Effects of vibrational excitation and dissociation of air on inviscid high speed flow past a circular cone, at zero incidence, with an attached shock wave, are studied on the assumption of thermal equilibrium. A numerical solution of the problem is outlined and an approximate analytic solution for the flow between the surface of the cone and the shock wave is developed. Two numerical examples are given as an illustration and compared with the corresponding solutions assuming constant air properties.

The thrust magnitude programme of a rocket missile being supposed specified, the problem is solved of programming the thrust direction to achieve maximum range on the Earth's surface. Earth curvature and rotation, and variation of gravity with height are taken into account, but air resistance is neglected. Motion is assumed to take place in the Equatorial plane. Tables are included from which the optimal trajectories of missiles may be computed when two design parameters are known and these tables are used to assess the advantage to be gained at extreme ranges by firing in the sense of the Earth's rotation rather than against it.

The differential equation considered is

where all the a’s and b’s are real constants.

The nature of the solution is investigated in the neighbourhood of the singular point and the conditions are found for logarithmic terms to be absent.

The conditions for stability for large values of τ are determined; the system is stable if

are all positive for large values of τ.

The form of the response is considered and its oscillatory (or non-oscillatory) nature investigated. The Sonin-Polya theorem is used to determine simple inequalities which must hold between the coefficients of the differential equation in any interval for the relative maxima of | x | to form an increasing or decreasing sequence in that interval.

Evvard’s technique is applied to the problem of a thin finite wing moving at a supersonic speed when the leading edge is subsonic. It is developed in two methods:—

• (i) in which the relationship between the pressure loading and the integrals of the downwash over the wing surface is extended as far as possible, and which has to be computed numerically;

• (ii) in which approximations are made for the upwash velocities in the neighbourhood of the leading edge, resulting in a series of standard integrals for the estimation of the pressure loading.

Method (ii) is applied to the pressure loading on a flat plate triangular wing and cropped delta wing, and the application to more general shapes is discussed.

Dr. Rockey, in his interesting paper on the design of vertical stiffeners for shear webs, perpetuates the idea of Timoshenko (Theory of Elastic Stability, McGraw-Hill, New York, 1936) that for stiffener rigidities above a certain value the stiffeners remain straight and the rigid stiffener buckling load is reached. It is my opinion that this is only so when the stiffeners happen to be placed along a straight node of one of the harmonics of the buckling pattern of the unstiffened plate. With unstiffened plates under shear loads, the nodes are not straight and consequently the buckling load will theoretically always increase with increase of stiffener rigidity, i.e. no buckling mode exists such that stiffeners of finite rigidity remain straight. It is suspected that Timoshenko was led to his conclusion by over-estimated buckling loads obtained by energy methods.

In this work the co-ordinates of three-dimensional nozzles of several types have been obtained as explicit functions, and some shapes have been plotted. It is hoped that some of these might be of use in cases where smooth uniform fluid flow is desired. The design of a particular nozzle shape in the presence of a plane boundary is given: previously any equations obtained have been too intractable to use.

A method is given for the solution of the flutter determinant on a general purpose electronic digital computer. The method has been programmed for the N.R.D.C. 401 Computer and details of this programme are given. A quicker programme, applicable when only structural damping is present and there are two degrees of freedom, is also discussed. Appendix I discusses in detail the types of errors which occur when the method is applied and Appendix II considers the anticipated loss of accuracy which will be encountered when using the method in cases where the number of degrees of fredom is large.

Modern turbine blades are generally twisted about their axes, the shape resembling that of a helicoid. This makes the determination of their overtone frequencies much more difficult. The equations governing the flexural vibrations may be obtained from the Clebsch-Kirchhoff theory for rods which are naturally twisted. By using these equations, this paper considers a first-order approximation for the effect of uniform twist.