The Effects of Nonstationary Aerodynamics on the Rigid-Body Dynamic Stability of an Airplane

A first order in frequency theory is developed for the aerodynamic loads on a harmonically oscillating thin wing of finite aspect ratio in a subsonic compressible flow. The downwash in the vicinity of a horizontal tail behind such a wing is also evaluated to the same order in frequency. The results are then used to determine the stability derivatives of a conventional-type airplane and to set up the stick-free longitudinal equations of motion including the unsteady flow effects. An important conclusion of this study is that, within the limitations of a "lifting-strip" theory, the airloads on the oscillating finite span wing are linear in frequency in the neighborhood of zero frequency. This is in contrast with the two-dimensional results which show a logarithmic singularity there. As an example of a practical application, calculations are made of the frequency, damping and transient responses of the stick-free longitudinal motion of an F-80A airplane and the results compared with those obtained using quasisteady aerodynamic coefficients. The indications are that, while nonsteady flow considerations show considerable influence upon the control surface motion, they have a negligibly small effect upon the airplane motion