The study of aerodynamics is still largely empirical, and there seems little hope at present that the gap between theory and practice will be sensibly diminished by any means at present known to the applied mathematician. Yet the light that would, in all likelihood, be thrown on a number of practical problems by the complete solution of even a single case of turbulent motion would be very great. Of the problems that can be attempted, that of the flow of a fluid past a circular cylinder is likely to prove the least intractable.

1. The object of this paper is to explain the principles upon which the flapping flight of birds depend and to show how the velocities, power expended and gliding angles can be approximately calculated. The birds are considered to be flying on a horizontal course with constant velocity. The calculations have been made for five birds, the Teal, the Grouse, the Common Swift, the Starling and the Stork, but the formulae given can of course be used for any bird.

2. The results obtained seem to show that:—

1st.—As regards velocities, the very high speeds given by some writers are by no means so impossible as is generally supposed.

2nd.—The power expended at these high speeds is much less than the estimates usually made.

In connection with gliding flight enough measurements of “ lift ” and “ drag ” have been made to enable us to calculate the conditions for success of an aeroplane fitted with wings of standard sections; but no attempt has been made, as far as the present writer is aware, to ascertain what would happen if a flying machine were fitted with wings of standard section and these were flapped in a rhythmical manner. Would it support and propel itself? Several authors, including M. F. Fitzgerald and Colonel J. D. Fullerton in the previous issue of this journal, have discussed various portions of this problem; but instead of appealing to wind-tunnel determinations the latter has used such expressions as pSUV or pSUV2 for the pressure on a wing of area S, where p is the density of the air and V, U are the component velocities along and at right angles to its surface.

In “Die Naturwissenschaften,” 6th February, 1925, p. 93, there appears an article by Prandtl entitled “ Magnuseffekt und Windkraftschiff,” giving the following explanation of the phenomena under consideration.

In a stream of viscous fluid a non-rotating cylinder builds up an accumulation of retarded fluid with considerable vorticity (Fig. 5). This fluid reaches the neighbourhood of the near dead water point with a loss of kinetic energy and velocity by dissipation. At the somewhat indeterminate boundary of the boundary layer it is in contact with fluid which has lost its kinetic energy and velocity in acquiring an increase of pressure approaching the dead water pressure. The retarded fluid is pushed away from the dead water point by the higher pressure fluid (Figs. 6, 7), and ultimately it breaks up into cylindrical masses which are detached and carried away by the stream (Fig. 8).

A technical discussion on the use of the wind channel to aircraft designers was held in the Library on Thursday, January 8th, 1925, when the following were present:—Wing Commander T. R. Cave-Browne-Cave (in the chair), O. T. Gnosspelius, Griffith Brewer, W. O. Manning, C. C. Walker, H. N. Wylie, G. T. R. Hill, A. P. Rowe, A. A. Hammond, B. W. Townshend, R. Reynolds, G. P. Douglas, J. S. L. Oswald, W. H. Sayers, T. M. Barlow, R. McKinnon Wood, N. A. V. Piercy, V. Gaunt, R. K. Pierson, F. L. Richards, A. H. Tiltman, S. H. Evans, N. S. Norway and A. V. Roe.

In opening the discussion, Mr. C. C. Walker said that the wind channel should be a means of supplying a mass of systematic data which will indicate the direction in which promising full-scale experiments may be made.

At the request of the Council the following notes on the subject have been prepared, with special reference to the Flettner “rotor ship” and to possible applications in aeronautics.

While it is necessarily somewhat provisional, the data available are pretty full, and it is hoped that no serious modifications will be required as a result of further experimental investigations.

In the now well-known Joukowsky transformation from a circle to a wing profile, maintaining the circulation G and the steady flow at a distance U, unaltered, the diameter of the cylinder 2a, its angular velocity ω, the chord of the profile 4a. (subject to a small correction of about – 5 per cent) and the effective incidence (β are connected by the relations G = 2πa2ω = 4πa sin βU so that aω/2U = sin β.