The velocity field around a circular cone in supersonic flow is determined by considering fluid injection and suction through the porous wall of the body. By using a new method of linearisation of the equations of motion, analytical formulae are obtained which yield almost exact results, as compared with numerical calculations. In addition, the method proposed suggests new problems related to fluid injection and suction which are important for practical applications.

This paper concerns the boundaries between flow regimes for sharp-edged delta wings in supersonic flow and the relation of some predictions of thin-shock-layer theory to these boundaries. In particular, it is shown that the theory predicts that the attachment lines on the lower surface of a thin delta wing at supersonic speeds suddenly jump from just inboard of the leading edges to the centre line in certain flight conditions. In general there is close agreement between the conditions for this jump and the flight conditions corresponding to the change-over from attached flow to the leading-edge separation on the upper surface. Since the movement of the attachment lines on the lower surface must change the position of the sonic line and the nature of the expansion around the edge, it is suggested that the two phenomena are directly related. Thus thin-shock-layer theory can be used to establish the boundaries of the various flow regimes for a wide range of Mach number, incidence and wing sweep. The theory can also be used to predict the effects of wing thickness on leading-edge separation, but here the experimental data is very sparse and somewhat contradictory, so the value of the prediction in the case of thickness requires further investigation.

This paper reports an experimental investigation into the stagnation bubbles found in the shock layers of some supersonic jets impinging on perpendicular flat plates at small nozzle-to-plate distances. The experiments used twelve contoured nozzles within the Mach number range 1.42 to 2.83. Surface pressures were measured on the plate and free-jet pitot pressure distributions were obtained at the level of the centre of the plate shock. Schlieren pictures were taken of both impinging and free jets. It was found that the bubbles result from the interaction of the plate shock with very weak shock waves which are produced in the jet either by small imperfections in the nozzle wall or by slight inaccuracies in the design or production of the nozzle contour. The bubbles can be eliminated by suitable improvements to the nozzle. Other anomalous flows produced by shock interactions are described and explanations offered. It is shown that the bubbles sometimes encountered at close plate spacings with conical nozzles are also due to shock waves. However, for wide-angled nozzles, internal shocks can be an inherent part of the flow from the nozzle and the bubbles which they produce are thus an inherent part of the impingement flow. From physical arguments concerning the main factors involved in producing a bubble, a parameter is constructed whose values are shown to be a good criterion for whether a bubble occurs or not.

Comparisons are made between some measurements of skin friction and heat transfer over five axisymmetric bodies and the predictions of a simple theory. The development of the theory is outlined and explicit expressions obtained for all the gross turbulent boundary-layer characteristics (δ*,θ,H,Cf and St).

An experiment was made on a turbulent boundary layer with adverse and favourable pressure gradients alternating twice along the stream. The most important findings of the present study are as follows. In the region of the adverse pressure gradient downstream of the strong acceleration, an internal boundary layer develops within the boundary layer. In this internal layer large advection of turbulent energy occurs and the flow is locally non-equilibrium even near the wall. As a result the usual logarithmic law and turbulence similarity in the viscous sublayer break down.

The equations of motion of a highly idealised model of a helicopter with a simple lag-hinged rotor are derived by Lagrange’s method. It is shown that the transformed equations governing Coleman instability (ground resonance) have a regular form involving wholly symmetric and skew-symmetric matrices. The work input to the unstable motions derives wholly from the torque applied to the rotor by the engine, but the torque equation is superfluous as far as the eigenvalues are concerned. Approximate stability criteria show that chassis and lag dampings per se are destabilising relative to the undamped reference condition and can lead to a substantial lowering of the critical rotor speed for instability onset. A necessary condition for instability (dynamic) is that two eigenvalues of the stiffness matrix are simultaneously negative.

A method of predicting body drag in subcritical axisymmetric flow is outlined which requires only detailed body shape, free-stream conditions and transition point to be prescribed. Results of calculations for a range of body shapes are shown essentially to confirm information in Royal Aeronautical Society Data Sheets but clearly demonstrate that fineness ratio alone is not sufficient to characterise body shape. For example, at a fixed fineness ratio of 0.18, detailed changes in body contour are shown to produce 10 per cent changes in drag coefficient.

