (5.15)

Where m and n are constants, e is vapour pressure in the lower levels of the atmosphere, - is the

Stefan’s constant and T is the absolute temperature. The convective heat flux is given by:

>� � �#��.�� 1 (5-16)

For high wind speed and low intensity radiation conditions there is negligible free convection

therefore from one of his previous thesis’, Kingsolver uses the relationship between the Reynolds

and Nusselt numbers for a bare cylinder (similar to butterfly models without fur) in eqn (5-17):

NO � 0.6��/� (5-17)

Conclusions

• Body emissivity of the butterfly is approximately 1.

• Free convection is negligible at high wind speeds and low solar intensity.

22

3.2 Behavioural Habits & Body Traits in Effecting

3.2.1 Posture

Research paper reference: (Kingsolver,

This section of the literature search deals with

increase or to reduce body temperature

Figure 12, Butterfly body (depicted by the cylinder) and

(normal to the thorax) and wing angle

Kingsolver (1988) outlines t

thermoregulation; they are lateral, dorsal and reflectance

wings are closed over the body

posture is mainly used to avoid temperature increases in the body. In dorsal

opens its wings normal to the solar rays

Finally, in reflectance basking the butterfly will open its wings

the reflective region of its wings onto the thorax and abdomen

Habits & Body Traits in Effecting Thermoregulation

(Kingsolver, 1988)

section of the literature search deals with the behavioural basking used by b

temperature depending on their required choice.

, Butterfly body (depicted by the cylinder) and corresponding orientation angle

(normal to the thorax) and wing angle θ (Kingsolver, 1988).

three main postures as the typical butterfly

they are lateral, dorsal and reflectance (figure 13). Lateral basking

body and orientated perpendicularly towards the sun’s solar beam.

posture is mainly used to avoid temperature increases in the body. In dorsal basking the butterfly

opens its wings normal to the solar rays (θ=90o) thereby directly heating the thorax and abdomen.

Finally, in reflectance basking the butterfly will open its wings at an angle, reflect

region of its wings onto the thorax and abdomen (figure 15).

Ψ

Ψ

Thermoregulation

by butterflies, to either

orientation angle Ψ

.

hree main postures as the typical butterfly postures for

ateral basking is when the

the sun’s solar beam. This

basking the butterfly

directly heating the thorax and abdomen.

reflecting solar rays off

23

Figure 13, Basking postures: lateral, dorsal and reflectance basking

The basal regions of the butterfly wing due to their melanisation

the larval stage) are responsible

Melanisation is the process by which butterflies have

to a local concentration of substance known as melanin.

that butterflies living in cooler habitats tend to

regulation conditions as opposed to butterflies

Furthermore Kingsolver

quantify the link between butterfly thermoregulation characteris

size (thoracic diameter), thermoregulatory posture (

Figure 14, Reflectance basking:

conduction. The hatched distal

radiation from the wings onto the thorax or abdomen

, Basking postures: lateral, dorsal and reflectance basking (Kingsolver, 1988)

terfly wing due to their melanisation (influenced by

are responsible for the majority of the conductive heat absorption

is the process by which butterflies have darker pigments on their wings and bodies

to a local concentration of substance known as melanin. For this reason the Kingsolver (1988)

that butterflies living in cooler habitats tend to be darker in colour, aiding

as opposed to butterflies living in more favourable mild climates.

Furthermore Kingsolver (1988) argues that there are primarily four parameters that help to

quantify the link between butterfly thermoregulation characteristics and flight activity time: b

size (thoracic diameter), thermoregulatory posture (figure 13), solar absorptivity

, Reflectance basking: The black basal absorption areas are responsible for heat

region has little or no effect. The white medial

radiation from the wings onto the thorax or abdomen (Kingsolver 1988).

(Kingsolver, 1988).

(influenced by photoperiod during

heat absorption by the wings.

darker pigments on their wings and bodies due

or this reason the Kingsolver (1988) asserts

be darker in colour, aiding the harsher heat

climates.

argues that there are primarily four parameters that help to

tics and flight activity time: body

), solar absorptivity and fur thickness.

absorption areas are responsible for heat

regions reflect solar

24

The author asserts that there is a link between

temperature based on figure 14

larger the wing angle required to maximise body temperature.

butterfly species and each species have their own proportions of basal, medial and distal wing

regions.

Figure 15, Melanisation in Pierid

where melanisation occurs. O corresponds to no effect and

wing is the dorsal side, right wing is ventral

As shown in figure 15 the author uses a functional map to show the effects of melanisation in

butterflies. There is a striking difference between the dorsal and ventral areas of the wing.

of the wing with the greater melanisation will have darker patt

coefficients). The only region of the wings where this may aid heat gain is in the near wing basal

region where small amounts of heat are conducted to the butterfly’s body.

regions are lighter in colour (coefficient of reflection

butterfly in reflecting solar radiation onto the body.

3.2.2 Shivering

Research paper reference: (Rawlins 1980)

Shivering occurs when the muscles contract

very expensive process in terms of energy

i.e. avoiding predators by sufficiently raising

considers minimum and maximum temperature ranges that the butterflies c

procuring fatal injuries (Rawlins, 1980)

Rawlins also asserts that shivering may be used by the butterflies to improve basking sites under low

solar radiation, selecting suitable

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 b

The author asserts that there is a link between wing melanisation (defined above)

temperature based on figure 14. He states that the greater the melanisation % on the wings the

to maximise body temperature. Figure 14 only applies to one set of


Pierid butterfly wings. Where + indicates an increase in temperature

melanisation occurs. O corresponds to no effect and – as a decrease in temperature.

wing is the dorsal side, right wing is ventral (Kingsolver 1988).

the author uses a functional map to show the effects of melanisation in

butterflies. There is a striking difference between the dorsal and ventral areas of the wing.

of the wing with the greater melanisation will have darker patterns (i.e. larger absorptivity

The only region of the wings where this may aid heat gain is in the near wing basal

region where small amounts of heat are conducted to the butterfly’s body. The

(coefficient of reflection ρ is higher) and this is more beneficial for the

butterfly in reflecting solar radiation onto the body.


when the muscles contract allowing for a quick increase in body temperature

in terms of energy dissipation, it is only used in situations of absolute need,

avoiding predators by sufficiently raising their body temperature for required

inimum and maximum temperature ranges that the butterflies can withstand without

(Rawlins, 1980).

asserts that shivering may be used by the butterflies to improve basking sites under low

suitable roosting sites in the evening and to regain a roosting spot after


butterfly from a predator) when ambient temperatures are below those required for flight.

