Page 228 - Aerodynamics for Engineering Students

Finite wing theory 21 1

5.1 The vortex system

Lanchester’s contribution was essentially the replacement of the lifting wing by
a theoretical model consisting of a system of vortices that imparted to the surrounding
air a motion similar to the actual flow, and that sustained a force equivalent to the lift
known to be created. The vortex system can be divided into three main parts: the
starting vortex; the trailing vortex system; and the bound vortex system. Each of
these may be treated separately but it should be remembered that they are all
component parts of one whole.

5.1.1 The starting vortex
When a wing is accelerated from rest the circulation round it, and therefore the lift, is
not produced instantaneously. Instead, at the instant of starting the streamlines over
the rear part of the wing section are as shown in Fig. 5.1, with a stagnation point
occurring on the rear upper surface. At the sharp trailing edge the air is required to
change direction suddenly while still moving at high speed. This high speed calls for
extremely high local accelerations producing very large viscous forces and the air is
unable to turn round the trailing edge to the stagnation point. Instead it leaves the
surface and produces a vortex just above the trailing edge. The stagnation point
moves towards the trailing edge, the circulation round the wing, and therefore its lift,
increasing progressively as the stagnation point moves back. When the stagnation
point reaches the trailing edge the air is no longer required to flow round the trailing
edge. Instead it decelerates gradually along the aerofoil surface, comes to rest at the
trailing edge, and then accelerates from rest in a different direction (Fig. 5.2). The
vortex is left behind at the point reached by the wing when the stagnation point

Fig. 5.1 Streamlines of the flow around an aerofoil with zero circulation, stagnation point on the rear
upper surface

Fig. 5.2 Streamlines of the flow around an aerofoil with full circulation, stagnation point at the trailing
edge. The initial eddy is left way behind