On a pitch control law for a constant glide slope through windshears

Abstract

SummaryThe equations of motion of an aircraft flying at a constant glide slope (Fig. 3), in the presence of arbitrary head- or tailwinds, and up- or downflows is considered. The equations are integrated analytically, in the case of an aircraft initially on a steady flight, perturbed by winds of ‘moderate’ strength, in the sense that the wind velocity is not negligible compared to the aircraft's steady speed, but the ratio of their squares is much smaller than unity. The case of an approach through a downburst (Fig. 1), leads to winds which can be simplified to a one-period sinusoidal wind along the flight path, changing from head- to tailwind, at the peak of a superimposed downflow (Fig. 2), of half-period sinusoidal shape, and this is discussed in some detail. Data sheets are presented for three combinations of amplitudes of the head-to-tailwind and downflow; each contains plots of the scheduling of incidence that exactly cancels windshear effects, and of the groundspeed a'nd airspeed profiles which will keep the aircraft flying along the original glide slope. Each plot is given for a range of values of the windshear susceptibility parameter, representing aircraft with small or large inertia, with high or low approach speeds, including light aircraft, jet fighters and large transports; the cancellation of windshear effects isachievable only if the incidence schedule lies wholly below the stall limit. Since the rotational inertia of the aircraft is neglected, the short period mode is absent, and the pitch control acts to cancel the ‘phugoid’ instability induced on the aircraft by the wind profiles typical of a microburst.