(defined above) and body

melanisation % on the wings the

only applies to one set of


an increase in temperature

as a decrease in temperature. Left

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 sides

erns (i.e. larger absorptivity

The only region of the wings where this may aid heat gain is in the near wing basal

The medial and distal

is higher) and this is more beneficial for the

allowing for a quick increase in body temperature. A

used in situations of absolute need,

required flight. Rawlins also

an withstand without

asserts that shivering may be used by the butterflies to improve basking sites under low

to regain a roosting spot after


low those required for flight.

25

3.2.3 Wing Level


Figure 16, Relationship betwe

swallowtails. Solid line indicate

temperature (i.e. Tb=Ta). Dotted line

temperatures and white ambient temperatures)

Based on figure 16, for a given ambient temperature

higher than the ambient temperature.

that for low ambient temperature conditions the

above the wings, exposing it to

Conversely for hotter weather conditions

just below thereby shading them


, Relationship between body and ambient temperature of perched male black

indicates a region where the body temperature is equal

. Dotted line represents the general pattern of spots (black being thoracic

temperatures and white ambient temperatures) (Rawlins, 1980).

for a given ambient temperature, thoracic and abdominal temperatures are

than the ambient temperature. In terms of thermoregulatory practise Rawlins (1980)

that for low ambient temperature conditions the butterflies would usually rais

to direct solar radiation and raising the abdominal temperature

onversely for hotter weather conditions, butterflies often level their abdomen

just below thereby shading them from direct sunlight.

of perched male black

equal to the ambient

spots (black being thoracic

thoracic and abdominal temperatures are

ulatory practise Rawlins (1980) states

would usually raise their abdomen

abdominal temperature Tab.

abdomens to wing height or

26

3.2.4 Abdominal pumping

Figure 17: A graph comparing the various postures taken up by the

ambient temperatures and levels of solar radiation


The author Rawlins (1980) in his research paper

sd (oC), the butterfly began struggling

of the abdominal muscles that results in the expansion of the air

insects are active and require

pumping there is a decrease between the thoracic a

net increase in thoracic temperat

temperature, indicating heat transfer

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

Moreover Rawlins (1980)

between the thorax and abdomen may depend

pumping. During abdomen-shade

hemolymph is maximised. In cases where

useful cooling procedure (heat transferred from thorax to abdomen)

excessive temperatures.

: A graph comparing the various postures taken up by the Swallowtail

ambient temperatures and levels of solar radiation (Rawlins 1980)


in his research paper states that at thoracic temperature

he butterfly began struggling, pumping its abdomen. Abdominal pumping is the

of the abdominal muscles that results in the expansion of the air sacs. This occurs mainly when

cooling through greater respiratory exchange.

s a decrease between the thoracic and abdominal temperatures. This is

net increase in thoracic temperature, where the abdominal temperatures are seen to

heat transfer from the butterfly’s thorax into the abdomen.


from the thorax to the abdomen reduces the likelihood of thorax

(1980) says that conditions under which heat exchange is carried out

between the thorax and abdomen may depend solely on whether the butterfly exhibits abdominal

shade posture, pumping occurs and heating exchange

ymph is maximised. In cases where the thorax is overheated and the

(heat transferred from thorax to abdomen) occurs to reduce stress from

Swallowtail butterfly for given

(Rawlins 1980).

thoracic temperatures Tth of 37.1 ± 1.5

Abdominal pumping is the contraction

sacs. This occurs mainly when

greater respiratory exchange. During abdominal

. This is due to a zero

s are seen to increase in

from the butterfly’s thorax into the abdomen. This practise is


thorax over-heating.

h heat exchange is carried out

on whether the butterfly exhibits abdominal

posture, pumping occurs and heating exchange via the

abdomen shaded, a

to reduce stress from

27

3.2.5 Tilting

Research paper reference: (Shelly and Ludwig, 1985):

A report by Shelly & Ludwig

butterflies under a forest location as opposed to the more common open land habitats from

previous reporters. Tilting behaviour was analysed and found to

the thorax and so reduce the time required for

occurs in lateral baskers (figure 13)

angle for increased rate of heat intake

basking where it is a useful way of heating the body more quickly

Figure 18,

An additional chapter of the literature

butterflies have, that aids thermoregulation

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 tha

when required.

3.2.6 Fur Thickness

Research paper reference: (Kingsolver and Watt, 1984):

The fundamental reason for this paper by Kingsolver

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 fr

height=2.8km and Mesa Seco h=3.3

understanding of the effects of pubescence (fur) on butterfly thermoregulation. According to Watt &

Kingsolver 1984, fur decreases the butterfly body’s sensitivity to temperature changes. This is

advantageous for high elevation butt

at higher wind speeds. Conversely butterflies dwelling in

allows them to fly for extended pe

(Shelly and Ludwig, 1985):

(1985) dealt with better understanding the behaviour of


Tilting behaviour was analysed and found to elevate the rate of he

the time required for thoracic temperature Tth to rise.

occurs in lateral baskers (figure 13), where the butterfly positions its body for the most effective

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.

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

of the literature survey has been assigned to general

, that aids thermoregulation. These include fur thickness, aposematic colouring of


alance that is to be carried out but provide useful background information that may be called upon

(Kingsolver and Watt, 1984):

The fundamental reason for this paper by Kingsolver & Watt (1984) lies with two important



habitats of butterflies ranging from low to mid and high elevations (Montrose h=1.5km,

height=2.8km and Mesa Seco h=3.3-3.6km. The main article of importance sprung from a better

of pubescence (fur) on butterfly thermoregulation. According to Watt &

, fur decreases the butterfly body’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

understanding the behaviour of Calisto


elevate the rate of heat intake in

to rise. Titling behaviour

, where the butterfly positions its body for the most effective

. It is especially used for short duration

general features that the

. These include fur thickness, aposematic colouring of


t may be called upon

lies with two important



Montrose h=1.5km, Skyland

The main article of importance sprung from a better

of pubescence (fur) on butterfly thermoregulation. According to Watt &

, fur decreases the butterfly body’s sensitivity to temperature changes. This is

their body temperatures

lower elevations have less fur but this

28

3.2.7 Aposematic Colours

Figures 19 & 20, Aposematic colours of the unpalatable Birdwing butterfly. Left (Wong, 2010),

Research paper reference: (Dudley 1991):

The author Dudley (1991) attempts

butterflies and the difference between the thoracic and ambient temperature labelled as thoracic

excess. Palatable butterflies according to Dudley

expensive energy consumption

rates. In contrast unpalatable Danaine

less need of avoiding predators and

speeds. This thesis didn’t bring to light

species but rather highlighted a reason for elevated or reduced body temperatures for butterflies

depending on their predatory desirability.

