Mr. Glauert's paper “Theoretical Relationships for the Lilt and Drag of an Aerofoil Structure ” strikes a bold note in asking us to discuss the fundamental principles of Prandtl's aerofoil theory rather than its detailed application. His suggestion is a particularly good one, however difficult the task. Justification of the geeneral truth of the suggestions brought forward by Lanchester, and so ably developed bv Prandtl and his colleagues and others, have frequently been afforded by the application of the theory, and similar support only awaits the seeking. But, to achieve its greatest utility, the theory should enable us to extrapolate experimental knowledge with confidence; an example is provided by the question as to what limit, if any, exists to the camber of wings on economic grounds and apart from burble considerations. An approximate tally—rough, in some cases—of the theory with observation over a limited range is inadequate to establish it sufficiently for such a purpose. The theory may indicate with truth the existence of, say, a limit to a certain development, but its numerical calculation of the limit may yet be widely wrong.

When engaged on war work as Chief Inspector for Fredk. Sage & Co. at Peterboro’, England, in the spring of 1918, I observed that when Honduras mahogany was compressed across the grain, and parallel, to the annular rings of the wood, a “first” or “natural” elastic limit was reached, after which the deflections increased more rapidly than the load, as has been commonly observed in all testing of all materials.

As it may be necessary in the future, as it has been in the past, to launch aircraft from ships, other than aircraft carriers with large aerodrome decks, the following investigation has been carried out.

It is required to find the minimum propeller thrust necessary to enable an aircraft (particularly a seaplane or flying boat) of known weight and fineness, to take off from a railway platform, on a ship steaming at given speed.

It is a fact of common experience that a body in motion relative to a gas or liquid is subject to a resultant force, and it is customary to resolve this force into two components, the drag opposing the relative motion and the lift at right-angles to the direction of this motion. In general the drag is the pre-dominant component, but the class of bodies known as aerofoils and used for the construction of aeroplane wings, is such that the lift is considerably in excess of the drag. The present discussion relates solely to this class of bodies whose essential characteristic is the production of a large lift correlated with a relatively small drag. It is a matter of very considerable importance to develop a theory which will explain the origin of the forces experienced by an aerofoil, and will provide a method of calculating the characteristics of any aerofoil structure from a knowledge of its geometrical form and of the physical properties of the fluid through which it moves. It is proposed to discuss the behaviour of aerofoils in two and in three dimensions, and in particular to discuss the vortex theory of lift and induced drag. The general nature of the flow pattern on which the theory is based has been described by Lanchester, but the mathematical development of the thcorv is due to Prandtl and his colleagues.

The object of the present paper is to give some account of certain methods developed by Joukowsky, Mises and others for calculating the forces experienced by a body of aerofoil shape placed in a stream moving in a fixed direction with uniform speed. The span of the aerofoil is supposed infinite and the cross section uniform and the motion thus becomes two-dimensional.