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 approximationsA 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

Literal Approximations to Aircraft Dynamic Modes

L'objectif de la these est de traiter quelques themes de la Dynamique du Vol par une approche analytique. Cette approche constitue un complement pertinent de l'approche numerique. C'est un outil d'analyse rapide et physique des phenomenes particulierement utile, notamment : Au stade de pre-developpement en phase conceptuelle - rapidite des calculs ; Pour cerner rapidement les axes pertinents de recherche - outil d'aide a la decision ; Pour interpreter et valider des etudes numeriques sophistiquees. Les themes suivants ont ete traites : Modeles des efforts exterieurs : propulsif (ex : poussee moteur F[indice max] et consommation speciﬁque C[indice SR]) ; massique (ex : masse moteur Mm et voilure M[indice w]) ; Performances operationnelles (ex : longueur de piste au decollage L[indice p]). La coherence du projet reside dans l'etat d'esprit commun et l'unite de la methode pour traiter les differents themes. Les modeles analytiques classiques sont revisites avec la puissance du calcul formel avec l'aide de logiciel tel que Maple. Si possible une generalisation est faite par une approche adimensionnelle qui rend le resultat universel, c'est-a-dire applicable a tout type d'avion.

Pour une approche analytique de la dynamique du vol

Longitudinal Long-Term Modes in Super- and Hypersonic Flight

Consistent Approximations to Aircraft Longitudinal Modes

The rst successful powered and controlled heavier-than-air igh t and the subsequent meteoric rise of aviation in the 20th century also brought with it mathematical models to understand the phenomenon of igh t. Though successful to a large extent as is obvious from their longevity, these models still suer from the odd anomalous results. 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 dieren t mechanisms that are responsible for the aerodynamic forces and moments generated due to body angular rates in igh t, this paper renes the existing model for igh t mechanics by redening 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 o w curvature eects. Further, new literal approximations to the longitudinal and lateral-directional modes have been obtained in terms of the redened dynamic stability parameters. The new approximations, for instance, correctly relate the short-period natural frequency to the longitudinal static stability parameter, Cm .

S. Pradeep

Papers

A century of phugoid approximations

Derivation of perturbed equations of motion of aircraft