The programming of the thrust direction of a rocket missile, to obtain maximum range over a flat earth by the most favourable employment of the aerodynamic forces, is considered for the special case when these forces are small by comparison with the missile weight. The cases of a V.2-type missile, (a) with lift and (b) without lift, are dealt with in detail and numerical results have been computed.

A number of results derived by the author in earlier reports on the flow of air around blunt bodies moving at high speed are here collected in a unified analysis. The theory predicts in a satisfactory way the shock shape and detachment distance for two blunt bodies, a flat disc and a sphere. It is shown that the density ratio across a normal shock is a useful parameter, combining the effects of both the free stream Mach number and the ratio of specific heats.

The responses of systems, whose equations of motion are linear, to arbitrary applied forces are conveniently calculable by the use of impulsive or indicial admittances. Expressions for these admittances are here given explicity for some simple dynamical chains and the procedure for their calculation in chains with more degrees of freedom is outlined. Some general characteristics of the dynamical chains are also examined.

Curves are presented which, together with a knowledge of the intake performance, enable ram-jet thrust coefficients and specific consumption figures to be obtained quickly and accurately in the range M = 1·0 to 3·0.

The problem of the best division of pressure ratio between the two spools is investigated by means of simplified expressions for component characteristics. It is found that a unique position of the L.P. compressor operating line (i.e. maximum L.P. flexibility) is obtained when the H.P. compressor operating line is vertical. This arrangement requires a low pressure ratio on the H.P. spool and gives an engine whose power is sensitive to air intake temperature changes, so that the H.P. rotor tends to overspeed at sea level and surge at high altitude. Checks by standard methods show that the algebraic approach is useful for understanding the two-spool matching problem.

Expressions are obtained for the radial, tangential, and shear stresses in an infinite plate containing a variably reinforced circular hole. The variation in the cross-sectional area of the reinforcement is chosen so that the maximum tensile resistance of the reinforcement occurs at points around the hole where the stresses in the plate tend to be high. It is shown that when the reinforcement has a given weight, the effect of varying its cross section is to reduce the stress concentration in the plate.

The following particular applied stress systems are considered:—

1. (i) Uniform tension or compression in one direction.

2. (ii) Uniform shear.

3. (iii) Unequal principal stresses.

For the particular cases of uniform end loading and unequal applied stresses in the ratio 2:1, data have been obtained which enable the designer to determine the stress distribution in plates with reinforcements having a reasonably wide range of practical dimensions.

A theory of the incompressible flow through two- and three-dimensional cascade actuator discs has been developed by several workers over the past ten years, and its accuracy has been confirmed in several experiments. This theory is briefly reviewed, and a parallel theory for subsonic compressible flow through actuator discs is developed. Approximate solutions for several examples are considered, including a compressible shear flow through a two-dimensional cascade, and a compressible flow through an annular cascade of guide vanes.

The natural transverse vibrations of a long cylindrical box of doubly symmetrical rectangular cross section are considered. Explicit stress-function solutions are obtained for the webs and the top and bottom surfaces so that the effects of shear lag and shear deflection are inherently included. The results are expressed simply in terms of an effective flexural rigidity, which may be determined with the aid of a number of graphs.

The block diagram representing an aircraft in either its lateral or longitudinal motion is given and is used to explain the aircraft response in the antisymmetric stick-fixed case. A generalised autopilot is added to the aircraft diagram and the method of analysing the combination by conventional servo techniques is indicated. It is shown how an estimate can be made of the effects on stability of non-linearities in the output member of the control system.

A model for the calculation of the “off-design” performance of turbo-machines has been suggested by Mellor, who proposed that the machine be split into an infinite number of stages, each producing a small change in stagnation enthalpy. This note suggests that the overall performance of a machine may be obtained in an integral form which permits a rapid calculation of performance maps for rotational speeds and flow rates not greatly different from design values. The method may be of use in preliminary design studies of multi-stage compressors and turbines.

In a conventional rate-of-turn measuring gyroscope the necessity to use a displacement transducer results in an appreciable zero error when a rapid response is required. Other types of instrument, employing alternating forces and force transducers, are also shown to have a relation between error and response time. An assessment is made of these relations and conclusions are reached concerning the relative merits of the different types. The results are given in terms of the estimated rate errors as functions of bandwidth.

The paper examines the error involved when the continuous distribution of lift on an unswept lifting surface is represented by a finite number of horseshoe vortices, the strengths of which are determined by a prescribed downwash. Attention is directed mainly to the case of elliptic loading, but an anti-symmetrical case is also studied to ensure that the conclusions are not peculiar to the elliptic case.

The reduction in stress concentration factors resulting from the introduction of an interference-fit pin in a circular hole in a flat plate to which a simple tension is applied has already been recorded. The same result is found to occur to an equally marked extent, and qualitatively in a very similar way, when the load is applied to the pin itself. When varying loads are applied to the pin or the plate, the effect of the interference is to produce a rise in the mean stress level at critical points on the hole boundary with a marked fall in the oscillatory stress. There appears to be an optimum value for the “interference stress” for given applied loading conditions at which the endurance of the plate will have its highest value.

