Reducing vortex-induced drag Aspect ratio

5.1 THE TRAILING VORTICES

The association between induced drag and the trailing vortices behind a wing was men­tioned in the closing paragraphs of Chapter 2. This will now be examined in more detail.

The cause of the vortices is the difference in pressure between the lower and upper surfaces of the wing when it is generating lift Near the ends of the wing the high pressure air below tends to flow outwards and round the tips towards the low pressure side. The main fore-to-aft flow stream is deflected slightly outwards on the under surface and slightly inwards above. There is also an upward component of flow outside the ends of the wing. A vortex forms behind the wing tip and trails off downstream as shown in Figure 5.1. In a simple theoretical representation, the tip vortices may be envisaged as continuations of the bound vortex of Figure 2.6. The bound vortex cannot end abruptly at the end of the wing, so it may be supposed to turn back through a right angle to form a U or horseshoe shaped vortex system as sketched in Figure 5.2.

The real picture is more complex. The cross flow at the tips influences the inner portions of the wing causing similar, though less pronounced, cross flows under and over the wing all along the span. This effect progressively weakens as distance from the tip increases, but the result is that behind the wing not a single pair, but a whole sheet of vortices forms as suggested in Fig. 5.3. Some distance behind the wing the vortex sheet rolls together into two simple vortices, the horizontal distance between them being somewhat less than the geometric wing span. The simple horseshoe vortex gives a comparable result well aft of the wing, but near the lifting surface itself a better image is of a large number of horseshoe vortices fitting one inside the other. The tip vortex at the ex­treme end of the wing remains the strongest, unless a very poor wing planform is chosen.