Metabolic power of European starlings Sturnus vulgaris during flight in a wind tunnel, estimated from heat transfer modelling, doubly labelled water and mask respirometry

Flight is the most energetically demanding, sustained activity that animals perform (Schmidt-Nielsen,1972; Norberg,1990). Each of the existing methods for estimating metabolic power during flight (P_met) has some drawbacks as well as advantages. Mask respirometry during flight in a wind tunnel (for references,see Rayner, 1994; Ward et al., 2001, 2002) is the only direct way to measure the rate of gas exchange, from which one can calculate P_met. However, this technique has the disadvantage that while being precise, P_met for an unencumbered bird is overestimated by 3–30% due to the additional work required to overcome the drag of the respirometry mask and tube(Tucker, 1972; Rothe et al., 1987; Ward et al., 2001, 2002). Doubly labelled water(DLW) is most useful for measuring the cost of long flights (e.g. Wikelski et al., 2003), but cannot resolve short-term variation in flight costs. Monitoring heart rate can provide information on short-term fluctuations in metabolism, but this method requires calibration against respirometry measurements before variation in metabolic rate can be quantified (Butler et al., 1998; Weimerskirch et al., 2001; Ward et al.,2002). P_met can also be inferred from the rate of mass loss during flight, which is simple to measure, but produces results that are prone to error since the energy content of mass changes is difficult to assess accurately (Nisbet et al.,1963; Butler et al.,1998; Kvist et al.,1998; Battley et al.,2000).

An alternative approach to estimating the energetic cost of flight is to determine mechanical power production for flight (P_mech)from an aerodynamic model (Rayner, 1979a,b; Pennycuick, 1989), direct measurements of the mechanical work performed by muscles during flight(Dial et al., 1997; Williamson et al., 2001; Tobalske et al., 2003) or from wake vorticity (Spedding et al.,2003). In principle, one can then readily predict P_met from P_mech using the efficiency with which the animal performs the mechanical work required for flight. However, such calculations could be in substantial error in practice because P_mech forms a small, but poorly known, proportion of P_met (between 7 and 9% with differences between species,flight speeds and individual birds; Norberg et al., 1993; Masman and Klaassen, 1987; Chai and Dudley, 1995; Ward et al., 2001; Kvist et al., 2001). Any inaccuracy in either P_mech or the value of whole animal efficiency (E_w, defined as P_mech/P_met) is therefore magnified in the estimated P_met.

We explore the suggestion (Ward et al.,1999) that it may be possible to measure the energetic cost of flight using a novel approach: quantification of heat production(P_heat) by heat transfer modelling. The majority of P_met is lost as heat due to the low conversion efficiency of chemical to kinetic energy in the flight muscles(Hill, 1938). Thus any errors in the assumed value of E_w will have a relatively small influence on P_met. Thermal imaging equipment allows measurement of radiative heat transfer and surface temperature from unrestricted animals during flight(Lancaster et al., 1997; Speakman and Ward, 1998; Ward et al., 1999). The metabolic rate of stationary animals has previously been modelled using heat transfer theory by assuming that an animal is a series of simple geometric shapes. For example, Williams(1990) used surface temperature measured by infrared thermography and heat transfer rates from plates and cylinders to calculate that the metabolic rate for an African elephant Loxodonta africana was only 6% lower than the allometric prediction based upon the animal's mass. However, relationships used to calculate heat loss during flight will differ from those that apply to stationary animals since convective heat transfer during flight occurs by forced convection, due to the movement of the animal through the air, while free convection will predominate in animals that are not moving(Holman, 1986).

In the present study, we compared estimates of the energetic cost of flight determined by heat transfer modelling with those obtained by two independent techniques (DLW and mask respirometry). We collected data using all three techniques from European starlings Sturnus vulgaris (hereafter referred to as starlings) that we trained to fly in a wind tunnel at speeds between 6 and 14 m s^–1. Previous studies have suggested that flight cost estimates may be technique-dependent(Masman and Klaassen, 1987; Pennycuick, 1989; Rayner, 1990). We examine whether this is the case when the same individuals fly under the same conditions, to test whether the apparent discrepancies between previous studies are due to biological variation in the energetic cost of flight,rather than being an artefact of the technique used to make the measurement. This is the first comparison of the results of three independent measurement techniques used with the same birds when flying under the same conditions. Our results therefore allow cross-validation of all the measurement techniques as well as permitting evaluation of heat transfer modelling as a novel method for measuring P_met.

