1 The figure 2.80 is correct for an equal span biplane with rectangualr wings of aspect ratio 6 and gap/span ratio 0.13. The corresponding figure for a rectangular monoplane of aspect ratio 6 is 3.50. Both figures should be reduced by 5 per cent, for wings of elliptic plan, by (A - 6) per cent, when the aspect ratio of rectangular wings is A, and by 100 (G - 0.13) per cent, when the gap/span ratio is G. These refinements are unnecessary in the present paper.

2 Transition curves of this nature have previously been calculated by Prandtl and shown to agree closely with direct measurements of drag. Ergebnisse der Aerodynamischen Versuchsanstalt zu gottingen. Vol. III., 1927. For assumptions made in calculating these curves see reply to discussion at end of paper.

3 The points in this diagram refer to minimum profile drags, which however are, for all the wings included, close approximations to the actual profile drag at the incidence corresponding to cruising or top speed.

4 For simplicity in calculating I have assumed that for wings E equals twice the conventional wing area, and for solids of revolution E equals three-quarters of the area of the circumscribing cylinder. These approximations are good enough for practical purposes, provided that the ratio of length to diameter—the fineness ratio—of the solids of revolution is not less than 3: 1.

5 My thanks are due to the National Advisory Committee of the United States and to the British Aeronautical Research Committee for permission to include in Fig. 2 data which has not yet been published.

6 These results are not shown in Fig. 2.

7 This argument is not true if the rotary velocity of the slipstream is taken into account, but the energy in the rotary motion is generally very small.

8 As an example of what is meant by a screw performing the service required: a screw of fixed pitch which has to give a compromise between the requirements of take-off, climbing and cruising speed will not have so high an efficiency as would be obtainable were it only required for cruising. η might thus be 75 per cent, cruising and 70 per cent. climbing, whereas were a screw of variable pitch contemplated η might be over 80 per.

9 I am aware that cruising speed is of more general interest than top speed, but I have used the top speed in computing these points because 6f the difficulty of estimating engine power at cruising speed. The broad conclusions would be much the same in either case.

10 I took the figures from Jane to avoid argument. Being, as I suppose, makers’ own figures, they are unlikely to be pessimistic as regards performance. Some of the more interesting aeroplanes are omitted because performance figures are not given in Jane and I was loth to introduce a new variable by writing to the firms concerned and getting up-to-date figures for some types as compared with the 1927 figures for others.

11 Zeit. f. ang. Math. u. Mech. Vol. 1, p. 436, 1921.

12 Fromm: Zeit. f. ang. Math. u. Mech. Col. 3, p. 329, 1923.

13 Notes on Model Experiments, Collected Researches, N.P.L., 1916.

14 Phil. Trans. Roy. Soc., 29/1/14, Vol. 214 A.

15 For permission to publish Figs. 7 and 8 I have to thank the Aeronautical Research Committee, to whom I have submitted the diagrams as part of a report on this matter.