A modified blade element theory for estimation of forces generated by a beetle-mimicking flapping wing system.

We present an unsteady blade element theory (BET) model to estimate the aerodynamic forces produced by a freely flying beetle and a beetle-mimicking flapping wing system. Added mass and rotational forces are included to accommodate the unsteady force. In addition to the aerodynamic forces needed to accurately estimate the time history of the forces, the inertial forces of the wings are also calculated. All of the force components are considered based on the full three-dimensional (3D) motion of the wing. The result obtained by the present BET model is validated with the data which were presented in a reference paper. The difference between the averages of the estimated forces (lift and drag) and the measured forces in the reference is about 5.7%. The BET model is also used to estimate the force produced by a freely flying beetle and a beetle-mimicking flapping wing system. The wing kinematics used in the BET calculation of a real beetle and the flapping wing system are captured using high-speed cameras. The results show that the average estimated vertical force of the beetle is reasonably close to the weight of the beetle, and the average estimated thrust of the beetle-mimicking flapping wing system is in good agreement with the measured value. Our results show that the unsteady lift and drag coefficients measured by Dickinson et al are still useful for relatively higher Reynolds number cases, and the proposed BET can be a good way to estimate the force produced by a flapping wing system.