Surface pressure distributions have been measured on a cylinder with a double-wedge cross section in a two-dimensional channel flow. The flow is sheared in the direction of the cylinder axis, using a grid of parallel wires with variable spacing, in order to simulate the type of geometry and velocity variation which occur for annulus support struts in turbomachines. The strut had a 38° included angle at the leading and trailing edges and an aspect ratio of 1.33 based on the maximum thickness. This was fixed between the parallel walls of a rectangular wind tunnel with end leakage eliminated. Surface pressure distributions were measured over a Reynolds number range of 0.5 × 105 to 1.5 × 105 for three different shear flow conditions. Despite the presence of sharp edges at the mid-chord position, delayed boundary-layer separation beyond the plane of maximum thickness has been found for sufficiently high spanwise shear in the upstream flow. Surprisingly, therefore, some similarity with previous results for struts of circular cross section appears to exist. The influence of the shear flow conditions on the pressure drag force has been determined by numerical integration of the data. Only a slight dependence on the upstream flow conditions is found, although the effect of secondary velocity components may still be observed if the spanwise variations in the local drag force are examined.

In the usual form of thin-shock-layer theory it is assumed that the flow about a lifting body can be expanded in terms of the inverse density ratio across a basic oblique shock wave lying in the plane of the leading edges of the body. In this paper it is shown that more accurate results can be obtained by moving the basic shock closer to the calculated shock wave below the body. The results obtained show why the original form of thin-shock-layer theory often gave good agreement with experiment in conditions which appeared to be outside the range of validity of the theory.

A novel low-speed wind tunnel which produces unsteady “gust” flows is described. The walls are sinusoidal in shape and are moved in the flow direction with a velocity Ww less than the mean velocity Wm of the free stream. The tunnel is useful for testing isolated aerofoils and aerofoils in cascade in non-convective gusts (Ww < Wm) so that comparisons with predictions by thin aerofoil theory may be made. However, it does not simulate precisely the unsteady flow that occurs in axial flow turbomachines.

A survey is given of experimental results on a series of aerofoils designed in recent years, first at the National Physical Laboratory and later at the Royal Aircraft Establishment, with the intention of operating at relatively high subsonic Mach numbers (around 0.8) with, on the upper surface, a large extent of supercritical flow, terminated by a weak shock wave. The paper describes the design of a basic aerofoil, together with some modifications to it which were successful in improving its performance at both high and low speeds. It is shown that the best of these aerofoils, with thickness/chord ratio 0.105, has a drag rise Mach number of 0.80 at a lift coefficient of 0.5, thus comparing favourably in this respect with other published examples; its maximum lift coefficient at low speeds, 1.2, is also satisfactory for an aerofoil of this thickness. In a final section some comparisons are given between these experimental results and some theoretical calculations by the finite-difference method of Garabedian and Korn, including a partial allowance for viscous effects. It is concluded that, although reasonable overall agreement with experiment is often obtained, further improvements in this theory are needed before it can be used with confidence for practical purposes.

The equations of motion of a vehicle entering the earth’s atmosphere (space shuttle) are expanded to give the incidence oscillation equation. The stability conditions for small free oscillations are deduced. These stability conditions apply equally to short-period and long-period oscillations. A special case of critical damping is investigated and more explicit stability conditions are derived for that case.

The usefulness of a probe which can sense the absolute value of the stagnation pressure in supersonic flow has long been recognised. In the past such a probe has not been available and therefore it has been necessary to infer this fundamentally important flow property from measurements of other properties. This paper describes a probe which has been developed specifically to measure accurately the stagnation pressure of a supersonic gas stream. Measurements of the performance of the probe to date show that it is capable of measuring absolute stagnation pressure with an accuracy of 0.1 per cent in the Mach number range 1.5 to 2.1. No measurements have yet been made in the transonic range, but at low subsonic speeds the probe has demonstrated its ability to measure dynamic pressure within an accuracy of 0.1 per cent at a Mach number of approximately 0.13. The permissible range of misalignment in pitch and yaw before the pressure recovery begins to deteriorate are functions of free-stream Mach number and are usefully wide.

Previous papers by the authors and others have developed exact methods for computing the critical buckling loads of prismatic assemblies of rigidly interconnected thin flat rectangular plates. The plates may be isotropic or anisotropic and can carry uniform in-plane shear stresses and transverse stresses in addition to a longitudinal stress which varies linearly over the cross section but is longitudinally invariant. Published results obtained using these methods have only covered a few of the types of structure and loading which are of interest. This paper presents results which complement those already published. For instance, interaction curves are given for common types of panel in combined in-plane shear and longitudinal compression and bending. About half of these curves are nearly parabolic while some others differ greatly from the parabola, which errs on the safe side for all the results presented. Other results cover critical loads other than the lowest, panels with bulb flat stiffeners, as used for bridge decks, and the effects of assumptions usually made when idealising real panels before computation.

The method of parameter differentiation is applied to the solution of the non-linear, two-point, ordinary differential equations resulting from an analysis of the finite bending of a thin-walled tube. Starting from a given set of solutions of the differential equations for a particular value of the curvature parameter α, solutions for a range of values of α can be obtained by this method non-iteratively. Very close agreement was obtained with solutions using iterative numerical methods.

An exact method has recently been presented for computing the critical buckling loads, or the natural frequencies of vibration, of prismatic assemblies of rigidly inter-connected, thin, flat, rectangular plates. The plates can carry uniform in-plane longitudinal, transverse and shear stresses and may be isotropic or anisotropic, with the elastic coupling stiffness matrix B = 0. This method can be used even if some of the plates have curved cross sections, are non-uniformly longitudinally compressed or, in certain circumstances, have B ≠ 0. However, approximations are then involved when representing the plates. Results presented herein indicate that good answers can be obtained despite these approximations.

