The properties of equilibrium turbulent boundary layers have been examined using Thompson’s family of velocity profiles along with alternative π – G relationships. The relationship which is in best agreement with measurements of equilibrium layers confirms an earlier suggestion that (νT/Uδ*)max is not a universal constant for such layers but decreases for small and negative values of π. A close relationship is established between eddy viscosity and entrainment, and it is shown that veδ/νT is effectively constant for π > 2.

A method is presented for determining the swirling compressible flow through a nozzle, given conditions at a reference section. The principal assumption is that changes in the nozzle cross-sectional area are sufficiently gradual for the radial velocity component to be neglected at each section, i e, the usual assumption of one-dimensional compressible flow theory. This method is used to determine choked-flow conditions in the case where there is solid-body rotation at the throat for a range of swirl intensities with the ratio of the specific heats taking various values. Mass-flux coefficients and impulse functions are determined. Sonic surfaces, velocity profiles and other characteristics of interest are also presented. An approximate analysis valid for low swirl intensities is developed and analytical formulae are derived for most quantities of interest. The main conclusion of practical importance is that the introduction of swirl to compressible nozzle flows need not lead to a significant reduction in specific thrust. Further exploration of the possible effects of swirl on noise during the relatively short take-off and landing periods cannot therefore be ruled out on the grounds that swirl would lead to excessive thrust losses.

For lifting re-entry there may be advantages in using wings which give as high a lift coefficient as possible at the design value of the lift/drag ratio. This paper presents the results of an experimental and theoretical study of wings with recessed lower surfaces designed to give high values of CL. The calculations show that a wide range of wing shapes can be found that give values of CL which are much larger than those on a flat wing with the same lift/drag ratio.

This paper extends the Wagner torsion bending theory for open section tubes to general systems of applied loading. An illustrative example is also included involving the calculation of the twisting and direct stress distribution in an axially loaded Z-section column.

A method which can be used for the design of blown or unblown wing sections is described in this paper. A brief description of a variety of theoretical methods for computation of different fluid flow phenomena encountered on high-lift wing systems is presented. The most significant type of viscous flow - a confluent boundary layer flow, which is present on the upper surface of the flap, the vane and the main component of a high-lift system – is described and its importance to the performance of high-lift systems is illustrated. Results of computation of pressure distribution, boundary-layer characteristic, and lift coefficient for two-dimensional high-lift systems are compared with experimental data in order to establish the validity and limitations of the method.

The time mean flow past a two-dimensional bluff body in a wind-tunnel is modelled by an adaptation of the numerical free-streamline method of Bearman and Fackrell. Provided the base pressure and separation positions are specified in advance, the method allows the calculation of the flow field outside the wake and in particular of the pressures on the wetted surface of the body. Good agreement of the predicted pressures with experimental results is obtained for a flat plate, wedge and circular cylinder at various blockage ratios. In addition to predicting the confined flow, it is shown that a free-air base pressure can be simply deduced from the confined base pressure. With an assumption that the separation positions are unaffected by blockage, this allows the free-air flow field to be calculated. By using an analogy to Roshko’s Strouhal number, which has been found to be invariant under constraint, a free-air Strouhal number can also be deduced.

Hypersonic small-disturbance theory is applied to the source flow over power-law slender bodies with conical or wedge type asymptote. The results for a point source flow with λ=2 over power-law cones of revolution show that the dominating equations in the first and second approximations are essentially the same as the ones for the parallel flow over power-law bodies of revolution. In the special case of a cone, results of a source flow and of a parallel flow are compared and it is shown that the surface pressure in a source flow at the nose is the same as the constant cone pressure in a parallel flow, but systematically decreases in the rear part. This is confirmed by comparison with a shock tunnel experiment.

The problem of the supersonic flow with attached shock wave past a circular cone at zero angles of attack is treated, using the thin-shock-layer expansion. The solution is calculated to the fourth approximation. A simple formula is then derived for the surface pressure coefficient by the application of the parameter-straining technique and it is shown to be very accurate for the whole Mach number range for which the shock remains attached to the cone vertex.

The formulation of mathematical models of aeronautical systems for simulation or other purposes, involves the transformation of aerodynamic stability derivatives. It is shown that these derivatives transform like the components of a second order tensor having one index of covariance and one index of contravariance. Moreover, due to the equivalence of covariant and contravariant transformations in orthogonal Cartesian systems of coordinates, the transformations can be treated as doubly covariant or doubly contravariant, if this simplifies the formulation. It is shown that the tensor properties of these derivatives can be used to facilitate their transformation by symbolic mathematical computation, and the use of digital computers equipped with formula manipulation compilers. When the tensor transformations are mechanised in the manner described, man-hours are saved and the errors to which human operators are prone can be avoided.

A unified treatment is given of the orbital and attitude stability of space shuttles in parking orbits (in vacuo) in the earth’s gravitational field. A shuttle in a circular orbit with a principal axis aligned with the horizontal in the orbital plane is found to be in stationary geostatic equilibrium. The demand for stability leads to a condition which must be satisfied by the principal moments of inertia. The stability which is achieved is not asymptotic without control. The stationary state is a stable centre about which a bounded perturbation oscillation without damping may exist.

A numerical method is described for predicting incompressible, attached flow round multiple-section aerofoils at high Reynolds number. Interaction between wakes and boundary layers is not accounted for, but the method is nevertheless suitable for optimisation of design in the take-off condition. The solution is obtained in three steps:

1. (i) The calculation of the outer, potential flow using a conventional Kutta condition for each aerofoil section.

2. (ii) The calculation of viscous boundary layers and wakes.

