The solution to the general problem of transferring a rocket between two terminals in space with minimum fuel expenditure is explained and the results obtained when application is made to a number of particular problems of space navigation are described. The mathematical techniques which may usefully be employed in the calculation of optimum rocket trajectories are exemplified by a method of solving the problem of obtaining maximum range from a rocket missile over the Earth's surface.

A transient sound wave is generated by discharging a spark in an air stream, the velocity and temperature of which are required. After a time interval of about 25 microseconds a shadowgraph photograph of the sound wave is taken; a second photograph is obtained after a further known time interval of the same order. The two exposures, both on the same negative, show the propagation of the sound wave in the air stream and from this the Mach number, the true velocity, the local velocity of sound, and hence the temperature, can be calculated.

Using this method, measurements of Mach numbers of the order of 0·5 gave values between 98 per cent, and 100 per cent, of those calculated from pressure measurements. Typical examples of the sound wave photographs are shown. With further development along the lines indicated in the paper greater accuracy should be possible. The local speed of sound was measured to an estimated accuracy of ±1·5 per cent.

Since only a very short time interval is needed to obtain the photographs, the method appears promising for investigating explosions of brief duration, or dealing with flows of pulsating character.

The equations of thin plate theory are expressed in polar co-ordinates and transformed using the Mellin transform. Problems involving discontinuous and isolated normal loadings may then be solved in the case of the built-in or freely supported wedge-shaped boundary.

Equations for the calculation of the subsonic flow of an inviscid fluid through given two-dimensional channels (the “ direct” problem), and for the design (the “ indirect” problem) of such channels are derived. The method is based on conformal mapping, and in the special case of channels with walls made from a number of straight sections, or with wall pressure prescribed as step-functions, yields the same results as the well-known Schwarz-Christoffel mapping theorem technique. However, it is more general than this latter method, since it is capable of dealing with curved walls or continuously varying wall pressures. The compressibility of the fluid is allowed for only approximately, the ideal gas being replaced by a Kàrmàn-Tsien tangent gas.

In Part II the theory is applied to various problems of aeronautical interest, perhaps the most important of which is to the setting of “ streamlined ” walls about a symmetrical aerofoil placed in the centre of the channel.

Experiments have been made to find the effect of the ratio of sting to base diameter on the base pressure of an axially symmetric body at zero incidence in a supersonic stream. The Mach number of the flow was 1·994 and the model boundary layer was turbulent. The model used was a one inch diameter circular cylinder without boat-tailing. It passed through and was supported upstream of the nozzle throat. This method of support allowed measurements to be made in the important (and hitherto unexplored) case of zero sting diameter.

As the sting to base diameter ratio was increased from 0 to 0·85, the base pressure decreased. The minimum value reached was approximately 0·8 of the value it would have at the base of a two-dimensional body with a similar ratio of boundary layer thickness to base height. The base pressure coefficient rose rapidly to zero as the ratio was further increased to unity.

Under the conditions of the experiments, with a sting to base diameter ratio of 0·4 the base pressure coefficient differed from that without a sting by approximately ten per cent. With the more modest ratio of 0·2, the difference was approximately three per cent.

The elastic stress distribution around a circular hole in a flat bar under simple tension, when the hole is filled by a push-fit pin, was investigated photoelastically. Over a range of values of the ratio of hole diameter to width of bar, and for pins of differing Young's moduli, the effect of the pin was sensibly the same, namely, to reduce the maximum tension on the hole boundary by about 15 per cent, as compared with that in the unfilled hole.

The maximum shear stress on the boundary was unaltered.