An expression is derived which relates the pressure on a wing in a supersonic free stream to the pressure on a thin wing with the same surface shape. The expression is used to find the pressure distribution for caret wings and flat delta wings with attached flow at their leading edges. The compression surface pressure distributions found are in good agreement with existing experimental and theoretical results, except when large pressure changes occur in the flow behind the attached shock wave. Some expansion surface results are also obtained for wings with an isentropic expansion at the leading edge. The effects of flow and geometry changes on the pressure distribution are investigated. It is found that a small improvement in the lift/drag ratio of a caret wing can be obtained by halving the anhedral required for the plane shock wave condition.

The paper considers the distribution of downwash at the surface of rectangular planforms with prescribed subsonic aerodynamic loading. Three separate aspects of the problem are treated analytically, the results of each being tested against those derived from an accurate numerical procedure (Section 2). Asymptotic expressions for large and small aspect ratio are formulated and shown to apply over a wide range of aspect ratio (Section 3). Downwash routines from certain existing lifting-surface methods are studied, and their patterns of convergence are illustrated and compared (Section 4). A logarithmic singularity near the leading tip corner is identified, but it is observed that this can exist without serious detriment to the lifting-surface methods (Section 5).

Measurements in two-dimensional flow on rectangular cylinders confirm earlier work of Nakaguchi et al in showing a maximum drag coefficient when the height h of the section (normal to the stream) is about 1.5 times the width d. Reattachment on the sides of the cylinder occurs only for h/d < 0.35.

For cylinders of D-shaped section (Fig 1) the pressure distribution on the curved surface and the drag are considerably affected by the state of the boundary layer at separation, as for a circular cylinder. The lift is positive when the separation is turbulent and negative when it is laminar. It is found that simple empirical expressions for base pressure or drag, based on known values for the constituent half-bodies, are in general not satisfactory.

By employment of the analytical method of characteristics and of a limiting procedure suitable for dealing with the trailing edge expansion, the influence of near-field flow on the far-field wave formation has been investigated for an incident flat delta wing with supersonic leading edges. Though confined in its scope to the front shock in the vertical plane of symmetry of the wing and to a homogeneous atmosphere without density and temperature gradients, the present analysis reveals features of flow which are interesting from the standpoint of the general theory of three-dimensional supersonic flow. It is found that the front shock due to a delta wing will as a rule be cancelled at a finite distance from the wing by the plane-wave expansion emanating from the trailing edge. The over-expansion must then give rise to a rear shock separate from the front one. Thus, at least in the plane of symmetry, a sharp-front wave signature can not, in general, be expected from the wing at a distance beyond the terminating point of the front shock. The boom signature then will be qualitatively different from that of a body of revolution. The general non-equivalence of a wing to a body of revolution in this respect should evoke some rethinking about sonic boom prediction and alleviation.

The three-dimensional equations of motion of a flexible towed cable are developed. A closed-form approximation for the equilibrium shape of a cable subjected to arbitrary aerodynamic loading is developed and used in the study of a heavy, vibrating tow cable. Natural frequencies of vibration and cable shapes are computed for typical cables and are shown to be in good agreement with exact, numerically obtained values.

A unified theory is given of hypersonic and supersonic flow over the lower surface of a caret wing at certain off-design conditions when the bow shock is attached to the leading edges of the wing and when there exists no internal shock. The flow field on the lower surface of a caret wing consists of uniform flow regions near the leading edges, where the cross-flow is supersonic, and a non-uniform flow in the central region, where the cross-flow is subsonic. The basic assumption is that the flow in the central region differs slightly from the two-dimensional supersonic flow over a flat plate at the same angle of incidence as that of the lower ridge of the wing. Based on this assumption, a first-order perturbation flow is first calculated and then strained and corrected so that it matches the uniform flow which is obtained exactly. Slope discontinuities of the pressure curve are found at the cross-flow sonic line. Numerical examples and comparisons with previous theories and experiments are included.

The BAC subsonic lifting-surface method is applied to the problem of evaluating the downwash at the surface of wings of rectangular planform subjected to particular loadings and the results are compared with a set of datum results. Over 95 per cent of the wing span the results of the BAC method are shown to be accurate to within 0.01 per cent, irrespective of chordwise position.

This paper gives qualitative descriptions of the wave patterns near a sonic line in non-homentropic flow. It is found that these wave patterns can be quite different from the homentropic forms. The most striking differences are that, under appropriate circumstances, the sonic line can produce expansion waves and receive compression waves. Three particular flow situations are then examined with the aid of the new descriptions.

An incompressible three-dimensional turbulent wall jet originating from a circular orifice located adjacent to a plane wall is studied both theoretically and experimentally. An approximate similarity analysis predicts that the two transverse length scales, l0 and L0, and the inverse of the mean velocity scale grow linearly with distance downstream x from the orifice. Experimental measurements of mean velocity and longitudinal turbulence intensity profiles were made both in air and water with hot-wire and hot-film anemometers respectively. The behaviour predicted by the similarity analysis was verified. It was found that the rate of growth of the length scale normal to the plane wall, dl0/dx, was somewhat less than that found for a two-dimensional wall jet, whereas the rate of growth of the length scale in the lateral direction, dL0/dx, was about seven times greater than dl0/dx.

To study the possibilities of reducing the base drag of profiles with a blunt trailing edge, experiments were performed in two low-speed wind-tunnels at the DFVLR-AVA, Göttingen, some on models between walls and some on rectangular wings with an aspect ratio of 2.5. The results show that the mean base pressure can be increased, and so the base drag reduced, by using a special form of the blunt trailing edge. The variation of local base pressure along the span, and the way in which this variation is influenced by the form of the trailing edge, is also shown. Some results for the total drag and lift are also indicated.

