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