We trained four adult female starlings (captured under licence from Scottish Natural Heritage in Aberdeenshire, UK) to fly in a closed section Göttingen-type variable speed wind tunnel at the University of the Saarland, Germany (Biesel et al.,1985; Ward et al., 1999, 2001). During collection of thermal images, the glass side wall of the flight section of the wind tunnel was replaced by a wooden panel with an opening that was filled by the lens of the thermal imager. The birds were trained to fly in the wind tunnel for 6–10 months before collection of the data that we report here. We used the equivalent air speed in the wind tunnel(Pennycuick et al., 1996) as the flight speed during each experiment. Since we could not control air temperature or atmospheric pressure, flight speed could vary by up to±0.2 m s^–1 from the intended 1.0 m s^–1 increments. The order of the speeds (6–14 m s^–1) at which each bird was flown was randomised.

We used DLW (Lifson and McClintock,1966; Nagy, 1983; Speakman, 1997) to measure the rate of carbon dioxide production(V̇_CO2) over 5.86±0.05 h (N=30), which included two flights in the wind tunnel of 1 h duration. The V̇_CO2 during 75±5% (N=30) of the time that the bird was not flying was measured by open circuit respirometry (Table A1 in Appendix; see supplementary material). The V̇_CO2 when the bird was neither in the wind tunnel nor the respirometry chamber was assumed to be double the mean value while in the respirometry chamber.

We injected the birds intraperitoneally with isotopically enriched water(0.217±0.001 g of an isotope mix consisting of 54 APE (atom percent excess) H₂¹⁸O and 33 APE ²H₂O (MSD Isotopes, Quebec, Canada). The birds were returned to the aviary for 60±2 min (N=30) while the isotopes equilibrated before taking the initial blood sample (100–200 μl) from the femoral vein. The birds were then placed in a darkened respirometry chamber (0.17 m×0.17 m×0.17 m) for 53±1 min at 15±1°C before transfer to the wind tunnel, where they flew for 1 h. The bird was allowed to drink for 10 min before transfer back into the respirometry chamber for a further 123±1 min. The final blood sample was taken after a second 1 h flight at the same speed (±0.2 m s^–1) as the first flight. The bird was weighed (to ±0.1 g) immediately after taking the initial blood sample and before and after each flight. A blood sample was also taken prior to each injection of the isotopes to determine the background levels of ²H and ¹⁸O. We measured the enrichment of the labelling isotopes using gas source isotope ratio mass spectrometers (Optima, Micromass IRMS, Manchester, UK) following vacuum distillation(Nagy, 1983), and small sample equilibration with carbon dioxide for ¹⁸O(Speakman, 1997) and reduction to hydrogen gas with LiAlH₄ for ²H(Ward et al., 2000).

We calculated the ¹⁸O and ²H enrichments of the injectate, the elimination rates of ¹⁸O (k_o)and ²H (k_d) and the ¹⁸O and ²H dilution spaces (N_o and N_d by the plateau method) following Speakman(1997) (Appendix; see supplementary material). We calculated V̇_CO2 from equation 36 of Lifson and McClintock(1966) using a dedicated computer program that took into account changes in the volume of the body water pool associated with changes in mass during experiments(http://www.abdn.ac.uk/zoology/jrs.htm; Speakman, 1997).

