The effect of a concentrated load, such as occurs in a wing spar at the fuselage, is to cause a discontinuity in shear strain of the spar web, which induces a bending moment in the booms through the medium of the rivets (or bolts) which attach the booms to the web. A mathematical theory is developed which shows that this bending induced in the boom is of a damped wave form starting at the point of application of the shear, and in practice the magnitude of the stresses produced by the bending moment may be appreciable at the wing root when the boom is deep compared with the spar depth (say 20 per cent.).

Further experimental verification is desirable, but a single wing test suggested the original investigation, and showed a measure of agreement with the theory.

It is fairly generally known that if, at any fixed speed of a compressor, either axial or centrifugal, the flow is reduced by throttling the outlet, then a point is eventually reached at which a complete breakdown of the air flow occurs and in most cases an actual flow reversal through the compressor takes place. Sometimes this phenomenon is gradual, taking the form of a sort of burbling, but more generally it takes the form of a sudden “ bang ” associated with a violent shake of the whole foundation of the bed on which the compressor is mounted. In most centrifugal compressors the flow reversal which takes place stops rapidly, the performance recovers, and a second “ surge ” occurs if the throttling is not reduced. The frequency of these individual surges varies greatly according to the degree of throttling and many other conditions; it may be only one isolated occurrence, in which case it would be concluded that the working point was just, but only just on the surge point, or it may take the form of a rapid series of thuds indicating that the working point is beyond the surge. In all cases of centrifugal compressors known to the authors reduction of the throttling will restore the compressor to its normal performance.

A method is described for obtaining the displacements (and hence the stresses) of a linear elastic system under a given transient load in a more accurate and more expeditious manner than is possible by the standard method. For simplicity, ho account is taken of damping forces in describing the method.

The method is of interest to engineers and others who require to obtain numerical answers to problems of the type described above. It depends upon the fact that in many practical cases of transient loads the inertia forces in the series of normal modes of an elastic system converge rapidly, compared with the series of “normal” loadings in terms of which the spatial distribution of the applied load can be expressed.

Many papers have been written on the measurement of strain by X-ray diffraction methods and on the interpretation of these strains in terms of stresses. Whereas, during the past few years, the experimental methods of determining the strains have. remained largely unchanged, research has shown that the older techniques for calculating stresses from strains are not always valid.

In this paper an attempt is made to describe some of the principles of strain measurement by X-ray diffraction methods to those who are unfamiliar with the methods. The types of stress and strain systems which may exist in polycrystalline metals are then considered, particular attention being paid to the effect of the elastic and plastic anisotropy of the individual crystals. Some indication is given as to how the earlier methods of interpreting X-ray strain measurements should be modified, but no rigid routine method is proposed for use in a general case.

The present position relating to the effect of repeated loads on aircraft structures is reviewed from the point of view of the capacity of aircraft structures to withstand such loads and also of their frequencies of occurrence in the life of the aircraft.

A rough account is given of the statistical methods by which such frequencies can be estimated, and the conclusions to which the use of these methods leads are discussed.

The note ends with an outline of a suggested programme of research and a brief statement of the conclusions reached.

Aileron reversal effects on swept-back wings in general and elevon reversal effects on tailless swept-back wings in particular are discussed on a non-mathematical basis, attention being confined to the orthodox flap type of control. The main purpose of the paper is to convey in the simplest terms possible a clear physical picture of the conditions producing loss of control power, emphasis being naturally laid upon the part played by structural wing distortion. Certain qualitative features relating to the two phenomena are also discussed. As a general introduction to the discussion on aileron reversal effects, the definition of “aileron power” in relation to the actual dynamic condition of rolling is described at some length. For elevon reversal effects on tailless aircraft the effect of wing flexibility on both “elevon power” and on trim in steady symmetric flight is considered.

With the descriptive treatment adopted the analysis is of necessity broad and general but is designed to appeal to those not too familiar with the subject. The results of certain calculations on a hypothetical wing, which may be of interest, are included. A mathematical analysis for the quantitative estimation of both aileron and elevon reversal effects is given in the Appendix.

From an analysis of the work of Crocco and others, semi-empirical formulae are derived for the skin friction on a flat plate at zero incidence with a laminar boundary layer. These formulae are

for the general case of heat transfer, and

when there is no heat transfer.

The problem of heat transfer and the effect of radiation are discussed in the light of these formula;. The second formula is then utilised in the development of an approximate method for solving the momentum equation of the boundary layer on a cylinder without heat transfer. The method indicates that with increase of Mach number there is a marked forward movement of separation from a flat plate in the presence of a constant adverse velocity gradient.

Once the linearised lift problem for a supersonic wing has been solved and the disturbance velocity potential or the pressure is known at every point on the surface, the complete flow round the wing and the downwash behind the wing may be found by the following procedure.