The results of an experimental study of the buckling and vibration behaviour of tensioned sheets with a rectangular opening are presented. The buckling phenomenon involves the existence of a non-uniform pre-buckle stress state in the vicinity of the opening. The local buckling load has been estimated on the basis of the modified Southwell method. The effect of parameters like cut-out size, sheet width, sheet thickness and cut-out corner radius has been investigated. The data from the vibration experiments indicate that the load versus frequency behaviour is dependent on the size of the test specimen and the opening shape. It has been observed that, for certain combinations of plate and opening parameters, the load versus frequency plot has a minimum corresponding to the local buckling of the free edge of the hole. For other plate and opening parameters it shows only a kink corresponding to the local buckling of the free edge of the cut-out. The buckling load for the opening shapes obtained from both the static and dynamic experiments are compared, showing good agreement.

This study is an investigation of the non-linear behaviour of an elastic spherical cap under the assumption of axisymmetric deformation. The types of axisymmetric loading under consideration are partially loaded uniform pressure, line load, “cosine” load with the maximum intensity at the apex and the combined action of uniform pressure and line load. The edge of the cap is assumed to be rigidly clamped, hinged, and unrestrainedly simply-supported. The method of solution is an extension of the iterative procedure for the integral equations formulated by Budiansky for uniformly loaded, clamped caps. In the cases of hinged and unrestrainedly simply-supported edges, the critical loads for the axisymmetric snap-buckling are presented for different types of loading and various values of the geometrical cap parameter. In the case of a clamped edge the load-deflection curves are established until no solution can be found for further increasing the load. The load corresponding to the limit point on the load-deflection curve is the critical load if the axisymmetric snap-buckling exists. The graphical results are presented for load-deflection curves, deflection profiles, bending moments, transverse shear and interaction of buckling pressures and buckling line loads. The present results are in good agreement with available data for uniform pressure distributed over the entire surface of the cap with three sets of edge conditions and over the central portion of a clamped cap.

The non-linear boundary-value problem resulting from an analysis of the stresses and deflections of an annular membrane is transformed into an initial-value problem, replacing the iterative and series methods of Pifko and Goldberg. A general solution valid for the complete range of values of the ratio of inner and outer radii is obtained and tabulated by this non-iterative method.

A wind tunnel technique has been developed to measure the aerodynamic forces acting on golf balls over a wide range of Reynolds number and spin rate. Balls with round dimples and hexagonal dimples have been investigated. The dimples are found to induce a critical Reynolds number behaviour at a lower value of Reynolds number than that experienced by a smooth sphere and beyond this point, unlike the behaviour of a sand-roughened sphere, there is little dependence of the forces on further increases in Reynolds number. A hexagonally-dimpled ball has a higher lift coefficient and a slightly lower drag coefficient than a conventional round-dimpled ball. Trajectories are calculated using the aerodynamic data and the ranges are compared with data obtained from a driving machine on a golf course.

The base pressure correlation proposed earlier by the authors, to take into account the effects of the boundary layer and of the boat-tail angle, is utilised in the design of two-dimensional aft bodies for minimum drag in supersonic flow. The general advantages of boat-tailing are indicated and charts of optimum profile parameters and minimum drag are provided for use in preliminary design. The effects on aft-body drag of possible reversion of the boundary layer at a sudden expansion are discussed, and the relevance of the optimum shapes found to the lifting case is indicated. The calculated optimum geometry is in good agreement with the experimental results of Fuller and Reid.

Among the many problems which face airframe manufacturers, cooling is certainly one of the most important, particularly as a special watch must be kept on the type of solution to be adopted, since the lowest fuel penalty must be incurred in flight.

Observed variations of eddy viscosity in the outer regions of turbulent boundary layers are here explained in terms of the reorientation and stretching of vortex elements. The explanation, which is purely qualitative, gives a clear and plausible physical picture.

