Dynamics of a passively flapping paper airplane*

Paper airplanes are commonly made to be good gliders. Interestingly, some can also be made to flap while flying. We study the dynamics of such a flapping paper airplane by John Collins named the “Bat Plane”. Flight experiments were recorded with 2 high speed cameras for 3D reconstruction of the paper airplanes in flight by tracking marker points. The paper airplanes were observed to have a periodic body pitch angle in sync with the flapping motion during flight. We propose displacement of the center of pressure (CoP) location about the center of mass (CoM) causing change in the direction of the aerodynamic moment about CoM. Steady state measurements of lift, drag and aerodynamic moments in a wind tunnel are used to explain this hypothesis. Moreover, the flapping frequency of these paper airplanes were observed to increase upon shortening wing dimensions (chord and span) and increasing material thickness. The flapping frequencies do not match with the corresponding natural frequency of the wing. Additionally, paper airplanes made with sufficiently thick paper and reduced wing dimensions were observed to transition to gliding. We attempt a theoretical model to understand the difference in the frequencies and the gliding transition.