The aerodynamic force platform as an ergometer

Abstract

Animal flight requires aerodynamic power, which is challenging to determine accurately in vivo. Existing methods rely on approximate calculations based on wake flow field measurements, inverse dynamics approaches, or invasive muscle physiological recordings. In contrast, the external mechanical work required for terrestrial locomotion can be determined more directly by using a force platform as an ergometer. Based on an extension of the recent invention of the aerodynamic force platform, we now present a more direct method to determine the in vivo aerodynamic power by taking the dot product of the aerodynamic force vector on the wing with the representative wing velocity vector based on kinematics and morphology. We demonstrate this new method by studying a slowly flying dove, but it can be applied more generally across flying and swimming animals as well as animals that locomote over water surfaces. Finally, our mathematical framework also works for power analyses based on flow field measurements.

Small deviations in kinematics and body form dictate muscle performances in the finely tuned avian downstroke

“…We determined the time-resolved aerodynamic force vector generated by each wing of the dove by measuring the net aerodynamic forces in the horizontal (back to front; x) and vertical (z) directions as in Deetjen et al 2020 [33] (Figure 1A,B, Figure 1-Figure Supplement 1). We then combined these 2D forces with our 3D wing kinematics measurements to reconstruct the final, lateral (right to left), component of the full 3D force vector (Figure 1C).…”

How oscillating aerodynamic forces explain the timbre of the hummingbird’s hum and other animals in flapping flight

“…Past the tenth harmonic, we approach the ambient noise floor for the measurements. 90.0 90.0 90.0 The aerodynamic force generated by each wing is equal to the vector sum of the lift (with magnitude and direction ̂) and drag (with magnitude and direction ̂) at 2 , the second moment of area (80). As the AFP measures net forces, the forces in the longitudinal ( ) and vertical ( ) directions can be measured directly since the contributions from the left and right wings sum together.…”

“…As the AFP measures net forces, the forces in the longitudinal ( ) and vertical ( ) directions can be measured directly since the contributions from the left and right wings sum together. On the other hand, because each wingbeat is symmetric about the bird's midline, the lateral force from the left and right wings cancel out when measured by the AFP (80). Thus, we defined the 3D force from each wing as:…”

“…The calculated lift, drag, and lateral forces are sensitive to measurement error when the vertical and horizontal components of lift and drag are near zero, which occurs at stroke reversal. To improve the calculated force accuracy at stroke reversal, we smoothed this singularity using a regularization developed by Deetjen et al (80).…”

“…The calculated lateral force and aerodynamic power were sensitive to error at stroke reversal, where the vertical and horizontal components of lift and drag are near zero. We incorporated a regularization developed by Deetjen et al (80). The sensitivities arise because solving Eqn.…”