A new method for evaluating determinants or matrices is given; it is rather tedious to describe and awkward to prove, but is very easy to use. The chief advantages this method is believed to possess are:

1. (i) It involves as few arithmetical manipulations as does the most rapid method of pivotal condensation currently used.

2. (ii) It is easier than any other known method to learn and to remember.

3. (iii) It can be adapted to routine computation, in such a way as to minimise the likelihood of error.

4. (iv) A digital computor can readily be programmed to use it.

For horizontal, or nearly horizontal, steady straight flight there exist some charts from which can be determined the speed at any altitude, the inclination of the flight path, and other quantities. This can be readily done, for instance, by a graphical comparison of the forces of drag and thrust, or by a corresponding representation of the powers, required and available. These charts, however, always involve the polar of the particular aeroplane, and are thus valid only for that aeroplane; they must therefore be replotted for each example. To avoid this and obtain a generally valid chart, the effect of the aerodynamic characteristics of the particular aeroplane must be eliminated; it is thus possible to prepare a chart even for the steady circling flight at any inclination of the flight path.

The three equations for the description of the flight path may be derived on the simple assumption that the thrust acts almost along the direction of flight, i.e., that the angles of attack and of sideslip are negligibly small.

Approximate Solutions obtained by the method of collocation are presented for the lowest critical buckling load of an isosceles triangular plate loaded as shown in Fig. 1. Also, the fundamental frequency is given. The base of the triangle is simply supported and the other equal edges are clamped. The usual assumptions regarding the bending of thin plates are made. The governing differential equation for the plate loaded as shown in Fig. 1 is

1

where D is the plate stiffness, N is axial load per unit length, w is deflection, positive downward, and the quantities a and h are dimensions shown in Fig.1.

The ability to manoeuvre at high altitude has become one of the main requirements in the design of modern military aircraft. Ability to manoeuvre enables the fighter pilot to execute tight turns during the attack on a bomber and the bomber pilot to perform evasive manoeuvres and so make the task of the fighter more difficult.

Normally the main manoeuvre considered is the application of increased normal acceleration, or g, and if we assume that (a) there is sufficient pitching power available from the longitudinal control surface to increase the wing incidence to give the necessary increase in normal force, and (b) that the new wing incidence is below the stalling incidence of the wing, then the degree of manoeuvrability available is a function of thrust and drag alone. In the past the manoeuvrability required at a given altitude has been expressed in terms of the rate of climb available at that altitude and thus we have such definitions as “ the 1,000 ft./min. ceiling ” and so on.

Boundary layer problems may be divided into two classes: (a) those for which similar solutions can be found, i.e. where the boundary conditions are such that similar profiles differing only in scale factor exist at different sections; and (b) those where the boundary conditions do not effect similarity, so that the development of the boundary layer must be calculated in stages. The latter class are known as “continuation problems,” and very few numerical solutions have been obtained because of the labour involved.

Approximate methods of solving continuation problems are known, using the Karman momentum integral method (e.g. Ref. 1) or variants. Some of these methods make use of velocity profiles calculated for “similar” boundary layers. This note presents a new approximate method which uses “similar” profiles but avoids using the momentum integral. Instead of characterising the boundary layer thickness by the “momentum thickness,” which needs to be calculated yet is of less direct interest, the wall shear stress is used; this stress usually has to be calculated in any case and the present method is therefore comparatively simple.

The Classical method of solution of the stability of an axially–loaded continuous beam is by means of the three moments equation, using the Berry Functions, which are functions of the axial load. As the axial load approaches a value equal to the critical value for a pin–jointed beam, the Berry Functions tend to infinity, and the use of the three moments equations —(i. e. treating the end fixing moments as the independent variables)—leads to certain difficulties in the complete solution of the problem.

The major difficulty lies in the question of stability. The critical value is determined by the vanishing of the determinant of the coefficients of the fixing moments in the three moments equations. This value could be found by plotting the determinant against end load (c. f. Pippard and Pritchard). However, in a problem involving a large number of bays, the calculation necessary to do this is likely to be considerable, for there may be many branches to the curve.

The Quasi-Cylinder and slender body theories for the supersonic flow past bodies of revolution have been much used in recent years because, for reasonably simple body profiles, these theories permit a simple and rapid calculation of the first-order pressure distributions and aerodynamic forces. It is assumed in both theories that the body profile slope is small; in the quasi-cylinder theory it is also assumed that the body radius is nearly constant, whereas in the slender body theory it is assumed that the thickness ratio of the body (maximum diameter/length) is small.

In the present note these two theories are combined completely. From a strictly mathematical point of view nothing is gained by this combination, and, furthermore,application of the combined theory to a particular case is in general a little more laborious than application of either of the original theories.

It would be possible to write a paper conforming, literally, to the above title in very few words by simply describing the behaviour of the crescent wing in various circumstances. Such treatment, however, would avoid what is really the prime question of all, namely, why is the crescent wing used? What is the attraction of this layout? The answer to that question is performance. One essential characteristic of the crescent wing is thus its performance characteristic.

Therefore, in this paper, the matter will be introduced from a performance angle and an attempt will be made to show, in general terms, why there should be a performance gain from the crescent layout. Having established the case, the aerodynamic and aeroelastic characteristics will be considered in some detail so that, with these properties explained, the way will be clear to consider a performance comparison in greater detail and thus gain a fuller appreciation of the situation.

