In studies of the stability of aeronautical systems, equations of motion are derived which have coefficients dependent on flight speed. Conventional practice treats the speed as constant, when a set of linear differential equations with constant coefficients results. Actually, since the speed varies during flight, it may be regarded as a prescribed function of time; the set of linear differential equations then has variable coefficients.

The treatment of the problem of stability then becomes much more complex in this case. A simple example is given to show that a system which is stable at any constant speed can become unstable during deceleration; the ordinary constant-speed criteria are, strictly, therefore inadequate. Some approaches to the discussion of stability during acceleration are suggested; a solution is given of the single second-order equation which enables the amplitude of oscillation of the solution to be studied. Inverse methods of approach are suggested, both for single and sets of equations, in which particular forms of acceleration corresponding to prescribed solutions are derived; and some tentative conclusions are drawn. As would be expected, the effects of acceleration depend on a dimensionless “acceleration number.”

The “second stage” two-dimensional jet flap experiments are briefly described and some of the results presented with comments. The relative simplicity of these experiments and the measure of their agreement with the theory provides, it is hoped, yet another illustration of the value of comparatively simple experiments in the early stages of work on a novel idea.

Tests have been carried out on a series of convergent-divergent nozzles and the results compared with those from a test on a convergent nozzle. At the design pressure ratio, reductions in the noise were found, particularly at 90° to the jet direction. For lower forward pressures the noise is also less, but above the design pressure the noise rises rapidly to the same level as that with a convergent nozzle. In the experiments cold jets were used, but the results are probably applicable in certain respects to hot jets.

By using the methods of the Calculus of Finite Differences, expressions are obtained for the nodal moments and deflections of a simply-supported grillage, subjected to a loading constant along one set of beams and having a sinusoidal variation along the other set of beams. A simple example verifies the expressions and illustrates their use.

A method is presented for the calculation of the streamwise component of vorticity, for flows in rotating passages. The method may be regarded as an extension of the methods applied in recent years to the calculation of secondary flows in stationary passages.

Attention is concentrated on the quantity I=p+½ρV2−½ρU2, where V is the fluid velocity relative to the rotor and U is the rotor tangential velocity. I remains constant along a streamline in the rotor, and is found to enter into the equation for the generation of vorticity in much the same way as the total head enters for flow in stationary passages.

An approximate calculation of the streamwise vorticity generated in a simple axial-flow rotor is made, and qualitative consideration is given to the flow in a centrifugal impeller. Just as for the calculation of secondary flows in stationary passages, an approximate shape of the streamline must be assumed before the secondary flows can be calculated.

Effects of vibrational excitation and dissociation of air on inviscid high speed flow past a circular cone, at zero incidence, with an attached shock wave, are studied on the assumption of thermal equilibrium. A numerical solution of the problem is outlined and an approximate analytic solution for the flow between the surface of the cone and the shock wave is developed. Two numerical examples are given as an illustration and compared with the corresponding solutions assuming constant air properties.

Dr. Rockey, in his interesting paper on the design of vertical stiffeners for shear webs, perpetuates the idea of Timoshenko (Theory of Elastic Stability, McGraw-Hill, New York, 1936) that for stiffener rigidities above a certain value the stiffeners remain straight and the rigid stiffener buckling load is reached. It is my opinion that this is only so when the stiffeners happen to be placed along a straight node of one of the harmonics of the buckling pattern of the unstiffened plate. With unstiffened plates under shear loads, the nodes are not straight and consequently the buckling load will theoretically always increase with increase of stiffener rigidity, i.e. no buckling mode exists such that stiffeners of finite rigidity remain straight. It is suspected that Timoshenko was led to his conclusion by over-estimated buckling loads obtained by energy methods.