The present article is an account of some calculations on helicopters.

Airscrews have been calculated for different conditions according to two theories: (1) the multiplane interference theory; (2) Glauert's vortex theor). According to both there should be no difficulty in designing a screw to give a good lift at a reasonable rate of climb, and the ceiling should also be quite good. When we consider the speed of falling, with the screws free-wheeling, the two theories give widely different results, and the practicability of the helicopter depends largely upon this question being settled. Simple airscrew theory shows that at least moderate speeds should be obtainable by inclining the airscrew axis. For many reasons it seems desirable that the screws should have at least four blades; gyroscopic couples on the whole machine are eliminated; the forces are widely fluctuating during forward motion with only two blades; the stability derivatives and equations are simplified; but the aerodynamic efficiency will be impaired. In general the stability equation is of the tenth degree, and the lateral and longitudinal stabilities are not separable when the machine, in a state of steady motion in a straight line, receives an asymmetrical disturbance.

The following notes are the results of an attempt to investigate the theoretical possibilities of the helicopter, and generally to develop some branches of the theory of helicopters. In this country extremely little work on the subject seems to have been published, and the only experiments I have been able to find are those given in the Report of the Advisory Committee for 1917-18 (Vol. II.). Several articles have appeared in “ L'Aérophile ” from time to time, notably by Lamé, Touissaint and Margoulis, and some experimental work has been done by Eiffel. But it is extremely difficult to find adequate experimental results with which to compare any theory ; for instance it is very rare to find results of tests on airscrews working under helicopteral conditions, and also the aerodynamic data of the aerofoil sections used. In the matter of stability I do not know of any experimental work at all.

I shall give first the results of my investigations into airscrews for helicopters, and then proceed to the consideration of the dynamics of helicopter flight and the development of the stability equations.