An approximate analytical method is presented for determining the swirling compressible flow through a nozzle. The method is developed from the techniques introduced by Carpenter and Johannesen. It is perfectly general in that the swirl distribution need not be specified a priori but the radial gradients of the stagnation enthalpy and entropy are assumed to be small. The principal assumption is that changes in the nozzle cross-sectional area are sufficiently gradual and smooth for the radial velocity component to be neglected at each section, i e the usual assumption of one-dimensional compressible flow theory. Analytical expressions are derived for various flow characteristics, e g mass-flux coefficient, impulse function and back-pressure ratio required for choking. The analytical results are compared to numerical results for two main classes of swirling flows. On the whole the analytical results are found to be good approximations for moderate swirl levels. The approximate numerical method is found to be reasonably successful at predicting flow reversal at the nozzle wall. The main result is that a swirl parameter is found such that, with the sole exception of the free-vortex case, the mass-flux-coefficient data for all swirling flows investigated collapse onto a single curve.

The effects of free-stream turbulence and of sinusoidal free-stream pulsations of controlled frequencies and amplitudes on the periodic wake of a circular cylinder are investigated experimentally by employing hot-wire and smoke visualisation techniques. In addition, the effects of cylinder yaw and mild favourable and adverse pressure gradients on the vortex shedding mechanism have been explored.

The data relating frequency to mean velocity follow Berger’s relation; this relation is uninfluenced by free-stream turbulence intensities up to 8 per cent. As the longitudinal turbulence intensity increases from 0.3 to 8 per cent, the downstream distance Lp behind the cylinder over which the hot-wire signal is periodic decreases progressively, indicating that the otherwise steady periodic wake interacts non-linearly with the three-dimensional free-stream turbulence and undergoes either transition or rapid diffusion by turbulence, depending on both the Reynolds number and the turbulence intensity. For a given turbulence intensity, Lp decreases also with increasing Reynolds number.

The shedding frequency behind a yawed cylinder does not vary as the cosine of the yaw angle ϕ for ϕ < 50°; the signal switches intermittently between periodic and irregular form as the yaw is increased from 0 to 70°. Mild pressure gradients (favourable as well as adverse) do not affect the shedding frequency; this is confirmed by smoke visualisation, which also shows that the pressure gradient changes the longitudinal vortex spacing downstream; the measured frequency is that determined by the local Reynolds number corresponding to the Berger relation.

Sinusoidal streamwise pulsations of controlled frequencies, and of amplitudes up to 10 per cent of free-stream velocity, have no effect on the natural shedding frequency; this is confirmed by smoke visualisation of the cylinder wake. However, the wake signal is amplitude-modulated at a frequency equal to the difference between the pulsation frequency and the natural shedding frequency corresponding to the free-stream mean velocity. The vortices are diffused faster in the presence of pulsation. When the pulsation amplitude is increased beyond 20 per cent, the hot-wire signal frequency in the wake equals the driving frequency; the frequency in the wake centre is also that of the pulsation. The effect of free-stream pulsation on the periodic wake is different from that due to longitudinal or transverse cylinder vibration, when lock-in has been observed.

It appears that free-stream disturbances – random or periodic – cannot account for the “Tritton jump”.

In an axisymmetric turbulent boundary layer along a circular cylinder at constant pressure, measurements have been made of mean velocity profile and turbulence characteristics: longitudinal velocity fluctuations, Reynolds shear stress, transverse correlation and spectrum. It has been found that the qualitative behaviour of an axisymmetric turbulent boundary layer is similar to that of a two-dimensional boundary layer in the wall region, where as in the outer region the effects of transverse curvature are observed.

This paper reports on an investigation of the effect of local elastic buckling of stiffener outstands on the overall behaviour of stiffened plates. A simplified mathematical model has been developed, based on the post-buckling analysis of the stiffener, and gives a simple expression which indicates that, for the plate geometry investigated, the maximum load carried varies asymptotically between the local critical load of the stiffener and a reduced Euler load. Also, there is a marked imperfection sensitivity arising from the interaction of the local and overall buckling modes. Experiments were carried out to confirm the analytical prediction for the elastic buckling behaviour of the stiffened plates. The models were constructed of Araldite, to allow large deformation within the elastic strain range. Experimental results showed very good agreement with the theory.

A theory is developed for the prediction of the pressure at the reattachment point in subsonic two-dimensional steady base flow. Theoretically estimated values of the reattachment pressure seem to agree well with experimental ones.

A detailed survey of a delta wing of 70° sweep has been performed at M = 2.5. The measurements include upper- and lower-surface pressure distributions, schlieren photographs, vapour-screen photographs and surface oil-flow visualisation. The results have been compared with thin-shock-layer theory and various other predictions.