Stabilisation of the Aeroplane in Symmetric Flight at Zero or Very Small Air Speeds

Summary

The possible use of jet thrust as a source of lift, either by deflection of the force from the normal propulsion axis, or by some other means, raises a new stability problem under conditions of hovering flight and flight at speeds for which the aerodynamic damping becomes insignificant. At the same time, despite the small dynamic pressure, the direct air loads cannot be neglected, for, due to the very large positive or negative incidences peculiar to the motion, the associated coefficients are of a compensatingly high order. Consequently, the problem retains an aerodynamic element, but is principally one of automatic stabilisation, amenable to treatment by ordinary mechanical or electrical circuit theory. The investigation has been restricted to the longitudinal-symmetric motion with virtually the only workable form of automatic control, namely, one responsive to the angular displacement and velocity in pitch, but these conditions undoubtedly embrace all the essentials of any practical application, e.g. in take-off and landing by the new technique. The solution to the stability in a gust, or in a succession of disturbances, may then be easily obtained in closed analytical form, but the more general case of unsteady motion, when the displacements are no longer purely oscillatory, necessitates, in part, the use of step-by-step integration. This arises from the added complexity of the aerodynamic terms, due to the appearance of significant changes of incidence, and to the very large and variable values of the resistance derivatives at the angles involved, so that, in the present state of knowledge, the forces determining the motion cannot be expressed functionally. The labour which such calculations entail may be considerably shortened, however, by the application of a procedure based on mean deviations, but it is also found that the conclusions to be drawn from the hovering case remain valid in a number of important respects for the general problem. This feature is demonstrated in the discussion at the end of the paper on a number of examples designed to illustrate the characteristics of the automatic control and the conditions necessary for stability in a variety of circumstances, both when the aircraft is hovering and when its displacement increases continuously with time.