It is now more than 25 years since Coker and Filon first developed photoelasticity as a practicable method of exploring the stress distribution in certain types of engineering components. All engineers must be familiar with the striking photographs of fringe patterns obtained by their method in stressed plates of various shapes viewed in a polariscope. In those early days observations were made on Xylonite models and the method was only applicable to components in which stress distribution was of a two-dimensional type. Moreover, with the apparatus then available investigations were somewhat difficult and many engineers at that time were very distrustful of the results obtained from what was, to them, a little understood laboratory technique.

The design of ducted fans, and the estimation of their performance for conditions other than those of the design, are usually based on the equations of the so-called strip-theory. Existing methods of solution invariably employ some form of iteration which is more or less rapidly convergent according to the experience of the computer and the detail of the method.

In this note, a solution is given which, although it is strictly an iteration, is explicit in the sense that in practice no iteration is necessary. It is shown how both design for a given performance and performance for a given fan can be calculated in one direct step.

Conditions for maximum efficiency are considered in an Appendix. Here a suggestion of R. Baldur's is used to give a simple approximate solution of the strip-theory equations which can be developed to give conditions for maximum efficiency, for the special case of a constant pressure rise through the fan.

The design of the damped tuned vibration absorber, which has previously been treated algebraically, is studied by the use of a three-dimensional admittance diagram. The advantages of this method are that the basic principles can be more easily understood and that it is not necessary to simplify the vibrating system so much. The results obtained by the use of the method show that under some conditions the algebraic treatment does not give the optimum tuning, but that the differences in performance of dampers which have been designed by the two methods will not be large. It is shown how the method may be extended to more complex problems.

The general technique for rendering approximate solutions to physical problems uniformly valid is here applied to the simplest form of the problem of correcting the theory of thin wings near a rounded leading edge. The flow investigated is two-dimensional, irrotational and incompressible, and therefore the results do not materially add to our already extensive knowledge of this subject, but the method, which is here satisfactorily checked against this knowledge, shows promise of extension to three-dimensional, and compressible, flow problems.

The conclusion, in the problem studied here, is that the velocity field obtained by a straightforward expansion in powers of the disturbances, up to and including either the first or the second power, with coefficients functions of co-ordinates such that the leading edge is at the origin and the aerofoil chord is one of the axes, may be rendered a valid first approximation near the leading edge, as well as a valid first or second approximation away from it, if the whole field is shifted downstream parallel to the chord for a distance of half the leading edge radius of curvature ρL. It follows that the fluid speed on the aerofoil surface, as given on such a straightforward second approximation as a function of distance x along the chord, similarly is rendered uniformly valid (see equation (52)) if the part singular like x-1 is subtracted and the remainder is multiplied by .

A method is developed for calculating the profile drag of a yawed wing of infinite span, based on the assumption that the form of the spanwise distribution of velocity in the boundary layer, whether laminar or turbulent, is insensitive to the chordwise pressure distribution. The form is assumed to be the same as that accepted for the boundary layer on an unyawed plate with zero external pressure gradient. Experimental evidence indicates that these assumptions are reasonable in this context. The method is applied to a flat plate and the N.A.C.A. 64-012 section at zero incidence for a range of Reynolds numbers between 106 and 108, angles of yaw up to 45°, and a range of transition point positions. It is shown that the drag coefficients of a flat plate varies with yaw as cos½ Λ (where Λ is the angle of yaw) if the boundary layer is completely laminar, and it varies as if the boundary layer is completely turbulent. The drag coefficient of the N.A.C.A. 64-012 section, however, varies closely as cos½ Λ for transition point positions between 0 and 0.5 c. Further calculations on wing sections of other shapes and thicknesses and more detailed experimental checks of the basic assumptions at higher Reynolds numbers are desirable.

In a previous paper it was assumed that the cross-girders are freely supported at their ends. In practice these ends can often be considered as clamped (“ built-in ”), for example, a span of continuous bottom-girders of a ship between two transverse bulkheads.

In the following discussion it is assumed that the ends of the cross-girders are clamped, conditions at the ends of the main beams remaining arbitrary, as in Ref. 1.

The expression for the induced velocity of a vortex element,in Glauert's notation (where K is the strength of the vortex, h the length of the normal, and r the distance from the field point to the element, of length ds) which is often known as the Biot-Savart law, and is of fundamental importance in aerodynamics, is frequently left unproved in textbooks. Sometimes reference is made to the electro-magnetic analogy, or to a standard treatise such as Lamb. One well-known work implies that the law is the solution of an integral equation derived from the known induced velocity of an infinite straight-line vortex, but this is misleading, since there is an infinite number of solutions, of which only one is correct. Another textbook gives a lengthy argument starting from the replacement of a line vortex by a sheet of sources and sinks, which is probably not too convincing to the average student. Lamb himself gives a long and rather involved proof based on Helmholtz and Stokes, with appeals to the Theory of Attractions, with which few are likely to be familiar. A simple and direct proof from fluid mechanics seems therefore worth while.