A Hemispherical Motor Oscillator for Experiments on Swimming and Flying of Small Animals

Abstract

The propulsors of organisms from paramecia to dolphins have ball-and-socket jointed bases that allow large-amplitude, low-friction swings. Their olivo-cerebellar control also remains unchanged. Yet, the propulsive surfaces of small animals vary widely from flagellar filaments (0 < Re < 5) to flapping fins (Re > 20) with an intermediate range of Reynolds number (5 < Re < 20) where both types are present in the same swimming animal. Analysis suggests that these unsteady surfaces are mechanical oscillators coupled to their nonlinear wakes. A low-friction-driven oscillator that can interact with the oscillators of models or live swimming and flying animals could help us understand the hydro-structural events prompting the evolution of such surfaces at specific Re values. A gearless underdamped (in air) hemispherical motor oscillator is described where energetic efficiency increases by a factor of eight as the forces drop by a factor of ten from 10 N. The electrical efficiencies at 0.8 N are comparable to the total thermal efficiencies of flies, and the quality factor is comparable. The continuously varying fin oscillation of penguin fins and abruptly varying fin oscillations of Clione antarctica and flies are reproduced. When flapping at 0.3 Hz, the oscillator would respond to all wake nonlinearities. Abrupt fin turning is modeled by switching the roll and pitch phase difference between −π/2 and π/2 in successive quadrants. Defining the fish-wake lock-in error as the difference between Triantafyllou's fish Strouhal number and the tangent of the vortex-shedding angle, an experiment is discussed for measuring the minimum drag of live fish.

Vortex bursting near a free surface

“…The full vortex is undergoing such axial oscillation and releases the bubbles radially from the root in the process in the unstable range 45 • < β 90 • only during one half of the oscillation. (In a low-friction mechanical apparatus of small forces (<1 N), up to five damped oscillations have been seen when the mass is released (Bandyopadhyay 2019).) The time period of axial oscillation is 0.067 s, which is two to three times the estimated bubble release time.…”

“…Background of the flow apparatus: wave-wave interaction Wave-wave interactions in oceans and olivo-cerebellar control dynamics (Kazantsev et al 2004;Bandyopadhyay et al 2008b) have been extensively studied. They are beginning to receive attention in modelling and laboratory fluid dynamic research (Bandyopadhyay et al 2012;Bandyopadhyay & Hellum 2014;Bandyopadhyay 2019). Swimming and flying mechanisms of animals show that the propulsive surfaces undergo orthogonal rolling and pitching oscillations (Bandyopadhyay et al 2012) given by…”

“…Here, φ controls the forces produced, θ controls the blockage and the timing of the vortex formation and bursting and θ t reduces the spanwise variation of the velocity field (Bandyopadhyay et al 2012). Equations (2.1)-(2.5) produce the vorticity spirals -uniform and conical -of Kelvin mode m = 1 in axis t and pitch f shown in table 1; for spatial trajectories of a particle obtained using these equations, see figure 2(d) in Bandyopadhyay (2019). The foil velocity is given by U foil (t) =φ(t)R avg , where R avg is the average foil span.…”

“…Then, the foil responds to all five dominant harmonics of the wake (Beal & Bandyopadhyay 2007). Theoretically, olivo-cerebellar ionic control has a similar self-regulation mechanism for ion-by-ion control of vortex shedding to control the hydrodynamics of swimming and aerodynamics of flying at all instants of time (Bandyopadhyay 2015(Bandyopadhyay , 2016(Bandyopadhyay , 2019. If the device producing the wake/jet has a high quality factor ratio (low friction), the foil and wake approach lock-in and self-regulation (Bandyopadhyay 2015).…”

“…If the device producing the wake/jet has a high quality factor ratio (low friction), the foil and wake approach lock-in and self-regulation (Bandyopadhyay 2015). Insect wings approach this condition (Ellington 1999;Bandyopadhyay 2019).…”