Figure 21, Aposematic colours of the white

Research paper reference: (Kingsolver,

In another paper on palatability, Kingsolver (1987)

butterfly wings that deter predators

, Aposematic colours of the unpalatable Birdwing butterfly. Left (Wong, 2010),

right (Mun, 2010)

(Dudley 1991):

attempts to link relations between palatability (figures 19 & 20


Palatable butterflies according to Dudley fly in arbitrary flight patterns at the cost of

expended due to the increased wing beat count and metabolism

Danaine butterflies fly more slowly and soar for longer

less need of avoiding predators and as there is a connection between predation rates and fly

bring to light direct heat transfer information for the

a reason for elevated or reduced body temperatures for butterflies

desirability.

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

Kingsolver, 1987)

In another paper on palatability, Kingsolver (1987) writes about a special white pigment on the

predators from attacking the butterflies as it’s a sign of un

, Aposematic colours of the unpalatable Birdwing butterfly. Left (Wong, 2010),

(figures 19 & 20) in


arbitrary flight patterns at the cost of

expended due to the increased wing beat count and metabolism

and soar for longer as they have

etween predation rates and flying

direct heat transfer information for the Danaine butterfly

a reason for elevated or reduced body temperatures for butterflies

, (Jack, 2010)

al white pigment on the Pierid

from attacking the butterflies as it’s a sign of un-palatability.

29

Kingsolver justifies a hypothesis that the white w

(figures 19 & 20) that may ward of predators.

from poisonous, dangerous or bas tasting animals, i.e. bright yellow colour of golden poison frog.

Furthermore from his previous studies Kingsolver

pigment-a reflective colour to aid reflectance basking in the

pigment assists predation avoidance as well as aiding thermoregulati

also argues that melanisation of the wings can increase

due to increased solar absorption

3.2.8 Wind Shielding

Figure 22, Wind shielding of the

Research paper reference: (Polcyn &

This paper throws light on thorax temperature

body at different angles. The

wind/light angles and wind velocities, citing

parameter has on the butterfly thorax.

(due to a reduction in convective cooling)

shielding of the thorax by the abdomen.

stationary against the wind direction and the abdomen acts as a buffer for the thorax from direct

convective cooling from the wind

Kingsolver justifies a hypothesis that the white wing pigment represents aposematic coloration

that may ward of predators. Aposematic colours specifically warn off predators

or bas tasting animals, i.e. bright yellow colour of golden poison frog.

from his previous studies Kingsolver relates a second useful function for the white wing

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.

nisation of the wings can increase the rate of thermoregulation during basking

tion.

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

(Polcyn & Chappell, 1986)

light on thorax temperatures when light and wind are applied

researchers Polcyn & Chappell attempt different combinations of

t angles and wind velocities, citing the different temperature variations

utterfly thorax. They also assert that closing the wings actually increases

(due to a reduction in convective cooling) by maximising the increases in temperature due to

shielding of the thorax by the abdomen. Wind shielding occurs when the butterfly flies

gainst the wind direction and the abdomen acts as a buffer for the thorax from direct

convective cooling from the wind (figure 24).

Wind

direction

The abdomen acts

as a ‘shield’ and

prevents

cooling of the thorax

from the wind

ing pigment represents aposematic coloration

Aposematic colours specifically warn off predators

or bas tasting animals, i.e. bright yellow colour of golden poison frog.

relates a second useful function for the white wing

Therefore this white

on through basking practise. He

the rate of thermoregulation during basking

thorax by the abdomen, (Toogood, n.d)

wind are applied across a butterfly’s

different combinations of

the different temperature variations that each

that closing the wings actually increases Tth

s in temperature due to wind

Wind shielding occurs when the butterfly flies/lies

gainst the wind direction and the abdomen acts as a buffer for the thorax from direct

Wind

irection

The abdomen acts

as a ‘shield’ and

prevents convective

cooling of the thorax

from the wind

30

3.3 Conclusions of the Literature Survey

∼∼∼∼ Conductive heat gain occurs strictly at the basal region of the butterfly wing. For heat

conduction to occur the butterfly exhibits the lateral basking posture and this allows the

solar radiation from the sun to directly heat the ventral basal region of the wings. The

heated basal region of the wings then proceeds to conductively transport heat into the

thorax. This 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 rate of the conduction is

however very slow as compared to the convection and radiation.

∼∼∼∼ The butterfly angles its body towards the solar rays thereby heightening its chances of heat

gain in a behavioural posture called tilting.

∼∼∼∼ Fur helps to reduce convective heat loss and is more apparent on butterflies existing in

colder climates.

∼∼∼∼ At high wind speeds and low solar radiation free convection is negligible.

∼∼∼∼ Changing the wing angles can either help to increase body temperature by reflecting solar

radiation onto the body: reflectance basking, or alternatively cool the butterfly down by

angling wings perpendicularly to the sun’s rays: lateral basking.

∼∼∼∼ 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 intake by wing reflection, especially in colder climates

where it is more present in the wings.

∼∼∼∼ 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.

31

4 Heat Balance

4.1 General Analysis and Key Assumptions

The purpose of the heat balance is to identify an equilibrium temperature that a butterfly species

may require for controlled body temperatures. In order to carry out an effective heat balance,

precise information on the butterfly’s body dimensions is required. Regular body dimensions where

taken from the Swallowtail species and are tabulated in table 1 below, where average values are

detailed in parenthesis. The butterfly body area is modelled as a cylinder for simplification.

Body part(s) Body dimensions [mm], [mm2]

Body length L (top of head to abdomen end) 25-32 (28)

Thorax width 3.5

Cylinder radius (thorax width/2) 1.75

Area of cylinder (2πr2+2πrL) 308 [mm

2]

Total wing area (both wings) 6643 [mm2]

Wing span 161.5

Wing thickness ~ thickness of paper (Kingsolver

& Koehl, 1985)

0.2-0.4 (0.3)

Table 1, Body dimensions

The thorax is the most crucial organ of the butterfly body in relation to its ability to regulate

temperature effectively. For this reason, the base of the energy balance model is set from the

thorax, whether the butterfly is heating up or cooling down. Initially, conduction was deemed to be

a part of effective heat transfer in the butterfly body yet after careful consideration of the literature

survey it became more feasible to abandon it. Conduction occurs only in the basal region of the

wings and there it is also very gentle, therefore negligible overall.

For the purposes of analysing the effects of wing angle on the heat transfer rates, four

different groups of wing angles were chosen: 10-44o, 45

o, 46-89

o, 90

o. 10

o is the estimated physical

minimum wing angle that the butterfly can achieve owing to its body radius (Kingsolver 1985). 45o is

a special case where reflection off incident radiation will mirror perfectly horizontally and either

reflect off the opposing wing and out into the surroundings or be intercepted by the butterfly’s

body. Between the wing angles of 46-89o it is expected that the area of the wing that is used for

heating the body reduces gradually with increasing wing angle up until 90o where it would have no

effect on heating the body. 90o is also another special case where the wings are essentially exclusive

of providing reflection radiation and consequently heat gain to the body. At 10o it is expected that

the highest concentration of radiation is reflected off the wings and onto the body due to the steep

gradient of the wings and the proportion of reflective wing length.

