Influence of aspect ratio on tumbling plates

Abstract

AbstractThe tumbling motion of freely falling plates with aspect ratio ranging from 2 to 10 is studied using both experimental measurement and simplified lifting line theory. The trajectories of plates are recorded by high-speed video camera and analysed to obtain instantaneous and average kinematic and aerodynamic parameters, including the descent angle, rotating speed, descent velocities, lift and drag coefficients, and their fluctuation spectrums. A double period rotation with period doubling is observed here for some range of aspect ratio and the double frequency is determined from a Fourier analysis. By adding a correction from the inducing effect of trailing vortices and wing-tip vortices to the corresponding two-dimensional force and torque expressions, a simplified kinematic model is obtained which successfully predicts the qualitative influence of aspect ratio on the averaged kinematics, that the descent angle and the vertical descent velocity component are decreasing functions of the aspect ratio, while the rotation speed and horizontal velocity component are increasing functions of the aspect ratio. For decreasing aspect ratio, the induced drag due to the trailing and tip vortices reduces the lift to drag ratio and thus increases the descent angle, while the dissipative torque due to translational induced drag decreases the rotation speed.