The power–speed relationship is U-shaped in two free-flying hawkmoths (Manducasexta)

Abstract

A flying animal can minimize its energy consumption by choosing an optimal flight speed depending on the task at hand. Choice of flight speed can be predicted by modelling the aerodynamic power required for flight, and this tool has previously been used extensively in bird migration research. For insects, however, it is uncertain whether any of the commonly used power models are useful, as insects often operate in a very different flow regime from vertebrates. To investigate this, we measured aerodynamic power in the wake of two flying freely in a wind tunnel at 1-3.8 ms, using tomographic particle image velocimetry (tomo-PIV). The expended power was similar in magnitude to that predicted by two classic models. However, the most ubiquitously used model, originally intended for vertebrates, failed to predict the sharp increase in power at higher speeds, leading to an overestimate of predicted flight speed during longer flights. In addition to measuring aerodynamic power, the tomo-PIV system yielded a highly detailed visualization of the wake, which proved to be significantly more intricate than could be inferred from previous smoke trail- and two-dimensional-PIV studies.

Indirect actuation reduces flight power requirements inManduca sextavia elastic energy exchange

“…The difference between the two P total values represents the maximum energetic benefit of elastic energy exchange. Using this general strategy in Manduca sexta but with different experimental approaches, Willmott & Ellington (blade element models), Sun & Du (computational fluid dynamics), and Warfvinge et al (particle image velocimetry) concluded that elastic energy exchange can reduce P total by up to 20 -35% [8,7,9]. To extend upon this work, Dickinson & Lighton utilized respirometric measurements combined with model based estimates of P aero and P inertial [5].…”

“…In this case, all excess inertial power (P inertial − P aero ) is stored in spring-like structures and returned to reduce P inertial for the subsequent half stroke [4,5]. Several modeling and indirect mechanical measures have estimated the potential benefits of elastic energy exchange afforded by the thorax and muscles during flight [6,7,8,9]. Blade element models, computational fluid dynamics, and tomographic particle image velocimetry estimates suggest that perfect elastic energy exchange could reduce P total by up to 20 -35% in Manduca sexta [8,9,7].…”

“…Several modeling and indirect mechanical measures have estimated the potential benefits of elastic energy exchange afforded by the thorax and muscles during flight [6,7,8,9]. Blade element models, computational fluid dynamics, and tomographic particle image velocimetry estimates suggest that perfect elastic energy exchange could reduce P total by up to 20 -35% in Manduca sexta [8,9,7]. These estimates indicate the potential benefits of elastic energy storage in flapping wing systems.…”

Mechanical power curve measured in the wake of pied flycatchers indicates modulation of parasite power across flight speeds

“…We used a modified version [38] of the method proposed by von Busse et al [7], in which Helmholtz-Hodge decomposition was used to infer the velocity fields beyond the measurement plane (to the cross-sectional limits of the wind tunnel, which was assumed to be a square with 1.2 m sides) based on the vorticity in the measurement area. Although the air outside the immediate wake is not accelerated to high speeds, the volume of this air is large and an extension of the vector field was necessary to capture all the added kinetic energy [7] (electronic supplementary material, figure S8).…”

“…The actual velocities in the masked measurement area were kept for the analysis. The average kinetic energy added to the wake (E wb ) during a wing beat was calculated by summing the kinetic energy over a fixed number of wingbeats, and subsequently dividing by the number of wingbeats [38]:…”