The solar irradiance was chosen to be 579 W/m2, a value consistent with typical ambient

conditions in the Colorado region in the USA, where the majority of the most progressive research

on butterflies has been carried out. This value assumes constant direct radiation as opposed to a

more genuine variation in a nominal day where periods of direct and diffuse radiation occur, owing

to interspersed cloud coverage. Diffuse radiation was primarily left out due to the lack of tangible

ambient data. The value of the body absorptivity is 0.95 (Berthier, 2005), with the solar absorptivity

0.54 (Kingsolver, 1983). This value of the solar absorptivity is consistent for weather conditions of

32

direct sunlight, in the summer months of June, where ambient temperatures may vary between 20-

40 oC in Colorado. The solar rays are assumed to be radiating from directly above (Ψ=0

o) the

butterfly’s body as shown by figure 23 below:

Figure 23, Proportion of solar radiation striking the butterfly body

The reflection coefficient of solar wings interacting with the wings is taken to be 1 from a similar

investigation carried out by Kingsolver (1985). All other parameters such as the wind speed and body

radius were taken for the most general cases of butterfly body dimensions and ambient conditions,

with the intention of drawing an overall understanding of the critical processes that are occurring.

An outlined picture of the butterfly wing angle and solar radiation orientation are shown in figure

24.

The heat balance is to be carried out without the addition of the fur thickness, with the

principal reason being that the effects of the fur become more pronounced for butterflies in flight,

whereas this study is strictly for stationary butterflies, adding unnecessary complexity to the

calculations. The fur thickness also becomes more important for the butterflies in colder conditions

(Ta<20o) whereas the ambient temperatures taken here are in the summer months. As stated above

the ambient temperature is generally above 20o

in the day (between 20o-40

o) when most

measurements were carried out in the literature survey in Colorado.

The temperature excess Tex= Tb-Ta was required in order to obtain a prospective value of the

Grashof number and subsequently the Nusselt and coefficient of convective heat transfer in free

convection. A value of 6oC was chosen and this is based on research carried out (in the literature

survey) on temperature differences between the surface of the body and ambient temperatures, a

reasonable average being 6oC for the stated environmental conditions.

33

Figure 24, Butterfly body, wings and interaction with incoming solar radiation

The nominal wind speed taken to calculate the Reynolds number and consequently the forced

convection is 3.14 m/s. This was taken from samples of data from ambient conditions of the most

typical weather conditions that the butterfly species may face. At this wind speed the ratio of free to

forced convection is approximately 0.84 at a wing angle of 90o. At 2.15 m/s the ratio of free/forced

convection is 1 and any further decreases in wind speed would represent a majority of free over

forced convection. Hence a wind speed of 2.15 m/s is the balancing tip between forced and free

convection. Increasing the wind speed from 3.14 m/s decreases the body equilibrium temperature

of the butterfly Tb.

For the previous calculations the temperature excess Tex=Tb-Ta was kept at 6oC in order to better

understand the effect of the other parameters in changing the heat transfer equations. Increasing

Tex by a constant amount does not affect the forced convection but rather decreases the free

convection. This is due to the fact that the film temperature rises and the inverse occurs with

coefficient of volumetric expansion β, thereby reducing the Nusselt number and subsequently

coefficient of convective heat transfer h.

In short, the key ambient conditions and constants for this study are under ambient conditions

based on Colorado, USA, in the summer month of June, under direct sunlight. A summary of the

parameters are shown below:

• Steady state heat balance (independent of time measurement).

• Butterfly body is approximated as a cylinder.

• Butterfly body will be assumed to be above the wings as opposed to being level with them.

• Butterfly is upright (i.e. no tilting is assumed for the heat balance).

• Orientation angle of butterfly body to the sun Ψ: 0o.

• Ambient temperature: 20oC.

34

• Solar absorptivity: 0.54 (Kingsolver, 1983).

• Body emissivity: 1 (Clark et al, 1973).

• Wind speed: 3.14 m/s.

• Solar irradiance: 579 W/m2.

• Temperature excess Tex=60 (required for Grashof number in free convection).

• Wing angle bands: 10-44o, 45

o, 46-89

o, 90

o.

• Yaw angle (direction of wing in relation to longitudinal length of butterfly body): 0o.

• The butterfly wing is taken to be totally reflective, i.e. (ρ=1) for all parts of the wing. This

assumption allows for a more general analysis to take place on the wing geometry with the

wing melanisation also being particularly complicated to examine, mainly because of the

uniqueness of each wing pattern for each species.

• Wind shielding by the abdomen has not been accounted for as it is assumed that the wind

direction is towards the head of the butterfly and along the body longitudinally.

• Radiation emitted by the butterfly that reflects off the ground and back onto the body has

not been considered to exclusively emphasise the effects of the wing angle(s) to the sun.

• Radiation heat transfer will be based on ambient sky temperature and the ground

temperature will be disregarded (eqn: 5-14).

4.2 Wing angle: 90o

Incident Radiation

The incident solar radiation is a function of the solar irradiance, absorptivity and size of the body

being radiated to. When the wings are held at 90o to the vertical there is no radiation from the wings

onto the body and the butterfly body receives all radiation directly. The equation for the heat

transfer onto the butterfly body is:

><��<��# � A / 7� / �

(6-1)

Convection model

Convection is split into its dual constituents of forced and free convection, and each will be derived

separately.

Forced Convection

Reference for derivation of equations: (Cotton, 2010)

Figure 25, Forced convection along the butterfly body

35

A research paper deemed paper to be a suitable approximation in place of the thermal conductivity

of butterfly wings. It is anticipated that other factors such as the specific heat capacity and the

butterfly body width were considered in choosing paper as a good estimate for thermal conductivity.

With this assumption it is then possible to estimate the butterfly body as a flat plate (as the wings

are very thing when facing the wind axially). The wind direction is taken to be facing the axial

direction of the butterfly body as shown above in figure 25.