A method is presented for predicting the behaviour of a two-dimensional supersonic turbulent near-wake during the recompression process. In contrast to most previous extensions of Crocco-Lees strong interaction theory, the proposed analysis includes a transverse momentum integral equation. In addition, a modified strip method for conservation of streamwise momentum replaces the usual integral equations. Although a straightforward treatment of the equations results in the appearance of a singularity analogous to the well-known Crocco-Lees critical point, it is shown that solutions can be obtained which do not exhibit a singular behaviour, either by posing the problem as a boundary-value problem rather than an initial-value problem or by making a suitable approximation which suppresses the quasi-elliptic behaviour of the equations. Both procedures lead to an unambiguously defined uniqueness condition for the near-wake recompression solution.

The response of a flexible helicopter rotor blade to random loading is investigated, the random input being the vertical velocity component. The model takes into account blade flexibility in bending as well as torsion, and also general root rigidity. The spectral density and the mean square value of the transverse displacement are computed for both hingeless and hinged rotor blades and the results are evaluated.

In previous papers the basis of a matrix approach to the initial buckling or vibration of prismatic structures consisting of a series of thin flat rectangular plates rigidly connected together along their longitudinal edges has been developed. The present paper provides numerical results for the buckling, under uniform longitudinal compression, of a series of panels with unflanged or flanged integral stiffeners, or with Z-section stiffeners; the results are compared with those obtained by other methods and with published results, including an appropriate Royal Aeronautical Society Structures Data Sheet. It was found that considerable inaccuracies can arise from the usual methods of analysis and the authors believe that these justify the use of computer programmes, such as the ones used to obtain the results of this paper, at least at the final design stage.

Measurements are presented of total pressure, static pressure, surface shear stress and yaw angle in the flow through several S-shaped ducts, each with a thin turbulent boundary layer at entry. The results show that the region of low total pressure in the exit plane, found by previous workers, is due to expulsion of boundary-layer fluid by a pair of contra-totating vortices in the boundary layer. The generation of these vortices is explained: similarly-produced vortices, with similar effects, occur in some types of wind-tunnel contraction and possibly in other three-dimensional flows.

Many investigators have studied the aerodynamics of axial flow turbomachinery but none has produced a complete map of the three-dimensional flow behind a rotor row. This is of considerable interest to the aero-acoustician. A system is described which uses a constant temperature hot-wire anemometer to analyse the flow behind such a rotor. Although much information may be extracted by using the technique, its interpretation depends to a large extent on its form of presentation. An analysis of the flow behind a research fan is used as a means of discussing various forms of visual presentation.

The three-dimensional motion of a body towed by a flexible cable is studied. An approximate solution is developed for the non-linear equations of motion of the system to determine cable shapes. This solution is then used to compute natural frequencies and damping rates for longitudinal and lateral motions of the system. Conditions necessary for the uncoupling of the lateral and longitudinal motions are defined.

Recent advances in the development of ground cushion vehicles have indicated the need for a more efficient means of providing lift at the higher speeds envisaged in the future. A wing operating in ground effect could provide this lift and might be far more attractive economically than the “Hovercraft”. This note investigates some of the stability aspects of such a “Ground Effect Wing” Vehicle, using linear analysis, by developing the relevant equations of motion and examining the characteristic equations using quasi-steady derivatives, at fixed heights, obtained from wind-tunnel tests. In addition comparison is made between an analogue simulation of a GEW and the flight paths obtained from a free-flight model. This investigation showed that the longitudinal mode of oscillation for both single and tandem-wings with endplates was unstable and artificial stability was necessary. The lateral mode of oscillation for a single wing was stable in both roll and yaw, the latter being subject to fin and endplate configurations. The effects of the force, and moment, rate of change of height derivatives were not considered, as values for these derivatives were not available. Some proposals for future work include the development of suitable aerofoil sections for operation near the ground and the investigation of slender bodies in ground effect.

Measurements are presented of the mean flow properties of some three-dimensional turbulent boundary layers re-developing after reattachment behind short separation bubbles yawed at 26.5° to the main stream. For these measurements, Rθ11 varied from about 550 to 1450. It was found that, where the pressure gradient parameter (ν/ρu3τ1)∂p/∂s was not greater than about 0.05, the flow in the local external streamline direction conformed well with empirical laws for fully-attached two-dimensional layers with regard to the mean velocity profiles, shape parameter relationships and skin friction laws, giving support to the usual assumption that these two-dimensional relationships may be applied to the streamwise flow in three-dimensional layers, subject to the limitation on the pressure gradient parameter. The cross-flow profiles, on the other hand, were not generally fitted well by the often-used representations of Mager and Johnston. The variations of the kinetic energy dissipation coefficient and the entrainment rate were deduced for one of the layers, both quantities being found to be higher than those predicted by empirical relationships for conventionally-developing two-dimensional layers. However, the energy dissipation is in fair agreement with that in a similarly re-developing two-dimensional flow.

Two prediction methods for compressible turbulent boundary layers with air injection have been developed. The results from the two methods are compared with experiment for constant pressure flows at Mach numbers from 1.8 to 3.6. In general the results from the two methods and from experiment are in close agreement. However, there are some differences at the higher Mach numbers and it is suggested that both methods need further development for use at Mach numbers above 3.

The impact of an axisymmetric jet onto a ground board is a flow of some interest in VTOL aircraft aerodynamics. This paper presents a simple argument for correlating data obtained in the impact region from different nozzle configurations and for different nozzle heights above ground. The argument is applied, in particular, to the static pressure on the ground board and to the peak dynamic head in the flow over the ground board.