The changes in stagnation pressure produced by movement of rows, arrays and sheets of vortices are derived. By applying Preston’s result for a single row of moving vortices to continuous vortex sheets, the time mean stagnation pressure downstream of a row of blades with fluctuating circulation is derived. It is shown that if the blade circulation varies due to the potential flow fields of the neighbouring blades then the time mean stagnation pressure may change with location.

In a recent paper, a theory explaining the wake-induced flutter of smooth circular cylinders was developed and vindicated. It was shown that, for moderate spacing of the cylinders (where the aerodynamic coupling between the constituent motions is small), flutter could occur only when the natural frequency, in still air, of vertical oscillations exceeded that of the horizontal motions. The theory, however, took no account of the possibility of mechanical coupling between the constituent motions and, while the results from this theory were corroborated by wind-tunnel tests in which a statically uncoupled mechanical support system was used, no indications were given of the changes in aeroelastic behaviour which might accompany the introduction of simple coupling terms.

In this paper, the class of cases wherein the mechanical support system for the leeward cylinder exhibits static coupling is studied using “undamped flutter theory”. It is demonstrated that the appearance of static coupling terms can lead to quite dramatic changes in the flutter characteristics, and that considerable care must be exercised in the design and operation of wind-tunnel dynamic models if meaningful results are to be obtained.

An Appendix deals with the general problem of mechanical coupling, using the normal coordinates approach, and aspects of the problem which bear on the subconductor oscillation phenomenon experienced on “bundled” overhead power transmission lines are highlighted.

The results obtained from exact numerical solutions to the laminar boundary layer equations are compared with those given by the approximate method of Luxton and Young and the comparison shows that the latter method may be used for cases involving non-constant wall temperatures. This satisfactory result arises essentially from the fact demonstrated by the calculations that the skin friction is relatively insensitive to wall temperature gradients. It is also shown from these results that there is a lag in the propagation of wall temperature changes through the boundary layer. In consequence the Stanton number is a heat transfer parameter of doubtful value in cases of non-uniform wall temperature.

For plane turbulent jets and wall jets in uniform streaming flow a simple method, based on a simple empirical formula for the rate of growth which differs from that proposed by Abramovich, is presented. The predictions of length scale, l0, and velocity scale, u0, are in good agreement with experimental results for all ratios of free-stream to jet exit velocity and the eddy viscosity Reynolds number has the correct asymptotic values.

Because of the lack of reliable data on heat transfer to long bodies, measurements have been made to cone-cylinder-flares at a Mach number of 5·2. Axial heat transfer distributions were closely predicted by a modified reference enthalpy method for both laminar and turbulent flows at zero incidence and the heat transfer to the flare windward generator at incidence agreed with laminar theory.

To study the effects of flow non-uniformities on the hypersonic flow past test bodies, perturbation analysis is applied to the hypersonic source flow past wedges and cones. In both cases it is shown that the effects of the source flow on the shock shape and velocity are small, while effects on the pressure and density are large. Curves are presented for various values of the Mach number from which these effects can be estimated.

For caret waveriders at the design condition the attached shock wave in the plane of the leading edges may correspond to either a strong or a weak oblique shock wave when viewed normal to the edges. In cases when the design shock wave corresponds to the strong oblique shock the off-design behaviour of the wing is not completely understood. In this note some measured results are analysed in an attempt to understand this off-design behaviour.

In constructing an X-type hot-wire probe it has been the policy of a number of experimenters and manufacturers to place the two wires forming the X close to each other to assure that they are both measuring in effectively the same plane. A number of important experiments have been made using such a probe design. Recent experiments at the University of British Columbia and McGill University have shown that an X-wire probe which has two wires almost in the same plane is quite sensitive to movements of the velocity vector out of that plane (defined as pitching motion). This has been attributed to the influence on one wire of the hot wake produced by the other. In this note a Disa X-type probe (type 55A32), with the wires 0·15 mm apart, is tested and found to have a static sensitivity to small angles of pitch, which is very significant for low wire Reynolds numbers (< 5) but becomes small for Reynolds number greater than 10. A modified probe, having the wires one wire length apart, is suggested and when tested was found to have no pitch sensitivity.