From figure 25 there is an indication of a growing boundary layer from the leading edge (or butterfly

head) in the x direction. The Nusselt number as well as the coefficient of heat transfer also varies

along the length of the body in the flow direction. The local Nusselt or Reynolds numbers may be

obtained along the length of the body, yet it is more appropriate to acquire the average values

across the whole body. The Reynolds numbers for typical wind speeds experienced by the butterfly

are Re < 5x105, i.e in the laminar region of flow. The equation for the average Nusselt number is:

NORSSSSS � �RSSS 2 (6-2)

Where NuVSSSSS is the average Nusselt number, hVSSS the average coefficient of heat transfer along the flat

length. L is the body length and k is the thermal conductivity. hVSSS may be further described by its own

definition as:

�RSSS � 1 X �Y

RZ

[Y (6-3)

In the laminar region of flow, the flat plate surface temperature Tw is constant and as the Nusselt

number is a function of the Reynolds and Prandtl numbers, the forced convection average Nusselt is

equal to equation (6-4) for a horizontal flat plate:

NOYSSSSSS � �RSSS\2 � 0.332 / ��Y

�� / _6�̀ (6-4)

Where The Reynolds and Prandtl numbers are defined as:

��Y � �$\a (6-5)

_6 � )*b2 (6-6)

36

Hence:

�YSSS2 � 0.332 / �$

�� / \��a�� / \ _6�̀

(6-7)

�YSSS2 � 0.332 / �$

�� / \c��a��

_6�̀ (6-8)

�RSSS2 � 0.332 / �$

�� _6�̀

a��1 X \c��

RZ

[\ (6-9)

�RSSS2 � 0.332 / �$

�� _6�̀

a��1 d2\�/�eZR (6-10)

�RSSS2 � 2 / 0.332 / �$

�� _6�̀

a�� c�� (6-11)

�RSSS 2 � 0.664 / �$a �

�� _6�̀

(6-12)

NORSSSSS � 0.664 / ��R��_6�̀ � 2NOR (6-13)

The average value of the Nusselt number is thus double the local Nusselt number along the flat plate

in the laminar flow region. The average Nusselt number is then used to obtain the coefficient of

convective heat transfer and subsequently the forced heat transfer rate:

��@�� NO / 2�

(6-14)

>��@�� @��.�� 1

(6-15)

37

Free Convection

An assumption is made here that the butterfly is stationary in a quiescent manner and thus can be

modelled as a horizontal cylinder. The derivation of the heat transfer is begun with the coefficient of

volumetric expansion below:

f � 1�

[�[��* � g[.hL�1

[� i*

� [.hL�1[� � 1

�� (6-16)

Where Tf is the film temperature (mean of the surface and free-stream temperatures). The Grashof

number is represented by:

76 � jf.�� 1�`a� (6-17)

Here D is the diameter of the cylinder and a is the kinematic viscosity of air taken from steam tables.

In order to obtain the Nusselt number for free convection, the product of the Grashof and Prandtl

numbers is required for a horizontal cylinder.

76_6 (6-18) Once the Nusselt is obtained, the coefficient of convective transfer can be calculated from the

equation below:

��@�� NO / 2� (6-19)

A value of the free convective heat transfer is then obtained:

>�@�� @��.�� 1

(6-20)

The total combined heat transfer from forced and free convection is:

>#�#�I � �#�#�I�.�� 1

(6-21) Where htotal is defined by:

�#�#�I � ��@�� = ��@��

(6-22)

Radiation Model

One assumption made in the radiation model is that the emitted radiation onto the surface of the

wings and body has 0 transmissivity, and all radiation is either due to absorption (direct radiation

onto the body) or reflected radiation (off the wings and deflected onto the body).

38

For the first case of radiative heat transfer where the wings do not provide any heat gain benefits,

the wing angle are set to 90o from the vertical. The equation for the radiative heat transfer is:

>@�� -,�k��0 � ��0

(6-23)

Where - is the Stefan-Boltmann constant, , the emissivity off the butterfly body and f is the view

factor to the surroundings. The view factor (0.5) was calculated based on the direct radiation to the

ambient surroundings as well as radiation reflected onto the surrounding off the wings. As shown by

figure 26 below, the highlighted blue portion of the emitted radiation returns to the body leaving

50% radiating to the surroundings.

Figure 26, View factor to the surroundings ~ 0.5

Overall Heat Balance

The overall heat balance states that the incident solar radiation must balance the heat lost by the

butterfly at the equilibrium body temperature:

A7��f � -,�.��0 � ��01 = �#�#�I�.�� 1

(6-24) The value of the equilibrium temperature may be obtained from an in-built feature (goal seek) in

Microsoft Excel that equates both sides of the equation to 0 and thereby obtains Tb.

39

4.3 Wing angle: 45o

For the special case of the wings being angled at 45o

to the vertical there will be an evident change in

the equilibrium body temperature Tb. It is predicted that this value will drop below the value

obtained when the wings were completely horizontal. The aided benefit of angled wings will aid

reflective basking and so reduce the equilibrium temperature.

Incident Radiation

Here the incident radiation is split into two entities, direct and reflected solar radiation. The direct

solar radiation will be exactly equal to case 1 (wing angle=90o) as the direction of the solar radiation

hasn’t changed and neither has the body area. As before the direct heat transfer is represented by:

>�<@��# � A / 7� / �

(6-25)

The reflected radiation will supplement the heat transfer to the butterfly body and a larger

proportion (579 W/m2) of the incident radiation will be used by the butterfly. Lr is the length section

of the wings that will reflect solar radiation onto the butterfly’s body and for this case can be

approximated to be the body radius of the butterfly (Kingsolver 1985). The radiation area is the

multiplication of the reflective wing length by the wing width (approximated to be the body length).

The total estimated wing area of reflection is stated below and is demonstrated in figure 27:

��kh�)%lm� nlLj o6�o � @ /

(6-26) Therefore the reflective heat transfer is:

>@��I��#�� p / 7� / / @

(6-27)

Figure 27, Proportion of body acquiring incident radiation

40

The total heat transfer emitted onto the body of the butterfly is a summation of the direct and

reflected radiation as stated in equation (6-28) below:

>#�#�I � >�<@��# = >@��I��#��

(6-28) Convection Model

Forced Convection

Forced convection for angled wings is the same as the horizontal wing case because the heat

transfer equations are exempt of geometric considerations.

Free Convection

Free convection can be split into two sections; from the upper/dorsal surface of the wings and from

the down/ventral surface of the wings. For the upside surface of the wings most of the parameters

required for the Grashof number originate from the film temperature (previously stated as being the

mean of the free stream and surface temperature of the body). For the ventral side of the wings

there are slightly different derivations for the Nusselt number owing to the geometry positioning of

the lower wing face.

4.4 Wing angles: 46o-89

o

In deciding which wing angles to use between 46o and 89

o for the analysis, it became clear that the

average value of the range of angles would give a realistic indication of the thermoregulatory

behaviour. For example the reflective wing length Lr was calculated based on the angle of the wings

and the reflective area of the wings was obtained by multiplying Lr by the body length. The accuracy

of this method of obtaining the capacitive area of the wings for reflection depends on the degree of

melanisation of the wings as well as the region of the wings that are melanised (distal, medial or

basal (figure 13)).

