A quasi-steady aerodynamic model in consideration of the center of pressure (C.P.) was developed for insect flight. A dynamically scaled-up robotic hawkmoth wing was used to obtain the translational lift, drag, moment and rotational force coefficients. The translational force coefficients were curve-fitted with respect to the angles of attack such that two coefficients in the Polhamus leading-edge suction analogy model were obtained. The rotational force coefficient was also compared to that derived by the standard Kutta-Joukowski theory. In order to build the accurate pitching moment model, the locations of the C.Ps. and its movements depending on the pitching velocity were investigated in detail. We found that the aerodynamic moment model became suitable when the rotational force component was assumed to act on the half-chord. This implies that the approximation borrowed from the conventional airfoil concept, i.e., the 'C.P. at the quarter-chord' may lead to an incorrect moment prediction. In the validation process, the model showed excellent time-course force and moment estimations in comparison with the robotic wing measurement results. A fully nonlinear multibody flight dynamic simulation was conducted to check the effect of the traveling C.P. on the overall flight dynamics. This clearly showed the importance of an accurate aerodynamic moment model.

No abstract

No abstract

This paper investigates the six degrees of freedom (6-DOF) flight dynamics and stability of the hawkmoth Manduca sexta using a multibody dynamics approach that encompasses the effects of the time varying inertia tensor of all the body segments including two wings. The quasi-steady translational and unsteady rotational aerodynamics of the flapping wings are modeled with the blade element theory with aerodynamic coefficients derived from relevant experimental studies. The aerodynamics is given instantaneously at each integration time step without wingbeat-cycle-averaging. With the multibody dynamic model and the aerodynamic model for the hawkmoth, a direct time integration of the fully coupled 6-DOF nonlinear multibody dynamics equations of motion is performed. First, the passive damping magnitude of each single DOF is quantitatively examined with the measure of the time taken to half the initial velocity (thalf). The results show that the sideslip translation is less damped approximately three times than the other two translational DOFs, and the pitch rotation is less damped approximately five times than the other two rotational DOFs; each DOF has the value of (unit in wingbeat strokes): thalf,forward/backward = 7.10, thalf,sideslip = 17.95, thalf,ascending = 7.13, thalf,descending = 5.77, thalf,roll = 0.68, thalf,pitch = 2.39, and thalf,yaw = 0.25. Second, the natural modes of motion, with the hovering flight as a reference equilibrium condition, are examined by analyzing fully coupled 6-DOF dynamic responses induced by multiple sets of force and moment disturbance combinations. The given disturbance combinations are set to excite the dynamic modes identified in relevant eigenmode analysis studies. The 6-DOF dynamic responses obtained from this study are compared with eigenmode analysis results in the relevant studies. The longitudinal modes of motion showed dynamic modal characteristics similar to the eigenmode analysis results from the relevant literature. However, the lateral modes of motion revealed more complex behavior, which is mainly due to the coupling effect in the lateral flight states and also between the lateral and longitudinal planes of motion. The main sources of the flight instability of the hovering hawkmoth are examined as either the longitudinal instability grown from the coupled forward/backward velocity and the pitch rate, or the lateral instability grown from the coupled sideslip velocity and the roll rate.

No abstract