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

Abstract

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.