The view factor to the surroundings was calculated by taking a line perpendicular to each

wing angle to the outer tangent of the butterfly’s body. This configuration for the view factor owes

to the fact that the reflective coefficient of the wings ρ is 1. A diagram of the geometric relationships

is shown in figures 28 & 29 and mathematically stated as being:

ml�n ko)%q6 %q %�� rO66qOL[lLjr � 180 = .90 � u1 / 2360

(6-29)

41

Figure 28, View factor to the surroundings for wing angles of 46-89o

4.5 Wing angles: 10o-44

o

Figure 29, View factor to the surroundings for wing angles of 10-44o

42

4.6 Results & Conclusions

Wing Angle(s) [o] Tb [

oC] QIR [W] Qwings [W] Qtotal [W]

10-44 (avg) 76.169 0.0481 0.818 0.866

45 26.131 0.0481 0.0284 0.0765

46-89 (avg) 26.976 0.0481 0.0134 0.0616

90 26.753 0.0481 0 0.0481

Table 2, Equilibrium temperature and proportions of solar radiation from sun and wings

As shown by table 2 above, widening the wing angle decreases the total heat transfer to the

butterfly body. The heat transfer to the body is constant as the angle of incident radiation was taken

to be 0o

or directly above the butterfly’s head and the wings do not obstruct direct radiation. The

maximum heat transfer reflected onto the body from the wings occurs at 10o and gradually reduces

until zero effect at 90o.

Table 2 shows final equilibrium temperatures obtained for each band of wing angle(s). As previously

stated, at 90o the wings provide no heat gain to the butterfly body via the wings and overall there is

minimum heat transferred to the body.

ΔT is approximately 55oC at wing angles of 10-44

o, with a high equilibrium temperature of 76.2

oC

due to the long reflective wing length apparent for this band of angles. This high value indicates that

wing angles lower than 45o can only be displayed by the butterfly for a finite amount of time. As

time was not reckoned into the study it is possible to deduce that any amount of time between

instant up until the fatal body temperature (~50oC) may be possible. Assuming it does take longer

than an instant transition from the body temperature to change to 76.2oC, it is possible for the

butterfly to apply this angled posture and swiftly change to wing angles of 45o and above when a

suitable body temperature has been acquired. This provides several advantages, particular in

emergency situations such as avoiding predation where body temperature can be raised above the

flight minimum in a very short amount of time.

Wing

Angle(s)

[o]

Hfree

[W/m2K]

Hforced

[W/m2K]

Htotal

[W/m2K]

Qtotal

[W]

Qconv

[W]

Qrad

[W]

Tb

[oC]

10-44

(avg)

32.644 11.000 43.644 0.866 0.101 0.00930 76.169

45 26.023 11.000 36.253 0.0765 0.0670 0.00815 26.131

46-89

(avg)

14.084 11.000 25.084 0.0616 0.0463 0.00688 26.976

90 9.201 11.000 20.201 0.0481 0.0373 0.00543 26.753

Table 3, Proportions of key experiment parameters

Table 3 shows that the forced convection was constant throughout the different wing angles, mainly

due to the wind direction that is travelling in the longitudinal direction of the butterfly’s body, and

therefore in exclusion of geometric wing changes. Any changes in Qconv would have therefore come

about from free convection. Qconv and Qrad gradually increase proportionally with decreasing wing

angle but at wing angles between 10-44o there is a sharp rise in Qtotal. There are two reasons for this;

43

firstly that the wing is considered completely reflective (ρ=1) along its entire length and secondly

due to the large increase in the reflective wing length (figure 29). Kingsolver (1985) states that any

reflective index less than 1 would see a decrease in the intensity (by a factor of ρ2) of the radiation

reflecting off each wing until it is intercepted by the body. This is the main reason for the large

increase of incoming radiation at wing angles less than 45o.

It is also remarkable that between 45-90o the equilibrium body temperature is fairly constant,

indicating that although decreasing the wing angle causes a rise in the incoming heat to the body,

there is a complimentary rise in heat loss via convection and radiation. This special occurrence is

only applicable for the conditions stated but may differ significantly when for example radiation is

diffuse, and other parameters are accounted for, such as wing melanisation, fur thickness and tilting

etc.

4.7 Summary of Conclusions

∼∼∼∼ The greatest heat gain was produced at lower wing angles (10-44o). At these wing angles

however, the equilibrium body temperature is fatal and so it is suggested that the butterfly

would only display these wing angles for a finite or very short amount of time (requires

experimental confirmation).

∼∼∼∼ An increasing wing angle lessens the heat loss via free convection, and perhaps would be

used in situations of low wind speed to conserve a favourable body temperature.

∼∼∼∼ At the equilibrium temperature of approximately 26o, the butterfly species are comfortable

in that they have the capacity to fly without requiring any heat gain or heat loss through

thermoregulation. Therefore between 45-90o, it is possible to say that the most stable body

temperatures are acquired for the stated conditions.

∼∼∼∼ The wing span as well as the reflective wing length can greatly increase the amount of

radiation received by the butterfly. This is particularly emphasised when the butterfly

species has a lighter coloured wing colour (higher coefficient of reflection ρ).

44

5 Future Works

�� 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 transmissivity 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?

�� Transient heat balance including time.

�� Comparing various body radius sizes and how each respective length can be

advantages/disadvantages for the given ambient conditions.

�� Use accurate CAD model of butterfly to simulate equilibrium body temperatures during

flight.

�� Consider how the uptake of solar radiation may be different for tilted body posture,

especially as wing patterns are different for the ventral side of the wings as opposed to the

dorsal.

�� Produce extended studies in ambient conditions of less than 20oC.

�� Current wind speed (3.14 m/s) is for average ground heights in Colorado USA, yet it may

become more remarkable to study how at higher altitudes where the wind speeds would be

expected to be much higher. This would change the proportion of forced/free convection

and help in understanding how the butterfly mitigates the effects of convective heat loss.

�� Fur has been reckoned to be an effective aid in battling the effects of convective heat loss

(literature survey) and yet was left out of the main study due to the lack of accurate data on

temperature changes in the body. It is desired that a greater understanding of the

relationship of the fur in regulating temperature is required particularly between warm and

cooler climates.

45

5.1 Solidworks Simulation

Figure 30,

Figure 30 & 31 show a model of the butterfly made on CAD software (Solidworks

to provide a more accurate study of the equilibrium body temperature with closer contour detail

being considered. Meshing the butterfly model (figure 31) allows for a more accurate analysis of the

areas which are more susceptible to he

feature for thermal analysis and it allows the three main modes of heat transfer to be

well as setting other parameters such as

Figure 30,

Solidworks Simulation

Figure 30, Solidworks model of the butterfly (view 1)

a model of the butterfly made on CAD software (Solidworks


Meshing the butterfly model (figure 31) allows for a more accurate analysis of the

areas which are more susceptible to heat gain or heat loss. Solidworks has an in-

feature for thermal analysis and it allows the three main modes of heat transfer to be

other parameters such as ambient temperatures, view factors and emissivities.