When loads are applied simultaneously to pin and plate the critical stress on the hole boundary is found to be the mean of the stresses which would be produced by the total load applied separately to the pin and to the plate.

The paper describes a method of estimating the frequency of gust components in the plane of a propeller from measurements of vertical gust components, which are those generally recorded. By this means additional flight recording is avoided and the danger of under-estimating the frequency of gusts affecting the propeller is reduced. Random distribution of gusts in space is assumed. It is found that gust components in the plane of the propeller of 10 ft./sec. or more occur 2·51 times as frequently as vertical components of 10 ft./sec. or more. For speeds greater than 10 ft./sec., the ratio is higher.

This paper is concerned with the drag, at zero lift, of wing-body combinations which are symmetrical about the wing plane. Only two assumptions are made: that surface slopes are sufficiently small for the application of linearised theory, and that it is sufficient to satisfy the body boundary condition on the surface of a circular cylinder.

The configuration is represented entirely by singularities along the body axis, and three drag formulae are derived. The first involves the Laplace transforms of functions representing the strengths of the sources and multisources; the difficult problem of inverting these transforms is thereby avoided. The second involves these strength functions themselves, and is of the form of a series of double integrals of the famous von Kármán type. The third involves functions describing the geometry of a very hypothetical quasi-cylinder which has the same drag as the Whole configuration in question. The convergence of these formulae is established.

These results are then used to make an order-of-magnitude analysis for wing-slender-body combinations: a large number of drag terms are seen to be negligible when the ratio of body radius to wing chord is small, and the dominant terms for smooth bodies are those appearing in Ward's drag formula.

Finally, the geometry of the “ equivalent quasi-cylinder ” is investigated.

A simple matrix method is presented for the deflection and stress analysis of cylindrical shell structures of arbitrary cross section stiffened by flexible frames. The method is an extension to fuselage structures of the Matrix Force Method developed by Argyris, in which the internal load system in the structure consists of two parts:—(a) synthetic load distribution, represented by the matrix b0, satisfying the external and internal equations of equilibrium, and (b) self-equilibrating load systems, represented by the matrix b1, which are introduced to satisfy compatibility conditions. The magnitudes of these self-equilibrating load systems are determined from the generalised compatibility equations formulated using the flexibility matrix f for the un-assembled elements of the structure. The self-equilibrating systems are non-orthogonal, but are arranged in such a way that the mixing between one system and another is kept to a minimum and, consequently, the resulting compatibility equations are well-conditioned. The three basic matrices, b0, b1; and f, are compiled using only very simple formulae. The matrices b0 and b1 depend on the geometry of the structure, while the flexibility matrix f is a function of geometry and elastic properties. The present analysis is applied to cut-out problems in fuselage structures. It can also be used for problems involving thermal loading and diffusion of loads in curved panels stiffened by flexible frames.

An approximate theory is described which takes into account the influence of the wake on the aerodynamic derivatives of an oscillating rotor blade. It is shown that the most important parameter is the number of cycles of the oscillation which occur during one revolution of the rotor. For integral values of this parameter the flexural damping is shown to become very small at small angles of incidence. The flutter characteristics of a simple rotor blade are calculated on the basis of this theory, and it is found that the wake causes radical changes in the critical speeds. The theory is in good qualitative agreement with experiment.

The position and strength of the front shock wave at large distances from a wing-body combination, are deduced from the linear theory for the combination, using a method developed by Whitham. The combination consists of a body of revolution and a wing which has thickness and is lifting. The effects of interference between the flow over the body and the flow over the wing are included. In any direction the flow far from the wing-body combination is equivalent to the flow past a body of revolution determined from the configuration of the combination. The modified formulae for unsteady flow are given and some results are evaluated for the combination of a body of revolution and a delta wing with subsonic leading edges.

This paper concerns the free vibration of linear systems which are subject to damping. The general theory for a system having n degrees of freedom is recalled and illustrated by means of a simple example. Using an analytical method, the approximate theory for small damping is derived, showing the nature of the entrainment of the principal modes; the results are found to confirm those of Southwell (who uses a physical argument) and they are illustrated by an example. The approximate theory is shown to need modification when there are two nearly-equal natural frequencies and the appropriate corrections are found. The analysis is made somewhat complicated by the existence of two criteria of “ smallness ” instead of one; these are the difference between the close natural frequencies and the amount of the damping.

It is shown from elementary considerations that the lift coefficient of a thin two-dimensional wing at zero incidence, with a narrow high-velocity jet of momentum coefficient Cj issuing from its trailing edge at a (small) downward inclination τ, is given by

and the loading on the chord line (0<x<1) by

(except in a certain neighbourhood of the trailing edge), for small values of Cj. These formulae agree well with known measurements. Interpolation formulae for derivatives of CL at larger values of CJ based on earlier work, are also given: