The flow past families of two-dimensional cylinders and bodies of revolution with elliptic noses at zero incidence has been examined at free stream Mach numbers between 1·42 and 1·82. The observations include schlieren photographs and measurements of the pressure distributions at the surface.

The measured pressure distributions and positions of the detached bow waves are found to be in fair agreement with values calculated by a number of methods. The drag coefficients of the slender two-dimensional elliptic noses are considerably higher than those calculated for wedges of the same axis ratio with attached shock waves, but the drags become almost equal when the axis ratio approaches the value for subsonic flow behind the bow wave of the wedge. For most axis ratios the drag coefficients of the elliptic-nosed bodies of revolution are lower than those for cones of the same axis ratio.

The problem discussed is that of the elastic local instability of a uniformly compressed thin-walled strut composed of a number of flat component plates. The strut is essentially “ open ” in cross-sectional form, while reinforcing flanges are attached to the extreme edges. An overall stability equation, based on the small deflection theory of plate bending, is derived from the conditions which must hold at the common and extreme longitudinal edges of the strut.

It is shown that the critical compression stress induces a mode of buckling which involves a whole number of sinusoidal half-waves in the longitudinal direction. Furthermore, the number of half-waves is common to all component plates of the strut. The general’ stability equation—a zero determinant of high order—lends itself to expansion in terms of 4th order minors, which may again be expressed in terms of seven basic functions. A knowledge of these functions is sufficient for the solution of any problem, however complex, within the scope of the general analysis.

Application of the basic functions to the solution of three different problems yields results which indicate the need for considerable care in the design of thin-walled struts with reinforcing flanges. In struts of this type a longer wavelength of buckling is possible than is commonly associated with local instability problems.

Schlieren photographs of a small scale approximately two-dimensional air jet in air above the critical pressure have shown the existence of an instability displaying an anti-symmetric pattern, and the associated sound field having several distinguishing characteristics, has been photographed. An elementary theory based upon the hypothesis that the acoustic energy originates from the interaction of the stream disturbances with the shock waves of the flow, and connecting the stream disturbances with the radiated sound, is suggested. This is shown to be consistent with the physical dimensions of the phenomenon and predicts a sound field in reasonable agreement with that observed after certain simplifying assumptions have been made.

An investigation has been made to determine the positions and directions of initiation and the directions of propagation of fatigue cracks and to examine the correlation between these positions and directions and the planes on which maximum tensile and maximum shear stresses are generated.

To afford as wide a range as possible of the ratio of maximum shear stress to maximum tensile stress, tests have been made under combinations of alternating bending and torsion; and in order to separate partially the regions of high shear stress from those of high direct stress, the tests have been made on pieces of square section with the plane of bending parallel to one diagonal of the section. Two series of tests have been made; one a preliminary series on pieces having no parallel portion and the other on pieces having a parallel portion about three times the length of the side of the square section. The positions and directions of initiation and the directions of propagation of fatigue cracks have been observed and compared with the positions and directions of the maximum tensile and shear stresses.

Fatigue cracks may be initiated as a result of either high shear stress or high tensile stress and in the present series of tests on mild steel, cracking in tension has occurred in preference to cracking in shear when the ratio of the tensile stress range to the shear stress range has exceeded about 1.6; for values of this ratio less than 1.6, the cracks started in shear (and vice versa); propagation along the plane of maximum shear appears to be preferred up to a slightly greater value of the tensile/shear ratio (about 1.7 possibly). The general direction of a crack formed as a result of high tension usually follows the plane of maximum tension and that of a crack formed as a result of shear usually follows the plane of maximum shear. In detail both types of crack—in this mild steel—deviate quite widely from their general directions but this deviation bears no obvious relation to the microstructure of the material. Cracks propagating along one plane of maximum shear occasionally show a marked tendency to branch along the associated plane of maximum shear; but this tendency is not always observed and in other cases no tendency to branch has been noted.

The noise levels of a jet issuing from a long pipe are compared with those of a jet having a square velocity profile at the exit. A subsonic noise reduction of between 2 and 5 decibels for various conditions is found for the case of the flow emerging with an approximately “turbulent pipe-flow” velocity profile for the same maximum jet velocity, but this is at the expense of a loss in thrust of a quarter. On comparison with a jet of smaller diameter which has an equal thrust for the same maximum jet velocity, it is found that the changes in noise level are rather smaller. For jets of equal diameters, the effects on the subsonic aerodynamic noise generated of a reduction of velocity gradient near the boundary are more than offset by the increased velocities necessary near the centre of the jet to obtain equal thrust. It is concluded that if the effect of differences in initial turbulence can be neglected the use of an auxiliary flow forming a comparatively thin sheath of slower moving fluid at the exit is not likely to result in large decreases in the subsonic noise level, and that a general reduction in jet velocity is more effective.

Above the critical pressure larger reductions of up to 10 decibels are found. These are consistent with a delay of the onset of the self-maintained shock-produced noise.

A simple method is given for calculating, in incompressible flow, the spanwise and chordwise loadings on thin swept wings with symmetrical aerofoil sections and of moderate and large aspect ratios. The present note is based on, and continues, the investigation described in an earlier paper. The design of swept wings with given spanwise and chordwise load distributions, obtained by modifying the plan form of the wing or by adding camber and twist, is briefly considered, as well as the design of swept wings which give minimum induced drag.

A simple theoretical analysis is given of the quantities affecting the sensitivity and range of a schlieren apparatus. In regions of large density gradient the deflections of the light rays may lie outside the normal working range. When this occurs, dark regions may appear in parts of the photograph that would normally be light. Examples of this effect are given, and it is shown that confusion can be avoided by taking photographs in pairs, with the knife edges or slits arranged to give sensitivities of opposite sign.

The deflections of light rays in various typical disturbances in a supersonic air stream are calculated, using geometrical optics. Prandtl-Meyer expansions, boundary layers, and plane and curved shock waves are considered. From these calculated deflections it is shown that some of the anomalous effects commonly observed in schlieren photographs can be explained.

An analysis has been made which suggests that, with the types of pressure distribution most usual in practice and free stream Mach numbers up to 10, no serious errors would be introduced into the calculation of the laminar separation point by the assumption that σ, the Prandtl number, and ω, the index of variation of viscosity with absolute temperature, are equal to unity. (Typical actual values of σ and ω for air are 0.72 and 0.89 respectively).

This problem arose in connection with the stabilisation of the spar flanges of an aeroplane, where the spar passes through the fuselage. The fore-and-aft stabilisation of a compression flange in these circumstances may often be effected by means of intermediate supports, which are necessarily flexible, and the reliability of any calculations of buckling load is somewhat doubtful, mainly due to the difficulty of estimating the stiffness of the supports. In view of this it was decided in a recent design to consider a continuous support for the spar flange in the form of a thin horizontal web riveted to the flange and to the sides of the fuselage, and having a small member attached to its other edge.

This paper gives a new calculation of the solid and wake blockage for compressible subsonic flow about a symmetrical two-dimensional aerofoil, midway between symmetrically disposed tunnel walls, which need not be straight. Previous calculations have been based on the theory of sources, and the results obtained have usually involved only first order terms. At high subsonic Mach numbers the second order terms become important; they are given in this paper. The theory is based on an integral equation, which is exact for incompressible flow, and which is more accurate than linear pertubation theory in compressible flow. The effect on blockage of a possible increase in the boundary layer displacement thickness on the tunnel wall, due to the presence of the aerofoil, is investigated, and finally a method of calculating the total blockage from wall pressure measurements is given.

The scheme for taking a pair of photographs of opposite sensitivity for each flow is a useful one in certain problems, but is unsuitable for use in a routine experiment (in which several hundred photographs may be required) because of the additional labour and expense involved. This is particularly so because, apart from resolving any ambiguity which may occur in regions of intense density gradient, the second photograph usually will not give much additional information about the flow. Moreover, the scheme does not overcome the other difficulties associated with the use of an apparatus having inadequate range. The most serious of these is that the apparatus is unable to differentiate between the strengths of density gradients when they exceed the value which deflects the image of the light source completely on to, or away from, the knife edge. Photographs illustrating this effect are reproduced in Ref. 1; the use of inadequate range (i.e. too much sensitivity) is a common fault in wind-tunnel photographs.

The problem of the buckling of flat oblique plates (i.e. in the shape of parallelograms) with all edges clamped under a uniform system of stress is considered. An energy method of calculating the critical stresses is developed and applied to the particular case of a clamped oblique plate under uniform compression parallel to two of the sides. Numerical values for the buckling stress coefficient are obtained for plates having acute angles of 60° and 45°, and side ratios varying between 3/5 and 5/3.

The paper contains an analysis of the flow of a perfect gas with constant specific heats through a rotating channel of constant cross-sectional area, as used in certain helicopter propulsion systems and wind-driven gas turbines. The analysis is restricted to the adiabatic one-dimensional treatment, the Coriolis accelerations acting across a section being disregarded.

The equations of motion and energy are deduced and, together with the equation of continuity, reduced to an ordinary non-linear differential equation of the first order, involving a dimensionless form of velocity and distance.

The patterns of the integral curves of the differential equation are discussed and sketched by examining their asymptotic behaviour as well as that in the neighbourhood of singular points. It is shown that there exists a critical value of the angular velocity below which the flow remains subsonic in the pipe, if the entrance velocity is subsonic; it may, however, become sonic at the exit of the pipe. For supercritical angular velocities the flow may become sonic or supersonic in the pipe if the entrance velocity attains a given “ correct” but subsonic value. A method of examining for the possibility of shock formation is indicated.

The initial conditions for the differential equation are deduced for the design and for the performance problem, two new flow functions being introduced and tabulated to facilitate practical calculations. Formulae are also deduced for the calculation of the pressure and Mach number variation from the previously calculated velocity variation along the pipe.

Finally an approximate solution in closed terms is given for the case of small entrance velocities.

The one-dimensional equations governing the mixing of compressible flows in a channel of constant cross-sectional area are derived and are used to investigate the running of an induction-type high-speed wind tunnel. While in practice it is usually difficult to achieve working section Mach numbers greater than about 1.8 to 20 in this type of tunnel, this simple theory gives no obvious reason for this and indicates that higher Mach numbers should be attainable.

It is also shown that an increase in efficiency is predicted, particularly at the higher supersonic Mach numbers, if the injected stream enters the mixing section at the same Mach number as that of the working section main stream.

The supersonic flow past a combination of a thin wing and a slender body of revolution is discussed by means of the linearised equation of motion. The exact equation is first established so that the linearised solution can be fed back and the order of the error terms calculated. The theory holds under quite general conditions which should be realised in practice.

The wing-body combination considered consists of a wing symmetrically situated on a pointed body of revolution and satisfying the following fairly general conditions. The wing leading edge is supersonic at the root, and the body is approximately cylindrical downstream of the leading edge. The body radius is of an order larger than the wing thickness, but is small compared with the chord or span of the wing.

It is found that if the wing and body are at the same incidence, and the aspect ratio of the wing is greater than 2 (M2-1)-½, where M is the main stream Mach number, the lift is equivalent to that of the complete wing when isolated. If the wing only is at incidence then the lift is equivalent to that of the part of the wing lying outside the body.

The presence of the body has a more significant effect on the drag. If, for example, the body is an infinite cylinder of radius a, and the wing is rectangular with aspect ratio greater than 2(M2-1)-½, then the drag of the wing is decreased by a factor (1-2a/b), where 2b is the span of the wing.

When these conditions do not hold the results are not quite so simple but are by no means complicated.

A simple system is considered in which a two-dimensional aerofoil in an air stream performs a coupled oscillation in pitching and vertical translation. An expression for the energy transferred from stream to aerofoil is derived as a function of the frequency parameter, amplitude ratio and phase difference, and the conditions under which positive energy can be extracted from the stream are investigated. The connection between the case of zero energy transfer, and the critical flutter state is noted.

Attention is confined to the incompressible case and diagrams show the results obtained when the air loads are obtained from (i) vortex sheet theory and (ii) the classical set of constant derivatives.

Vortex sheet theory leads to the conclusion that, provided that the amplitude ratio and phase difference satisfy certain conditions, energy can be extracted from the stream for all values of the frequency parameter. On the other hand, the use of a set of constant derivatives places an upper limit on the values of the frequency parameter for the extraction of energy.

The strip-theory equations of flow through a ducted fan were the basis of a method of designing a fan for a given performance. The merit of the method was that it amounted to an explicit solution of the design problem, no iteration being necessary.

In the inverse problem, of determining the flow past a given fan in conditions other than those of the design, two relations—the motor or tunnel characteristics, for example—will be given between the four quantities P, Ω, η, u (the motor power and angular velocity, the fan efficiency and the air speed at the fan). The problem is to determine the values of these four quantities together with details of the flow past any blade element.

This paper shows that to a high degree of accuracy the performance of a ducted fan can be summed up by saying that P/Ω3 and η are both functions of Ω/u only, functions which depend only on the fan shape. Solution by graphical means is therefore almost instantaneous.

The fan-tunnel combination is shown to be governed by extremely simple equations which amount to saying that the tunnel power factor is a function of Ω/u only which, again, can be calculated once for all for a given fan and tunnel.

An instrument is described which detects total pressure, total temperature, and direction of flow simultaneously in a stream tube of one-sixteenth inch diameter. The observed directions and pressures are transmitted electrically to a remote station where they appear as pencil traces on a paper record which moves at a rate proportional to the traverse rate of the instrument. The temperature is noted at intervals and added manually to the trace. Integrators are included which permit rapid assessment of mean pressure and direction at the conclusion of a traverse, the control and maintenance of setting of the instrument being semi-automatic. A further development is also noted whereby total pressure and direction in three dimensions can be observed either manually, or remotely, by automatic means.

A method is developed for the calculation of the aerodynamic forces acting on a “swallow tail” wing (Figs. l(a) and l(b)) of small aspect ratio. For a given incidence, lift and induced drag coefficient are, within the limits of the theory, proportional to aspect ratio and independent of Mach number. The exact solution is derived for the limiting case of small sweepback of the trailing edge. A numerical method is indicated for the more general case.