The paper contains a generalisation of the conformal transformation by means of which a circle is converted into Joukowski aerofoils. The transformation is applied to a cascade of oval bodies which is the corresponding generalisation of the isolated circle; and it converts the oval bodies into a wide variety of cascades of curved shapes, which are generalisations of the isolated Joukowski aerofoils. In one particular case, the transformation yields a grid of flat laminae. Since the perfect fluid flow through such a grid is known (it appears to have been first given by Joukowski) the perfect fluid flow past the ovals, in any direction, and with equal but otherwise arbitrary circulation round each, is obtained. Accordingly, the perfect fluid flow through any of the derived cascades can be obtained.

The water tunnel, closed-return type, described in the paper is especially suitable for the observation of flow near the surface of a long streamline body of revolution at Reynolds numbers up to 1.3 × 106. The observation chamber is 32 ins. long and it has a circular cross-section of diameter 7 ins. The stream in the observation chamber although slightly disturbed at the higher speeds of flow is substantially free from turbulence (except near the wall) at all speeds and throughout its entire length.

The tunnel is equipped with two instruments designed for flow observation. The first instrument, named fluid-motion microscope, allows the movements of small particles in a bright beam of light to be observed and measured. This instrument is suitable for the study of details of flow too small to be seen with the unaided eye, but which are revealed under a microscope at a medium magnification. The second instrument, the fluid-motion microscope with an interrupter, allows the speed of a particle to be determined from a measurement of the length of its track recorded for a known time of exposure on a photographic plate. This instrument can be used to measure the velocity distribution in a boundary layer to a distance of about four thousandths of an inch from the surface.

The formation of shock waves as a limitation in aircraft design has been considered only, as far as the author knows, in the cases of wing sections at low operating lift coefficients and of the airscrew efficiency. There is, however, a further limitation for high flying aircraft in that the small air density causes the aircraft, even at the stall, to travel at a value of Mach number (V/a) which will cause a shock stall to form on the wing. In some cases the aircraft will be able to prevent this shock stall at high CL by flying faster, but in others, due to high wing loading, the wing sections will be shock stalled at all CL values and the only remedy will be to decrease the wing loading.

Fog is the result of a condensation process near the earth's surface when the air is cooled below its dew-point temperature by one or more of the processes which will be discussed in the second part of this paper.

The classical experiments of Wilson (I) showed that some types of particles, now called nuclei of condensation, must be present in the air if condensation is to occur with a reasonable degree of supersaturation.

Propeller theory has always been a subject of extreme difficulty, and those who riginated the screw propeller as a means of propulsion and developed itduring the latter half of last century were in most part guided by common senseand empiricism. Without much in the way of theory to guide them the results thus achieved in connection with marine propulsion were remarkable—but little short of the best possible. The designers of the early experimental aircraft were able to make use of the wealth of experience thus placed at their disposal; nevertheless, some new aspects of the problem presented themselves—fortunately the vortex theory, newly developed to deal with the problem of sustentation in flight came to their aid, though the manner of its application was not obvious or easy. The writer's first attempt consisted in treating the propeller blade as an aerofoil connected to the boss by an arm of spar section, geometrically related to a helical surface, in which the tracks of the blades relatively to the fluid follow these surfaces.

That this distinguished gathering has convened here to-day, amid the chaos of a war-torn world, for a lecture on civil aeronautics is indeed a singular expression of the true spirit of our profession. It is, I think, graphic proof of the fact that all of us in aviation are looking forward to the day when the aeroplane can lay aside its duties of destruction and once more assume its truly great role as a constructive force in world civilisation.

I am, therefore, particularly sensible of the privilege of delivering, at this historic meeting, the Twenty-ninth Wilbur Wright Memorial Lecture. Under any circumstances, we in America feel that an invitation to address you, the parent body of the aeronautical profession, is one of the highest honours which can be attained by an individual engaged in aviation.

My role here, of course, is hardly that of an individual. In the narrowest justifiable sense, I can but speak for what has been accomplished by the 7,000 men and women who are the Pan American Airways System.

Box beams, built up essentially with flanges and webs are widely used in aircraft construction and much has been written about their calculation. But often assumptions are implicitly made without reason. The first aim of this paper is to point out which assumptions must be chosen and why, and to show what results may be expected from them. The calculations are then developed in the. cases of the quadrangular box beam and the wing with three spars (redundancy of the first degree).

A graphical method is developed for solving the problem of the beam with variable section, bent by transverse loads and an axial load. The latter may be either tensile or compressive. The beam on statically determinate supports is first dealt with, successively as regards the stress and the deformation. Then a similar procedure is followed for a beam with redundant supports. Finally, the case is studied when there is no transverse load at all, that is buckling only.

Under the influence of civil engineering construction the part played by shear in the deformation of beams is usually neglected. In aircraft construction, where weight is important, the approximation is sometimes rough. It is shown that, in I-beams, it is simple to take the deformation due to shear into account, and it appears due chiefly not to elementary deformations distributed along the length, but to discontinuities in the slope wherever there is a concentrated load, namely, at the supports.

The torsion of box beams of rectangular section, the edges of which are strengthened by flanges, and of which one side is lacking, is analysed by the energy method. The torsional stresses are generally taken up by the bending of the two parallel walls, the rigidity of which is augmented by the third wall. The result was checked experimentally on duralumin and plywood boxes. The torsion recorded was 10 to 30 per cent, less than that given by the calculation, owing to self-stiffening.

In most of the problems concerned with the buckling of plates it is assumed that the length of the plate is greater than its width, and that the edges of the plate, at which the compression loads are applied, are simply supported. The method of support of the side edges vary with the actual conditions.

In the case of short wide plates or plates with many lateral stiffeners, as shown in Figs, 1 and 2 respectively, the effect on the buckling load due to the conditions of support at the two side edges will become less, and that due to the conditions of support at the end edges will become important, so that they can no longer be assumed to be simply supported. For ease of calculation the side edges are assumed to be simply supported.

The concept of “mechanical impedance,” a quantity equivalent to Biot's Dynamic Modulus (reference i), has been utilised since 1939 by the de Havilland Aircraft Company as a standard method of treatment of vibration problems inengine airscrew systems, the method being applied principally to torsionalvibrations. In this work the effect of damping forces was neglected, on theassumption that the resonant frequencies of a system are not affected appreciablyby such forces so long as they remain of small magnitude.

The desire to justify this assumption by theoretical reasoning, and to evolve a method of attack for problems in which the damping forces are too large to be neglected, led to the application of the concept of mechanical impedance to damped systems.

In reference 1 Biot has given a simple and valuable formula for what he calls the “ dynamic modulus “ of a flywheel system or airscrew in terms of resonance and anti-resonance frequencies. The resonance frequencies are the natural frequencies when the systems are free, and the anti-resonance frequencies are the natural frequencies when the end of the flywheel shaft (or the airscrew boss) is fixed. The dynamic modulus is defined to be the ratio of the amplitude of the applied periodic couple to the amplitude of the angular movement produced at the point of application, and is a function of the frequency of the periodic couple. A very useful application of the dynamic modulus can be made to engine-propeller systems, for the natural frequencies of the combination are such that the dynamic moduli of the two components are equal and opposite.

If A, B, C,… be the successive bending- moments involved, the equations to find them have the following characteristics : The first involves A and B only, the second A, B and C only, the third (if more than three) B, C and D only, and so on for all intermediate equations; finally, the last equation contains only the last two unknowns.

The method to be considered applies more generally, however, when each equation in succession contains only one additional unknown, so that the third may contain A, B, C and D, the fourth A, B,C, D and E, and so on.