ORIGINAL ARTICLE

The effect of an external transmitter on the drag coefficientof a bird’s body, and hence on migration range, and energyreserves after migration

C. J. Pennycuick • Peter L. F. Fast •

Ninon Ballerstadt • Niels Rattenborg

Received: 19 February 2011 / Revised: 11 October 2011 / Accepted: 28 October 2011 / Published online: 19 November 2011

� Dt. Ornithologen-Gesellschaft e.V. 2011

Abstract Externally mounted transmitters or loggers may

adversely affect migration performance for reasons other

than the effects of added mass. The added frontal area of a

payload box increases drag, and if the box triggers sepa-

ration of the boundary layer over the posterior body, the

drag coefficient could also be increased, possibly by a large

amount. Any such effects would lead directly to a

decreased migration range and reduced energy reserves on

completion of migration. We measured the body drag

coefficients of Rose-coloured Starlings in the Seewiesen

wind tunnel by the wingbeat-frequency method. The speed

at which the wingbeat frequency passed through a mini-

mum was taken to be an estimate of the minimum-power

speed (Vmp), from which the body drag coefficient was

calculated in turn. Dummy transmitter boxes were mounted

on the bird’s back by attaching them with Velcro to a side-

loop harness pad. The pad alone projected 6 mm above the

bird’s back, and increased the drag coefficient by nearly

50%, as compared to the ‘‘clean’’ configuration with no

harness. Adding boxes (square-ended or streamlined)

produced no further significant increase in the drag coef-

ficient, but the addition of a sloping antenna increased it to

nearly twice the clean value. These increases are attributed

to separation of the boundary layer over the posterior upper

body, triggered by the payload. We then ran computer

simulations of a particular Barnacle Goose, for which

detailed information was available from an earlier satellite-

tracking project, to see how its migration range and

reserves on arrival would be affected if its transmitter

installation also caused flow separation and affected the

body drag coefficient in a similar way. By representing the

range calculation in terms of energy height, we separated

the effect of the transmitter’s mass, which reduces the fat

fraction (and hence also energy height) at departure, from

that of flow separation, which steepens the energy gradient.

The effect of the mass is small, and increases only slightly

with increasing distance, whereas a steeper energy gradient

not only reduces the range but also reduces the reserves

remaining on arrival, to an extent that increases with

migration distance. Energy height is related to the fat

fraction rather than the fat mass, and is therefore preferable

to energy as such, for expressing reserves in birds of dif-

ferent sizes.

Keywords Flight mechanics � Bird migration �Transmitter � Energy height � Aerodynamics

Zusammenfassung

Der Einfluss eines externen Transmitters auf den Wi-

derstandsbeiwert eines Vogelkorpers und folglich auf

Zugstrecke und Energiereserven am Ende des Zuges.

Extern angebrachte Sender oder Datenlogger konnten außer

ihrem zusatzlichen Gewicht einen weiteren nachteiligen

Communicated by A. Hedenstrom.

C. J. Pennycuick

School of Biological Sciences, University of Bristol,

Woodland Road, Bristol BS8 1UG, UK

e-mail: c.pennycuick@freeuk.com

P. L. F. Fast

Departement de Biologie et Centre d’etudes nordiques,

Universite du Quebec a Rimouski, 300 Allee des Ursulines,

Rimouski, QC G5L 3A1, Canada

N. Ballerstadt � N. Rattenborg (&)

Max Planck Institut fur Ornithologie,

Haus 11 Eberhard-Gwinner Str, 82319 Seewiesen, Germany

e-mail: rattenborg@orn.mpg.de

123

J Ornithol (2012) 153:633–644

DOI 10.1007/s10336-011-0781-3

Effekt auf die Arbeitsleistung beim Vogelzug haben. Die

durch eine Zuladung vergroßerte Stirnflache erhoht den

Luftwiderstand und der Widerstandsbeiwert konnte—

moglicherweise um einen großen Betrag—ebenfalls anste-

igen, wenn es durch die Zuladung zu einer Ablosung der

Grenzschicht uber dem Rumpf kommt. Jeder dieser Effekte

konnte direkt zu einer Verringerung der Reichweite beim

Vogelzug fuhren sowie zu reduzierten Energiereserven am

Ende der Wanderung. Im Seewiesener Windkanal (Max-

Planck-Institut fur Ornithologie) ermittelten wir den

Widerstandsbeiwert von Rosenstaren (Sturnus roseus) uber

die Flugelschlagfrequenz-Methode. Die Geschwindigkeit,

bei der die Flugelschlagfrequenz ein Minimum durchlief,

wurde als Abschatzung fur die Minimum Power Speed

(Vmp) herangezogen, aus der wiederum der Widerstands-

beiwert des Korpers berechnet wurde. Sender-Attrappen

wurden am Rucken der Vogel angebracht, indem sie mit

Klettband an einem rucksackahnlichen Geschirr befestigt

wurden. Der ‘‘Rucksack’’ohne Zuladung ragte dabei

6 mm uber den Vogelrucken hinaus und erhohte den

Widerstandsbeiwert um fast 50% im Vergleich zum Vogel

ohne Geschirr. Die zusatzlich auf dem Geschirr angeb-

rachten Sender-Attrappen (kantig oder stromlinienformig)

