One of the main problems associated with the “ Jet Flap ” concerns the discrepancy in thrust between idealised theory and the experimental results. This discrepancy is attributable to the mixing with the surrounding flow of the thin two-dimensional jet while still in close proximity to the aerofoil. The effect of the mixing may be calculated to a first approximation from a formula derivable from first principles, while certain second order effects, which can be significant, may be considered qualitatively.

It is concluded that.

• (i) the full thrust should be experienced by a jet flapped aircraft at cruise,

• (ii) it should be possible to attain a low form drag at cruise in comparison with a conventional aircraft,

• (iii) at take-off, an aircraft using a shrouded jet flap would have better thrust recovery than one using a pure jet flap (which shows appreciable losses),

• (iv) the use of by-pass engines would further improve the thrust characteristics,

• (v) the practical gains from thrust augmentation, as obtained by controlling the mixing, seem likely to be small.

The result derived in a previous paper for the primary effect of the jet mixing on the thrust is confirmed, both by an investigation using momentum principles and by a quantitative examination of the sink effect. Boundary layer behaviour still cannot be predicted with accuracy, but it is suggested that, even under cruising conditions, a jet flapped aerofoil may exhibit unconventional properties.

A theory of creep buckling is presented in which the instantaneous elastic and plastic deformations following the application of a load, as well as the steady creep deformations, are considered in an approximate manner. Equations are given from which the critical time, that is, the time elapsing between load application and the collapse of the column, can be computed.

When a flow with a non-uniform velocity passes through a cascade, the blades impose on each layer of the flow local pressure changes which are roughly proportional to the dynamic head in the layer. This results in local pressure differences which, within the blade passages, produce rotational secondary flows and which also cause overall spanwise accelerations and displacements. These effects are analysed for frictionless flow by treating the blade row as an actuator plane whose outlet angle is determined by the secondary velocities in the blade passages.

At low outlet angles or large deflections the secondary flows effectively control the downstream flow angles. When the outlet angle is large the displacement effect can result in downstream flow angles of opposite sign to those induced by the secondary flow alone.

Measurements on cascades with small spanwise variations induced in the approaching stream confirm the main predictions of the first order theory.

The correct design of intermediate vertical stiffeners on web plates subjected to shear becomes very important when the web plates are designed to operate at loads close to their buckling loads. This paper presents details of an extensive series of tests conducted on stiffened web plates subjected to shear. From the analysis of the results obtained from these tests, new empirical relationships between the flexural rigidity and spacing of the intermediate stiffeners and the buckling stress of the stiffened web plate have been obtained.

One interesting and important feature of these new relationships is that they define more clearly than hitherto the difference in the behaviour of single-and double-sided stiffeners.

The longitudinal stability derivatives and stability loci for a single-degree-of-freedom, pitching oscillation of a rectangular wing having an effective aspect ratio less than unity have been calculated from the results of a previous, analytical investigation. The results extend those previously available for a rectangular wing of effective aspect ratio greater than unity.

In this paper a non-linear theory of the supersonic bangs from an accelerating body is worked out, using an extension of Whitham’s method. The strength of the bow shock is determined, and it is shown that the effect of acceleration on the pressure rise is appreciable at large distances from the nose for Mach numbers near unity. The results are compared with those of linear theory; the estimate for the pressure rise is found to be about a half of the linear value. The results also include an expression for the curvature of an attached shock at the nose, and a formula for the decay of a shock after it is detached from a decelerating body.

Kinetic heating associated with supersonic flight presents new problems to the aircraft structural engineer. Some of these can be resolved by the use of the theorems of thermo-elasticity. This paper outlines the foundations of this subject and derives generalisations of the usual variational theorems, which are so often used in structural analysis.

The mathematical theory of nosewheel shimmy is given, with particular reference to twin nosewheel assemblies. It is shown that a sovereign remedy for shimmy is to make the castor length greater than what is here called the “ creep distance,” which in practice is found to be approximately equal to the tyre radius. Lateral flexibility of the oleo leg is disadvantageous but elastic constraint at the pivot is a good feature. The one necessitates an increased castor for stability while the other allows a smaller castor. It is also shown how, by the use of a compact linkage mechanism, the effective castor length can be made independent of the wheel-leg offset and can have any desired value. Model experiments that confirm the theoretical conclusions are described.

An historical sketch shows how the basic ideas of the jet flap were evolved. The exploratory work included the prediction that lift would be induced on an aerofoil by a two-dimensional jet deflected from the trailing edge, and that the magnitude of the total lift would be of the order of four times the direct jet lift. The prediction was confirmed experimentally and a first quantitative theory evolved. Meanwhile the hypothesis was put forward that, ideally, the forward thrust on the aerofoil would be independent of the deflection angle of the jet.

This paper is the first of a series of papers that will describe the development and present state of knowledge of the jet flap.

The introduction of an interference-fit pin in a circular hole in a flat plate is found to result in a reduction in the stress concentration factor at the hole boundary under tension applied to the plate. The S.C.F. decreases rapidly with increase in the ratio of interference stress to applied tension, and decreases also with increase in the ratio of hole diameter to width of plate. Very little difference in the S.C.F. is found for different ratios of Young's modulus of pin and plate.

In the investigation of approximate numerical values of overtone frequencies of a turbine blade it is desirable to know formulae for certain integrals of the modes of vibration of an ordinary cantilever beam. The first object of this paper is to obtain such formulae and to arrange them in tabulated form. By proceeding along the lines of the calculus of perturbations, these results may then be used to obtain new formulae which give second order approximations for the effects of uniform breadth and thickness tapers on the overtone frequencies. The theory gives good agreement with experiments for tapers which do not exceed about 0·5, which is present-day practice for turbine blading.

This paper is concerned with the solution of the creep buckling of columns. Instantaneous elastic and plastic deformations, as well as the transient and secondary creep, are considered. Formulae for the critical time at which a column fails are presented for integral values of the exponents appearing in the creep law.

This paper is the second of a series of three. The first dealt with the steady forced harmonic motion of a simple oscillator with one degree of freedom when “ hysteretic damping ” is present; by this it is meant that a damping force exists which is in phase with velocity but whose magnitude is proportional to displacement. The present paper is devoted to the formulation of a general theory of small hysteretically damped vibration in which the existence is postulated of damping forces which act between pairs of points such that they are in phase with the relative velocities and their magnitudes are proportional to relative displacements. The theory is presented in general terms and use is made of Lagrange’s equations with a new type of “ dissipation function ”; this is comparable with that of Rayleigh for viscous damping. It is shown that this theory generally leads to simpler algebra than does that of viscous damping. Moreover, it will be shown in a later paper that the nature of forced and damped oscillation may be thought of in terms of modes more simply than is the case with the more familiar viscous damping.

The climb performance of a turbo-jet transport aircraft is considered, using the concept of the energy height. The analytical formulae used in evaluating the time needed, distance covered and fuel consumed during climb under various conditions are developed. It is concluded that the application of this energy approach method to the climb performance estimation of a turbojet transport aircraft will prove satisfactory from the points of view both of the accuracy of the results and of saving some of the considerable time needed for the climb calculation by the conventional method. A numerical example is given to illustrate the usefulness, applicability and flexibility of this method.

Approximate solutions are given for the lowest natural frequency of flexural vibration of isosceles triangular plates which have the equal edges simply-supported and the base clamped. The results are presented graphically to allow rapid determination of a desired fundamental frequency.

Small, steady perturbations of general two-dimensional steady, shock-free, supersonic flows are studied and the perturbation fields of symmetrical nozzle flows are described in detail. The relation between errors in the shape of the supersonic part of the nozzle liners and the deviations from uniformity of the flow in the test section is given to an approximation sufficient for the treatment of a number of problems arising from experiment and in the design of nozzles.

The class of incompressible axially-symmetric laminar viscous flows considered are exact invariant (similarity) solutions of the Navier- Stokes equations. The functional forms of the velocity components are deduced by group-theoretic arguments. The system of governing partial differential equations is reduced to a system of ordinary differential equations and these in turn are reduced to a single first order non-linear ordinary differential equation for the dimensionless tangential velocity component. The general solution of this equation is obtained in terms of hypergeometric functions.

The classes of laminar viscous flows bounded by a right conical surface or by right inner and outer conical surfaces with a common apex obtainable from the previously mentioned (similar) solutions of the Navier-Stokes equation are studied. Suction/injection velocities (inversely proportional to the distance from the apex) normal/parallel to the conical boundaries are admissible for the classes of flows considered. If the flow is bounded by impermeable conical surfaces, then it is shown that these solutions of the Navier-Stokes equation imply that it must be identically quiescent.

When the bounding cones are not impermeable, closed solutions for the single-cone case are found in terms of elementary functions. A numerical example of such a flow, with fluid injected normal to the conical boundary, is given. Such a simplification of the hypergeometric functions entering into the problem, however, cannot be achieved in the two-cone case.

Using Rayleigh's principle, the natural frequencies of thin isotropic rhombic plates, with three possible combinations of boundary conditions obtained by combining clamped-clamped and clamped-supported edge conditions, are determined in Part I of this paper. To introduce constant limits of integration, non-orthogonal co-ordinate systems are used and the wave shape for the vibrating plate is approximated by using normal functions representing mode shapes of corresponding bars. To estimate the accuracy of these eigenvalues, Kato's theorem is used and the lower bounds for the natural frequencies are determined in Part II of the paper. It is also shown that normal beam functions are not generally suitable for the determination of eigenfrequencies of skew plates with large skew angles.

The non-linear theory of supersonic bangs, obtained in Part 1 for a body accelerating along a straight path, is extended to include curved paths. The basic theory remains the same. The important parameter, which appears in the theory, is the acceleration component along the ray, the rays being lines drawn from points on the flight path at an angle cos-1 (1/M) with the direction of motion. It is found that the only essential effect of the curvature of the path is in the modification of this acceleration component to include a term due to the transverse acceleration. With this modification the main results are formally the same as in Part I.

The strength of the bow shock is obtained, and it is found that the effect of the curvature of the path is more pronounced at points on the inside of the curve, and in general it becomes greater as the distance from the body increases. A simple asymptotic formula is obtained which predicts the strength of the shock with an error of less than five per cent, at distances of the order of a hundred body-lengths. Finally, the theory is compared and contrasted with the recent work by Warren.