An appropriate introduction to the topic of this lecture is the following comment taken from Cierva's third and last lecture presented before this Society in 1935:

“Perhaps the most irritating of the secondary difficulties met with in the Autogiro development have been those of a dynamical nature. The dissymmetry of speed on both sides of the rotor produces periodical variations in the lift and drag…“

The Fourth Cierva Memorial Lecture, which it is my privilege to present, is concerned with these periodic variations and their contribution to what remains one of the most irritating problems in rotary wing design.

From time to time in the course of my practice as a Solicitor I have the privilege of coming into contact with people who are concerned, as designers, engineers, pilots, operators, commercial and technical staff and insurance brokers and underwriters, with the actual business of designing, manufacturing, flying, operating and insuring aircraft.

Several of them have said to me that the Air Law Group of the Royal Aeronautical Society would fulfil a useful and worthwhile function, so far as they were concerned, if it would try to give them a basic but overall picture of what “air law” was and how their own day to day actions could be affected by it.

A choked nozzle with an appropriate wall contour has adischarge coefficient, CD, so close to unity that a theoretical calculation of (I—CD) would allow the nozzle to be used as an absolute meter for air flow. The high discharge coefficient results basically from the fact that ∂(ρv)∂p=0 at M=1.

Simplified calculations yield formulae for the boundary layer displacement thickness and for the flow reduction resulting from the variation in static pressure across the throat. The optimum profile for the wall at the throat of an absolute meter is suggested to be a circular arc of radius of curvature equal to about twice the throat diameter. For such a meter the theoretical discharge coefficient is found to be within ¼ per cent of 0·995 over a wide range of Reynolds numbers.

The uncertainty in the discharge coefficient for a steady flow at Reynolds numbers of 106 and over appears to be less than ±0·15 per cent, both when the boundary layer is known to be entirely turbulent and when it is known to be entirely laminar. When the state of the boundary layer is not known the corresponding figure appears to be ±0·25 per cent. Experimental information might therefore be helpful on transition—under the appropriate conditions of flow unsteadiness and rig vibration. Available experimental results with known boundary layers tend to confirm the theoretical discharge coefficients down to a Reynolds number of 0·4x106.

A pressure ratio of about 1·1/1 or less would probably be sufficient to establish fully supersonic flow if the nozzle were followed by a suitable diffuser.

Recently, the effect of sweepback on the boundaries of supersonic panel flutter was studied in Ref. (1), (2) and (3), all of them dealing with rectangular plates.

The present note considers the problem of panel flutter boundary of plates in the shape of a parallelogram with all edges clamped.

It is assumed that Ackeret's theory of linearised two-dimensional supersonic aerodynamic loading gives an adequate approximation to the air forces for high Mach numbers.

The criterion of instability is the coalescence of frequencies.

A four-mode solution was obtained by means of Galerkin's method using first two streamwise and spanwise deflection modes. The results are represented in the form of diagrams for different aspect ratios (a/b) and sweep angles(ϕ).

The initial buckling stresses of rectangular panels under applied axial loads are in general increased both by circumferential tensile stresses and by the curvature of the panel. The present Note gives theory to estimate these stresses for panels forming part of an unstiffened cylindrical shell. All edges are free to rotate. This condition is often closer to the actual rotational edge restraint of curved panels in conventional stressed-skin construction than the clamped condition, especially in the case of lightly-reinforced shells. The axial generators in the mid-plane of the panels are held straight at the longitudinal edges. All other axial generators are also assumed to remain straight before buckling (no “mattress effect”). The middle surface is restrained at the curved edges of the panel against radial deformation during and after buckling.

Design curves are presented for several values of the parameter (ab/Rt), followed by a typical example.

The natural frequency of the fundamental mode of star-shaped membranes whose boundary is given by an equation in polar form is determined. The boundary conditions are satisfied identically by conformally transforming the complicated shape onto a unit circle. The transformed partial differential equation is solved by two different collocation techniques.

An attempt is made in this note to extend Glauert(1948) analysis to predict the increase in induced drag and decrease in lift due to a split in an aerofoil of finite span placed in a free stream. The values of induced drag obtained from this analysis is compared with Munk and Cario's (1917) experimental values and Prandtl and Betz's (1927) theoretical values. A modified analysis for low gap/length ratio, which takes into account the lift retained at the tip, gives better agreement with Munk's experimental values for gap/length ratio (Ω) less than 0·012. The effect of slot diminishes as the aspect ratio is increased.

Bending analysis of rectangular orthotropic plates due to lateral loads has been considered by many writers. A small initial curvature has no effect on the bending of a plate due to the action of a lateral load, and the final deflection curve may be obtained by superposing the ordinates due to the initial curvature on the deflections calculated as for a straight plate, but when the plate is subjected to compressive forces acting in the plane of the plate, the initial curvature influences considerably the deflections produced by these forces. The analogy between bending of orthotropic plates with small initial curvature and the plate vibration is established here by expressing the ratio of the initial deflection to the additional deflection in terms of the frequencies of free vibration.