A multibody approach for 6-DOF flight dynamics and stability analysis of the hawkmothManduca sexta

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.

Direct lateral maneuvers in hawkmoths

“…Results here compliment wing velocity mediated roll damping described in the turning free-flight of cockatoos, ( Hedrick et al, 2007 ), and computational studies which predict heavily damped roll in M. sexta ( Kim and Han, 2014 ). Effective angle of attack asymmetry induced by rolls, as in fixed-wing aircraft, almost assuredly dampens movement in moths as well.…”

“…Velocity decay half-lives (i.e. time constants), estimated from the differential solutions to Eqns 1-2, are similar to those extracted from two computational models of passive theoretical M. sexta ( Hedrick and Daniel, 2006 ; Kim and Han, 2014 ). Coefficients values from observed data and the blade element model also agree ( ).…”

“…However, the velocities moths encountered in our experiments cover a small range, over which we might expect to reasonably linearize an exponential trend. Furthermore, computational analysis of the flight of M. sexta suggests that, on the time scale of half wing-strokes, passive resistance to movement during horizontal and vertical movement is roughly linearly proportional to velocity rather than velocity squared for both horizontal and vertical movement terms, ( Cheng and Deng, 2011 ; Kim and Han, 2014 ). Further velocity damping effects have also been proposed ( Faruque and Humbert, 2010 ).…”

The effect of the abdomen deformation on the longitudinal stability of flying insects

“…Equation (9) represents the derived nonlinear equations of motion for the 4-DOF system, where F G represents periodic aerodynamic forces and moment in global axis. When the torsion spring constant k is more than 1.5 N-m/rad, the solution of equation (9) becomes almost the same as that of a standard 3-DOF rigid body formulation, and we define this k value as the rigid case. where…”

Body flexion effect on the flight dynamics of a hovering hawkmoth

“…For example, the abdominal responses of a hawkmoth, Manduca sexta, under visual stimuli are observed in pitch direction more than yaw or roll direction (Hinterwirth andDaniel, 2010, Dyhr et al, 2013). Even though the body flexion looks small, it can affect the flight dynamics and stabilities (Kim andHan, 2014, Yokoyama, et al, 2013). In order to understand the flight dynamics of insects with the body flexion and to find novel control strategies for MAV, we investigate the effect of the longitudinal active and passive body flexion on flight dynamics by using an in-house CFD and FBD solver.…”