fuhrten zu keiner weiteren Erhohung des Widerstands-

beiwerts. Mit einer schrag nach hinten oben gerichteten

Antenne jedoch stieg dieser Wert auf annahernd das

Doppelte gegenuber dem Vogel ohne Zuladung und Ges-

chirr. Die Erhohungen des Widerstandsbeiwerts lassen

sich auf die Ablosung der Grenzschicht uber dem hinteren

Ruckenteil des Vogels durch die Manipulationen zur-

uckfuhren. Im Anschluss fuhrten wir Computersimulatio-

nen fur eine ganz bestimmte Nonnengans (Branta

leucopsis) durch, fur die detaillierte Daten aus einem

fruheren Projekt (Standortverfolgung via Satellit) vorla-

gen, um zu sehen, wie ihre Reichweite und die Energie-

reserven bei der Ankunft im Zielgebiet beeinflusst worden

waren, falls ihre Besenderung zu einer ahnlichen Ablo-

sung der Grenzschicht am Rucken gefuhrt und damit den

Widerstandsbeiwert ihres Korpers verandert hatte. Bei der

Darstellung der Reichweite in Abhangigkeit vom Ener-

gieaufwand unterschieden wir zwischen dem Einfluss der

Masse des Senders, die beim Abflug zu einer Reduzierung

des Fettanteils fuhrt (und damit auch des Lei-

stungsvermogens) und dem Effekt der Ablosung des

Luftstroms vom Korper, die den Arbeitsaufwand steil

ansteigen lasst. Der Einfluss der Masse ist gering und

steigt bei zunehmender Entfernung nur leicht an,

wohingegen der Anstieg des Arbeitsaufwands nicht nur

die Reichweite verkurzt, sondern auch die verbleibenden

Energiereserven bei der Ankunft verringert und bei weit-

eren Entfernungen immer großere Ausmaße annimmt. Um

die Reserven von Vogeln unterschiedlicher Große dar-

zustellen, ist das Leistungsvermogen, das eher an den

Fettanteil als an die Masse des Fetts gebunden ist, der

Energie als solcher vorzuziehen.

Introduction

The use of back-mounted satellite transmitters and data

loggers to study bird migration always raises doubts as to

whether the package itself degrades the flight performance

which it is being used to study (Barron et al. 2010; Casper

2009). Most researchers discuss this exclusively in terms of

the added mass of the payload package. This is indeed a

legitimate concern, but a package which alters the external

shape of the body may also increase the body drag, and this

may degrade flight performance in ways that are different

from the effects of added mass. The added frontal area of

the package inevitably introduces some extra drag, but a

much larger effect might result if the package were to

trigger separation of the boundary layer over the posterior

end of the body. An earlier attempt to quantify any such

effects by measuring the drag of frozen bird bodies in a

wind tunnel failed, because it turned out that the boundary

layer always separated from a frozen body, whether or not

a dummy payload package was attached (Pennycuick et al.

1988; Obrecht et al. 1988). However, no such effect was

seen when a method was devised to measure the drag

coefficient of the body of a living bird flying in a wind

tunnel (Pennycuick et al. 1996). In this paper, we describe

how the same method was used to measure the body drag

coefficients of Rose-coloured Starlings (Sturnus roseus)

flying in the wind tunnel at the Max Planck Institute for

Ornithology at Seewiesen, Germany, with and without

back-mounted boxes of various shapes.

Background to drag measurements

In the special case of horizontal flight, in which a bird or

aircraft moves steadily along in a straight line, the drag force

acts backwards along the flight path, and has to be balanced

by an equal, forward horizontal force supplied by a propel-

ler, jet, or flapping wings. The nature of the drag force, along

with its magnitude and its causes, has been the subject of

intense study since the early days of aeronautics, because the

rate at which work is done in level flight (the mechanical

power) is directly proportional to the drag, and this in turn

determines the rate at which fuel is consumed, whether in an

aircraft, a bird or a beetle. Hoerner (1951) reviewed classical

drag studies at scales ranging from small insects up to

supersonic aircraft and integrated them into a theoretical

structure that remains the backbone of the subject today.

The drag (D) is a force whose magnitude varies with the

air speed (V), the air density (q), and the frontal area of the

634 J Ornithol (2012) 153:633–644

123

body (Sfr), and the first step in any study of drag is to

eliminate these variables by converting the drag into a

dimensionless drag coefficient (Cd), where

Cd ¼ D=ð1=2qV2SfrÞ: ð1Þ

V is the relative speed at which the air flows past the body

(or alternatively, at which the body moves through sta-

tionary air) and Sfr is the body’s frontal area, meaning the

cross-sectional area at its widest point, in a plane perpen-

dicular to the flow. The denominator in Eq. 1 is approxi-

mately equal to the drag of a disc of area Sfr, perpendicular

to a flow of air of density q at a relative speed V, and the

drag coefficient can be seen as the ratio of the drag of a

particular body to this ‘‘reference drag’’. For example, if

the drag coefficient of a bird’s body is 0.1, this means that

its drag is the same as that of a disc whose area is one-tenth

the body’s frontal area.

Hoerner (1951) shows that the drag coefficient of a

given body is a function of just two dimensionless num-

bers, the Mach number and the Reynolds number. The

Mach number (ratio of the air speed to the speed of sound)

can be neglected at the low speeds at which birds fly, and

drag coefficients then become functions of the Reynolds

number (Re) only. It is defined as

Re ¼ Vd=m; ð2Þ

where V is the air speed, d is a reference length, and m is the

kinematic viscosity of the air; that is, the ratio of its vis-

cosity to its density. The value used here for the reference

length is the diameter (d) of the body at its widest point,

although Reynolds numbers for wings (not considered

here) are usually calculated using the mean chord, which

usually gives a higher Reynolds number at the same speed.

The drag of any object is made up of two components,

skin friction, which is due to the tangential motion of air

sliding over the skin, and pressure drag, which is due to air

pressure acting normally to the skin. The pressure varies

over different parts of the surface; it is highest at the front

and rear ends, and less in between. The pressure on the

forward-facing parts of the skin integrates to a backward

force, which is always larger than the forward force due to

the integrated pressure over rearward-facing parts. The

pressure drag is the difference between the backward and

forward force components. At Reynolds numbers below

100, as in insect-sized bodies at low speeds, air is effec-

tively a viscous fluid, skin friction predominates, and the

drag varies in proportion to the speed. At the scales at

which aircraft operate, with Reynolds numbers of a million

and up, the drag is nearly all pressure drag, and varies in

proportion to the square of the speed. Birds occupy the

region between these two very different regimes, and the

drag of their bodies is difficult to predict for that reason.

Our Reynolds numbers begin at about 17,000 (see

‘‘Results’’ below), which is well into the region where

pressure drag predominates, according to Hoerner (1951).

This means that the drag coefficient (Eq. 1) remains

approximately constant as the speed is varied, but may

change if the pattern of flow changes. In particular, a large

increase in the drag coefficient can result if the boundary

layer separates from the surface of the body, creating a

region of low-pressure, turbulent air over the downstream

end. Our experiment was intended to show whether adding

a back-pack transmitter box would result in an increase in

the drag coefficient, such as would be caused by boundary-

layer separation. If any such effects can be quantified, the

results can be used directly to estimate the effect of a

transmitter box on a migrating bird’s range, using software

which is already freely available (http://books.elsevier.

com/companions/9780123742995).

