The overall effective efficiency of a jet-propelled flight may be defined as the net useful work that is done in accelerating the vehicle, raising it to height and combating its drag, divided by the calorific value of the propellants used. The analysis presented here shows that for a single-stage vehicle this overall efficiency is equal to the integral of the fraction

with respect to each element of propellants used. In this expression u'is the effective jet velocity (allowing for jet deflection, this is √(1 + k2) times the actual exhaust velocity), υ the vehicle velocity, q the fuel/air ratio and H the calorific value of the fuel in dynamic units. The mean lift/drag ratio of the vehicle is taken as 1/k, so that the last three terms of the numerator represent the work lost in dragging, raising and accelerating each element of propellant to the range R, height h and flight velocity υ at which it is burnt. The fraction may therefore be considered as the efficiency with which that element of propellant is used with respect to the whole flight plan.

For advanced air-breathing projects—by-pass engines up to aircraft speeds around Mach 2 and ramjets between Mach 4 and 9—the analysis shows that the sum of the υ-dependent terms in the efficiency factor is practically constant. The potential energy term is insignificant in the normally accepted flight corridor. Thus the overall efficiency with which propellants are consumed in covering a range R1 at flight speed υ js closely approximated to by the fraction

and the useful work done by the mass mm of propellants is

The vehicle mass (including engine, payload, and so on) that can be dragged over the range R1 by unit mass of propellants can then be calculated.

Although such simplified expressions cannot substitute for the final detailed analysis of a projected flight plan, it is hoped that they will prove more useful in preliminary analysis than the figures based entirely on cruise performance which have often been quoted in the past.

An investigation has been made into the errors involved in using certain lumped parameter methods for the solution of beam frequencies. It is found that existing methods are not consistent for all boundary conditions. A new dynamic stiffness matrix has been formulated, which gives consistently good results for even a few elements. The error in the solution is always inversely proportional to the fourth power of the number of elements used.

The vorticity shed behind a finite wing has been studied and a condition found for steady circulation. This condition is then combined with three-dimensional boundary layer theory to find the lift of a finite wing. An example shows that on a thin ellipsoid of aspect ratio 6·37 the lift as found by the present method is 2 per cent lower than the lift obtained using a sectional boundary layer approach.

The stress concentration factors for equilateral triangular holes, with varying degrees of curvature at the corners, and with varying amounts of compact reinforcement on the boundary, have been computed for each of three loading cases. Poisson's ratio was assumed to be 1/3.

The stability of the phugoid motion of an aircraft in the presence of wind shear is investigated. The effect of the wind shear on the phugoid frequency increases with increasing aircraft speed and can be stabilising or destabilising, depending on the aircraft orientation relative to the wind shear. The destabilising effect of wind shear is alleviated by the stabilising effect of the density gradient of the atmosphere. At the most critical combination of speed and altitude a strong wind shear may lead to divergence, with a time to double amplitude of the order of 10-15 seconds.

A numerical study of the aircraft motion with controls fixed when descending through a wind profile similar to that in a jet stream indicates that the increase in the aircraft indicated speed can be of the same magnitude as, or larger than, the maximum wind velocity increment in the jet stream core. However, as the time to reach the excess speed is of the order of one minute, the actual behaviour of the aircraft strongly depends on the pilot's action and thus is not fully predictable by theoretical analysis.

The method of generalised conical flows has previously been developed subject to the condition that the upwash divided by the streamwise co-ordinate to the power ĸ, where ĸ is the order of the conical flow, must have vanishing (ĸ+1)th derivative with respect to the conical co-ordinate. In the present paper this restriction is removed. The results are also used to discuss the effect of the application of the leading edge attachment condition on the wing pressure and geometry.

An exact plate analysis is given for torsion-type modes whose wavelength and deflection pattern are repetitive in the spanwise direction. It is shown that for short wavelengths there are regions of localised curling at the leading and trailing edges.

An investigation of the effect of a root gap is extended to the oscillatory pitching motion of a slender wing. Potential theory is used and the unsteady forces are shown to be reduced by the gap as drastically as the steady. These results cast doubt on measurements made by the technique of half-model testing. Viscous flow in the gap is discussed with reference to the possible types of model mount. The effect of viscosity may be to reduce the gap loss, but the extent of the improvement is uncertain.