In recent papers Squire has presented results for the shock shape and pressure distribution on the lower surface of unyawed, lifing, conical bodies with sharp leading edges. The work, a development of Messiter’s first-order correction to Newtonian theory, was successfully applied to wings of diamond and caret section. This paper shows how the method may be used to include the effects of yaw. Results are presented here for the flat wing and some biconvex sections. Comparisons are made with experiment for both the flat and biconvex wings and agreement is shown to be good.

An approximate theory, which yields the minimum induced drag of a planar wing with end-plates in ground effect, is presented. As a check on the accuracy of the method, it is compared with the exact linearised theory in the case of end-plates of vanishing depth (planar configuration). This shows that, within the limitations of the linearised lifting-surface theory, the present method is accurate in the range of wing heights of interest. In Section 5 the theory is compared with experiment. In this comparison two interpretations of the theory are employed. The first assumes that the vortex trace is the projection of the trailing edge of the configuration onto a plane normal to the direction of motion when the wing incidence is zero. The second is different from this only in that no constraint is placed on the wing incidence. Of the two interpretations the first is found to be in better agreement with experiment than the second for the planar configuration. However, the opposite is found to be true when end-plates of sufficient depth are fitted. A reason for this is proposed in Section 5.

When an aircraft flying at a constant airspeed performs circular orbits relative to the ground, its path relative to the air has interesting features if a wind of uniform velocity is blowing. The locus, which is here called an aeroid, bears some resemblance to a prolate trochoid; its equation is obtained in parametric and intrinsic forms, and its curvature and other fundamental properties are derived.

In the final section of the paper some practical implications are considered, including the effect of wind on the fuel consumption per orbit of a circling aircraft and the influence of winds of different headings on the path for a landing approach.

Bradshaw’s method of calculating the development of two-dimensional turbulent boundary layers involves the simultaneous solution of partial differential equations of mean motion and turbulent kinetic energy. The present approach avoids the computational complexities of this procedure.

The use of Thompson’s two-parameter family of velocity profiles and associated skin-friction law enables the momentum integral equation to be satisfied, along with Bradshaw’s version of the turbulent kinetic-energy equation at a specified fraction of the boundary layer thickness. This fraction (y/δ = 0·5) is chosen as representing the position in the boundary layer where Bradshaw’s equation, which contains several empirical functions, is shown by comparisons with experiment to hold with greatest accuracy. Thus the present simplified approach leads not only to a reduction in computing time but also to an appreciable increase in the general accuracy of prediction.

Cylinders of non-circular cross-section which can be constructed by circular arcs and straight line segments are analysed. Differential equations and boundary conditions for the buckling of eccentrically stiffened, isotropic or orthotropic, circular panels of zero Gaussian curvature are derived through variation of the total potential. Eight equations of continuity along the generators of adjacent arc-segments are enforced simultaneously through the use of Lagrangian multipliers which, with the potential minimised with respect to the admissible displacement functions, constitute an approximate solution of the cylinder problem. Numerical examples include stiffened cylinders with oval and egg-shaped sections. The buckling strengths of these non-circular cylindrical shells under bending are compared with their circular counterparts on the basis of equal circumferential length.

A method for the generation of assumed modes in beams with arbitrary boundary conditions is described. The method is applied to two cantilevered beams using a modified Rayleigh-Ritz vibration analysis. The results obtained show excellent agreement with those obtained by exact methods of analysis.

The paper first describes an approximate method for calculating inviscid flows round arbitrary aerofoils at sub-critical Mach numbers, based on second-order theory with empirical improvements to give better agreement with exact theory; several comparisons are shown. This method is then used as the basis of an iterative procedure for calculating the effect of the boundary layer on the surface pressures and overall forces; several comparisons are given with recent experimental results.