Page 229 - Aerodynamics for Engineering Students

21 2 Aerodynamics for Engineering Students

reached the trailing edge. Its reaction, the circulation round the wing, has become
stabilized at the value necessary to place the stagnation point at the trailing edge
(see Section 4.1.1).* The vortex that has been left behind is equal in strength and
opposite in sense to the circulation round the wing and is called the starting vortex or
initial eddy.

5.1.2 The trailing vortex system
The pressure on the upper surface of a lifting wing is lower than that of the
surrounding atmosphere, while the pressure on the lower surface is greater than that
on the upper surface, and may be greater than that of the surrounding atmosphere.
Thus, over the upper surface, air will tend to flow inwards towards the root from the
tips, being replaced by air that was originally outboard of the tips. Similarly, on the
undersurface air will either tend to flow inwards to a lesser extent, or may tend to
flow outwards. Where these two streams combine at the trailing edge, the difference
in spanwise velocity will cause the air to roll up into a number of small streamwise
vortices, distributed along the whole span. These small vortices roll up into two large
vortices just inboard of the wing-tips. This is illustrated in Fig. 5.3. The strength of

Fig. 5.3 The horseshoe vortex
*There is no fully convincing physical explanation for the production of the starting vortex and the
generation of the circulation around the aerofoil. Various incomplete explanations will be found in the
references quoted in the bibliography. The most usual explanation is based on the large viscous forces
associated with the high velocities round the trailing edge, from which it is inferred that circulation
cannot be generated, and aerodynamic lift produced, in an inviscid fluid. It may be, however, that local
flow acceleration is equally important and that this is sufficiently high to account for the failure of the
flow to follow round the sharp trailing edge, without invoking viscosity. Certainly it is now known, from
the work of T. Weis-Fogh [Quick estimates of flight fitness in hovering animals, including novel mechanisms
for lift production, J. Expl. BioZ., 59, 16%230, 19731 and M.J. Lighthill [On the Weis-Fogh mechanism
of lift generation, J. FZuidMech., 60,l-17,19731 on the hovering flight of the small wasp Encursiu formom,
that it is possible to generate circulation and lift in the complete absence of viscosity.
In practical aeronautics, fluid is not inviscid and the complete explanation of this phenomenon must take
account of viscosity and the consequent growth of the boundary layer as well as high local velocities as the
motion is generated.