We used a paramagnetic oxygen analyser (Taylor Servomex OA184, Crowbourgh,UK) and an infra-red carbon dioxide analyser (Hartmann and Braun URAS MT,Frankfurt, Germany) to measure the concentrations of oxygen and carbon dioxide in excurrent air while the bird was in the respirometry chamber. We used a customised BASIC program running on a microcomputer to sample gas analyser output at 30 Hz and stored the mean of 900 observations twice each minute. We used a wet test gas flow meter (Wrights DM3A, Zeal, London, UK) to measure the flow rate of gases through the chamber. Gases from the chamber were dried with silica gel before and after passing through the flow meter. The gas analysers were calibrated daily by setting the zero points with oxygen-free nitrogen gas(Messer Griesheim, Krefeld, Germany), the span of the oxygen analyser with ambient air and the span of the carbon dioxide analyser with a gas mixture of known carbon dioxide content (1.85%, Messer Griesheim). V̇_CO2 was calculated from the proportional increase in the carbon dioxide content of the gases leaving the chamber attributable to the presence of the bird, multiplied by the flow rate (corrected to stpd). The rate of oxygen consumption (V̇_O2)was calculated from equation 3b in Withers(1977). The respiratory quotient (RQ) was calculated from V̇_CO2/V̇_O2. We estimated metabolic power during the part of the DLW measurement that the bird spent flying (P_met,DLW) using a RQ of 0.71(Torre-Bueno, 1977).

We filmed one of the birds (bird 15; Table 1) during stable flight to measure wing beat frequency, amplitude and fluctuation in the area of the wings during the wing beat cycle by stereophotogrammetric resection(Albertz and Kreiling, 1980). We obtained lateral and dorsal images taken simultaneously from near-perpendicular viewing angles during flight at approximately 1 m s^–1 increments in speed between 6 and 14 m s^–1 (Photo-Sonics Series 2000 16 mm-1Pl cameras, Burbank, CA,USA; 255 frames per second; shutter speed 1/1500 s; 16 mm Agfa XTR 250/XTS 400 colour negative film) (Möller,1998). We used two 16 mm film projectors (NAC Analysis Projector DF-16C; Stuttgart, Germany) connected with a synchronisation unit (NAC SYNC Conti Box) to project images on to a digitiser board (Kontron DK 1515 OP,Munich, Germany) using a silver-plated mirror. Both digitiser boards were connected to a PC (Intel Pentium II 266 MHz) and data was digitised using a customised program. We calculated wing beat frequency from the number of frames required to complete between 34 and 71 complete wing beats during periods when the birds flapped constantly and maintained station in the flight chamber. We determined wing beat amplitude from projected dorsoventral excursions of the wing tip over five consecutive wing beats. We measured wingspan from the maximum extension of the wings in the dorsal view during the downstroke. We calculated the fluctuations in wing area during flight at 6, 8,10 and 13 m s^–1 and used interpolation and extrapolation to determine the area during flight at 12 and 14 m s^–1. Wingbeat frequency, amplitude and wing span were measured at 6, 8, 10, 12 and 14 m s^–1. Details of the calculations are given in Möller(1998) and Ward et al.(1999, 2001).

We used an Agema Infrared Systems Thermovision 880 system (FlirSystems,Portland, OR, USA) with a 20° lens linked to a dedicated thermal imaging computer (TIC-8000) running CATS E 1.00 software to measure the intensity of radiation from starlings during wind tunnel flight. We used the software to calculate the surface temperature (T_s, measured to±0.1°C) of each section of the surface of the bird assuming an emissivity of 0.95 (Cossins and Bowler,1987). The principals by which the thermal imager measures radiative heat transfer and calculates T_s are explained in Speakman and Ward (1998).

We obtained thermal images from the same birds that were used in the DLW measurements during flights in the wind tunnel at approximately 6, 8, 10, 12 and 14 m s^–1. Thermal image collection and analysis followed Ward et al. (1999). We calculated the convective heat transfer coefficient (h), taking into account the build up of a thermal boundary layer as air flowed from the head to the tail of the bird (method 2 in Ward et al., 1999). We calculated fluctuations in air speed past the wings due to flapping by taking into account changes in air speed and wing area measured for one of the birds (bird 15) for six sections of the wing,which we divided into 10 strips along the wings at 50 steps in the wing beat cycle (Ward et al., 1999). The value of h for the legs was estimated from equations applicable to cross flow over isolated cylinders, taking into account the extent to which the legs were extended into the air stream (method 3 in Ward et al., 1999).