Figure 30, Solidworks model of the butterfly (view 2)

a model of the butterfly made on CAD software (Solidworks), which can be used


Meshing the butterfly model (figure 31) allows for a more accurate analysis of the

-built simulation

feature for thermal analysis and it allows the three main modes of heat transfer to be evaluated as

ambient temperatures, view factors and emissivities.

46

Figure 31,

Applying mesh to butterfly body & hind-wings

47

6 Appendix

6.1 DataBank

Figure A1, Body temperatures of

Figure A2, Various parameters in relation to different wing and abdominal posi

of Swallowtails in field studies (oC). Mean ± sd above, range below

(Rawlins, 1980).

Various parameters in relation to different wing and abdominal posi

(Sample size), (Rawlins, 1980).

± sd above, range below,

Various parameters in relation to different wing and abdominal positions Mean ± sd.

48

Figure A3, Critical thoracic temperatures for various activities of black

cage. Mean (N = sample size) above, range below (

Figure A4, Identification, sex, means and standard deviations (SD) of body mass

length R [mm], wing loading pw

thoracic excess ΔT=Tth-Ta [oC] and solar irradiance

Figure A5, Solar absorptivity, thoracic fur thickness and thoracic diameter of four

in central

Critical thoracic temperatures for various activities of black Swallowtail

cage. Mean (N = sample size) above, range below (oC), (Rawlins 1980).

Identification, sex, means and standard deviations (SD) of body mass

w [N m-2

], thoracic temperature Tth [oC], ambient temperature

and solar irradiance I [W m-2

] for two species of

(Dudley, 1991).

Solar absorptivity, thoracic fur thickness and thoracic diameter of four

in central Colorado, (Kingsolver, 1983).

Swallowtails in the flight

(Rawlins 1980).

Identification, sex, means and standard deviations (SD) of body mass m [mg], wing

], ambient temperature Ta [oC],

] for two species of Danaine butterfly,

Solar absorptivity, thoracic fur thickness and thoracic diameter of four butterfly species

49

Figure A6, Cumulative daily flight activity time (KFAT) in hours for the three sites o

elevational heights,

Figure A7, Sensitivity analysis of the energy balance model,

(labelled as Tex in the nomenclature)

the butterfly’s

Figure A8, Table of results for experiments carried out at high elevations

Cumulative daily flight activity time (KFAT) in hours for the three sites o

elevational heights, (Kingsolver 1983).

Sensitivity analysis of the energy balance model, where Td is body temperature excess

in the nomenclature), Tex = Tb-Ta. This graph relates how each parameter may affect

butterfly’s body temperature, (Kingsolver, 1983).

Table of results for experiments carried out at high elevations, (Kingsolver & Watt,

1984).

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

is body temperature excess

This graph relates how each parameter may affect

, (Kingsolver & Watt,

50

6.2 Nomenclature

Symbol Quantity Units

A Effective area of butterfly model m2

Ar Archimedes number:

Ar = Gr/Re2

---

Ac Convective heat transfer surface area m2

As,dir Direct solar radiative heat transfer surface area m2

As.ref Reflected solar radiative heat transfer surface area m2

As.ttl Total solar radiative heat transfer surface area m2

At Thermal radiative heat transfer surface area m2

Aw Cross-sectional area of wire m2

cp Specific heat of butterfly model J kg-1

K-1

Deff Characteristic dimension of the butterfly model (maximum

width of mesothorax including the fur):

Deff = (4V/πL)1/2

m

e Vapour pressure Pascals

g Gravitational constant m s-2

Gd Solar radiation intensity W m-2

Gr Grashof number = (gβ(Tb-Ta)D3eff/ν

2) ---

hb Boundary layer conductance W m-2

K-1

hc Conductive heat transfer coefficient W m-2

K-1

hf Convective heat transfer coefficient W m-2

K-1

hfur Fur layer conductance W m-2

K-1

hr Radiative heat transfer coefficient W m-2

K-1

ht Total heat transfer coefficient W m-2

K-1

Hs.dir Direct solar radiative horizontal flux densities W m-2

Hs.dif Diffuse solar radiative horizontal flux densities W m-2

Hfree Coefficient of free convective heat transfer W m-2

K-1

Hforced Coefficient of forced convective heat transfer W m-2

K-1

Htotal Total coefficient of convective transfer (free+ forced) W m-2

K-1

Hs.ttl Total solar radiative horizontal flux densities W m-2

I Solar Irradiance: amount of solar power received over a certain

area

W m-2

k Thermal conductivity of air W m-1

K-1

ke Thermal conductivity of fur W m-1

K-1

kW Thermal conductivity of wire W m-1

K-1

L Length of butterfly model m

Lw Length of wire m

m Mass of model kg

Nu Nusselt number:

Nu = hfDeff/k

---

pw Wing loading: the weight of the butterfly divided by its wing

area

N m-2

v� conv Heat transfer rate by forced convection W

v� in Rate of internal heat input W

QIR Incident radiation heat transfer W

Qconv Convective heat flux W

51

Qrad Radiation heat transfer W

Qs Total Solar radiative heat flux W

Qs.dif Diffuse solar radiative heat flux W

Qs.dir Direct solar radiative heat flux W

Qs.ref Reflected solar radiative heat flux W

Qt Thermal radiative heat flux W

Qwings Wing reflected heat transfer W

rg Ground solar reflectivity ---

ri Body radius m

R Wing length m

Re Reynolds number:

Re = UDeff/ν

---

t Time s

T Absolute temperature K

Ta Ambient temperature K

Tab Abdominal temperature K

Tba Basking temperature = steady state thoracic temperature of

butterfly in basking posture with the wings held at a

perpendicular angle to the sun’s beams.

