Generic Analytical Thrust-Force Model for Flapping Wings

The purpose of this paper is to propose a generic analytical flapping-wing cycle-average thrust-force estimation method by implementing elongated body theory into actuator disk theory. Compared with previous a flapping-wing analysis based on actuator disk theory, the proposed method relates wing geometry and kinematics directly to induced velocity, and the periodical pressure pulsation correction factor measurement for every different flapping-wing design is no longer necessary. The proposed method is much simpler than unsteady aerodynamics or computational implementations, and thus the complex multiparameter optimization can be avoided at the early design stage of flapping-wing vehicles. Theoretical deviation of the proposed thrust model is evaluated by a numerical simulation method, and a correction term is proposed. The corrected method is then validated by wind-tunnel experiments on an 850-cm-wing-span active-twisting flapping-wing model and experimental data from previous studies that were over large parameter ranges. The results suggest that the proposed method is valid for the flapping-wing cycle-average thrust estimation over a large range of variables. Theoretical deductions about the effects of dominant factors of flapping-wing propulsion behavior and application of the present method in both passive- and active-twisting flapping-wing designs are also discussed.