The stability of a smooth circular cylinder, free to translate horizontally and vertically against linear springs in the wake from an identical neighbouring cylinder, is studied using quasi-static aerodynamic derivatives and simple flutter theory. It is found that at spacing values between ten and twenty cylinder diameters (typical of the spacings employed on “bundled” overhead transmission lines) classical flutter of the leeward cylinder can occur in a certain critical range of wind speeds at certain orientations of this cylinder in the wake. However, the occurrence of flutter appears to be conditional on a positive difference of natural frequency between vertical and horizontal motions of the leeward cylinder in still air.

Classical static instability (divergence) of the leeward cylinder is also shown to be possible over the entire “incidence” range in the wake, but this occurs in a much higher wind speed range than that associated with flutter.

The method of characteristics and an implicit finite-difference scheme are used to investigate the interaction between the internal flow field and laminar boundary layer in ducts of circular cross-section under the conditions of high Mach number and low Reynolds number. The displacement thickness is added on to the body to form a new “effective body shape” which is used to re-calculate the inviscid flow. Iterations are performed and a solution is obtained when the surface pressures in two consecutive iterations converge to within a specified tolerance. The calculated surface pressures on a 10 degree conical duct placed in a hypersonic stream at M∞=8·34, Re∞=7·5 × 106 and M∞=10·4, Re∞=4·625 × 106 with γ=1·4 show good agreement with experiments. The results are computed for constant wall temperature, using a value of Tw/Tstag=0·23, and the Prandtl number is assumed to be constant and equal to 0·7 throughout the calculations. The type of shock-wave interaction near the axis of symmetry is determined and the computation terminates after the fluid properties behind the reflected shock have been calculated.

This paper presents the results of some calculations of the incompressible turbulent boundary layer on an infinite yawed wing. A discussion is made of the effects of increasing lift coefficient, and increasing Reynolds number, on the displacement thickness, and on the magnitude and direction of the skin friction. The effects of the state of the boundary layer (laminar or turbulent) along the attachment line are also considered.

A study is made to determine whether the behaviour of the boundary layer can adequately be predicted by a two-dimensional calculation. It is concluded that there is no simple way to do this (as is provided, in the laminar case, by the principle of independence). However, with some modification, a two-dimensional calculation can be made to give an acceptable numerical representation of the chordwise components of the flow.

Using a perturbation method, the formulae for the pitching stability derivatives of sharp wedges at zero incidence in viscous hypersonic flow are obtained in closed form. The results include the effect of unsteady reflected waves from the bow shock and may be applied to any wedge provided that the bow shock is attached. The effect of viscosity of the gas is included in two parts: first, it thickens the wedge, thus introducing the concept of an effective wedge, thicker than the original wedge by a semi-vertex angle equal to the average inclination of the displacement boundary layer; secondly, it makes this effective wedge deformable. Comparison with previous theories is given.

This paper presents a theoretical analysis of the behaviour of thin-walled lipped channel beams subjected to end moments. In the analysis the beam section is assumed to be composed of a number of flat plates, joined at the edges. The mechanics of local instability of the walls of the beam are examined from a consideration of the strain energy stored in the component plates, and critical moments to cause local buckling are evaluated. The behaviour of the beam after local buckling is studied using a semi-energy method, whereby the stress and deflection systems throughout the section are linked by solving von Kármán’s compatibility equation for the component plates and the stress and deflection magnitudes are found from energy considerations. As collapse of the beam is approached, a simple plasticity analysis is incorporated in the theory in order to evaluate the collapse moment for the beam.

The results of the analysis are compared with the findings of an extensive experimental investigation and it is shown that the theory is very accurate in its prescription of the experimental stresses and deflections. Comparison of the theoretical and experimental collapse moments also verifies the validity of the theoretical analysis.

