Structural scaling and functional design of the cercal wind-receptor hairs of cricket

Abstract

We have estimated the intrinsic mechanical parameters of cricket cercal wind-receptor hairs. The hairs were modeled as an inverted pendulum, and mechanical parameters of the equation of notion were determined from data given by a systematic measurement of mobility by the least-square error method. The theoretical torque which turns the hair shaft is given by the drag force due to the moving air. The drag force is given by the method of Stokes' mechanical impedance of an oscillating cylinder in viscous fluid. The effect of the boundary layer in which air is stagnating on the substrate surface is also taken into account. The moment of inertia of a hair shaft shows a clear length dependency to the power of 4.32 of the hair length. The torsional resistance within the hair base and the stiffness of hair-supporting spring also show clear length dependencies to the power of 2.77 and 1.67, respectively. The torsional resistance within the hair base is so large that the hair is a strongly damped non-oscillatory second-order system. The large resistance within the hair base represents an efficient energy absorption by the sensory bell. The resistance seems to match with the source impedance, i.e., the frictional resistance at the site of air-hair contact. The impedance matching provides the condition of maximum power transmission from the moving air to the sensory cell. Structural scaling is discussed in relation to the functional scaling of the frequency-range fractionation of the mechanical filter array with a common biological design.