Infinite Span Research Articles

Official Publications Received

BRITISH AND COLONIAL. Aeronautical Research Committee: Reports and Memoranda. No. 989 (Ae. 200): An Investigation of the Flow of Air around an Aërofoil of Infinite Span. By L. W. Bryant and D. H. Williams; with an Appendix by G. I. Taylor. (A. 3. a. Aeroloils, General, 132.—T. 1185.) Pp. 44. Is. Pd. net. No. 995: The Behaviour of Simigle Crystals of Aluminium under Static and Repeated Stresses, Parts 1, 2 and 3. By H. J. Gough, Dr. D. Hanson and S. J. Wright. Work performed for the Engineering Research Board of this Department of Scientific and Industrial Research. (B. 1. a. Metals, 40, a and b.—T. 1983, a and b.) Pp. 54+35 plates. 3s. Gd. net. No. 1015 (Ae. 218): On the Drag of an Aerofoil for Two. dimensional Flow. By A. Fags and L. J. Jones. (A. 3. A. Aeroioils. General, 154.—T. 2135.) Pp. 14. 7d. net (London: H.M. Stationery Office.)

On the drag of an aerofoil for two-dimensional flow

(1) According to modern aerofoil theory, the drag of an aerofoil of finite span is compounded of two parts, one a profile drag associated with the shape and attitude of the section, and the other an induced drag connected with the variation of lift along the span. The magnitude of this induced drag can be determined when the forces acting on the aerofoil are known. As the span increases, the profile drag per unit length approaches a limiting value, whereas the induced drag becomes relatively smaller, because of the more uniform distribution of lift, and would disappear completely if the span were infinite. The present paper deals exclusively with the profile drag of an aerofoil of infinite span, or, in other words, the drag for two-dimensional flow. L. W. Bryant and D. H. Williams have shown from explorations of velocity in the wake of an aerofoil mounted between the walls of a wind tunnel, that the flow around the central part of the aerofoil, at a sufficient distance from the walls, is, for all practical purposes, two-dimensional. In an Appendix to the above paper, Prof. G. I. Taylor shows that there is good reason to believe, on theoretical grounds, that the drag of an aerofoil can be determined with good accuracy from observation of total-head losses in the wake, provided that these observations are taken in a region where the velocity disturbances are relatively small, that is, at a sufficient distance behind the aerofoil. The present investigation has been undertaken to examine experimentally this method of measuring drag, and also to throw light, in a general manner, on some characteristics of the wake. The experiments were made on an aerofoil of 0·5 foot chord mounted in a 4-foot wind tunnel, with small clearances between the tips and the tunnel walls (0·15 inches). Preliminary observations of total head showed that the wake was uniform along the span, except in the neighbourhood of the walls, where it opened out appreciably. To establish the fact that the drag could be determined from the total-head losses, observations—for 0° incidence—were taken in the wake at several sections, chiefly near the aerofoil tips. The drag of the entire aerofoil was then estimated from the integral along the span of the losses at each section. This value of the drag was found to be in close agreement with that measured directly on a balance, and it was concluded that the drag for two-dimensional flow could be estimated with good accuracy from the measurements of the total-head losses in the wake behind the median section.

V. An investigation of the flow of air an aёrofoil of infinite span

1. A great deal of attention has been directed of late years to the development of a rational theory of the aёrofoil. Prof. L. Prandtl and others in Germany have applied the principles of the hydrodynamics of a perfect fluid to the aerofoil with remarkable results, whilst investigators in this country have extended this work and have verified experimentally many of the deductions of the Prandtl theory. The assumptions underlying the work of Prandtl are, however, of uncertain validity, and it has become a matter of great importance to add to existing experimental evidence of the fundamental characteristics of the motion of a viscous fluid round an aёrofoil. With this purpose in view an aerofoil section of fairly high lift coefficient was selected, and a model of it tested in the Duplex Tunnel at the National Physical Laboratory, the field of flow being thoroughly explored with a wind-velocity meter. At the same time the theoretical stream-lines corresponding to inviscid fluid flow were determined experimentally, as described in Part II of this paper. The case considered is that of an aerofoil of infinite span, the flow being two-dimensional. A comparison was made of the theoretical and experimental distributions of pressure over the surface of the aёrofoil, as well as of the two sets of superposed stream-lines. The work has provided an experimental verification of the law of Kutta and Joukowsky, that the product of the mean velocity and density of the fluid and of the circulation (according to the hydrodynamical definition of this term) around a contour enclosing the aerofoil is equal to the lift of the aёrofoil (per unit length). It has further shown that the circulation around the aёrofoil is constant within the limits of experimental error and independent of the contour of integration chosen, provided that the contour line does not at any part approach too near to the aerofoil, and also that it cuts the trailing “wake” approximately at right angles to its core. The lowest value of the circulation found (calculated for a contour as close to the aёrofoil surface as the observations permitted) was about 6½ per cent, less than the value corresponding to the lift coefficient; this is hardly outside the limits of experimental accuracy in the neighbourhood of the aёrofoil.

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