The generation of lift by a wing

In order to understand how the planform of the wing affects lift and drag, we need to look at the three-dimensional nature of the air flow near a wing.

You may remember, that we described in Chapter 1, how the wing pro­duced a circulatory effect; behaving like a vortex. A major breakthrough in the

Fig. 2.1 Wing geometry understanding of aircraft aerodynamics came at the end of the nineteenth century, when the English engineer F. W. Lanchester reasoned that if a wing or lifting surface acts like a vortex, then it should possess all the general prop­erties of a vortex. Long before the Wright Brothers’ first flight, a theory of vortex behaviour had been developed which indicated that a vortex could only persist if it either terminated in a wall at each end, or formed a closed ring like a smoke ring. In Fig. 2.3 we show in very simplified form, how this requirement of forming a closed circuit is met. In the diagram we see that the circulatory effect of the wing, which is known as the wing-bound vortex, turns at its ends to form a pair of real vortices, trailing from near the wing tips. The ring is com­pleted by a so-called starting vortex downstream.

These vortices do exist in reality and we can easily detect the trailing vortices in a wind tunnel by using a wool tuft which will rotate rapidly if placed in the appropriate position behind a model. On a real aircraft they can sometimes be seen as fine lines of vapour streaming from near the wing tips, as seen in Fig. 2.4. This often occurs at airshows, particularly on damp days. They are most likely to be seen when an aircraft is pulling out of a dive, and is therefore

generating a large amount of lift, so that the wing circulation and trailing vortices are strong.

In the wing trailing vortex, as in a whirlwind or whirlpool, the speed of the rotating fluid decreases with distance from the central core. From the Bernoulli relationship, we can see that, since the air speed in the centre of the vortex is high, the pressure is low. The low pressure at the centre is accompanied by a low temperature, and any water vapour in the air tends to condense and become visible in the centre of the trailing vortex lines, as in Fig. 2.4. Note that the vapour trails frequently seen behind high-flying aircraft are normally formed by condensation of the water vapour from the engine exhausts, and not from the trailing vortices. Figure 2.5 is a flow-visualisation picture showing the trailing vortices forming at the wing tips.