Unsteady aerodynamic theories are essential in the analysis of bird and insect flight. The study of these types of locomotion is vital in the development of flapping wing aircraft. This paper uses potential flow aerodynamics to extend the unsteady aerodynamic theory of Theodorsen and Garrick (which is restricted to rigid airfoil motion) to deformable thin airfoils. Frequency-domain lift, pitching moment and thrust expressions are derived for an airfoil undergoing harmonic oscillations and deformation in the form of Chebychev polynomials. The results are validated against the time-domain unsteady aerodynamic theory of Peters. A case study is presented which analyzes several combinations of airfoil motion at different phases and identifies various possibilities for thrust generation using a deformable airfoil. / Master of Science

This dissertation presents both analytical and numerical approaches to optimizing thrust and thrust efficiency of harmonically deforming thin airfoils and membrane wings. A frequency domain unsteady aerodynamic theory for deformable thin airfoils, with Chebychev polynomials as the basis functions is presented. Stroke-averaged thrust and thrust efficiency expressions are presented in a quadratic matrix form. The motion and deformation of the airfoil is optimized for maximum thrust and efficiency. Pareto fronts are generated showing optimum deformation conditions (magnitude and phase) for various reduced frequencies and constraints. It is shown that prescribing the airfoil to deform in a linear combination of basis functions with optimal magnitude and phase results in a larger thrust as compared to rigid plunging, especially at low reduced frequencies. It is further shown that the problem can be constrained significantly such that thrust is due entirely to pressure with no leading edge suction, and associated leading edge separation. The complete aeroelastic system for a membrane wing is also optimized. The aerodynamic theory for deformable thin airfoils is used as the forcing in a membrane vibration problem. Due to the nature of the two dimensional theory, the membrane vibration problem is reduced to two dimensions via the Galerkin method and nondimensionalized such that the only terms are nondimesional tension, mass ratio and reduced frequency. The maximum thrust for the membrane wing is calculated by optimizing the tension in the membrane so that the the aeroelastic deformation due to wing motion leads to optimal thrust and/or efficiency. A function which describes the optimal variation of spanwise tension along the chord is calculated. It is shown that one can always find a range of membrane tension for which the flexible membrane wings performs better than the rigid wing. These results can be used in preliminary flapping wing MAV design. / Ph. D.