We calculated heat loss by evaporation using the relationship between air temperature and evaporative heat transfer for starlings during flight in a wind tunnel (Torre-Bueno,1978). We calculated overall heat transfer(P_heat) from the sum of heat transfer by radiation,convection and evaporation. We calculated metabolic power during flight from heat transfer (P_met,heat) from P_heat/(1–E_w). We assumed that E_w was 0.15 (the mean value determined for two of the birds in a previous study; Ward et al.,2001). We also examined the effects of varying E_w in the range 0.07–0.19.

We examined relationships between metabolic power and flight speed using linear regression and curves of the form P_met=αV^–1+βV³+γ,where V was flight speed (m s^–1). The latter curve describes the approximate power–speed relationship that is expected from aerodynamic models in which induced power is proportional to V^–1, parasite power (and profile power in some aerodynamic models) varies with V³, and basal metabolism(and profile power in some aerodynamic models) is constant (Rayner, 1979a,b; Pennycuick, 1989; Ward et al., 2001). When more than one form of relationship provided a significant fit to the data, we present the one with the highest coefficient of determination. We used general linear models analysis of covariance (GLM ANCOVA), with bird and measurement technique as factors and flight speed and air temperature as covariates, to analyse the effects of these variables upon P_met or upon heat transfer by radiation or convection. We included interactions between terms in our initial models and performed stepwise elimination of non-significant terms till only those that contributed significantly to the model remained. When the slopes of relationships did not differ significantly between birds, we used a common slope and common intercept to describe the relationship. We used Tukey's post-hoc multiple comparisons to test for differences between factors. We performed our statistical analyses following Zar (1996) and Winer(1971). Two-tailed tests of statistical significance were applied to all analyses. Differences where P<0.05 were regarded as significant. Regression coefficients are presented ± standard error (s.e.) and means ±standard deviation (s.d.). Mean values across birds are averages of the mean values for each of the birds.

Radiative heat transfer decreased with increasing air temperature(T_a), increased with flight speed (V) and did not vary between birds (GLM ANCOVA with T_a and V as covariates and bird as a factor: T_a, F_1,19=4.8, P=0.05; V,F_1,19=9.4, P=0.008; bird, F_3,19=1.4, P=0.3; radiative heat transfer=0.03±0.01V–0.03±0.01T_a+1.05±0.22). Radiation accounted for 8.6±0.1% of P_heat(N=20, Fig. 1). Convective heat transfer decreased with increasing T_a,increased with V, and did not vary between birds (GLM ANCOVA with T_a and V as covariates and bird as a factor: T_a, F_1,19=5.1, P=0.04; V,F_1,19=62.5, P<0.001; bird, F_3,19=1.0, P=0.4; convective heat transfer=0.50±0.06V–0.21±0.10T_a+6.40±1.64). Convection was the most important mechanism for heat transfer from flying starlings, representing 79.9±2.7% of P_heat(N=20, Fig. 1). Heat transfer by evaporation was 1.03±0.16 W (range 0.78–1.32 W, N=20) in the 15.6–23.2°C range in T_a at which we collected thermal images from starlings flying in the wind tunnel. Air temperature (and hence evaporative heat transfer) did not vary systematically between birds or with V (GLM ANCOVA with V as a covariate and bird as a factor: V, F_1,19=3.3, P=0.09; bird, F_3,19=1.2, P=0.3). Evaporation accounted for 11.6±2.3% of P_heat(N=20, Fig. 1).

Metabolic power calculated from heat transfer modelling(P_met,heat) increased linearly with flight speed(V) from 8.1±0.8 W at 6.0±0.1 m s^–1 to 12.4±1.2 W at 14.0±0.1 m s^–1 and did not vary between birds (GLM ANCOVA with V as a covariate and bird as a factor: V, F_1,19=50.2, P<0.001; bird, F_3,19=0.5, P=0.7, N=20, Fig. 1). The scatter in the DLW data and the uncertainty inherent in each measurement meant that although the best-fit line through the these data was a U-shaped curve with a minimum of 9.4±2.7 W at 10.3±0.8 m s^–1, both the coefficients of the relationship and the minimum power speed and P_met are only approximate(Fig. 2).

