Small-Perturbation Analysis of Airplane Dynamics With Dynamic Stability Derivatives Redefined

Abstract

The first successful powered and controlled heavier-than-air flight and the subsequent meteoric rise of aviation in the 20th century also brought with it mathematical models to understand the phenomenon of flight. Though successful to a large extent as is obvious from their longevity, these models still suffer from the odd anomalous result. Upon careful examination, the source of this problem can be traced to an inappropriate choice of dynamic stability derivatives that is inconsistent with the aerodynamics. In order to correctly distinguish between the different mechanisms that are responsible for the aerodynamic forces and moments generated due to body angular rates in flight, this paper refines the existing model for flight mechanics by redefining the dynamic stability derivatives with respect to, i) relative rate of rotation between the body and wind axes, and ii) the rate of rotation of the wind axis with respect to the earth axis, sometimes called flow curvature effect. Further, new literal approximations to the longitudinal and lateral-directional modes have been obtained in terms of the redefined dynamic stability parameters. The new approximations, for instance, correctly relate the short-period natural frequency to the longitudinal static stability parameter Cmα.