The beam on elastic supports is often considered as a beam on a continuous elastic medium. This method can be applied only to a large number of equally spaced supports having equal rigidities. The method proposed by the author, giving the solution in the form of rapidly converging series, is not bound by this restriction, and when applied to the problem of beams supported by cross-girders reduces it to a system of linear equations, their number being equal to the number of cross-girders, while the existing approximate method leads to the same number of simultaneous differential equations.

The statement that with modern aircraft and jet propulsion engines it is essential to match the engine and aircraft has become a platitude, without the reasons being quite so well appreciated. It is well known that should the aircraft be operating away from its “ design point,” involving throttling back of the engine, then the loss of efficiency with either jet or turbine airscrew engines is liable to be serious, and to have a large effect on the range. There is also a firm conviction that very high altitude is necessary in order to give a jet aircraft any range worth mentioning.

It seems worth while to examine in a simple way on what qualities of the engine the range depends. The object of this simplified attack on the problem is two-fold; first of all it enables the factors to be readily appreciated, and second it provides rapid methods of comparing the qualities of two different engine types for range.

Following the original work of Munk, Jones, and Ward for steady flow, a solution is given for unsteady, supersonic flow over very slender bodies of revolution and wings. The results are subject to the restriction (M2- l)δ2 loge [(M2- 1)½ δ]«1 where δ is the slenderness ratio, M is the Mach number and, in addition, to the usual restrictions imposed by linearisation. As examples, the lifts and pitching moments on flat wings and bodies of revolution executing pitching motion and the damping moment on a rolling wing are calculated.

It is shown that the order of approximation is consistent with the limitations already imposed by linearisation, at least in supersonic flow, where no Kutta condition is required.

The paper is concerned with the two-dimensional, steady, irrotational, isentropic flow of a perfect gas in a wind tunnel nozzle which is found to produce a flow in the test rhombus deviating slightly from the desired uniform flow.

The minimum corrections are derived that must be applied to the liners in order to produce a uniform flow in the test rhombus. If the uncorrected nozzle produces a flow of uniform direction, measurement of the pressure on the axis, in the test rhombus, suffices to determine these corrections (Section 5). If not, further pressure measurements are required (Section 6). A simple test is indicated for checking whether the flow stream direction is uniform (Section 6).

The method cannot be used to correct for deviations from a two-dimensional flow.

In a theoretical flutter analysis, the real zeros x˂0,y˃0, of a stability determinant Δ(√x, y) which is a polynomial in y are required, and can readily be evaluated once the polynomial expansions are known for assigned values of x. When the air loads are estimated on the basis of classical derivative theory, Δ becomes a bivariate polynomial in √x and y of a special type. Direct expansion of the stability determinant becomes too involved when the number of degrees of freedom is large and indirect methods of expansion are needed.

A method of bivariate expansion which uses a framework of lines subject to certain restrictions is examined in Part I, and is applied to a quaternary wing-flutter problem. The analysis shows that frameworks previously proposed, having all intersections outside the flutter quadrant (x˂0, y˃0), demand very high computational accuracy. A new framework is suggested having all intersections inside the flutter quadrant. The improvement in computational accuracy is considerable.