Estimation of force generated by a beetle-mimicking flapping-wing system by using the blade element theory

In this paper, 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. Beside the aerodynamic forces, the inertial force of the wings is also calculated, and added mass is included to accommodate unsteady force. All of the force components are considered based on the full 3D motion of the wing. The BET model is validated with the model presented in a reference paper. The difference between the averages of the estimated forces (lift and drag) and those in the reference is about 4.2%. Later on, the BET model was also used to estimate the force produced by a freely flying beetle. The wing kinematics used in the BET calculation of a real beetle was captured by high-speed cameras. The results showed that the estimated vertical force is close to the weight of the beetle. Finally, the model is used to estimate the force produced by a beetle-mimicking flapping-wing system. The averages of the estimated force and the measured one are in a good agreement. These results show that the unsteady lift and drag coefficients measured by Dickinson et al. are still useful for the relatively higher Reynolds number cases, and the BET can be a good way to estimate the force produce by a flapping-wing system.