Methods

Principle of the method

Our method of estimating the bird’s body drag coefficient

(Cdb), with or without added hardware, is based on mea-

suring the minimum-power speed (Vmp), which is the speed

at which the least mechanical power is required from the

flight muscles when the bird is flying horizontally at a

constant air speed. According to the model given by

Pennycuick (2008),

Vmp ¼ 0:807 k1=4m1=2g1=2=ðq1=2b1=2S1=4fr C

1=4db Þ; ð3Þ

where k is the induced drag factor, m is the bird’s all-up

mass (including the mass of a harness and dummy

transmitter, if fitted), g is the acceleration due to gravity,

q is the air density, b is the wing span, Sfr is the total frontal

area (including the frontal area of any harness and

transmitter) and Cdb is the drag coefficient of the body

including the transmitter. If Vmp has been measured, and

Cdb is to be determined, Eq. 3 can be rearranged to give an

estimate of Cdb from the measured Vmp:

Cdb ¼ 0:424 km2g2=ðq2b2SfrV4mpÞ: ð4Þ

Apart from Vmp, all of the variables on the right-hand

side of Eq. 4 can be measured to a precision of 1% or

better, except for the induced power factor (k). This is

somewhat conjectural in flapping flight, but it was shown in

an earlier paper (Pennycuick et al. 1996) that improbably

large deviations from the default value (1.2) would have

little effect on the estimated value of Cdb. Gravity was

assumed to be constant at 9.81 m s-2.

Equation 4 does not require an estimate of the power as

such, but it requires the speed (Vmp) at which the power

J Ornithol (2012) 153:633–644 635

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passes through a minimum. We estimated this speed indi-

rectly by measuring wingbeat frequency over a range of

speeds. The variation of wingbeat frequency versus air

speed is much smaller than that of power, but it was shown

in an earlier project (Pennycuick et al. 1996) that the curve

is U-shaped, and that the minimum occurs at the same

speed in both curves, at least under the restriction that the

bird is flapping steadily and flying at a constant speed. The

evidence for this came from a Teal (Anas crecca) flying in

the Lund University wind tunnel, which can be tilted.

Although the absolute mechanical power could not be

measured, tilting the tunnel by a small amount (making the

bird fly ‘‘uphill’’ at a shallow angle) imposed a known

increment of power, equal to the bird’s weight times the

vertical component of speed. Varying the tilt over a range

of climb and descent angles while keeping the air speed

constant showed a linear relationship between the wingbeat

frequency and the power over the narrow range that con-

cerns us here. In other words, when the power increases by

a small amount, the wingbeat frequency also increases, and

when the power goes down, so does the wingbeat fre-

quency. On this basis, we identified the minimum-power

speed with the minimum-frequency speed. Deviations from

the assumed condition of steady, unaccelerated flight

would be a potential source of error (below).

Birds and their measurements

We used three Rose-coloured Starlings from a group that

were raised at Seewiesen in 2003 by their own parents, who

had themselves been brought from Ukraine. These birds

were trained and handled by one of us (N.B.), having been

originally been trained to fly in the wind tunnel for phys-

iological experiments (Engel et al. 2006; Schmidt-Well-

enburg et al. 2008). Their wing spans, aspect ratios and

average masses were closely similar, and are listed in

Table 1, while Table 2 shows the payload configurations

that we tested. The birds were trained to perch on a balance

before and after each flight, and we took the all-up mass

(m) of the bird, including a harness and a dummy trans-

mitter box (if fitted), to be the average of these two mea-

surements. The body mass (mbody) was then found by

subtracting the mass of the particular harness–box combi-

nation (Table 2) from the all-up mass. The bird’s frontal

area (Sbody) was estimated from the body mass for each

flight using the formula from Pennycuick (2008):

Sbody ¼ 0:00813 m0:666body : ð5Þ

It varied from 1,360 to 1,630 mm2. The total frontal area

(Sfr) was the sum of the body frontal area from Eq. 5 and

the frontal area of the harness–box combination (Sbox) from

Table 2:

Sfr ¼ Sbody þ Sbox: ð6Þ

This was calculated separately from Eq. 6 for each

flight, and used to calculate the drag coefficient from Eq. 4.

The Seewiesen wind tunnel

The wind tunnel at the Max Planck Institute for Ornithol-

ogy at Seewiesen, Germany, was built by the Swedish

engineering firm Rollab of Solna, who had previously built

the wind tunnel at Lund University to the same basic

design as described by Pennycuick et al. (1997). It is a

closed-circuit, low-turbulence tunnel, with an octagonal

test section measuring 1.24 m wide by 1.08 m high, a

contraction ratio of over 12:1, and a settling section with a

honeycomb and five screens. The first 2 m of the test

section is enclosed by transparent plexiglass walls, fol-

lowed by a 0.5 m gap, where the pressure equilibrates with

the surroundings, allowing free access to the test section

Table 1 Wing measurements

for Rose-coloured StarlingsBird ID Sex Mass (kg) Wing

span (m)

Wing

area (m2)

Aspect

ratio

Successful

flights

A M 0.0737 0.360 0.0221 5.86 18

B M 0.0728 0.360 0.0226 5.73 41

C F 0.0842 0.360 0.0226 5.73 14

Table 2 Harness and

transmitters. Bird body frontal

area varied from 1,360 to

1,630 mm2

Payload Mass (g) Length

(mm)

Width

(mm)

Height

(mm)

Fr. area

(mm2)

Added

area (%)

Harness only 1.2 18 16 6 96 7

Harness ? box 1 (rectangular) 1.8 24 13 15 195 13

Harness ? box 2 (with fairings) 2.0 24 13 15 195 13

Harness ? box 3 (with antenna) 1.9 24 13 15 240 19

636 J Ornithol (2012) 153:633–644

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without disturbing the air flow. The fan is driven by a

variable-frequency AC motor, allowing the wind speed to

be continuously controlled down to below 5 m s-1. The

wind speed display is derived from a dynamic-pressure

source in the contraction, but a dedicated computer uses

readings of temperature in the tunnel and barometric

pressure to calculate and display the true (as opposed to

equivalent) wind speed. Although no test data were avail-

able, the performance may be assumed to be similar to that

of the Lund wind tunnel, with a turbulence level in the test

section of around 0.05%. During part of our study period, a

net of 15 9 15 mm mesh made from 0.7 mm diameter

nylon thread was installed near the outlet of the contrac-

tion, and this would, of course, introduce a substantial

amount of turbulence. Some of our measurements were

made with the net in place, and some with it removed, so

that we could check for any effects. We checked the cali-

bration of the wind speed display against an Airflow

MEDM-500 micromanometer and pitot-static tube, and

detected no discrepancies between the displayed reading

and the true air speed with or without the net.

