Empirical Method to Extract Steady-Level Flight Conditions of a Stroke- and Pitch-Controlled Flapping Wing

An experimental procedure has been developed to extract the steady-level flight conditions of a flapping-wing drone from wind-tunnel experiments, where the wing motion is comprised of two degrees of freedom: stroke and pitch angle. The manipulable variables in flight are taken to be reduced frequency of flapping, $k$, and mean pitch angle, $\overline{\theta}$, and these variables were varied in the wind-tunnel experiments while stroke amplitude, mean stroke angle, and pitch amplitude were held constant. Contours of mean lift, thrust, and power coefficients on the two-dimensional $k$--$\overline{\theta}$ space were generated from force and motor-power measurements. These charts allow the reader to extract the expected steady level flight conditions once the required mean lift and thrust coefficients are known, as derived from the expected wing loading, flight dynamic pressure, parasitic drag, and trim drag. The mean lift coefficient was found to increase with both $k$ and $\overline{\theta}$, but more strongly with the latter. Mean thrust tended to decrease with $\overline{\theta}$ and increase with $k$ for $k>1.1$. Power coefficient increased exponentially with $k$ but was insensitive to $\overline{\theta}$. The corresponding insensitivity of power coefficient to mean lift or thrust suggests a hypothesis for future testing: namely, that a significant portion of the power expended in these tests went into generating non-useful lateral flow.