Literal approximations to aircraft dynamic modes

Derivation of literal approximations to the aircraft dynamic modes remains one of the central problems in the theory of aircraft flight dynamics, and one that has never been satisfactorily resolved. Although approximations to the fast modes (short period, roll) are generally good, the slow modes (ph ugoid, dutch roll, spiral) seem to have several competing approximations, n one of which are uniformly satisfactory. This paper examines the fundamenta l assumptions behind the traditional approach to the derivation of literal approximations. A major flaw in all previous derivations resulting in incor rect slow-mode approximations is uncovered. In following a formal procedure , improved literal approximations are derived for the slow modes. In this p rocess, a new condition for onset of directional departure is obtained, whi ch is related to the dutch-roll frequency. Predictions from the literal app roximations derived in this paper are compared with actual numerical values for an example aircraft to illustrate conditions under which the approxima tions work well, and to point out the fundamental limitations of the litera l approximations derived by the traditional approach.