Fig. 3 compares the estimates of P_met made using heat transfer modelling with an E_w of 0.15 (N=4 birds), DLW (N=4 birds) and previously published data obtained by mask respirometry(P_met,resp excluding the estimated additional cost of carrying the respirometry mask and tube, N=2 birds; Ward et al., 2001, 1998). P_met did not vary systematically between measurement techniques when we assumed that E_w was 0.15 (ANOVA with bird and measurement technique as factors and flight speed V as a covariate: measurement technique, F_2,94=1.26, P=0.289; V, F_1,94=10.87, P<0.001;bird, F_3,94=3.43, P=0.020) or when we assumed that E_w was 0.19 (ANOVA: measurement technique, F_2,94=0.22, P=0.807; V,F_1,94=11.36, P<0.001; bird, F_3,94=3.35, P=0.023; Fig. 3). P_met,heat was significantly lower than P_met,resp or P_met,DLW if we assumed that E_w was less than 0.11 (ANOVA when E_w=0.10: measurement technique, F_2,94=3.66, P=0.030; V,F_1,94=10.30, P=0.002; bird, F_3,94=3.52, P=0.018).

The estimates of P_met,DLW were influenced by our assumptions of RQ during flight and V̇_CO2 while the bird was not flying or inside the respirometry chamber. Some of the other sources of error normally associated with DLW(Lifson and McClintock, 1966; Speakman, 1997) will be reduced by the high k_o:k_d ratio during flight (3.0±1.7, N=30 in our birds)(Kvist et al., 2001). The RQ typically declines during flight from close to 1.0 at the start of flight,when carbohydrate is the primary fuel, to around 0.7 as fuel use shifts to fat and protein (Rothe et al.,1987; Schmidt-Neilsen, 1990; Ward et al., 2001, 2002). The RQ during flight can also vary with the length of time since a bird ate or flew previously(Rothe et al., 1987; Gannes et al., 2001). We were not able to measure RQ directly during 1 h flights using mask respirometry because our starlings were only willing to fly for up to 12 min carrying a respirometry mask (Ward et al.,2001). Extrapolation of the decline in RQ that we measured during the flights made with the respirometry mask[log₁₀(RQ)=–0.078±0.004log₁₀t–0.017±0.003(where t is time into flight in min), r²=0.88, N=44 measurements of RQ made at 15 s intervals, in which each measurement was the mean of three flights by each of two birds] predicted that the mean RQ during a 1 h flight would be 0.75. Most of the mask respirometry measurements were made from the first flight performed by a bird each day, so since RQ during subsequent flights can be lower than that during the first flight made in a day (Rothe et al., 1987), average RQ across both flights during DLW measurements was probably less than 0.75. The RQ inside the respirometry chamber declined after exercise (RQ was 0.74±0.01 before and 0.72±0.01 after flight (N=34). However, RQ during flight may differ from that measured during resting before and after flight. Further estimates of RQ during flight in wind tunnels by starlings are 0.69±0.08 after 30 min of flight (Torre-Bueno and Larochelle,1978) and 0.71±0.02 measured from gas composition in the air sacs by Torre-Bueno(1977). If RQ were 0.75 (the highest of the estimates above) rather than 0.71 (the value that we assumed), P_met,DLW would be 4.4% higher than the values that we present. Variation in RQ from the value that we used therefore does not have a large influence upon P_met,DLW.

Calculated P_met,DLW was increased by 7.3±0.9%(N=30) if V̇_CO2 when the bird was not flying or inside the respirometry chamber was decreased to the mean value inside the respirometry chamber. Calculated P_met,DLW was decreased by the same amount if V̇_CO2 during transfers was raised to three times that when the bird was inside the respirometry chamber. Metabolism during transfers probably did not vary as much as this from the value used in our calculations, so the change in P_met,DLW calculated here is the upper limit of that introduced by this assumption.

