| The tumbling motion of freely falling plates with aspect ratio ranging from 2 to 10 is studied using both experimental measurement and theoretical analysis and the influence of aspect ratio on tumbling motion is obtained by this study.A plate releasing platform is built for purpose of experimental study.The trajectories of plates are recorded by high speed video camera and analyzed 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 ratios and the double frequency is determined from a Fourier analysis.For theoretical study of the in?uence of aspect ratio on tumbling plate,the problem is rather complicated,due to rotation of the plate and high angle of attack flow phenomena such as vortex shedding and unsteady flow behavior.By adding a correction from the inducing effect of trailing vortices and rotation related wing tip vortices to the corresponding two dimensional force and torque expressions,a simplified aerodynamic model for lift,drag and torque is obtained.Some factors that are independent of aspect ratio are determined by experimental data for high aspect ratio.With the aerodynamic properties thus determined,a kinematic model is obtained which successfully predicts the qualitative influence of aspect ratio on the averaged kinematics,that compare very well with experimental data.By this study,we find 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. |
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