Air density

The wind tunnel is situated 688 m above sea level, and there

was no extreme weather during our 36-day study period in

October to November 2010. There were some temperature

fluctuations when the tunnel was started up each day,

because part of the circuit was inside a heated building, with

the settling section and part of the contraction in an unhe-

ated shed outside. Once the air was mixed, the temperature

in the tunnel settled at a value between the ambient tem-

perature outside the building and the internal room tem-

perature. We read the tunnel temperature and the ambient

barometric pressure at the beginning and end of each flight

from the main monitor display, and used the average of the

two resulting values of the air density when calculating the

bird’s body drag coefficient from Eq. 4. This was done

separately for each flight. The mean air density in the tunnel

was 1.121 kg m-3 ± SD 0.013 kg m-3. This corresponds

to a density altitude of 933 m, slightly higher than the

elevation above sea level of the wind tunnel site, meaning

that the mean air density observed during our project was

below the value expected in the International Standard

Atmosphere. The kinematic viscosity corresponding to the

observed mean density altitude was 1.56 9 10-5 m2s-1

(Pennycuick 2008), and this value was used for estimating

Reynolds numbers (Eq. 2).

Stroboscope observations

Wingbeat frequency was measured with a stroboscope

based on a pair of liquid–crystal shutter glasses, which were

driven by an RC oscillator that made both shutters ‘‘open’’

(clear) for one-sixteenth of each cycle period and ‘‘closed’’

for the remainder of the cycle. Details of the stroboscope

and its calibration, including a circuit diagram, can be

downloaded from http://books.elsevier.com/companions/

9780123742995. If the shutter frequency was near but not

equal to the wingbeat frequency, the observer would see the

bird at a slightly different phase in successive wingbeat

cycles, so that the wings appeared to move slowly up and

down. The observer then adjusted the stroboscope fre-

quency until the wings appeared to stop, and the frequency

was recorded from the display to a nominal precision of

0.01 Hz. The inherent precision of the measurement was

derived from a 4 MHz crystal.

Our observation procedure involved taking six obser-

vations of wingbeat frequency at each of eight wind speeds,

i.e. 48 measurements in a period that never exceeded

15 min. This was easily achieved with the stroboscope,

although it would have been impracticable with video.

Also, video has insufficient precision for measuring

wingbeat frequency in this type of experiment, because the

variation of wingbeat frequency is small (although con-

sistent), and a video measurement is based on timing a

series of wingbeats to the nearest whole wingbeat by

counting frames. The precision in this case depends on

identifying the same phase of the cycle in the first and last

wingbeats, effectively discarding information from inter-

vening wingbeats. Wingbeat irregularities are apparent to

the stroboscope operator and can be avoided, but they are

difficult to detect from video.

An inherent limitation of the wingbeat-frequency

method is that each estimate of the body drag coefficient

requires a complete set of wingbeat-frequency measure-

ments, from the lowest to the highest speed at which the

bird will fly, spanning the range of available Reynolds

numbers. It is therefore not possible to use this method to

study the effect of varying the Reynolds number on the

drag coefficient, or to look for the classical hysteresis

effects described by Schmitz (1960).

Harness and dummy transmitters

The harness followed a design by Rappole and Tipton (1991)

consisting of a small rectangular pad (18 9 17 mm) for

mounting dummy transmitters and leg loops at the sides

made of elastic tubing. This harness was recommended for

starlings by Woolnough et al. (2004) as preferable to glued

backpack or tail-mount designs. The side loops were slipped

around the bird’s legs to install or remove the harness, and

we added a layer of Velcro loops to the top surface of the pad

for the quick attachment and removal of dummy transmit-

ters. The harness pad with the Velcro stood up 6 mm from

the bird’s back, and the three transmitter shapes tested added

J Ornithol (2012) 153:633–644 637

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a further 9 mm above the back. The three shapes were a

simple rectangular block (box 1), an identical block with

added nose and tail fairings (box 2), and a block with an

antenna made from 1.5 mm diameter aluminium tube, pro-

jecting upwards and backwards at 45� (box 3). The five

payload configurations tested are shown to scale in Fig. 1,

and their masses and dimensions are listed in Table 2.

Results

Drag coefficient estimates

Figure 2 shows two curves of wingbeat frequency versus

true air speed from the same bird on different days. In one

curve, the bird was ‘‘clean’’, i.e. without a harness, while in

the other it was wearing a harness with box 1 (rectangular

block) attached. Each of the eight points in each curve

represents the mean of six stroboscope readings, with a

nominal precision of 0.01 Hz, and the vertical bars are the

standard errors. Each curve required 10–15 min of con-

tinuous flight, and 89 curves of this type were obtained

from three birds during the 36 days of the project. Fifty-

nine of these are represented in Fig. 1. The remaining 30

were rejected, either because we were unable to estimate

Vmp owing to excessive scatter or anomalies caused by

unsteady flight (below), or because the flights referred to

further types of dummy transmitters that were dropped

following preliminary tests.

