A decomposed Fourier series solution to Prandtl's classical lifting-line theory is used to predict the lift, induced-thrust, and power coefficients developed by a flapping wing. A significant advantage of this quasi-steady analytical solution over commonly used numerical methods is the utility provided for optimizing wing flapping cycles. The analytical solution involves five time-dependent functions that could all be optimized to maximize thrust, propulsive efficiency, and/or other performance measures. Results show that by optimizing only two of these five functions, propulsive efficiencies exceeding 97% can be obtained. Results are presented for untwisted rectangular wings in pure plunging, rectangular wings with linear washout and the minimum-power washout magnitude, and rectangular wings with the minimum-power washout distribution and magnitude.
Decomposed Lifting-Line Predictions and Optimization for Propulsive Efficiency of Flapping Wings31st AIAA Applied Aerodynamics Conference
Document TypeConference Paper
PublisherAmerican Institute of Aeronautics and Astronautics
Citation InformationPhillips, W. F., Miller, R. A., Hunsaker, D. F., “Decomposed Lifting-Line Predictions and Optimization for Propulsive Efficiency of Flapping Wings,” 31st AIAA Applied Aerodynamics Conference, San Diego, California, June 24 – 27, 2013, AIAA-2013-2921.