Finite state induced flow models. Part I: Two-dimensional thin airfoil

A new finite state aerodynamic theory is presented for incompressible, two-dimensional flow around thin airfoils. The theory is derived directly from potential flow theory with no assumptions on the time history of airfoil motions. The aerodynamic states are the coefficients of a set of induced-flow expansions. As a result, the finite state equations are hierarchical in nature and have closed-form coefficients. Therefore, the model can be taken to as many states as are dictated by the spatial texture and frequency range of interest with no intermediate numerical analysis. The set of first-order state equations is easily coupled with structure and control equations and can be exercised in the frequency or Laplace domain as well as in the time domain. Comparisons are given with Theodorsen theory, Wagner theory, and other methods. Excellent results are found with only a few states.