Each curve was analysed using the multiple regression

method given by Bailey (1995) to fit an equation of the

form

f ¼ Aþ B1=V þ B2V3; ð7Þ

through the eight observations of mean wingbeat

frequency, where A, B1 and B2 are regression constants, f

is the measured wingbeat frequency, and V is the true air

speed. This is a generic bird power curve (Pennycuick

2008). The speed at which it passes through a minimum is

an estimate of Vmp, given by

Vmp ¼ B1=3B2ð Þ1=4: ð8Þ

In the example shown in Fig. 2, the effect of adding the

harness and box 1 was to raise the high-speed end of

the curve more than the low-speed end, so shifting the

minimum-frequency speed downwards. The minimum-

frequency speed from Eq. 8 served as an estimate of the

minimum-power speed (above), and this was used in turn to

estimate Cdb, the drag coefficient of the composite body,

made up from the bird’s body plus the added harness and

dummy transmitter. The estimates of the body drag

coefficient that were obtained from Eq. 4 for five different

configurations are summarised in Table 3 and Fig. 1.

Drag coefficient of the clean bird body, and with added

hardware

The mean of 20 estimates of the ‘‘clean’’ body drag coef-

ficient (i.e. with no harness or box) was 0.116

(SD ± 0.0394). This is a little higher than the value of

0.080 found earlier for both a Teal and a Thrush Nightin-

gale in the Lund wind tunnel (Pennycuick et al. 1996), but

we do not propose to change the default value for the body

drag coefficient in the Flight program (0.10) because of

probable upward bias in the present experiment due to

unsteady flight behaviour (below).

0

0.1

0.2

0.3

Dra

gco

effi

cien

t

N=20 19 6

P<<0.001

P<<0.001

Clean

Harness only

Box 1 Box 2

Box 3

Not sigNot sig

7 7

0 20 6040 80 100 mm

Fig. 1 Scale drawings of the five payload configurations in frontal

view with the bird’s frontal profile (top) and in side view (bottom).

The box measurements are in Table 2. The points show the drag

coefficients and their standard deviations, measured for each config-

uration, from Table 3

6 7 8 9 10 11 12 138

9

10

11

True Air Speed m/s

Win

gbea

tfre

qH

z

9.04 m/s

7.65 m/s

= 0.157Db

C = 0.285Db

Clean

Harness+ Box 1

C

Fig. 2 Two curves of wingbeat frequency versus true air speed from

the same bird (B) on different days. Each point is the mean of six

stroboscope observations, with standard error bars. Circles: clean, i.e.

with no payload. Crosses: with harness and box 1 (see Fig. 1). The

minimum in each curve is an estimate of the bird’s minimum-power

speed (Vmp), and is the basis of the drag coefficient estimate

638 J Ornithol (2012) 153:633–644

123

When the harness was installed, with its Velcro pad

standing 6 mm above the surface of the back, the mean of

19 measurements of Cdb rose to 0.167 (SD ± 0.0519). This

differed significantly (P \ 0.001) from the clean Cdb esti-

mate, according to a t-test for the means of two small

samples given by Bailey (1995).

The addition of box 1, a rectangular balsa-wood block

which stood up a further 9 mm above the top of the harness

pad, made no significant difference to the drag coefficient

of the composite body when compared to the harness alone.

Neither did box 2, which was identical to box 1 but with

added streamline fairings at the front and back ends. Box 3

was also identical to box 1 but with the addition of an

antenna, and this raised the drag coefficient to 0.225 (SD

0.0638, N = 6), which differed significantly (P \ 0.001)

from the ‘‘harness-only’’ value. These findings are sum-

marised in Fig. 1 and Table 3.

Reynolds number

Reynolds numbers were calculated using a fixed value of

43 mm for the body diameter. This is the diameter of a

circle with the same area as the body frontal area from

Eq. 5 (shown to scale in Fig. 1). Using this as the reference

length, and a value of 1.56 9 10-5 m2s-1 for the kinematic

viscosity of air, the Reynolds number in each flight varied

from about 17,000 to 40,000. Vmp was typically at a Rey-

nolds number of around 25,000 to 30,000. Reynolds

numbers for the wings were about 45% higher, being based

on the mean chord.

Effect of upstream net

In the case of ‘‘clean’’ and ‘‘harness-only’’ configurations,

we had enough data to compare the drag coefficients with

and without the upstream net, which would have

introduced an unknown amount of small-scale turbulence

into the air stream. We observed significant differences for

both configurations, but in opposite directions (Table 4).

Flight behaviour

As our birds had been trained to keep flying, but not to hold

a steady position in the test section, their appearance

through the stroboscope showed variations from the pattern

described above. A common variant was for the wing to

appear momentarily stationary but to jump between dif-

ferent positions, meaning that the phase suddenly shifted,

probably due to a momentary pause during the upstroke. It

was still possible to set the stroboscope if the bird did this,

but if the bird started to move erratically about the test

section, the scatter in the frequency measurements became

excessive. We minimised this by selecting three birds that

often flew steadily for periods of a few seconds at a time,

and preferred to fly at the upstream end of the test section,

where they could be observed at close range through the

plexiglass wall. In this position, the birds often flew with

the head turned to one side, watching the trainer who stood

by the gap at the downstream end, and they also often flew

with the feet partially lowered, especially at low speeds.

Our best bird (B), who was responsible for more than half

of our observations, happened to moult his body feathers in

the middle of our study period, which resulted in a some-

what tousled appearance for a few days. All of these

variations would be likely to bias the drag coefficient

estimates upwards.

As noted above, deviations from steady flight may

invalidate our basic assumption that the minimum-fre-

quency speed and the minimum-power speed are one and

the same, and one particular form of unsteady flight biased

the observations in an unexpected way. One of our birds

(C) sometimes, but not always, flapped intermittently,

Table 3 Observed drag coefficients (Cdb) of the composite bird’s

body, including payload

Payload Mean Cdb SD N

Clean (no payload) 0.116 0.0396 20

Harness only 0.167 0.0519 19

Box 1 (square ends) 0.172 0.0542 7

Box 2 (box 1 ? fairings) 0.177 0.0729 7

Box 3 (box 1 ? antenna) 0.225 0.0638 6

Testing difference between t Deg. freedom P

Clean versus harness only 14.83 37 \0.001

Harness only versus Box 1 0.738 24 Not sig

Harness only versus Box 2 1.24 24 Not sig

Harness only versus Box 3 7.22 23 \0.001

t-Tests follow Bailey (1995)

Table 4 Effect of upstream net on body drag coefficient

Payload Clean (no harness) Harness only

With net

Mean drag coefficient 0.108 0.223

Std dev. drag coeff. 0.0384 0.0397

N 11 4

Without net

Mean drag coefficient 0.127 0.152

Std dev. drag coeff. 0.0407 0.0445

N 9 15

Difference between means

t 3.205 8.723

Degrees of freedom 18 17

P \0.01 \0.001

J Ornithol (2012) 153:633–644 639

123

alternately gliding and dropping back to the downwind end

of the test section, and then flapping extra hard to get back

to the upwind end. This behaviour invalidates the basic

wind-tunnel assumption that the bird’s air speed is the

same as the wind speed. Also, the stroboscope could only

be used while the bird was flapping, and it was then flying

faster than the wind speed, thus biasing the observed

wingbeat frequency upwards. However, the bird only did

this at medium speeds, where it had muscle power to spare.

