It is Sometimes required to find the maximum amplitudes of vibration attained and the speeds at which they occur when a machine is run through its critical speed with different accelerations. The solution of this problem for single degree of freedom systems has been obtained by Lewis and by Ellington and McCallion for mechanical vibrations and by Hok for the equivalent electrical case. These solutions require higher mathematics (contour integration, Fresnel's integrals or series solutions leading to Bessel functions). The purpose of this note is to show how, by using simple integration only, an alternative method of solution can be obtained for both zero and small values of damping.

A Method is presented for determining approximately the effects of small changes in the characteristics of a dynamical system on its free motion. Successive factorisations of the determinantal equation, as the system is altered, are avoided at the expense of accuracy, but the influence of the small changes on, for example, the stability of the system, are quite easily determined.

A New type of auxiliary equation is given for calculating the development of the form-parameter H in turbulent boundary layers with adverse pressure gradients. The chief advantage of this new method lies in the rapidity and ease of calculation which has been achieved, without apparent sacrifice of accuracy.

Whereas the growth of momentum thickness in the turbulent boundary layer can now be rapidly calculated by methods involving only simple quadrature, the prediction of the form parameter development remains a laborious task, while the results obtained do not always appear to justify the complexity of the calculations.

At the start of the discussions, the Chairman (Major G. P. Bulman) gave a warning that parts of the subject of transonic wind tunnel testing were still classified and therefore he asked speakers to be careful in what they said. In spite of this, it was possible to discuss a wide range of topics without transgressing security restrictions. Those members of the audience who were familiar with the subject were able to put many questions to the lecturers and to raise several new points, while the large proportion of the audience to whom the subject was relatively new were able to gain a useful insight into the problems involved in the operation and design of transonic tunnels.

The Function of the air intake of a gas turbine engine is to deliver whatever air mass flow is required, with the best recovery of ram stagnation pressure, over the desired range of flight speeds and altitudes.

Although it is generally shown in other forms, the performance of an air intake for supersonic flight can be represented on charts very similar to those of a rotating compressor. In Fig. 1 the ratio between ambient (static) pressure and stagnation pressure at the diffuser of a typical intake is shown as a function of corrected inlet and outlet air mass flow (which are themselves functions of the local flow Mach numbers), for a series of flight Mach numbers.

Crabtree (July Journal, page 525) has suggested a simple method for estimating the transition position on an aerofoil, based on the use of a single curve of momentum thickness Reynolds number (Rδ2) against a pressure gradient parameter at transition, mr. This curve makes some allowance for the effects of pressure gradient and laminar separation on the transition “point”, neglecting the effects of roughness, free-stream turbulence, and so on, but is considered “adequate for most practical purposes”. However, transition is a complex phenomenon, sensitive to a great variety of factors, so that Crabtree's method should be accepted with some reservations.

The Calculation of the roots of an algebraic or transcendental equation in a single unknown is a problem of frequent occurrence. For a real root the usual procedure is to obtain a first approximation to the required quantity, graphically or otherwise, and to improve this approximation by successive applications of the Newton-Raphson process. The extension of this process to the improvement of an approximate solution of a set of non-linear simultaneous equations in n unknowns is fairly obvious, but it does not seem to have received much attention in text books, although the case of two unknowns is dealt with in Ref. 2.

For a Flat Surface at zero incidence in a deep uniform stream, the total frictional drag F per unit width of the surface can be calculated from the well known equation

Using the momentum principle in the usual way, it can be shown that when fluid is added locally to the flow through the surface, the total frictional drag F1 is given by

Now a Days, the phenomenon is well known of the plane normal shock waves set up in the divergent section of a convergent-divergent nozzle, and the oblique shocks which occur in the resultant jet downstream of the nozzle exit when operating under overall pressure ratios less than the design value. Stodola was among the first to demonstrate experimentally the effect on the flow within the nozzle of increasing the back pressure above the design value, and work by Schmidt, Martin) and others, has been concerned with the theoretical changes in pressure, temperature, density and Mach number across a normal shock wave whose position varies along the nozzle axis. The effect of working substance on these changes, which is taken into account by the ratio of specific heats, has also been investigated.

Two methods are given concerning the following problems of linear algebra over the field of complex numbers (or, less rigorously, linear problems with complex coefficients): the solving of a system of linear algebraic equations, the inversion of a matrix and the evaluation of a determinant. The second method is especially suitable for use with computers. In addition to the usual numerical checking, the second method also provides an effective form check.

A Method is described for providing warning of the onset of undesirable effects produced by flow separation on an aircraft wing. It is based on static pressure measurements near the trailing edge and appears to have advantages over alternative methods.

Recent work has suggested that certain effects of flow separation such as buffeting, aileron buzz and undesirable changes in loading, occur when a “ bubble ” of separated flow originating at the leading edge of a wing, or at a shock wave on its surface, first becomes sufficiently large to affect the flow at the trailing edge.

The Important characteristics of the turbulent velocity profile of a plain concentric annulus and some of the methods of correlating the velocity distribution are briefly reviewed. The average velocities in an annular section are examined and some experimental data is correlated by a modified power law.

Perforated Plates have been used at large angles of incidence to produce drag forces and evidence on their properties has been published by de Bray. Less appears to be known about the drag forces on such surfaces at zero incidence, although they are usually considered to be aerodynamically rough. This has been confirmed by Ambrose, who carried out pipe flow experiments using perforated liners which fitted tightly in the bore of a pipe. Perforated plates used in this way do not allow flow completely through them and give “pitted” surfaces. If a perforated plate is mounted so that it is possible for cross flows to occur between the main flows on both sides of the plate the drag forces on it may be affected, and in this case the perforations will be referred to as “holes.”

MR. Harpur's interesting and stimulating paper (page 363, May 1958 Journal) is obviously of great importance to all who have to face the problem of fatigue strength of aircraft. These comments all refer to Section 3—Design Loads. Mr. Harpur's conclusions are based on analysis of a typical flight plan of a medium haul civil transport, and are formulated as a proposal for two fail-safe design requirements.

In a previous note a method was developed for calculating the exhaust port area for two-stroke cycle engines assuming the cylinder length to be constant. It was pointed out by Williams and Pullman that the effect of the variation in cylinder length was important, this was appreciated in the preparation of the note, but it was necessary to assume a constant length in order to obtain an analytical solution. In this note the method given earlier is extended to cover a cylinder discharging direct to atmosphere with a moving piston.

It has been suggested to the Divisions of the Society overseas and to the Singapore Branch that, instead of publishing their Annual Reports, it would be of more general interest to publish, two or three times a year, news of their activities and of aeronautical developments in their areas. This month we publish reports from the New Zealand and Southern Africa Divisions and hope that we shall have news soon from the Australian Division and the Singapore Branch.—Ed.