• (a)Purpose of Investigation. To determine the least size of stringers necessary to prevent overall buckling of a flat stiffened panel before buckling of the plates between stringers.

• (b)Range of Investigation. The conditions for buckling of a longitudinally stiffened flat panel are established on the assumption that the rotational stiffness of the stringers is negligible. The results are applied to determine the limiting characteristics of the stringers to ensure that these members remain straight up to the stress at which the plates buckle between stringers. The analysis has been carried through in detail for panels with one, two, or three stringers and is capable of extension to four, five or more stringers. This extension appears unnecessary, because the three stringer case is moderately close to the limiting case of a wide panel with an indefinitely large number of stringers.

• (c)Conclusions. The stiffening effect of the stringers, having each the area of section A, and modulus of section AsK2, when attached to a sheet of thickness t and length a, at spacing b depends upon the three ratios (k/t), (a/b) and (As/bt) In general, the size of stringer necessary to ensure that the stringers remain straight until the plates buckle between stringers may be represented by the conditions

  .

  For a panel stiffened by one stringer only suitable values are λ = 4.5 and μ = 12.5, independent of the value of (a/b), while v=0.366 (a/b)2or 23 if 8>(a/b)>6.

  For two or more stringers the same general conditions hold, but it is impossible to assign values to λ and μ which would be fully satisfactory for all values of the ratio a/b. In these cases, therefore, it is more satisfactory to select the values of λ and μ appropriate to each value of the ratio a/b. These values may be obtained from Figs. 2 and 3 where curves of bt/As against (k/t)2for varying values of (a/b) are shown for two and three stringers respectively. For an indefinitely large number of stringers the corresponding condition is

  

  and the second condition (k/t)2 0.366 (a/b)2 is virtually included in the first.

• (d)Further Developments. In the present analysis the resistance of the stringers. to rotation is neglected. Inclusion of this characteristic in the basic analysis is straightforward, but practical interpretation of the results becomes much more difficult. Moreover, the effect of this stiffness in modifying the condition for buckling between stringers is likely to affect the conclusions more than the direct effect of their torsional stiffness in modifying the condition for buckling of the stiffened panel. This consideration is particularly important in cases of light stringers and heavy sheet, when the effective rotational stiffness of the stringers at buckling of the plates between stringers may be greatly reduced as a result of the end loading and may even be negative. Representation of the effect of both longitudinal stiffeners (stringers) and lateral stiffeners (ribs), including their stiffnesses to rotation is also straightforward; but interpretation of the results in forms suitable for practical application would be extremely difficult.

The approximate supersonic flow past a slender ducted body of revolution having an annular intake is determined by using the Heaviside operational calculus applied to the linearised equation for the velocity potential. It is assumed that the external and internal flows are independent. The pressures on the body are integrated to find the drag, lift and moment coefficients of the external forces. The lift and moment coefficients have the same values as for a slender body of revolution without an intake, but the formula for the drag has extra terms given in equations (32) and (56). Under extra assumptions, the lift force due to the internal pressures is estimated. The results are applicable to propulsive ducts working under the specified condition of no “ spill-over “ at the intake.

Following a brief discussion of various methods of measuring combustion efficiency in gas turbine chambers, the superiority in accuracy of applied gas analysis is stated. Factors leading to inefficiencies in combustion are outlined and the exhaust constituents requiring measurement are deduced. The chief difficulty in the past in the application of gas analysis methods to combustion efficiency determination has been the time consumed in actual analysis of samples; at Thornton Research Centre means of overcoming this difficulty have been investigated and several rapid and accurate analytical techniques have been developed and used successfully. These techniques are described, together with other promising methods at present under development. The broad requirements of obtaining exhaust gas samples for analysis are discussed and typical sampling systems described; precautions necessary in applying these systems are given. Formulse for the calculation of combustion efficiency from analytical results, together with any assumptions made, are given in the text and their derivation explained in an Appendix. The techniques described have been developed primarily for use in conjunction with rig testing of aircraft gas turbine combustion chambers; the broader application—for instance, to engine testing—of the principles involved are considered briefly.

A method is given for calculating approximately the changes in the roots of a stability secular equation caused by a change in any of the parameters involved. General formulas are given applicable to any quartic equation, and special formulae are also given applicable to the stability of an aeroplane: lateral stability in the text, and longitudinal stability in an appendix.

The method of using the formulae is illustrated by applying them to a particular calculation of the lateral stability of an aeroplane, and a check of the results is made by comparing the predicted approximate changes with those calculated by solution of the modified period equations. It is shown that the formulae are reliable, for this typical case, for any reasonable changes in any parameter other than nv.