At low and high speeds, where more power was required, it

flapped steadily. The result was that the curve was biased

upwards in the middle, but not at the ends, sometimes

resulting in an inverted frequency curve, with a maximum

instead of a minimum. We were unable to get a drag

coefficient estimate if this happened, or if the scatter of the

points was so large that we could not identify a minimum

in the wingbeat frequency, within the range of speeds that

we tested.

Discussion

Implications of the results

Our results indicate that the addition of the harness pad by

itself, which only projected 6 mm above the bird’s back,

was enough to trigger a highly significant increase in the

body drag coefficient, but the addition of boxes (faired or

not) projecting a further 9 mm above the pad did not result

in a further significant increase in the drag coefficient. This

suggests that the pad triggered separation of the boundary

layer over the posterior end of the body, over an area that

stayed much the same when additional boxes were added,

although the addition of a sloping antenna caused a further

increase in the drag coefficient.

This does not, of course, mean that the drag stayed the

same when we added a box to the harness. The drag coef-

ficient stayed the same, meaning that the drag would be

proportional to the total frontal area, provided that the speed

and air density remain constant (Eq. 1). Bowlin et al. (2010)

observed a ‘‘significant’’ increase in drag when they

attached a box to the back of a stuffed swift, approximately

matching the increase in frontal area, but they did not cal-

culate the drag coefficient. Our drag coefficient calculation

takes account of the added frontal area, and so does the

migration range calculation in the Flight program (below).

The boundary layer over a feathered surface

It has been known for some years that the boundary layer

will not remain attached to a frozen bird body in a wind

tunnel, even at Reynolds numbers as high as 100,000,

whereas there are no signs of boundary layer separation in

living birds at much lower Reynolds numbers (Pennycuick

et al. 1996). A smoothly streamlined outer shape, faired by

the body contour feathers, is typical of even the smallest

birds, which fly (at Vmp) at body Reynolds numbers below

8,000. Streamlining would serve no useful function if the

boundary layer did not remain attached at these small

scales, and indeed large insects, which fly at Reynolds

numbers in the same range, do not have such smoothly

faired body shapes. Lowson (2012) has proposed a way in

which the feathered surface could inhibit boundary-layer

separation on the upper surface of the bird’s wings by

preventing reversed flow along the surface in regions where

the pressure gradient is reversed, and his explanation, if

correct, would also apply to feathered bodies. It might be

possible to test this by the same method that we used here,

measuring the body drag coefficient with and without an

elastic jacket, which would prevent the feathers from lift-

ing up in reversed flow without altering the bird’s external

body shape. Such an experiment would require more con-

sistent measurements than we were able to achieve, but

might be achievable with birds that were trained to hold

their position and speed more steadily in the test section.

Application of the results to range calculations

Although it is obvious that adding to a bird’s body drag is

likely to impair its flight performance, a formal theory is

needed to link our drag coefficient measurements with

practical estimates of migration range. The range calculation

has been understood in its simplest form since the early days

of aviation (Breguet 1922), for an aircraft that uses only one

type of fuel and whose external shape remains the same as the

fuel is used up. However, birds differ from aircraft in that

they use fat as the primary fuel, but they also consume some

protein as a secondary fuel with a lower energy density

(Lindstrom and Piersma 1993). It is impractical to modify the

original theory to take account of this complication in a

simple ‘‘range equation’’ for birds, but it is straightforward to

simulate a migrating bird by a numerical computation that

can incorporate alternative hypotheses as to how the con-

sumption of flight muscles and other body components is

actually implemented. This approach has been described in

detail elsewhere (Pennycuick 2008; Pennycuick and Battley

2003). It is implemented in the ‘‘time-marching’’ numerical

computation used in the program Flight 1.23, which can be

downloaded free from http://books.elsevier.com/compan

ions/9780123742995.

Migration range in terms of energy height and energy

gradient

The range calculation can be simplified by splitting Breg-

uet’s (1922) original range equation into two components,

640 J Ornithol (2012) 153:633–644

123

the energy height at which the bird starts migrating, and the

energy gradient at which it descends from its initial energy

height. A bird’s energy height at any point in a flight is the

height to which the bird would be lifted if all of its

remaining fuel energy were converted progressively into

potential energy. The energy height is a logarithmic func-

tion of the fuel fraction, meaning the ratio of the mass of

usable fuel to the bird’s all-up mass, which includes the

mass of any added hardware. The definition of energy

height also takes into account the energy density of the

fuel, the strength of gravity, and the efficiency with which

the bird’s muscles convert fuel energy into work (Penny-

cuick 2003, 2008). The birds’ use of protein as a supple-

mentary fuel complicates the calculation of energy height,

but Flight 1.23 calculates it automatically during data

entry, and displays it on the main setup screen.

The energy gradient is identical to the quantity known to

engineers as the effective lift-to-drag ratio for the whole

bird. It is a measure of the bird’s aerodynamic efficiency,

and is calculated routinely by Flight 1.23. The body drag

coefficient, measured in our experiments, is one of its

major components.

