# Subsonic and supersonic trailing edges

For an untapered wing the trailing edge is parallel to the leading edge. Thus if the leading edge is subsonic then the trailing edge is likely to be so as well. In this context the terms ‘subsonic’ and ‘supersonic’ mean exactly the same as they did for leading edge; if the trailing edge has a higher angle of sweep than the local Mach angle then it is subsonic – if the sweep angle is lower than the Mach angle then it is supersonic.

It is perhaps worth pointing out here that, unless the wing is swept forward rather than back, the trailing-edge sweep must be less than the leading-edge value if an inverse taper is to be avoided (Fig. 8.12). The trailing edge of a conventionally swept wing is therefore likely to be less swept than the leading edge.

We already know what happens if we make both the leading and trailing edges either subsonic or supersonic. What happens, though, if we make the leading edge subsonic and the trailing edge supersonic? Once again it is a matter of working out the zones of influence. First let us look again at the wing with both leading and trailing edges subsonic, this time concentrating on what happens to the Mach lines in relation to the trailing edge. Considering the point A on the trailing edge (Fig. 8.13), this will be able to influence the shaded area. Note, once more, that if the wing had no centre section, but went on to infinity, any point on the wing would be influenced by some point on the trailing edge and we would be back to the equivalent subsonic flow.

If we now reduce the sweep at the trailing edge it will not be able to make its presence felt anywhere on the wing surface (Fig. 8.14). The flow in this region will then look like that of the unswept supersonic aerofoil where the flow is turned through a pair of trailing-edge shock waves and a pressure

Fig. 8.12 Backward and forward sweep Unless wing is swept forward, trailing-edge sweep is less than leading-edge sweep for conventional taper |

Fig. 8.15 Loading on section of swept wing (a) Supersonic leading and trailing edges (b) Subsonic leading and trailing edges (c) Subsonic leading edge and supersonic trailing edge |

difference between upper and lower surfaces is sustained right to the trailing edge.

With the subsonic trailing edge there can be no such loading because no shock waves will be present. Consequently there can be no pressure discontinuity at the trailing edge between the upper and lower surfaces.

Figure 8.15 shows a comparison of the load distribution (the pressure difference between bottom and top surfaces) for all the cases we have considered so far:

(a) supersonic leading and trailing edges

(b) subsonic leading and trailing edges

(c) subsonic leading edge and supersonic trailing edge.

Above we saw that one of the main advantages of the subsonic leading edge was that its performance would not appear too violently different as the aircraft accelerated from subsonic to supersonic speed, while remaining reasonably economical in terms of drag production under supersonic conditions. The main trouble with the unswept wing is that the thin sections and sharp leading edges required for good supersonic operation lead to poor low speed performance because of boundary layer separation. No such difficulty exists with the supersonic trailing edge and the main problem here is the rearward movement of the centre of lift caused by the change in load distribution (Fig. 8.15(c)).

It is worth noting that option (c) is one of the most frequently encountered solutions to the problems of supersonic flight. This is because advantages, such as improved structural properties, offered by a small trailing-edge sweep angle can more than outweigh the aerodynamic penalty mentioned above.

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