The properties of weak shock waves in a vibrationally relaxing gas are discussed with particular application to waves in carbon dioxide. An account of various methods of generating weak shock waves in a shock tube is given. The best method requires the insertion of a perforated plate in the low pressure section of the shock tube. A suitable choice for the open-to-total area ratio of the plate leads to transmitted waves in the appropriate strength regime. These waves were observed using a Mach-Zehnder interferometer and were either fully or partly dispersed by vibrational relaxation. Values for the relaxation frequency of carbon dioxide at room temperature were obtained.

The governing elasticity equations for sandwich shells of double curvature are discussed. No restriction is placed on the thickness of the honeycomb core, and the faces are taken to be made up from fibre reinforced plastic laminations. Some numerical results are given for a circular cylinder subjected to uniform internal radial loading. The results show the importance of treating the core as a thick shell, and of including the bending effects and coupling terms in the laminated faces.

This paper treats theoretically the problem of the minimum induced drag of non-planar ground effect wings with both tips very close to the ground, within the limitations of the linearised lifting-line theory. The gap clearance between the wing tip and the ground is assumed to be very small and, using this small parameter, an approximate theory, which yields the minimum induced drag of a non-planar ground effect wing, is formulated by the method of matched asymptotic expansions. As a check on the accuracy of the method, this theory is compared with the exact theory for a semicircular wing. This shows that the present method is accurate within the small gap clearance. Moreover, the present method is applied to other wing configurations, such as semi-elliptic wings and wings with endplates, circular arc wings in a tube and circular arc wings. These computations show the theory to be very effective and it can be easily extended to various spanwise cambers.

The aerodynamic derivatives for a two-dimensional aerofoil with an oscillating control surface in a high subcritical flow are calculated using the method of Nixon. The aerofoil is assumed to be symmetric and at zero incidence with a zero mean control surface deflection angle. With the exception of the control surface stiffness derivative the magnitudes of the aerodynamic derivatives are greater than the corresponding linear values by between 15–35 per cent; the greatest difference occurs for low values of the frequency parameter. The magnitude of the control surface stiffness derivative is less than the corresponding linear value by the order 10–15 per cent.

A simple formulation is established for the determination of vibration characteristics of pre-twisted beams by the matrix displacement method. An important point in the analysis is the assumption of complete polynomial displacement distribution in the principal directions. In particular, two twisted elements which employ quintic polynomials are introduced and used in the calculation of natural frequencies of pre-twisted beams for several boundary conditions. The results demonstrate rapid convergence.

The exact expressions for the partition function Q and the coefficient of specific heat at constant volume Cv for a rotating-anharmonic oscillator molecule, including coupling and rotational cut-off, have been formulated and values of Q and Cv have been computed in the temperature range of 100°K to 100 000°K for O2, N2 and H2 gases. The exact Q and Cv values are also compared with the corresponding rigid-rotator harmonic-oscillator (infinite rotational and vibrational levels) and rigidrotator anharmonic-oscillator (infinite rotational levels) values. The rigid-rotator harmonic-oscillator approximation can be accepted for temperatures up to about 5000°K for O2 and N2. Beyond these temperatures the error in Cv will be significant, owing to anharmonicity and rotational cut-off effects. For H2, the rigid-rotator harmonic-oscillator approximation becomes unacceptable even for temperatures as low as 2000°K.

An analysis is presented for the non-linear vibrations of an elastic rectangular plate resting on a viscoelastic foundation. Hamilton’s principle is used for obtaining coupled non-linear partial differential equations of the system. These equations are uncoupled with the help of Berger’s approximation and the Galerkin method is used to obtain the solution of the resulting equations. Particular cases of the plates on an elastic foundation are also discussed.

For the turbulent boundary layer it is shown that, if an initial velocity profile is given, along with the local pressure gradient and shear-stress distribution through the layer, then the shape of the velocity profile a short distance downstream is unaffected by flow convergence or divergence, provided this is constant through the layer. For flow approaching an obstacle, increased divergence close to the surface is shown to account for the marked changes in profile shape that have been observed.

A simple integral method is described for the calculation of a thick axisymmetric turbulent boundary layer. It is shown that the development of the boundary layer can be predicted with acceptable accuracy by using an approximate form of the momentum-integral equation, an appropriate skin-friction law, and an entrainment equation obtained for axisymmetric boundary layers. The method also involves the explicit use of a velocity profile family in order to interrelate some of the integral parameters. Available experimental results have been used to demonstrate the general accuracy of the method.

Results are presented of an experimental study of the pressures on the flat windward surface of a Gothic wing at a free-stream Mach number of 3.5 and at moderately high angles of attack, including the effects of yaw. The results show that the perturbation in pressure due to yaw is almost independent of the streamwise distance from the vertex. As a result, it has been possible to calculate the pressure distribution on the yawed wing using the appropriate yawed conical wing results, the zero yaw results being calculated by the “equivalent” delta wing method. The calculations show reasonable agreement with the experiments and confirm that the perturbation due to yaw generates a stabilising rolling moment.

The methods suggested by Ross and by Fraser for dealing with turbulent boundary layers in adverse pressure gradients using semi-empirical data are extended to the prediction of boundary layer growth in conical diffusers, the new method making no recourse to measured static pressures, as previously required. Predictions agree closely with published experimental data by Fraser and give some justification for the use of the Ross model for the turbulent boundary layer in a diffuser provided that the diffuser is not too long and that the inlet boundary layer is thin.