Planforms for supersonic flight

So far we have only looked at the effect of the aerofoil cross-sectional shape on the aerodynamic performance of the lifting surface. We know that in subsonic flight the planform shape has a vital role to play, and the same is true above the speed of sound.

The unswept wing

Let us first take a look at the unswept wing. We have already seen what the flow is like when we consider a two-dimensional section and ignore any

3-dimensional flow at wing tip

Intersection of wing surface and tip Mach cone

Wing trailing edge

Shock wave

Mach cone

Curved shock wave

Fig. 8.7 Wing-tip effect in supersonic flow (unswept wing)

influence from the tips. Let us now consider the more realistic situation in which the wing has a finite span so that the tips will have an influence on the wing behaviour.

When we considered subsonic wings (Chapter 2) we saw how the tip affected the flow everywhere. In a supersonic flow we found (Chapter 5) that because of the way pressure disturbances are propagated, only a limited region of the flow can be affected by the presence of an object. Thus we find that the influence of the tips is restricted to a limited region and the centre section of the wing behaves in a purely ‘two-dimensional’ way as though the tips were not there at all.

The region over which pressure disturbances from the tip can propagate will be bounded by the ‘Mach cone’ (Fig. 8.7). The Mach lines making up the surface of this cone are determined by the local flow conditions at each point along their length. Thus, in general, the local slope of the Mach line, and consequently that of the surface of the Mach cone, will vary and the surface will be warped slightly. Further the geometry of the cone will also depend on the wing incidence. In the centre region, outside the tip Mach cones, the flow knows nothing about the existence of the tip region and the flow is the straightforward two-dimensional flow discussed earlier.

Further from the surface the tip Mach cone intersects the oblique bow shock wave generated by the wing centre section (Fig. 8.7). The shock is therefore

Fig. 8.8 Unswept wing for supersonic flight In supersonic flight the unswept wing of the F-104 is relatively efficient, but in subsonic flight, the highly loaded razor-thin wing gives poor handling, and a high stall speed. Like the Lightning, it was designed as a high performance interceptor at a time when almost total reliance was placed on air-to-air missiles. Manoeuvrability and dog-fight capability were considered of little importance (Photo by N. Cogger)

altered in the tip region and the outer region of the tip flow becomes bounded by a conical shock wave as shown in the figure.

Because the tip can influence the flow within its Mach cone, the flow in this region develops a spanwise component which is absent in the two-dimensional centre region of the wing. This spanwise velocity results in a circulation around the tip from the high-pressure lower surface to the low-pressure upper surface. Trailing vortices are thus formed in a manner similar to a subsonic wing.

If the wing is unswept a sharp leading edge is required to reduce the wave drag and, since such wing sections have poor low speed performance, they are not employed when this aspect is important. Figure 8.8 shows the F-104, one aircraft where such a planform was employed for high speed.

Swept wings

In Chapter 2 we saw how wing sweep could be used to reduce the component of velocity approaching at right angles to the wing leading edge. If the wing is

swept back sufficiently to make this velocity component less than the velocity of sound then the wing will behave as though in a subsonic air stream.

In order to simplify the discussion we will return to the consideration of a wing of infinite span. In this way we can initially ignore both the problem of the wing tip and that of the ‘cranked’ centre section of the wing.