3. (iii) The combination of the inviscid and viscous solutions to effect proper matching at the edges of the boundary layers and wakes and a more accurate specification of the circulation in the inviscid flow.

A theoretical and experimental study is made of the stresses and strains around circular holes in plates reinforced with carbon fibre filament-wound discs. An analytical solution is given for infinite isotropic plates subjected to uniform tension, but for orthotropic carbon fibre plates the finite-element displacement method of analysis is used. The filament-wound discs are found to be efficient in reducing the stresses around the holes with the principal stresses being taken, in the main, by the strong fibres. There is reasonable agreement with the experimental results for the uniform tension cases, but results from tests on bolt-loaded holes do not correlate as well with theory.

Results are presented of an experimental investigation on a non-conical wing which supports an attached shock wave over a region of the leading edge near the vertex and a detached shock elsewhere. The shock detachment point is determined from planform schlieren photographs of the flow field and discrepancies are shown to exist between this and the one calculated by applying the oblique shock equations normal to the leading edge. On a physical basis, it is argued that shock detachment has to obey the two-dimensional law normal to the leading edges. From this, and from other measurements on conical wings, it is thought that the planform schlieren technique may not be particularly satisfactory for detecting shock detachment. Surface pressure distributions are presented and are explained in terms of the flow over related delta wings which are identified as a vertex delta wing and a local delta wing. The forces acting on the wing are calculated and are shown to be very close to the two-dimensional wedge values over a wide range of incidence. In particular, it is shown that this wing, compared to one which supports a fully detached shock wave, generates a higher lift/(pressure drag) ratio at a given lift coefficient.

The velocity defect in the wake and its curvature lead to a pressure jump across it. As a result the pressure distribution on the aerofoil and the lift are modified.

In this paper, a systematic study of the triple shock confluence point is presented for the case of an overexpanded jet which impinges on a perpendicular flat plate at small displacements from the nozzle. The jet is uniform upstream of the free jet shock wave. Non-homentropic effects are taken into account and lead to modifications to the accepted flow patterns at a triple point for the case of strong incident shock waves. Where more than one thermodynamically possible solution to the triple point equations exists, the alternative solutions are re-examined, taking non-homentropic effects into consideration. Some discussion of the possibility of infinite shock curvatures is also included. Qualitative flow patterns of the impinging flow are constructed, based on the triple point solutions and the known boundary conditions. The interesting cases where the tail shock flow is supersonic are given particular attention and two possible flow patterns are distinguished. Finally, some experimental evidence in the form of schlieren pictures is presented. Although not conclusive, this evidence supports the theory.

The present experiment describes the behaviour of a turbulent boundary layer on a concave wall. At the onset of curvature there appears a fairly coherent wavelike transverse profile of mean velocity. This disturbance might be interpreted as a kind of large scale Taylor-Görtler type instability superimposed on a conventional turbulent boundary layer; further downstream the coherence degenerates as the turbulence level increases. Boundary-layer profile measurements were made at positions of maxima and minima of transverse profiles of (U-component) mean velocity. The boundary layer at the minima positions is found to be twice as thick as that at the maxima positions. Also, turbulent intensities inside the boundary layer are substantially increased as a result of the concave curvature of the surface.

This paper gives details of theoretical and experimental investigations into the behaviour of simply-supported uniformly compressed square and rectangular plates with central circular holes. The theoretical analysis employs an approximate approach using a combination of Rayleigh-Ritz and finite-element methods. The experimental investigation consisted of a number of experiments on plates with hole diameters from one- to seven-tenths of the plate width. Agreement between experiment and theory is shown to be good at buckling. In the post-buckling range it is found that the theoretical analysis is reasonably accurate for small holes, but loses accuracy when dealing with large holes.

To obtain profiles of shear stress and eddy viscosity, the boundary-layer equations in finite-difference form have been applied to published turbulent-boundary-layer developments measured in nominally two-dimensional conditions. In applying this procedure, measured velocity profiles have been represented by members of Thompson’s profile family. Except close to separation, these representations are very satisfactory, and derived shear-stress profiles are generally in good agreement with direct measurements. Various eddy-viscosity and mixing-length models are compared with the results of the analysis and are found in general to differ widely among themselves and from the present results. The widely used assumption, l = ky in the wall region, appears to be invalid.

Measurements of mean velocity and Reynolds shear stress have been made in a turbulent boundary layer downstream of a small step change in surface roughness. Upstream of the step the surface is smooth, while downstream it consists of a d-type rough wall made up by a series of two-dimensional elements of square cross section placed transversely across the flow and spaced one element width apart in the direction of the flow. The calculated mean velocity and Reynolds shear stress profiles obtained using the method of Bradshaw, Ferriss and Atwell are in good agreement with the measurements throughout the relaxation region of the layer. Well downstream the calculation method adequately reproduces the self-preserving features of a d-type rough wall.

A subsonic, lifting-surface method is extended to apply to low-frequency oscillations of wind-tunnel models, taking into account both longitudinal and lateral variations of tunnel lift interference. Rectangular sectioned tunnels with closed, slotted or open roof and floor and closed sidewalls are considered. A comparison is made between the aerodynamic derivatives obtained by this method and those calculated with the assumption that the model span is small compared to the tunnel width. Three models of aspect ratio 2.67 and different sweepback are considered in rigid pitching oscillations in tunnels of width/height ratio 2.5. The greatest differences between the results from the two methods occur for the tunnel with closed roof and floor and for the unswept planform. The least differences occur for the slotted tunnel and for the planform of greatest sweepback. The results indicate that, for models of conventional size [up to span/(tunnel width) ratio of 0.4], the “small-span” assumption is satisfactory in tunnels with slotted roof and floor and closed side walls, but not in fully closed tunnels.