Synopsis
The need for long dispersal flights can drive selection for behavioral, physiological, and biomechanical mechanisms to reduce the energy spent flying. However, some energy loss during the transfer of momentum from the wing to the fluid is inevitable, and inherent to the fluid–wing interaction. Here, we analyzed these losses during the forward flight of the mango stem borer (Batocera rufomaculata). This relatively large beetle can disperse substantial distances in search of new host trees, and laboratory experiments have demonstrated continuous tethered flights that can last for up to an hour. We flew the beetles tethered in a wind tunnel and used high-speed videography to estimate the aerodynamic power from their flapping kinematics and particle image velocimetry (PIV) to evaluate drag and kinetic energy from their unsteady wakes. To account for tethering effects, we measured the forces applied by the beetles on the tether arm holding them in place. The drag of the flying beetle over the flapping cycle, estimated from the flow fields in the unsteady wake, showed good agreement with direct measurement of mean horizontal force. Both measurements showed that total drag during flight is ∼5-fold higher than the parasite drag on the body. The aerodynamic power estimated from both the motion of the wings, using a quasi-steady blade-element model, and the kinetic energy in the wake, gave mean values of flight-muscle mass-specific power of 87 and 65 W kg muscle−1, respectively. A comparison of the two values suggests that ∼25% of the energy is lost within the fluid due to turbulence and heat. The muscle mass-specific power found here is low relative to the maximal power output reported for insect flight muscles. This can be attributed to reduce weight support during tethered flight or to operation at submaximal output that may ensure a supply of metabolic substrates to the flight muscles, thus delaying their fatigue during long-distance flights.
Exact functional derivative of the nonadditive kinetic-energy bifunctional in the long-distance limit