SUMMARY It is technically demanding to measure the energetic cost of animal flight. Each of the previously available techniques has some disadvantage as well advantages. We compared measurements of the energetic cost of flight in a wind tunnel by four European starlings Sturnus vulgaris made using three independent techniques: heat transfer modelling, doubly labelled water (DLW)and mask respirometry. We based our heat transfer model on thermal images of the surface temperature of the birds and air flow past the body and wings calculated from wing beat kinematics. Metabolic power was not sensitive to uncertainty in the value of efficiency when estimated from heat transfer modelling. A change in the assumed value of whole animal efficiency from 0.19 to 0.07 (the range of estimates in previous studies) only altered metabolic power predicted from heat transfer modelling by 13%. The same change in the assumed value of efficiency would cause a 2.7-fold change in metabolic power if it were predicted from mechanical power. Metabolic power did not differ significantly between measurements made using the three techniques when we assumed an efficiency in the range 0.11–0.19, although the DLW results appeared to form a U-shaped power-speed curve while the heat transfer model and respirometry results increased linearly with speed. This is the first time that techniques for determining metabolic power have been compared using data from the same birds flying under the same conditions. Our data provide reassurance that all the techniques produce similar results and suggest that heat transfer modelling may be a useful method for estimating metabolic rate.

Results of experiments with thermocapillary flow in shallow liquid layers heated from the side are presented. The fluid has Prandtl number 17 and the main configuration investigated is an annular gap to avoid side-wall effects. The liquid depth d was d≤3.00 mm to have negligible buoyancy effects. Various instabilities have been observed. At a Marangoni number M≂6⋅102, a transition to steady multicellular flow occurred. The convection cells are longitudinal rolls embedded in the main flow all rotating in the same direction. At M≂3⋅103, a transition of the steady multicellular flow to time-dependent flow states (t) was observed. Two different t-flow states have been identified by thermocouple measurements and by visualization of the dynamic-free surface deformations of oscillatory flow. Both t states can be described by disturbances in the form of traveling waves. A short-wavelength t state with small surface deformations and with waves traveling in azimuthal direction is the preferred mode for d≤1.4 mm. A long-wavelength t state with larger surface deformations and with waves traveling in radial and in azimuthal directions is preferred for d≥1.4 mm. The stability diagram, wavelength, frequency, and phase speed of both t states are presented and the findings in comparison to an already existing theory by Smith and Davis [J. Fluid Mech. 132, 119, 145 (1983)] are discussed.

Convective motions in rectangular boxes with one side horizontal have been studied. The critical Rayleigh numbers were determined. In most cases cell patterns with rolls parallel to the shorter side wall of the rectangular box were observed. The results have been compared with the known theoretical results of Davis (1967). In general, good agreement has been found.

Infrared thermography was used to measure heat transfer by radiation and the surface temperature of starlings (Sturnus vulgaris) (N=4) flying in a wind tunnel at 6–14 m s-1 and at 15–25 degrees C. Heat transfer by forced convection was calculated from bird surface temperature and biophysical modelling of convective heat transfer coefficients. The legs, head and ventral brachial areas (under the wings) were the hottest parts of the bird (mean values 6.8, 6.0 and 5.3 degrees C, respectively, above air temperature). Thermal gradients between the bird surface and the air decreased at higher air temperatures or during slow flight. The legs were trailed in the air stream during slow flight and when air temperature was high; this could increase heat transfer from the legs from 1 to 12 % of heat transfer by convection, radiation and evaporation (overall heat loss). Overall heat loss at a flight speed of 10.2 m s-1 averaged 11. 3 W, of which radiation accounted for 8 % and convection for 81 %. Convection from the ventral brachial areas was the most important route of heat transfer (19 % of overall heat loss). Of the overall heat loss, 55 % occurred by convection and radiation from the wings, although the primaries and secondaries were the coolest parts of the bird (2.2-2.5 degrees C above air temperature). Calculated heat transfer from flying starlings was most sensitive to accurate measurement of air temperature and convective heat transfer coefficients.

SUMMARYWe trained two starlings (Sturnus vulgaris) to fly in a wind tunnel whilst wearing respirometry masks. We measured the metabolic power (Pmet) from the rates of oxygen consumption and carbon dioxide production and calculated the mechanical power (Pmech) from two aerodynamic models using wingbeat kinematics measured by high-speed cinematography. Pmet increased from 10.4 to 14.9 W as flight speed was increased from 6.3 to 14.4 m s–1 and was compatible with the U-shaped power/speed curve predicted by the aerodynamic models. Flight muscle efficiency varied between 0.13 and 0.23 depending upon the bird, the flight speed and the aerodynamic model used to calculate Pmech. Pmet during flight is often estimated by extrapolation from the mechanical power predicted by aerodynamic models by dividing Pmech by a flight muscle efficiency of 0.23 and adding the costs of basal metabolism, circulation and respiration. This method would underestimate measured Pmet by 15–25 % in our birds. The mean discrepancy between measured and predicted Pmet could be reduced to 0.1±1.5 % if flight muscle efficiency was altered to a value of 0.18. A flight muscle efficiency of 0.18 rather than 0.23 should be used to calculate the flight costs of birds in the size range of starlings (approximately 0.1 kg) if Pmet is calculated from Pmech derived from aerodynamic models.