Similar solutions of the boundary layer equations for incompressible flow with external velocity u1 ∞ xm and suction velocity υw ∞ x(m-1)/2 are obtained for negative values of m, in the range −0-1 to −0-9, and a wide range of suction quantities.

The results are used, in combination with, existing solutions for positive m, to provide a guide to the ranges of m and suction parameter [(υw/u1√x] for which a general form of the classical asymptotic solution can be regarded as a good approximation to the exact solution.

It is shown that the values of both m and suction parameter are generally important in this comparison, but for values of the latter greater than about 8 the approximation is a very good one for all values of m considered. For m≃−0·14 the approximation is good (i.e. the error is less than about 1 per cent) down to values of the suction parameter as low as 1·0.

The effect of depth taper on the flexural vibration characteristics of a beam of uniform width is investigated in this paper. The frequency parameters and mode shapes for the first five modes of vibration of tapered beams are presented for a wide range of depth taper. The Euler-Bernoulli equation of a beam is reduced to an eigenvalue problem and its eigenvalues and eigenvectors are obtained by using a digital computer. The theoretical results are compared with those of other authors and with the experimental results.

The effects of base bleed on the flow about a two-dimensional model with a blunt trailing edge were examined at Reynolds numbers, based on model base height, between 1·3×104 and 4·1×104. The ratio of boundary layer thickness at the trailing edge to half the model base height was approximately 0·4. Measurements were made of base pressure, vortex shedding frequency and the distance to vortex formation. With a sufficiently large bleed quantity the regular vortex street pattern disappeared and the base drag of the section was reduced to about a third of its value without bleed. The base pressure was found to vary linearly with the inverse of the vortex formation distance. Results of a previous splitter plate investigation were found to agree closely with those of the present experiments.

In this paper lower bounds are obtained for the intensity of the sonic bang resulting from a slender aircraft flying straight and level at supersonic speeds. The lower bounds are obtained for an aircraft subject to various constraints on its total lift, volume, area distribution and centre-of-pressure position. The work described proves the results quoted in an earlier paper, corrects the results given in that paper for the general configuration, and extends the results to cover more constraints, mainly the centre-of-pressure position.

A simple potential theory for flow through cascades of low solidity is developed. The analysis is an extension of Glauert’s theory for single aerofoils. The variation of outlet angle and lift coefficient with space/chord ratio and stagger angle is predicted. The simple analysis is shown, by comparison with other methods of computation, to be valid for cascades of space/chord ratio in excess of 1·5 and staggers over 50 degrees.

The various methods which axe available for controlling the rolling motions of a model suspended in an electro-magnet system are discussed. Data on the moment capability and damping achieved with some of the possible control techniques are presented, together with details of the roll control system adopted for the six-component magnetic balance which has been developed at Southampton University for an 8 in × 6 in supersonic wind tunnel.

A simple analysis is presented for the air flow and nozzle power requirements of hovercraft fitted with skirts on which the peripheral jet is blown down the inner skirt face—the “single-wall” type. The theory, which utilises experimental wall-jet data, is applicable to the equilibrium jet state.

A comparison is made with analyses for the air flow and nozzle power requirements of plenum chamber craft and hovercraft fitted with twin-wall skirts. It is concluded that, for a given gap between the skirt bottom and the terrain, at normal operating conditions the order of merit is twin-wall skirt, single-wall skirt, plenum chamber.

The paper describes an “explicit” method of predicting the flow properties of a turbulent boundary layer; particular attention is paid to the region in which the growth of the layer is characterised by the decay of a velocity maximum. The validity of the method is tested against the data of Wieghardt and against new data of the present authors; it is shown to be satisfactory. The integral flow properties predicted by the method are used, together with a further assumption, to predict velocity profiles; these closely resemble the measured ones.

Simple expressions are derived for predicting the spread of turbulent jets issuing into parallel moving airstreams. Difficulties with applying these expressions to practical problems are discussed and comparisons with experimental results are given.

The problem considered is the theoretical analysis and design of reinforcement around holes in plane sheets subjected to prescribed stresses at infinity. The reinforcement is taken to be an extensive thin plate attached to the sheet rather than the usual “compact bead” placed around the inside of the hole. The optimum design of the hole and the reinforcement is treated in two ways, firstly as an attempt to produce a “neutral hole” and secondly, to achieve the smallest stress concentration with the minimum amount of reinforcement. It is found in two cases that the plate-reinforcement can be as efficient as the bead but that, for both types, the validity of the theory is doubtful just when they are most efficient.

This paper presents a summary of a multi-moment method for solving the laminar boundary layer equations. Results obtained with the method tend to converge to the exact values as higher moments are used. Both similar and non-similar external flow fields are considered. The present results are compared with those obtained by another multi-moment method, a finite-difference method and a refined Pohlhausen-type method.

An experimental investigation of natural transition and turbulent boundary layers on a cold flat plate in hypersonic flow was carried out in the Imperial College Gun Tunnel. Studies were also made of the effects of both two- and three-dimensional roughness elements including vortex generators.

