1.1. Abstract. Tests at various staggers and gap chord ratios.

2.1. Abstract. The investigation relates to flat elastic strip, of uniform breadth, thickness and material, upon which a uniform shear is imposed by tangential tractions applied at its edges and in its plane. The tractions appear in the expression for the change of potential energy which occurs when the strip is bent, and they must therefore affect both the modes and the frequencies of its free transverse vibrations. If sufficiently intense, they will bring about a condition of limiting elastic stability, since they can neutralize, in certain types of distortion, the restoring effects of the flexural stresses. The results have some bearing on the stability of the webs of deep plate girders, which take the greater part of the total shear transmitted. The correspondence must not, however, be pressed unduly, because in a girder uniform shear will be accompanied by a varying bending moment which imposes additional stresses upon the web. It is more accurate to describe the sheared strip (of which the length, in this paper, has been assumed to be infinite) as the limiting case either of a narrow annular disc, or of a short tube, subjected to torsion. The similarity of the three problems is illustrated by the specimens shown in fig. 1, which have buckled under conditions of limiting elastic stability.

2.2 Note. With this paper, Southwell and Skan were distinguished as giving the pioneer solution for the shear buckling analysis of isotropic plates.

5.1. Note. This is the paper with the Falkner-Skan boundary layer.

6.1. Summary. A particular solution of the boundary-layer equations is given for the case where the tangential velocity at the outer limit of the boundary layer is proportional to a power of the distance measured along the boundary from the stagnation point, and the results are presented graphically for a range of values of the index. It is shown that Blasius' solution for a flat plate is a particular case of this solution. By a consideration of the necessary agreement between the solution of the equations of potential flow and that of the boundary-layer equations as the distance along the boundary from the stagnation point is decreased indefinitely, it is shown that the solution of the boundary-layer equations reduces to the particular solution described as the stagnation point is approached. This particular solution is used as a basis for two approximations of varying complexity to the solution in the general case; the second of these gives the correct value of the surface friction. These solutions are given graphically, and the method of application to problems is described. Close agreement is found between the calculated and experimental values of the tangential velocity in the boundary layer for a flat plate and a cylinder and of the surface friction for a cylinder.

9.1. Introductory Remarks. The present brief paper gives some comparisons between the three known methods of approximation, which will be referred to as (i) collocation, (ii) least squares, (iii) Galerkin's method. A fuller account, with numerical examples, is given in No 1799 of the Reports and Memoranda of the Aeronautical Research Committee. The term collocation is here used in connection with approximations to mean the act of assigning the error at one or more given points or stations. For example, when a polynomial approximation to a given function is constructed by Lagrange's interpolation formula, the errors are made zero at specified points, and the approximation is accordingly collocated in the sense just defined. In relation to differential equations an approximation will be understood to be collocated if given errors (usually zero errors) in the differential equations are assigned at given stations. The solution of differential equations by methods (ii) and (iii), which depend on the minimisation of average errors, has been considered recently by W J Duncan. The original papers by V G Galerkin, describing method (iii), do not appear to be available in this country, but accounts with references are given in two papers by E P Grossman. Galerkin's method reduces t the method of least squares when it is applied to obtain approximate representations of functions.

9.2. Abstract. The paper provides comparisons between three known methods of approximation, which are referred to for brevity as (i) collocation, (ii) least squares, (iii) Galerkin's method. The term "collocation" is here used to mean the act of assigning the error at given points or stations: in applications to differential equations the normal procedure is to make the error in the differential equations zero at specified stations. Part I is restricted to linear problems including approximate representations of some simple functions and examples of solutions of linear differential equations. The methods are particularly valuable for the calculation of characteristic numbers (e.g. natural frequencies). Part II discusses briefly certain difficulties connected with the solution of non-linear problems by Collocation, and contains a description of a method for the numerical solution of simultaneous non-linear algebraic equations. The general conclusions can be summarised as follow: (1) As the number of disposable constants is increased, the sequences of representations derived by the three methods will cither all converge to the same limit, or else will all diverge. (2) the methods may be expected to be successful provided the total interval of representation or solution is not taken too large; (3) Galerkin's method is usually the most rapidly convergent, but collocation has the advantage of simplicity.