Most (79.9±2.7%) heat transfer from starlings during flight occurs by convection, so our calculation of P_met,heat is most sensitive to any error in convective heat transfer. An increase of 10% in convective heat transfer would raise P_met,heat by 8.0±0.3%. Accordingly, we paid most attention to computation of convective heat transfer, especially how we expected convection from the wings to vary during the wing beat cycle. Comparison between the heat transfer coefficient that we calculated for the wings and those determined empirically from a heated model of a starling suggested that the assumptions that we used were realistic (Ward et al.,1999). A possible source of error is our assumption of laminar flow over the surface of the wings and body. Turbulent flow would increase convective heat transfer, especially towards the trailing edge of the wings and towards the tail, because turbulence prevents the build-up of a thermal boundary layer (Holman, 1986). Maybury and Rayner (2001) have shown that turbulent flow occurs towards the tail of taxidermic model starlings; however, it is not known how flapping wings or any differences in plumage position between living birds and models may influence the build-up of turbulence over flying starlings. The primary, secondary and tail feathers that are found on the trailing edges of the wings and body (where air flow may be turbulent) are the coolest parts of a flying starling(Ward et al., 1999), so there is less potential for raised heat transfer from these surfaces than would be the case from hotter parts of the body such as the head(Ward et al., 1999) where air flow is thought to be laminar. Since convective heat transfer represents such a large proportion of overall heat transfer, the accuracy of the calculated values of the convective heat transfer coefficient could be checked empirically in a future study by using a heated flapping model bird at a range of air speeds. However, the overall agreement between P_met,heat, P_met,DLW and P_met,resp suggests that the convective heat transfer used in our calculation is close to the correct value.

Although evaporative heat transfer may have differed between our birds and those studied by Torre-Bueno(1976, 1977, 1978; Torre-Bueno and Larochelle,1978), P_met,heat was relatively insensitive to changes in evaporative heat transfer because this contributed only 11.6±2.3% to overall heat transfer. A change of 10% in evaporative heat transfer would alter P_met,heat by 1.2±0.2%(N=20). Heat transfer by radiation contributed only 8.6±1.0%to overall heat transfer. A 10% change in radiative heat transfer would only alter P_met,DLW by 0.9±0.1%.

Heat generated during flight could potentially be stored in the body of exercising animals, and this may account for reductions in metabolic rate following flight, because heat generated during exercise could substitute for thermoregulatory heat production (Webster and Weathers, 1990; Bautista et al., 1998; Edwards and Gleeson, 2001). Heat storage typically occurs during wind tunnel flight by birds (Butler et al.,1977; Rothe et al.,1987), but does not account for an important proportion of heat production during long flights(Torre-Bueno, 1976; Craig and Larochelle, 1991; Butler and Woakes, 2001). Cloacal temperature did not vary between measurements made before and after the flights during which we obtained thermal images of the starlings(Ward et al., 1999), so our assumption that no heat was stored in the body of the birds was unlikely to introduce a significant error into P_met,heat.

Most metabolic power during flight is converted to heat(P_heat) rather than to mechanical work(P_mech) due to losses in conversion of chemical energy to kinetic energy (Hill, 1938). Thus, P_mech is 7–19% of P_metwhile P_heat forms 81–93%(Kvist et al., 2001; Ward et al., 2001). Efficiency can vary between individuals, with bird mass and with flight speed(Kvist et al., 2001; Ward et al., 2001). Uncertainty in the value of efficiency presents a problem when predicting P_met from P_mech, but has a much smaller effect on P_met,heat since much less extrapolation is needed to calculate P_met from P_heatthan from P_mech. The mean P_heat during flight by our starlings at 10 m s^–1 was 9.63 W. The mean P_mech predicted from Pennycuick's aerodynamic model was 1.55 W (Pennycuick, 1989). Changing the assumed value of E_w from 0.19 to 0.07 would increase P_met predicted from P_mechfrom 8.2 to 22.2 W (a 2.7-fold increase). The same change in E_w would alter P_met,heat from 11.9 W to 10.4 W (a 13% decrease). Heat transfer modelling therefore produces predictions of P_met that are much less sensitive to the variation in the assumed value of efficiency than those that are based on P_mech.