Results indicate that the Reynolds number based on the end of transition consists of two separate parts. These are the Reynolds numbers based respectively on the position of the apparent origin of the transition region behaviour, Ri, and on the length of the transition region measured from this origin. Ri is shown to be independent of unit Reynolds number for a sharp leading-edge model, and by correlations of other published data to vary little with Mach number. This origin is perhaps the most relevant point when comparisons are made between experiment and classical stability theory. The variation of the heat transfer rate during the transition region is compared with findings at low speed and shown to be similar to that expected from the turbulent spot concept of Emmons. The measured variation of the length of the transition region (x) from this origin gives an explanation for the unit Reynolds number effect on transition, and the rapid increase of transition Reynolds number with Mach number in hypersonic flow. The effect of bluntness on these factors is discussed.

The virtual origin of the turbulent boundary layer is shown to lie close to the measured beginning of transition. At these high Mach number and low wall temperature conditions experimental values of heat transfer and values of skin friction coefficient derived from the estimated momentum thickness growth in the turbulent region are found to be appreciably higher than predictions by present theories.

Roughness trips were found to bring the whole transition region forward. Only small differences in the measured boundary layer thickness, shape and heat transfer rates in the turbulent region (referenced to the estimated virtual origin in each case) were found after natural and forced transition. The transition point locations on a flat plate with either spherical roughness elements or vortex generators were found to agree with values predicted by the method of Potter and Whitfield as modified by Luxton to account for the effects of heat transfer.

A method of calculation has been developed in which all terms in the momentum integral equations in the streamwise and cross-flow directions are taken into account so that no restriction to small cross-flows is imposed. The essential feature of the method is the use of an entrainment equation which enables the development of the streamwise form parameter to be calculated along with the streamwise and cross-flow momentum thicknesses. Mager’s quadratic expression is used to relate streamwise and cross-flow profiles. The method has been applied to the idealised case of an infinite swept wing with free-stream velocity over the forward part of the chord and a linear adverse velocity gradient over the rear. The position of separation, the directions of the surface streamlines and the development of streamwise and cross-flow profiles have been calculated for a series of angles of sweep and for adverse pressure gradients of varying severity.

It is shown that considerable improvement is achieved in the most popular classical approach to the vibration of structural members by giving new meaning to the generalised coordinate term in the infinite series expansion of the product of the generalised coordinate and eigenfunction. A transform employing the eigenfunction as a kernel efficiently generates a universal solution that embraces arbitrary loading, time-dependent boundary conditions, and such in-span conditions as supports and changes in cross section, axial load, and elastic foundation modulus. The method is applied to the Timoshenko beam as a representative structural member.

A recent calculation method proposed by Curle has been applied to the flow U=U0ξe-ξ for which a computer solution exists. An earlier approximate method due to Head, presented here in a simplified form, has been applied to the same problem. All three solutions are found to be in close agreement. A further problem, already examined by Curle, is treated by Head’s method. Again the results are in good agreement with each other and with an exact solution obtained subsequently.

The asymptotic solution, valid near the centre of a rolled-up vortex sheet, obtained by Mangier and Weber, is generalised to include the effects of compressibility. The vortex sheet is taken to be embedded in a potential flow, and the flow field is assumed to be conical.

An earlier paper described a method of calculating the turbulent boundary layer flow over the rear of an infinite swept wing. It made use of an entrainment equation and momentum integral equations in streamwise and cross-flow directions, together with several auxiliary assumptions. Here the method is adapted to the calculation of the turbulent boundary layer flow along the attachment line of an infinite swept wing. In this case the cross-flow momentum integral equation reduces to the identity 0 = 0 and must be replaced by its differentiated form. Two alternative approaches are also adopted and give very similar results, in good agreement with the limited experimental data available. It is found that results can be expressed as functions of a single parameter C*, which is evidently the criterion of similarity for attachment-line flows.

This paper investigates the effect of the torsional stiffness of the ribs on the buckling strength of stiffened plates compressed in the direction of the ribs. For the case of plates simply-supported on all sides, a closed form formula is derived for calculating the buckling load.

An exact analysis is made of reinforced sheets having three fibre directions using netting analysis. Load envelopes of shear combined with both uniaxial and biaxial tension are assumed and optimum fibre arrangements are determined on the assumption that limits exist on the compressive and tensile forces which may be developed in a fibre. Such optimum fibre arrangements are compared with the best-arranged isotropic reinforced sheets and with hypothetical solid sheets having the same properties as the fibres. Elastic constants are derived for the optimum systems. The total allowable load envelopes of the optimum arrangements are found and are related to the prescribed load envelopes.

This paper describes the application of a previously published variational method to the solution of problems of holes in plane elastic sheets and is used to obtain numerical values for the specific case of an elliptic hole in an infinite sheet under tension at infinity. Two kinds of boundary condition at the hole are discussed. The first is that when the hole is unreinforced and stress free, and the second that when the hole is uniformly reinforced by a compact member. The results of the calculations are compared with those from known solutions to the problem, and the accuracy of the present method is investigated. These results provide a useful background to wider application of the method.