The mechanical power requirements of avian flight

Abstract

A major goal of flight research has been to establish the relationship between the mechanical power requirements of flight and flight speed. This relationship is central to our understanding of the ecology and evolution of bird flight behaviour. Current approaches to determining flight power have relied on a variety of indirect measurements and led to a controversy over the shape of the power-speed relationship and a lack of quantitative agreement between the different techniques. We have used a new approach to determine flight power at a range of speeds based on the performance of the pectoralis muscles. As such, our measurements provide a unique dataset for comparison with other methods. Here we show that in budgerigars (Melopsittacus undulatus) and zebra finches (Taenopygia guttata) power is modulated with flight speed, resulting in U-shaped power-speed relationship. Our measured muscle powers agreed well with a range of powers predicted using an aerodynamic model. Assessing the accuracy of mechanical power calculated using such models is essential as they are the basis for determining flight efficiency when compared to measurements of flight metabolic rate and for predicting minimum power and maximum range speeds, key determinants of optimal flight behaviour in the field.

Figure 1

Mechanical performance of pectoralis muscle fascicles in vitro. (a,d) The imposed strain trajectory(dashed line), stimulus and resulting force production(solid line), relative to peak isometric tetanic force, P₀. The bold line indicates the period of stimulation. (b,e) Instantaneous power output. (c,f) The force–length relationship or ‘work loop’. The work loops are anticlockwise (indicated by the arrows) and therefore represent net positive work. Data are typical examples obtained from (a–c) zebra finch and (d–f), budgerigar pectoralis muscle.

Figure 2

Pectoralis muscle power output and its relationship with flight speed. Power output was calculated using an aerodynamic model for a range ((a,c) minimum: C_D,par 0.05 (Tucker, 2000), C_D,pro 0.01 (Tobalske et al., 2003), k 1.0; S_b=0.00813M_b^0.666 (Pennycuick et al., 1988); and (b,d) typical: C_D,par 0.13 (Rayner, 1999), C_D,pro 0.02 (Rayner, 1979), k 1.2 (Pennycuick, 1975), S_b=0.00813M_b^0.666 (Pennycuick et al., 1988)) of aerodynamic coefficients from the literature and is compared with pectoralis muscle power output (mean±s.e.m.) determined in vitro, corrected for recruitment and intermittent flight. Data are from (a,b) zebra finch and (c,d) budgerigar pectoralis muscle. In vitro muscle power data are presented as mean±s.e.m. (budgerigars N=11, 9, 9, 6, 9, 5, 7 for speeds 4, 6, 8, 10, 12, 14, 16 m s⁻¹, respectively; zebra finches N=7, 6, 3, 5, 4, 4, 7 for speeds 0, 4, 6, 8, 10, 12, 14 m s⁻¹, respectively). Aerodynamic modelling was carried out on seven budgerigars at all speeds except 4 and 16 m s⁻¹ where data are from four and six individuals, respectively. In zebra finches, modelling was performed on six individuals at all speeds, except 4 and 14 m s⁻¹ where data are from four individuals.