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 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.

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.

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.

Static pressures have been measured in the separated flow region behind backward-facing steps in a wind tunnel, suitable corrections being applied for the model blockage. The results indicate a reasonably well defined similarity in the pressure distribution.

A numerical method which solves the time-dependent Navier-Stokes equations for plane, two-dimensional, compressible flow problems is presented. The method was applied to obtain the steady-state flow field about a flat-based 20° wedge at a free-stream Mach number of 6.05, a free-stream Reynolds number (based on the base height of the wedge) of 1.41 × 104, and a Prandtl number of 0.75. Two wedge surface temperature boundary conditions were investigated: adiabatic and isothermal walls. Convergence of the numerical solutions was demonstrated using two different finite-difference meshes. Numerical errors in the static pressure, velocity, and static temperature were generally less than 8 per cent in the wake of the body. Comparisons with experimental results and other independent theories were also made. For the isothermal wedge, calculated pressures on the surface of the body (including its base), static pressure profiles, pitot pressures profiles, and velocity profiles in the near wake were in agreement with corresponding experimental data. A comparison of static temperature profiles in the near wake of the isothermal wedge produced significant differences between numerical and experimental results near the wake shock. It was found that these differences could be explained in terms of uncertainties in the accuracy of the experimental measurements and thermal boundary conditions on the wedge surface. For the adiabatic wedge, the ramp boundary layer profiles and pressure distribution were in agreement with theoretical predictions coming from hypersonic interaction theory.