There was no statistically significant difference between P_met estimated by heat transfer modelling, DLW and mask respirometry when we assumed an efficiency between 0.11 and 0.19. Since previous data from the same birds suggested that efficiency lies in this range(Ward et al., 2001), we concluded that all three techniques provided consistent estimates of P_met. The DLW data were more variable than those obtained by the other techniques, both between birds at the same flight speed and across increments in flight speed (Figs 2 and 3). Variability in individual data points is typical of DLW data(Speakman, 1997), so the trend in P_met,DLW across all birds and speeds rather than individual data points should be used to evaluate these results (Figs 2 and 3). P_met,DLW appeared to show a U-shaped power-speed curve while the P_met,heat and P_met,respincreased linearly with flight speed. Our results therefore do not enable us to determine the form of the relationship between metabolic power and speed,and further experiments are needed to resolve this issue. The differences between the results may be due to the greater flight time during collection of DLW data (2 × 1 h flights) than of mask respirometry (12 min) or thermography data (up to 30 min).

Our measurements of P_met during flight in the wind tunnel were similar to those of free-living starlings measured using DLW(8.4–12.5 W; Westerterp and Drent,1985) and those predicted from modelling cardiac output(11–12 W; Bishop 1997). These results suggest that flight in wind tunnels does not have a different energetic cost than free flight (Masman and Klaassen, 1987; Rayner,1990; Wikelski et al.,2003). The somewhat higher values of P_metmeasured in our starlings than in the birds studied by Torre-Bueno and Larochelle (1978) (9–10 W) may be due to the greater mass of our birds (mean mass 82.0 g during doubly labelled water measurements compared with a mean mass of 72.8 g in Torre-Bueno's birds).

Heat transfer modelling based on thermal images is a novel technique by which to calculate P_met, which has an advantage over calculations based on P_mech in that the result is much less sensitive to the assumed value of efficiency. Heat transfer modelling also has an advantage over DLW or mask respirometry since it is non-invasive and the bird can fly without encumbrance from a respirometry mask and tube. Heat transfer modelling could be used to study P_met during free-flight rather than in a wind tunnel. Our results show that DLW, mask respirometry and heat transfer modelling produced consistent estimates of P_met. Heat transfer modelling could be used as an additional method by which to measure P_met, particularly if the potential influence of turbulent air flow on heat transfer could be better modelled.

List of symbols and abbreviations

 
• DLW

  doubly labelled water

 
• E_w

  whole animal efficiency

 
• h

  heat transfer coefficient

 
• k_d

  elimination rate of ²H

 
• k_o

  elimination rate of ¹⁸O

 
• N_d

  ²H dilution space

 
• N_o

  ¹⁸O dilution space

 
• P_heat

  heat production

 
• P_mech

  mechanical power

 
• P_met

  metabolic power

 
• P_met,DLW

  metabolic power estimated from DLW

 
• P_met,heat

  metabolic power estimated from heat production

 
• RQ

  respiratory quotient

 
• t

  time

 
• T_a

  air temperature

 
• T_s

  surface temperature

 
• V

  flight speed

 
• V̇ _CO2

  rate of carbon dioxide production

 
• V̇ _O2

  rate of oxygen consumption

We are very grateful to Deitrich Bilo for help collecting and analysing the kinematic data, to Imke Breves and Michael Stephan for help looking after the starlings, to Peter Thomson for mass spectrometry, to Martin Mörz for writing the digitisation program, to Michael Glander, Wyn Pattullo and Peter Anthony for technical assistance, to the EPSRC Equipment Loan Pool for the use of the thermal imaging equipment and to two anonymous referees for their help in improving this manuscript. Our work was supported by BBSRC grants to J.R.S. and J.M.V.R. and a British Council grant to J.R.S., S.W. and W.N.