The primary purpose of this note is to draw attention to the powerful influence of Coriolis forces and flapping pin offset on helicopter stability. It is shown that, for a conventional rotor of small offset, the damping in pitch and the flight stability are greatly reduced by the absence of drag hinges, an effect which may explain the use of stabilising bars on the successful helicopters which use this configuration. A “see-saw” rotor without some form of synthetic damping would be very unpleasant to fly by present-day standards.

When tip–mounted engines are employed on a helicopter rotor, such as lightweight turbines, ram-jets or pulse-jets, the action of the fuel flowing along the blade gives rise to a power loss. For a ramjet helicopter this is of the order of 6 per cent, of the total power requirement of the rotor system. In addition, if the fuel injection nozzles in the combustion chamber face upstream this leads to an additional power loss of 1-6 per cent, of the total power, and it is evident that these effects should be allowed for in helicopter performance calculations. It is shown for a ramjet helicopter that the total spraying and centrifugal pumping loss is of the same order as the total transmission and tail–rotor power loss for a conventional shaft-driven helicopter. The same effect can be demonstrated for pressure-jet rotors, where it has an even greater magnitude.

From Mr. A. M. Dobson's Note (July 1955 Journal, page 506) which dealt with the stability of an axially loaded continuous beam, and other contacts we have had with the Aircraft Industry, it would appear that the very considerable developments of structural theory which have taken place in relation to continuous beams subjected to axial load, as employed in normal structural steel work, are not well known in aircraft stress offices. The list of references appended may then be found helpful.

In many engineering problems it is necessary, from time to time, to deduce from only a few characteristic values data which would ideally be obtained from a complete stress-strain curve. For instance many handbooks, used in design offices and published by materials manufacturers and others, contain values of Young's modulus and minimum guaranteed, or typical, values of various proof stresses for materials. From these, estimates of strain, tangent modulus or ratio of stress to tangent modulus appropriate to known stress values may be required, or various processes involving integration of the stress-strain curve may have to be carried out. Even when a complete stress-strain curve is available from a special test, the differentiation and integration of it, which may have to be repeated several times, are timeconsuming processes. Also, in analytical work involving the use of materials beyond the limit of proportionality, it is desirable to have available a generalised mathematical form of the stress-strain curve in order that the results obtained may be applied to a wide range of actual materials simply by the substitution of appropriate coefficients. These and many other applications will be familiar to the reader.

The Paper by A.C.Nicholls in the October 1954 Journal (p. 724) describes two empirical equations neither of which possesses the first essential of an acceptable strain hardening function, namely that the stress attained in a preliminary straining operation shall become explicitly the threshold stress at which subsequent deformation begins. Eight years of study and the analysis of hundreds of published curves have convinced me that the exponential function put forward in 1948 faithfully reflects the strain hardening process. Far from being empirical, it can readily be deduced from a few simple and credible assumptions, and has counterparts in many branches of physics.

Attention is confined to civil aviation and the present scope of investigating procedures is outlined on a world-wide basis. Deficiencies in these procedures are noted and some suggestions are made for possible future developments of technique. In particular it is suggested that there can be little progress in air safety without the assimilation of “ human engineering data” by investigators and the Industry alike. Opinions expressed are entirely personal to the author and are not associated in any way with the official views of The British Aviation Insurance Co. Ltd.

In a recent articlein the Journal Dr. Syed Yusuff complains of a lack of “analytical work on compression panels of integral construction … . to provide an insight into the mechanism of the various instabilities involved and also to enable the designer to evaluate its advantages more precisely.” It may therefore be pertinent to point out that there is no fundamental difference between the modes of instability of integral panels and those of conventional panels with riveted or bonded stringers, except in so far as certain modes such as inter–rivet buckling cannot arise. Consequently the analyses discussed by Argyris and Dunne in the Handbook of Aeronautics and the more recent paper by Argyris on flexure-torsion panel failure are immediately applicable to integral panels; indeed with an enhanced degree of accuracy due to the monolithic character of the integral panel. Thus, such uncertain factors as the rivet stiffness need no longer be considered. In fact, in the last mentioned paper the analysis is illustrated by application to an integral panel with flanged stiffeners.

Reinforced rectangular plates find frequent application in the field of aeroplane structures, ship structures and allied fields. The stability of a structural element, if its critical load in compression is rather low, is normally influenced by its own weight. Usually the ratio of the body forces of the stiffened plate to the critical load is a considerable amount and the influence of the body forces of the plate and the ribs on the critical load of the stiffened plate is discussed here.

In this note (following Timoshenko), the extensional deformation of the middle surface during buckling is neglected, which greatly simplifies the analysis. Although it leads to an under-estimation of the critical load (of the order of 10 per cent at most) it is not likely to influence the general conclusions. Strain energy method of analysis is used.

The laws of reflection of pressure waves at temperature discontinuities are well known. Of particular interest is the effect of temperature discontinuities on the pressure conditions in the exhaust pipes and cylinders of two-stroke cycle engines, both models and running engines. Model experiments are usually performed at low temperatures with the cylinder release temperature and exhaust pipe temperatures of the same order; under these conditions the reverse type of temperature phenomenon occurs to that in running engines with excess scavenge air. In the case of a model during the exhaust blowdown the gas from the cylinder reaches the exhaust pipe with a greater density than that of the gas initially in the exhaust pipe.