Aerodynamics Flapping-Flight Robotic Bird using Unsteady Lifting-Line Method

The Robird is a bird-like drone, or ornithopter, that generates lift and thrust by flapping and pitching its wings, which performance resembles that of a Peregrine falcon. This paper describes an extension, from steady flow to unsteady flow, of Prandtl’s Lifting-Line method to predict the unsteady lift, thrust, pitching-moment, root-bending moment, required-power and propulsive-efficiency of the robotic bird. The extension comprises the derivation of the Kutta-Joukowski Theorem for unsteady flow, an unsteady trailing-edge Kutta condition and the representation of the wake as a stationary transpiration-type of planar surface carrying a time-dependent dipole distribution. Its instantaneous strength is obtained from the spanwise distribution of the circulation of the lifting line at earlier times. For the cases considered, the numerical method predicts that the section-lift, section-thrust, section-pitching-moment and section-required-power of the wing vary in time. During flapping flight, the cycle-averaged section-lift and section-thrust, as well as the cycle-averaged overall lift and thrust, are mostly positive. The spanwise distributions of cycle-averaged sectional aerodynamic quantities like circulation, lift, etc., as well as the corresponding span-integrated overall quantities and the propulsive efficiency, depend on flight parameters Strouhal number, but not all on pitch amplitude, cycle-averaged effective angle-of-attack nor phase difference between pitching and flapping. The topology of the wake in terms of the unsteady wake dipole distribution, as well as its corresponding vortex distribution, predicted by the unsteady-lifting-line method depend on all flight parameters. The paper provides the relation between wake topology and the generation of lift and thrust.