Computed example for a particular bird

The range calculation is not a statistical procedure. It

applies to an individual bird, not to a sample or a popu-

lation, and it requires physical information about the bird,

including its wing measurements. We will illustrate the

effects of an external payload on the initial energy height

and on the energy gradient of a particular Barnacle Goose

(Branta leucopsis) whose spring migration was tracked in

2008 (Pennycuick et al. 2011). Its wing span and area were

measured, and its mass and fat fraction at departure were

estimated for input to the program (Table 5). The input

information for Flight 1.23 can optionally include the mass

of a ‘‘payload’’ to represent crop contents or a transmitter,

and a payload ‘‘drag factor’’, which is a multiplier for the

body drag coefficient. The default value for the drag factor

is 1.0, meaning that although the payload increases the

frontal area, it does not affect the drag coefficient. Figure 1

and Table 3 indicate that the payload drag factor was about

1.4–1.5 when we added a harness pad to our starlings, with

or without a box, and over 1.9 if we added a box with an

antenna. These estimates have a direct interpretation in

terms of the air flow around the body (above), and can be

transferred to other species. The effect of the transmitter on

the goose’s body drag coefficient was unknown, so we tried

hypothetical values of 1.0 (no effect), 1.5 and 2.0, as we

saw in the starlings.

The results of four program runs are summarised in

Table 6 and Fig. 3. The effect of adding a 70 g payload, in

the form of a satellite transmitter and harness, is to increase

the all-up mass by 70 g, leaving the fat mass unchanged, so

that the fat fraction (ratio of fat mass to all-up mass) is

reduced from 0.290 to 0.282. This in turn reduces the

starting energy height (which is a logarithmic function of

the fat fraction) by 13 km, from 349 to 336 km. The

transmitter increases the body drag by a small amount

because its frontal area is added to that of the body, but if

the drag coefficient is assumed to be unchanged at the

default value (0.1), the effect of the added frontal area on

the energy gradient is barely perceptible. The energy height

curve comes down nearly parallel to the no-payload curve,

but as the starting energy height was lower, the range when

the energy height reaches zero (fuel finished) is about 5%

less than without the payload.

If the presence of the payload box triggers separation of

the air flow over the back, the effect would be to increase

the drag coefficient of the combined body and payload.

This is shown in two further curves in Fig. 3, which start

from the same initial energy height but descend more

steeply. If the body drag coefficient is increased by a factor

of 1.5 or 2.0, as seen in our experiments on starlings, the

range is reduced to 78 and 68% of its original value,

respectively, without the payload. These estimates take into

account both the loss of energy height due to the payload

mass, and the steepening of the energy gradient due to

separation of the air flow, but for a long flight, an increase

in the drag coefficient clearly has a larger effect than the

loss of energy height due to the added mass.

The calculated lines in Fig. 3 are nearly but not quite

straight. The program assumes that the bird is capable of

flying no faster than 1.2 Vmp at departure because it is

heavily laden with fat, and this is below Vmr, the speed for

maximum lift-to-drag ratio. Therefore, the gradient is

Table 5 Data for Barnacle Goose DLT from Pennycuick et al.

(2011)

Initial body mass 2.33 kg

Initial fat fraction 0.290

Initial energy height 349 km

Wing span 1.35 m

Aspect ratio 8.14

Body drag coefficient 0.10

Table 6 Energy gradients from Fig. 3

Payload

mass

Payload

drag

Energy

height

Energy

gradient

Overall

(g) factor (km) Start Fuel finished

None 1.0 349 12.6 15.9 15.5

70 1.0 336 12.5 15.8 15.4

70 1.5 336 10.2 12.9 12.6

70 2.0 336 8.9 11.3 11.0

J Ornithol (2012) 153:633–644 641

123

initially steeper than it becomes after the first few hundred

kilometres, when some fuel has been used up, and the

speed has been allowed to build up to Vmr (which has itself

come down a little). The gradient continues to flatten very

gradually after the bird is able to track Vmr, because the

consumption of fat and muscle tissue leads to a reduction

of frontal area, which in turn reduces the body drag, and

increases the lift-to-drag ratio. Variations on these

assumptions can be selected when the program is run, to

see what assumptions best account for field observations.

Obviously, the energy gradient depends on the wing mor-

phology as well as on the body drag, and it is not possible

to do valid range calculations that do not take wing mea-

surements into account.

Reserves for laying eggs

On reaching the nesting area, the remaining fuel reserve is

available for energy-intense activities related to nesting,

and in the case of female birds, that includes laying eggs.

As a rough approximation, an egg can be regarded as a

fixed fraction of the bird’s body mass, and hence the

number of eggs that any bird can lay would be roughly

proportional to its fat fraction at the start of laying. The

energy height on arrival in the breeding area is also directly

related to the fat fraction, and may thus serve as an indi-

cator of the number of eggs that the bird is able to lay. If

the number of eggs is limited by other considerations, then

the energy height becomes a measure of the reserve left

over after the clutch is complete, which is then available

for such activities as territorial defence and dealing with

predators. Energy height is a better measure of reserves

than energy as such, because the amount of energy needed

to lay an egg is obviously larger if the egg is larger, as it

usually is in a larger bird.

The addition of an external backpack box is likely to

reduce the energy height available on arrival, not only

because of the reduction in initial energy height due to the

payload mass, but also because of the steeper energy gra-

dient due to the added frontal area, possibly exacerbated by

an increase in the body drag coefficient. The vertical line in

Fig. 3 at 1,000 km from the start is approximately the

distance that the Barnacle Geese have to fly on the second

leg of their migration from the stopover area in Norway to

the nesting areas in Spitsbergen, and the numbers in the

top-left quadrant of the graph show estimates of the Bar-

nacle Goose DLT’s remaining energy height on passing the

1,000 km point with the same four payload configurations

considered above. In this scenario, which is presumably

much the same for a female goose, the effect of the payload

mass by itself is to reduce the arrival energy height by

about 5%; increasing the payload drag factor from 1.0 to

1.5 increases the energy-height penalty to about 10%, and

increasing it to 2.0 makes the penalty about 15%. The line

for payload mass alone is lower than the line for no payload

but nearly parallel to it, so that the absolute loss of energy

height does not change much for a longer flight (i.e. if the

vertical destination line is moved to the right). However,

the other two lines diverge downwards, meaning that the

energy-height penalty due to an increased drag coefficient

continues to increase as long as the bird keeps flying. For a

flight of 2,500 km, a payload that doubles the body drag

coefficient could reduce the arrival energy height to half of

the value that it would have without the payload, while the

proportional loss due to the mass of the payload is much

smaller.

