An account of the solution of a quadratic equation associated with a gas dynamic problem is given. Numerical examination of the equation Indicated that a conditional statement was required In a computer programme to determine the sign to be used in front of a square root. The necessity for this conditional statement was examined by studying a general quadratic equation. The study has also led to the formulation of a rule on the selection of a “desired root” of a quadratic equation.

The purpose of this note is to draw a formal parallel between the fundamental hodograph flow equations in subsonic and supersonic regimes when expressed in terms of a generalised velocity parameter. This parameter can cover, by simple algebraic extension, hodograph flows in either regime; it has simple geometrical and dynamical interpretations and models of the combined hodograph plans in terms of this parameter are also suggested.

A similar, and perhaps familiar, velocity parameter appears to have been first used in the solution of certain subsonic flow problems by Tsien, following a suggestion of von Kármán, although a more general and basic form was not described.

In the course of a recent meeting of the Performance Data Sheets Committee of the Royal Aeronautical Society to discuss thrust measurement in flight, it was pointed out that it is easy to apply the equations of motion incorrectly to the case of an aircraft which is losing mass due to fuel consumption. The rate of change of aircraft momentum is obviously affected by the loss of mass and so, at first sight, it may appear that the margin of thrust over drag required to achieve a given acceleration and /or rate of climb at any particular instant would be affected also. In fact this is not the case. To clarify this point, this account of the momentum and energy balances of an aircraft with an air-breathing engine has been prepared at the suggestion of the Performance Committee.

It is commonly stated in the literature on laminar flow control (see, for example, ref. 1) that the important parameter controlling the height of tolerable roughness is the Reynolds number per foot, or unit Reynolds number, Vh; provided this parameter is the same in any two cases (which are closely geometrically similar) then it is assumed that the tolerable roughness height will also be similar. It is the object of the present note to point out that this is true only in very restricted circumstances and that in general the actual physical scale is also of considerable importance, as the following shows.

A large lump of ice fell from a cloudless sky one morning in September 1964 and landed only ten yards from a farmer in the Brits district of the Transvaal, South Africa. A whirring sound shortly before the impact alerted the farmer so that he saw the ice as it struck the ground.

The lump was flattish-shaped and irregular, estimated at 11 x 9 x 6 inches, and gave off a peculiar odour. The farmer also observed that the ice was composed of numerous layers and that parts of its interior were brownish-coloured. He did not recall noticing aircraft in the vicinity at the time of the incident.

There seems to be a disturbing rate of increase in new scientific and technical terms. The purpose of these notes is to stimulate a discussion of this trend.

When inventing or introducing new terms the following points should be borne in mind: (1) is a new word necessary or desirable, (2) is it apt and well-constructed?

As regards (1) the usual justification is that science and engineering are developing so fast that in order to communicate new ideas and new concepts an increase in the vocabulary is essential. This, however, can be overdone. The very act of coining a new word implies a theoretical assessment, almost an acknowledgment of the fact that a concept or phenomenon, or particle has a well defined identity. The following, somewhat exaggerated examples, illustrate this point. It would have been most unfortunate if spectroscopists at the end of the last century had insisted on giving one and the same chemical element different names according to the wavelength of the light they emitted. I wonder whether the many names allocated to elementary particles today may not become an embarrassment should it turn out that they are in many cases just excited states of one and the same particle. Conversely, one must applaud the restraint of the nuclear physicists for not giving separate names to various radioactive isotopes. After all, as far as nuclear properties go, many isotopes (e.g.57Co, 58Co, 60Co) have very little in common. And, although we have a separate name for the heavy hydrogen isotope (deuterium), physicists and chemistsi have so far resisted the temptation to give the light isotope of helium (3He) a name and we are still spared “trelium”.

A few years ago the United States Air Force became interested in developing a higher temperature version of its standard pitot-static tube capableA of accurate operation to Mach number 5 and 150 000 ft with angles of attack up to 14°. It soon became evident that the existing aerodynamic configuration was inadequate because (a) the sharp pitot pressure source could not be protected from high heat fluxes and temperatures, (b) the static pressure source geometry produced serious errors at Mach numbers above 3·0 for α> 5°, and (c) the static pressure source geometry could be responsible for unacceptably high lag above 100 000 ft altitude because it consists of two orifices of only 0·070 in diameter.