If the changes in the derivatives are made equal to the probable error with which they can be measured, the formulae enable us to evaluate the probable errors of the roots. These are found to be considerable, and to arise mainly from uncertainties in yv, nv and nr: if these could be reduced to 0.03 in yv and 0.006 in the others, the uncertainties in the roots would be reduced to some ten per cent, of their values, except for a larger uncertainty in the root corresponding to the slow spiral motion.

This note is concerned with a general and exact solution of the two-dimensional equations of motion of a compressible fluid, which is steady, irrotational and isen-. tropic. The solution arrived at is the generalisation of the Prandtl-Meyer celebrated “wedge solution” to include an expansion around any smooth (or abrupt) convex boundary.

We shall obtain the solution of equations for the most general type of motion in which the Cartesian components of velocity are connected by some functional relation throughout the field of flow.

Taking into account the conditions of continuity, zero rotation and Bernoulli's equation, together with the fundamental assumption, which implies that the components of fluid velocity are each a function of fluid speed only, it is found that the motion is necessarily supersonic.

It is shown that the lines of equal speed, pressure (isobars) and density are all straight lines, although they are not necessarily concurrent as in the original Prandtl-Meyer theory, and further that the component of fluid velocity perpendicular to the isobar is equal to the local velocity of sound.

The extended Prandtl-Meyer solution for the flow past an arbitrary fixed boundary is obtained analytically.

The steady two-dimensional flow of viscous incompressible fluid in the boundary layer along a solid boundary, which is governed by Prandtl's approximation to the full equations of motion, presents a problem which in general is as intractable as any in applied mathematics. The problem, however, has such an immediate and necessary application that approximate methods of varying accuracy which go beyond the formal processes of expansions in series and so on, have been devised for the rapid calculation of the principal characteristics of the laminar boundary-layer, the variation of pressure along the surface being known. Such methods usually represent approximately the boundary-layer velocity distribution at any point by one of a known family of distributions whose spacing along the surface is determined by some means, often by the use of Kármán's momentum equation.

Exact solutions for the steady circulatory flow about a circular cylinder with suction applied at its surface have been obtained for the following cases: —

• (a) the cylinder at rest and a circulation at infinity,

• (b) the cylinder rotating and zero circulation at infinity,

• (c) the cylinder rotating in either direction with a circulation at infinity,

provided that, in general, the suction velocity is greater than a certain limiting value.

There is a particular case of (c) when the circulation at the cylinder equals that at infinity in magnitude and direction, for which the circulation is constant at all radii, for all values of R—presumably for blowing as well as suction.

The addition of a uniform stream parallel to the cylinder axis does not affect the circulatory motion, and the solution for the combined flow, which is exact, has some practical interest in that it demonstrates that the boundary layer on a long, circular, rotating boss can be kept thin and that the circulatory motion outside the boundary layer can be prevented by the suitable application of suction before starting the rotation.

The flow (a) is important in connection with the withdrawal of the Thwaites flap. The existence of steady state solutions, coupled with the arguments of Section 5.2, make it appear highly probable that a wing employing this device will retain its lift indefinitely, when the flap is withdrawn.

For high rates of suction flow, the flows exhibit the characteristics of boundary layer flows, in that the vorticity is confined to a narrow annulus enveloping the cylinder and the velocity distribution near the wall tends to the well-known asymptotic distribution of Griffith and Meredith.

It would be interesting to investigate these flows experimentally and to examine the stability of the laminar flow under suction conditions.

The analysis throughout is simple and expressions are obtained for the velocity distribution, the stresses, the vorticity and the torque, and so on.

Experience has shown that it is often necessary to retain many degrees of freedom in order to calculate critical nutter speeds reliably, but this entails much labour. Part I discusses the choice of a minimum set of freedoms and suggests that this should be based on the equation of energy and the use of the Lagrangian dynamical equation corresponding to any proposed additional freedom. The methods for conducting flutter calculations so as to minimise labour are treated in Part II.

Mr. Templeton's paper “Control. Reversal Effects on Swept-back Wings” (page 3, The Aeronautical Quarterly, Volume I, Part I) contains in Section 2 of the Appendix an argument which does not appear to be applicable to any but the simplest type of wing, namely one in which all the flexural and torsional rigidity is given by a single spar.

It has been shown that since the performance of a turbo-jet engine can be expressed theoretically as a function of the two variables and , the performance of a turbo-jet aircraft can also be expressed as a function of two variables, and Two methods can then be used for the reduction of the performance to standard conditions. In the “non-dimensional” graphical method, flight test measurements of, for instance, are plotted against and , and the standard value of is read from these curves at the standard values of and . In this way, the relation between the parameters is established during the tests. The alternative method is an analytical one in which corrections are applied to, for example, the level speed for differences from standard in the independent variables. For this method the effect on the performance of changes in these variables must be predetermined.