11.1. Abstract. A brief description is given of Cicala's theory of the non-uniform motion of wings of finite span, with special reference to wings of rectangular plan form. The method is applied to calculate by successive approximations values of the derivatives appropriate to two simple modes of motion, namely: (1) pitching oscillations of a rigid aerofoil about the half-chord axis; (2) torsional oscillations of a semi-rigid wing about the half-chord axis, with the twist assumed to increase linearly with distance along the span. The aspect ratios assumed are 6 and 2.7 in Case (1) and 6 in Case (2). The results are plotted against the frequency parameter $\lambda = pc/V$, where $p/2\pi$ denotes the frequency, c the chord and V the airspeed. Cicala's method is definitely superior to Lyon's method from the standpoint of rapidity of convergence. However, the limiting values given by Lyon's method may be expected to be closer to the true derivatives than those given by Cicala's method, since Cicala introduces certain extraneous vortices for convenience and treats their effects as and also makes a number of questionable assumptions in his analysis. Before the relative merits of the two theories could be fully judged in relation to practice more complete experimental information would be necessary.

12.1. Abstract. Critical speeds and critical frequencies for flexure-torsion flutter of a tapered model wing have been measured in a wind tunnel by Jones and Lambourne. The stiffness-ratio parameter covered the range 1·5 to 17·5 in the tests. In the present paper these experimental results are compared with the flutter characteristics predicted for the wing by the strip-theory method developed in R & M 1942. The principal formulae required are summarized and certain difficulties connected with accuracy in the calculation of the air forces appropriate to large values of the frequency parameter ª0 are explained. The actual predictions for the model wing are described and the results are given.

14.1. Introduction. Calculations based on Possio's subsonic derivative theory and on vortex strip theory were made to obtain preliminary information on the influence of compressibility and flying height on the critical speed for flexural-torsional flutter of a tapered cantilever wing moving at subsonic speed. The results are summarised by curves corresponding to constant altitude H, which show the variation of N with wing stiffness r, where N denotes the ratio of the critical speed for flutter of the wing in compressible air at a Mach number of 0.7 to the critical speed for flutter of the same wing in incompressible air. The results indicate that for 1 ≤ r ≤ 3 the compressibility correction is insignificant at sea level, and that N is of the order 0.95 to 0.92 at H = 30,000 ft. More extensive test calculations are very desirable.

14.2. Review by: C C Chang. The paper gives the calculations based on Possio's subsonic derivative theory and on vortex strip theory in order to determine the influence of compressibility and altitude on the critical speed for flexural torsional flutter of a tapered cantilever wing. It is found that for normal stiffness ratio and a given altitude, the compressibility effect on critical speed for flutter is insignificant at Mach number 0.7. The critical speed at 30,000 feet altitude is about 5–8% lower than that at sea level. The corresponding divergence speed ratio confirms a result of Theodorsen and Garrick.

16.1. Review by: E Isaacson. A complete introduction to the elementary mathematics and to some of the techniques of computation that are required of junior computers is clearly presented with many illustrative examples. These chapters would constitute the basis for an on-the-job training program for an audience with limited mathematical background. The mathematical topics range from the solution of quadratic equations to an introduction to the calculus. The numerical techniques that are described range from finding square roots to numerical differentiation and integration of functions. Throughout there is the necessary emphasis on the numerical checks and the arrangement of work sheets which insures accuracy in a computation laboratory.

17.1. Summary. Some new solutions for steady incompressible laminar boundary layer flow, obtained by Gortler, have been used to test the accuracy of two methods which are commonly used to predict separation. A modification of Stratford's criterion for separation is given in this paper and is probably the most accurate and the simplest of all methods at present in use. Modified numerical functions are also given for Thwaites's method of predicting the main characteristics of the boundary layer over the whole surface, which improve the accuracy of the method.

18.1. Summary. Some When separation occurs at the leading edge of a thin aerofoil, the Reynolds number at separation largely indicates whether a long or short separation bubble is formed. This Reynolds number depends upon the boundary-layer development, which is governed in turn by such parameters as the lift coefficient and the ratio r/c of the nose radius to the aerofoil chord. In this paper calculations have been carried out to determine separation conditions, when these parameters are varied, for the RAL 100-104 family of aerofoils.