An investigation is made into the possibility of the completely automatic longitudinal control of an aircraft in the deck landing approach. The method presupposes the existence of a radio beam system transmitted from the carrier and a study is made of the motion of the aircraft down this beam under automatic control.

The longitudinal motion alone of the aircraft and carrier is considered. The motion of the carrier is assumed to consist of a steady forward velocity modified by a non-pitching sinusoidal oscillation in the vertical plane.

The most successful method of approach control proposed is based on the use of a single beam emanating from a source at a fixed distance above the carrier deck and fixed in direction. The preliminary pilot-controlled approach is assumed to be down the mean position of the beam, and the auto-control requires, over and above certain ideal variations of elevator angle and thrust, additional types of control of the following forms. On the elevator, displacement pitch and displacement track error control; and on the thrust, displacement track error control.

Information is also forthcoming regarding the unsuitability of certain other types of control which at first sight seem promising.

The inverse problem of determining the supersonic flow past a thin symmetrical wing at zero incidence with given surface pressure distribution is solved for wings of arbitrary plan form. Expressions are obtained for the vertical derivative of the potential on the wing surface from which, using the linearised boundary condition of zero normal velocity at the surface, the profile of the wing can be designed. The integral equation method adopted by J. C. Evvard and extended by G. N. Ward is used. The analysis cannot be applied to pointed wings, whose leading edges are subsonic. The results in Part I are completely general and are applied to specific problems in Part II.

The elementary engineering theory of longitudinal waves in beams allows for no dispersion, whereas Love's corrected version of it predicts that very short waves are not propagated. A new correction is added which overcomes these defects. To do this, a simple theorem is proved concerning certain types of closed region. A method of improving Love's formula and the present one is illustrated.

The integral equations for the pressure distribution on an oscillating thin wing having a prescribed velocity distribution in a supersonic flow are developed.

The theory of aerofoils in unsteady flow, which has made substantial progress in the last decade due largely to the ground work of Küssner and his co-workers, is presented here in a form suitable for application in aeroelastic problems, particularly those concerned with the dynamic loads on aircraft arising from gusts.

Exact expressions are given for the aerodynamic lift and moment for an oscillating aerofoil as well as for the case of arbitrary motion through disturbed air. The expressions for the latter case involve two special functions, generally referred to as Wagner and Küssner functions. Exact values of these functions are tabulated together with useful approximations. The problem of a wing-tail combination is discussed and a method of solution indicated. The bibliography at the end of the paper lists the most important publications in this field.