The paper considers a body, or space vehicle, of arbitrary shape, with conductivity K and specific heat c. It is first assumed that K and c are invariant with time and the body, with a given initial temperature, is assumed to be heated by a distribution of heat sources that varies with space co-ordinates and time. It is shown that a rigorous analytical solution to the problem is possible, provided that the distribution function satisfies prescribed regularity conditions.

The same problem is then considered, but with a heat-source distribution which is also a function of temperature. In this case the problem can be reduced to a Volterra-type integral equation amenable to step-by-step solution. Convective heating and radiation are specific examples of this second case.

The third case considered is that of a body whose geometry and thermal coefficients K and c are all time-dependent, and this problem is reduced to the fixed-geometry case by the addition of a hypothetical heat-source distribution which is a function of the velocity of ablation, of temperature and of its time derivative; an integral equation of Volterra type again results.

Finally, an example is given of the application of the analysis to the ablation of a conductive spherical shell.

Previous papers have examined the implications of an assumed polytropic expansion law on the performance of nozzles. In this paper a peculiar anomaly is examined when the convergent nozzle is exhausting into a vacuum. It is shown that, on the strict assumptions of a polytropic expansion law, and the assumption that the flow will maximise for a given throat area, the thrust per pound of air increases progressively with falling polytropic efficiency, becoming infinite when the polytropic efficiency is zero. The author suggests that this anomaly is either concerned with the assumption that the flow will maximise or means that polytropic expansion efficiencies below a certain limit are theoretically impossible, but he believes that there may be some other explanation.

The problem considered is the buckling of a rectangular plate, tapered in thickness in a direction parallel to two sides, and uniformly compressed in that direction. Curves are presented showing the variation of buckling stress coefficient with the side ratio and the amount of taper, for each of two types of thickness variation, namely exponential and linear, and for each of two sets of boundary conditions, namely all edges simply-supported, and ends clamped and sides simply-supported. It is shown that, unlike the case of a uniform plate, there are no discontinuous changes of buckling mode.

Newtonian impact theory has been used to estimate the external pressure forces on ducted bodies of rectangular, circular and semi-circular cross section. With an allowance for skin friction (or other incidence-independent drag) it is shown that maximum lift/drag ratios of about three to four are possible with little effect of body geometry provided that short and very divergent, or tall and narrow rectangular ducts are avoided.

Large changes occur in the separate lift and drag at maximum lift/drag ratio and these have to be made compatible with the weight and thrust capacity of the configurations. The maximum lift/drag ratio of a duct can be improved by the addition of wings, especially for a duct with poor lift/drag ratio, but the best overall performance is with a duct of good lift/drag ratio and low drag.

It is anticipated that impact theory underestimates the pressure forces, and hence the lift/drag ratios, which would obtain at finite Mach numbers but the trends with geometrical changes should be reasonably reliable.

A method of calculation is developed to compute the overall performance of a multi-stage axial compressor, from a knowledge of the individual stage characteristics, by a “stacking” technique. Compressor models are designed and their overall performance calculated. These results are compared to show, qualitatively, the effect of alterations in design and stage performance on overall performance and to find how compressors should be designed for optimum performance.

During thermal fatigue testing of a specimen with a thin edge, or during rapid temperature changes in the gas flow past turbine blades, the thin edges are deformed plastically in compression during heating and subsequently creep in tension as the bulk of the specimen or blade heats up. The plastic deformation is determined from temperature distributions, which are calculated by Biot’s variational method. The creep deformation is determined as a function of time by a differential equation, which expresses the balance between increasing elastic stress and reduction of stress due to creep relaxation, and which is solved (i) by digital computer, (ii) by transformation to a Riccati equation soluble in terms of Bessel functions, or (iii) by transformation to a second-order differential equation with a periodic coefficient. Using the thermal stresses obtained from the solution of the differential equation, the theoretical thermal fatigue endurance is determined from cyclic (mechanical) stress endurance data. Agreement between theoretical and experimental thermal fatigue endurances is obtained, over ranges of temperature, strain and strain rate, or, equivalently, over ranges of temperature, edge radius and heat transfer coefficient. This agreement supports the use of the theoretical methods in wider contexts. The accuracy of the temperature distributions is better than the accuracy of other factors entering into the correlation between theoretical and experimental endurances. Improvement in the interpretation of experimental results requires consideration of the alteration of the stress cycles during the course of thermal fatigue testing. This requirement is catered for partially by the various solutions of the differential equation for thermal stress.