Abstract
Derivation of literal approximations to the aircraft dynamicmodes remains one of the central problems in the theory of aircraft ight dynamics, and one that has never been satisfactorily resolved. Although approximations to the fast modes (short period, roll) are generally good, the slow modes (phugoid, dutch roll, spiral) seem to have several competing approximations, none of which are uniformly satisfactory. This paper examines the fundamental assumptions behind the traditional approach to the derivation of literal approximations.A major aw in all previous derivations resulting in incorrect slow-mode approximations is uncovered. In following a formal procedure, improved literal approximations are derived for the slow modes. In this process, a new condition for onset of directional departure is obtained, which is related to the dutch-roll frequency. Predictions from the literal approximationsderived in this paper are compared with actual numerical values for an example aircraft to illustrate conditions under which the approximationswork well, and to point out the fundamental limitations of the literal approximationsderived by the traditional approach.
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