K

Tb Body temperature K

Tex Temperature excess, which equates to the body temperature

minus the ambient temperature:

Tex = (Tb - Ta)

K

To Initial body temperature K

Tsky Black body sky temperature K

Tt Body temperature at time t K

Tth Thoracic temperature K

Tw Wire temperature K

T∞ Final body temperature K

U Wind velocity m s-1

V Volume of body m3

y Yaw angle Degrees

z Zenith angle Degrees

α Solar absorptivity of wing ---

β Thermal expansion coefficient K-1

w Thoracic fur thickness m

ε Thermal emissivity of model (=1) ---

σ Stefan-Boltzmann constant W m-2

K-1

τ Transient time constant s

ν Kinematic viscosity of air m2

s-1

Ψ Orientation angle o

52

7 References

Anonymous 1, 2010 ‘Painted Lady Butterfly’

Anonymous 2, 2010 ‘High Mag Butterfly Focus Stack Tutorial’

http://www.fredmiranda.com/forum/topic/936420/0#8841929

Anonymous 3, n.d, ‘no title’,

Berthier, S., 2005 ‘Thermoregulation and spectral selectivity of the tropical butterfly Prepona

meander: a remarkable example of temperature auto-regulation’

Clark, A. J., Cena, K., Mills, J. N., 1973 ‘Radiative Temperatures of Butterfly Wings’

Dudley, R., 1991, ’Thermoregulation in unpalatable Danaine Butterflies’

Heimbuch, J., 2010, ‘Researchers create artificial spider’s silk spinner’

Heinrich B., 1986 ‘Thermoregulation and Flight Activity Satyrine’

Hicker R., n.d, ‘Pink Cattlefish Butterfly’, http://www.hickerphoto.com/pink-cattleheart-butterfly-

10295-pictures.htm,

Horton. J., 2008 ‘Where do butterflies get their striking colors?’, Available at:

http://animals.howstuffworks.com/insects/butterfly-colors.htm

Kingsolver J., 1983 ‘Thermoregulation and Flight in Colias Butterflies: Elevational Patterns and

Mechanistic Limitations’

Kingsolver, J., 1985, Thermoregulatory significance of wing melanisation is Pieris butterflies: physics,

posture, and pattern

Kingsolver J., 1987, ’Predation, Thermoregulation, and Wing Colour in Pierid Butterflies’

Kingsolver J., 1988, ‘Thermoregulation, Flight, and the Evolution of Wing Pattern in Pierid Butterflies:

The Topography of Adaptive Landscapes’

Kingsolver, K., Koehl M., 1985 ‘Aerodynamics, thermoregulation, and the evolution of insect wings:

differential scaling and evolutionary change’ Evolution,39(3), pp. 488-504

Kingsolver, J., Moffat, R., 1982 ‘Thermoregulation and the Determinants of Heat Transfer in Colias

Butterflies’

Kingsolver, J., Watt, W., 1984, ‘Mechanistic Constraints and Optimality Models: Thermoregulatory

Strategies in Colias Butterflies’

Miakar, P., n.d, ‘Boquet’, Available at: http://pixdaus.com/single.php?id=268335&f=rs

Mun B, 2010 ‘Butterfly of the Month’, Available at:

http://www.butterflycircle.com/?m=201001&paged=2

Polcyn, D., Chappell, M., 1986 ‘Analysis of Heat Transfer in Vanessa Butterflies: Effects of Wing

Position and Orientation to Wind and Light’

Rawlins J., 1980 ‘Thermoregulation by the Black Swallowtail Butterfly, PapilioPolyxenes’

Shelly, T., Ludwig D., 1985, ‘Thermoregulatory Behaviour of the Butterfly Calisto nubile in a Puerto

Rican Forest’

53

Smetacek, P., 2000, ‘The Study of Butterflies’, Resonance-The study of Indian Butterflies’, No.6, pp 8-

14 Sutton, O. G., 1965 ‘Biographical Memoirs of Fellows of the Royal Society’, Vol. 11, pages 41-52

Thinkquest, n.d, Available at: http://library.thinkquest.org/C002251/cgi-

bin/default.cgi?language=english&chapter=3&section=2&mode=chapter&outputmode=0&navmenu

=0&javascript=0

Toogood, P., n.d, ‘Mission Beach High Resolution Image Gallery’, Available at:

http://www.missionbeach.me/cairns-birdwing.jpg

Valentino, J. A., 2006, ‘Butterfly portrait’, Available at:

http://www.pbase.com/alvalentino/image/59094508

White, F., n.d, ‘Heat Transfer’

Wong A., n.d, ‘Great Mormon’, Available at: http://butterflycircle.blogspot.com/2009/08/life-

history-of-great-mormon.html

Wong A., 2010 ‘Butterfly of the Month’, Available at:

http://www.butterflycircle.com/?m=201001&paged=2, 2010

54

8 Gantt Chart

Thermoregulation By Butterfly Wings

Project Author Milad Arkian

Start Date: 17/06/2010

Main Tasks Start End Du

rati

on

(D

ay

s)

We

ek

Sta

rtin

g

27

-Se

p-1

0

04

-Oct

-10

11

-Oct

-10

18

-Oct

-10

25

-Oct

-10

01

-No

v-1

0

08

-No

v-1

0

15

-No

v-1

0

22

-No

v-1

0

29

-No

v-1

0

06

-De

c-1

0

13

-De

c-1

0

20

-De

c-1

0

27

-De

c-1

0

03

-Ja

n-1

1

10

-Ja

n-1

1

17

-Ja

n-1

1

24

-Ja

n-1

1

31

-Ja

n-1

1

07

-Fe

b-1

1

14

-Fe

b-1

1

21

-Fe

b-1

1

28

-Fe

b-1

1

07

-Ma

r-1

1

14

-Ma

r-1

1

21

-Ma

r-1

1

28

-Ma

r-1

1

04

-Ap

r-1

1

11

-Ap

r-1

1

18

-Ap

r-1

1

25

-Ap

r-1

1

02

-Ma

y-1

1

Pre term workResearch and acquire relevant thesis information 17/06/10 03/05/11 320

Matlab programming practise 17/06/10 03/05/11 320

Background reading on butterfly biology 17/06/10 03/05/11 320

Initial Report workBegin write up and organisation of the initial report, including abstract and introduction 27/09/10 17/12/10 81

Select research papers that will provide the main backbone of the project 27/09/10 17/12/10 81

Build up data bank of useful information 27/09/10 29/11/10 63

Research key features of the butterflies anatomy that relates to its thermoregulation 27/09/10 18/11/10 52

Derive the general heat balance equations 25/10/10 29/11/10 35

Sum up the report with a conclusion 06/12/10 17/12/10 11

Check report, organise and label figures, tables, glossary and nomenclature 02/12/08 09/12/08 7

Poster workResearch graphics tools and software that may be required for the poser 20/12/10 04/03/11 74

Research colour designs and effective use of space on the poster 20/12/10 31/01/11 42

organise material that will be used on the poster from the report 31/01/11 04/03/11 32

Design final poster 20/12/10 04/03/11 74

Final Report workResearch the gaps in knowledge from the initial report 31/01/11 21/02/11 21

carry out training of simulation software for the modelling of the heat equations 31/01/11 18/04/11 77

Obtain a better understanding of the butterfly wing structure 31/01/11 18/04/11 77

Refine asbtract, introduction and the literary survey 18/04/11 04/05/11 16

Develop links between biology of the butterfly and possible engineering applications 04/04/11 03/05/11 29

Refine reference list, nomenclature 25/04/11 03/05/11 8

Prepare final report structure 25/04/11 03/05/11 8

Finish final report 25/04/11 03/05/11 8

Documents

Temperature Control Mechanism by Butterfly Wings