The paper presents a theoretical investigation of the flow when the wake from a single vibrating aerofoil interacts with a fixed downstream cascade set normal to the mean flow direction. It is concluded that the effects of the cascade extend upstream by a distance of about one quarter of the wavelength of the fluctuations in the wake. It is also found that the wake passes through the cascade unchanged in strength, but that the cascade sheds vorticity of equal and opposite magnitude, so that, if an average is taken in the direction parallel to the cascade, the wake is annulled.

The natural frequencies and mode shapes of vibration of cantilever aerofoil cross-section blades of pre-twist angle in the range 0 to 90 degrees are obtained. The beams are 152·4 mm long and the width / thickness ratio is such that they may be regarded as slender. Theoretical frequency ratios and mode shapes of vibration, neglecting shear and rotary inertia effects, are obtained for two sets of beams, one with clockwise pre-twist relative to the root cross-section and the other with anti-clockwise pre-twist. The effect of variation in the value of the centre-of-flexure coordinates upon the natural frequency ratios and mode shapes of vibration is investigated. The theoretical results are compared to corresponding experimental results.

In many flight situations an automatic control is used to minimise the deviation of one or two aircraft motion variables from their trim values. The same effect may be brought about, in certain cases, by pilot action. If the control is very strong it may be imagined that the aircraft motion is kinematically constrained in the sense that the controlled motion variables are actually held irrevocably at their trimmed values throughout a disturbance.

More than fifteen years ago Neumark presented an analytical treatment of startling simplicity which dealt with the motion of an aircraft under strict kinematic constraint. By adopting the concept of kinematic constraint and so eliminating one or more variables the motion of the aircraft is described by a simpler set of equations: yet, clearly, the addition of a control system to the aircraft will, in fact, increase the complexity of the complete set of describing equations. However, there is no doubt that Neumark’s theory does give meaningful and useful results.

The analysis described in this paper shows how the motion of a strongly controlled aircraft can be described in terms of simpler sub-systems and indicates that Neumark’s theory appears as the limiting case of infinite control strength. The role of the pilot in applying strong control is placed in the context of the general theory.

Earlier papers described a method of calculating three-dimensional turbulent boundary layers based on the use of momentum-integral equations in the streamwise and cross-flow directions. Here the method is applied to a problem which is initially formulated in a coordinate system appropriate to the somewhat complex body geometry. Transformation to a streamline coordinate system is then made before the application of a rapidly converging iterative method of solution. The calculations, which are confined to single Reynolds number and a particular value of the rotation parameter, show the very large increases in drag and torque that accompany early transition.

The prediction procedures of Bradshaw and Ferriss and Spalding and Patankar are compared with a wide range of experimental data obtained in turbulent, supersonic, two-dimensional flow. Both procedures are shown to result in satisfactory predictions of mean velocity profiles and wall shear stress in adiabatic-wall situations: in addition, the procedure of Spalding and Patankar is shown to be satisfactory in heat transfer situations. The Bradshaw and Ferriss procedure employs a turbulent energy hypothesis in contrast to the mixing-length assumptions used in the present version of the Spalding and Patankar procedure. The close agreement between the predictions of the two procedures indicates a lack of experimental data obtained in flow configurations with suddenly imposed or relaxed pressure gradients.

This paper describes an experimental study of the interaction between a hypersonic flow and a transverse jet which issues radially from a slender conical model. Measurements in the region far upstream of the jet show qualitative agreement with free interaction analyses, while downstream a film cooling effect appears to reduce the heat transfer rate substantially. The effect of changes in Reynolds number, jet pressure ratio and mass flux is examined and compared with similar phenomena caused by fixed disturbances such as compression corners. The shape of the interaction shock wave is found to agree with the predictions of the second-order blast wave theory. Finally a correlation is found between the boundary layer separation length and a local mass flux parameter.

Shear stress, eddy viscosity and mixing length distributions have been obtained from measured boundary-layer developments over porous surfaces with air and carbon dioxide injection at Mach numbers up to M=3·6. It is found that, if the eddy viscosity is non-dimensionalised by dividing by the product of the free-stream velocity and the kinematic displacement thickness then this non-dimensional ratio is almost independent of injection ratio, but decreases slightly with Mach number.