Diagonal tension analysis of flat panels in shear is commonplace in aircraft design; such an analysis is presented in detail in the Royal Aeronautical Society Structures D.S., 02.03 series. In their present form, although well presented, they are time consuming and laborious to the engineer. It is therefore desirable to transform these data sheets into a form which can be easily programmed for solution by computers. The aim of this paper is to present such a format. The method is adequately covered in the data sheets, but important points are listed here. A step by step procedure for the analysis is given with a suggested programme input sheet and output format. An example is given with corresponding output data to be used for programme check-out purposes.

The dynamic analysis of heated structures is of considerable importance. Significant heating of a flight vehicle may take place at high speed causing reduction in its structural stiffness and vibration frequencies. Such changes in frequencies and mode shapes can substantially affect various static and dynamic aeroelastic instabilities.

In general, availability of a similarity law simplifies the solution of a problem. The following presentation studies similarity relations existing between an unheated vibrating cylinder and one with temperature gradient across its thickness.

The Free and damped vibrations of a circular plate with given initial conditions, which is either free or elastically restrained along its outer edge, are discussed using the method developed by Reid and some numerical results are also given.

The vibration of a circular plate has been studied considerably and most of the authors seem to be interested in determining the frequencies of vibration and the nodal patterns. A few investigators have studied the problem of determining the subsequent motion of a thin plate started with some given initial displacement or velocity. Sneddon has attempted this problem, taking into account an approximate boundary condition. Recently Reid has discussed this problem without taking recourse to any approximate boundary condition. He has developed a method of analysis to determine the displacement of a freely vibrating thin circular plate with the given initial conditions, using the norm of the eigen functions.

It is shown that, in regions near peak strains, improved accuracy of measurement with a strain gauge or extensometer, can be obtained by taking readings over more than one distance including each point. A better estimate of the true strain can then be derived than will be given by a single reading. Peak errors in the region of 8 to 10 per cent can thus be reduced to 1 or 2 percent.

Two methods are described: one in which measurements are made at equal intervals along a line, keeping the gauge length constant; the other using different gauge lengths centred on the point concerned, the latter being suitable where a grid can be marked on the surface.

Perhaps the most encouraging thing about the article by Mr. J. R. Cooper entitled “Future relationships between Air and Ground transport” which appeared in your issue for November, is that someone at least is ready to consider unorthodox methods of solving some of our present problems. It is a difficult paper on which to comment effectively because its does, as the author admits, embrace three separate principles.

The Navier-Stokes equations are solved iteratively on a small digital computer for the class of flows generated within a rectangular “cavity” by a surface passing over its open end. Solutions are presented for depth/breadth ratios ƛ=0.5 (shallow), 10 (square), 20 (deep) and Reynolds number 100. Flow photographs ore obtained which largely confirm the predicted flows. The theoretical velocity profiles and pressure distributions through the centre of the vortex in the square cavity are calculated.

In an appendix an improved finite difference formula is given for the vorticity generated at a moving boundary.

Since Thorn began his pioneering work some thirty-five years ago the number of numerical solutions which have been obtained for the equations of incompressible viscous fluid motion remains small (see bibliographies of Thom and Apelt, Fromm). The known solutions are principally for steady streaming flows, although two methods have now been used with success for non-steady flows (Payne jets and Fromm flow past obstacles). By contrast this paper is concerned with the class of closed flows generated in a rectangular region of varying depth/breadth ratio by a surface passing over an open end. This problem has been considered for a number of reasons.

The use of multilobed pressure vessels is not new. Such structures have been used in civil engineering applications for many years. It has been recognised that substantial weight savings are possible by reducing the radius of curvature by lobing. Usually the resulting discontinuity stresses at the junctions of the lobes have been balanced by attaching flat plates.

An analytical solution is given for the one-dimensional distribution of temperature in a web of an idealised multi-cell wing structure when the adiabatic wall temperature variation is assumed to be either an instantaneous or a linear function of time. The maximum temperature difference between skin and web centre is computed for a range of structural geometries and thermal parameters. Thermal stresses are calculated assuming a parabolic temperature distribution in the web.