Connecting experimental results with migration theory

The physiological experiments of Engel et al. (2006) and

Schmidt-Wellenburg et al. (2008) were intended to shed

some light on migration performance, and the results of their

extensive statistical analyses could indeed be used to predict

the migration range of Rose-coloured Starlings (only) flying

under the same conditions as prevailed in the Seewiesen

wind tunnel during the experiments. However, these purely

empirical studies cannot be transferred to other species, or

even to the same species flying in different conditions, for

instance at a higher altitude. A theoretical framework is

needed to do that, and the underlying theory is mechanical,

not physiological. The chemical power depends on such

mechanical quantities as the bird’s wing span and the air

density, which have to be known before empirical

0 1000 2000 3000 4000 50000

100

200

300

Air distance flown (km)

Ene

rgy

heig

htre

mai

ning

(km

)

68% 78% 95%

100%Payload 70gDrag factor 1.5

Payload 70gDrag factor 2.0

No payload

Payload 70gDrag factor 1.0

Overall gradient

11.0 12.9 15.8

15.9

276 km263 km

248 km235 km

Fig. 3 Energy height versus air distance flown by a migrating

Barnacle Goose, using data from Pennycuick et al. (2011), showing

the reduction in range caused by the mass of a transmitter that does

not increase the body drag coefficient (Cdb), and by the same

transmitter if it increases Cdb by factors of 1.5 or 2.0. The numbers at

top left are the energy height remaining when the bird passes

1,000 km (vertical line), which is roughly the distance that Barnacle

Geese have to fly from their spring stopover area to their nesting area.

Curves calculated by Flight 1.23

642 J Ornithol (2012) 153:633–644

123

measurements of fuel consumption can be related to a gen-

eral body of theory. Unfortunately, these details were not

mentioned by Engel et al. (2006) or Schmidt-Wellenburg

et al. (2008), but we can approximate them now, as we have

wing spans from four of the same Rose-coloured Starlings

that they used (all between 360 and 370 mm), and a sample

of air densities measured in the Seewiesen wind tunnel

which averaged 1.121 kg m-3 (above).

In one of their graphs, Schmidt-Wellenburg et al. (2008)

plotted the measured chemical power against the body

mass of their birds, which varied between individuals and

also from day to day. Their graph showed a cloud of 57

points, which we have enclosed within the tinted polygon

in Fig. 4, but they did not have ‘‘expected’’ values of the

power to compare their measurements with. The two lines

in Fig. 4 show expected values calculated from Flight 1.23

for one of our starlings (bird B) using default values for

input variables, including Cdb = 0.10 for the body drag

coefficient. They show how this individual’s chemical

power would be expected to vary if his body mass were to

change through the full range shown by Schmidt-Wellen-

burg et al. (2008). The lower line shows the power at the

minimum-power speed (Vmp), while the upper one is the

power at the maximum-range speed (Vmr). For reasons

explained by Pennycuick (2008), the power cannot be

below the lower line and it is unlikely to be above the

upper one; in other words, we expect the measured points

to lie between the two lines, but they are actually above

both lines. This could be because the theory underestimates

the power, but more probably the main reason was that the

measured power was biased upwards.

The calculated curves of chemical power in Fig. 4 are

based on the assumption that the bird is flying steadily

along at a constant speed without gaining or losing height,

but our starlings only did that for short periods of time.

Over longer periods, they moved about the test section,

often showing cyclic behaviour in which they moved for-

ward and back, or up and down, or from side to side.

Physiologists also note this, but do not attach any impor-

tance to it, assuming that it makes no difference to the

measured power, whether the bird is flying steadily or

doing cyclic or irregular manoeuvres. We do not know for

certain whether these continual manoeuvres require more

power on average than steady, unaccelerated flight, but it

seems likely that they do, and some other ways in which

irregular flight behaviour might have biased the power

upwards (if we had been measuring it) were noted above.

Besides these direct effects, the catching and handling

required for such methods as doubly labelled water must

inevitably introduce an additional expenditure of chemical

energy, which cannot be distinguished from the energy

actually required for locomotion.

Alternative power measurements in wind tunnel

experiments

The effect of irregular flight behaviour on chemical power,

measured by such methods as oxygen consumption or

doubly labelled water, can only be investigated by training

a bird to fly steadily for a matter of hours, due to the time

required for metabolic processes to settle into a steady

state. This is difficult, and has rarely (if ever) been

achieved. The mechanical power, i.e. the rate at which the

bird does mechanical work with its wings, does not involve

metabolic processes, and may provide a better route for

linking experimental results to migration performance. It

is, of course, also affected by irregular flight, but can be

measured in a much shorter period of steady flight than is

needed for any physiological experiment. In principle, the

video method of measuring mechanical power (Pennycuick

et al. 2000) only requires the bird to fly steadily in a fixed

position for a few seconds, which can be achieved by

conditioning the bird using small food rewards. Whatever

method is used to measure power (mechanical or chemi-

cal), the underlying theory is the same, and provides the

link between wind tunnel observations and the life of the

bird in the wild. The link is broken if flight conditions in

the wind tunnel are not as assumed, or if quantities that are

central to the theory—such as wing measurements and air

density—are not recorded.

Acknowledgments We thank J. Lesku, D. Martinez-Gonzales and

the Max Planck Institute for Ornithology for their hospitality, support

and advice. We also gratefully acknowledge support from the

40 50 60 70 80 90

0

2

4

6

8

10

Body mass (g)

Che

mic

alpo

wer

(W)

Power at Vmr

Power at Vmp

Schmidt-Wellenburg et al2008

Fig. 4 Measurements of chemical power from Schmidt-Wellenburg

et al. (2008) for Rose-coloured Starlings whose body masses varied

between 55 and 88 g (tinted polygon), compared with estimates for

one of our birds over the same mass range that was flying at the

minimum-power speed (lower curve) and the maximum-range speed

(upper curve). Curves were calculated by Flight 1.23

J Ornithol (2012) 153:633–644 643

123

W. Garfield Weston Award for Northern Research, Universite du

Quebec a Rimouski, Centre d’etudes Nordiques, and thank J. Bety, M.

Fast and S.A.Pennycuick for assistance and helpful comments.

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