Changes

In a sense, we have shown that, for a wing of finite span, a '''sheet of vorticity''' is trailed behind it because vorticity is being shed off from the root to the tip of the wing. But this does not remain as a sheet forever. For the third time according to Helmholtz’s theorems, these vortex lines move with the fluid, but do not forget that the vortices can introduce swirling flow themselves. The result is that this vortex sheet rolls up into a single vortex with all the strength there is. For an aeroplane, because of the obvious symmetry, a pair of vortices are formed. These are known as tip vortices. Despite the name, it is good to understand that '''they are not in general produced by flow escaping around the tip''', but it is a result of a finite span wing generating lift in general. A more detailed examination of the rolling up process reveals that the distance between these tip vortices is less than the geometrical span of the wing, i.e. ''the tip vortices are closer to the fuselage than the tips are''. === Implications === Tip vortices can be '''very strong''': they are as strong as vorticity required to keep the aeroplane in the air. In a sense they are a pair of tornados trailed behind an aeroplane which contains an enormous amount of kinetic energy (hence the induced drag on the aeroplane). In the real world, air is viscous, and these tornados are eventually dissipated, but this dissipation needs time, and in the world of aviation, time means distance. Therefore, it is generally not a good idea to stay too close behind other aeroplanes, especially the heavier ones, whose tip vortices are strong and generally highly turbulent (with the additional interaction with the wake). Airliners that generate tip vortices of significant strengths have the suffix “heavy” or (for an A380) “super heavy” on their callsigns to warn air traffic controllers to keep other traffic well separated, and you do not want to be anywhere close with your glider. Downwash is a consequence of having these trailing vortices (and this is used in the '''force approach''' to explain induced drag, contrasted to the energy approach we have been using). Viewing from behind, the left-hand vortex rotates clockwise and the right one counter-clockwise. Therefore, between these vortices there is a region where the flow is effectively going down (apart from the going back component which we take for granted). This is known as the downwash. Similarly, on either side of these vortices there is upwash. It is also important to remember that, because the flying speed we consider is subsonic, vorticity downstream can have an effect upstream, so downwash and upwash exists even in front of an aeroplane, although the strength is questionable. The understanding of these vortices is important to the competency in aerotowing. You will have a chance to appreciate the strength of these vortices and the degree of turbulence caused when the exercise “boxing the wake” is done. Ask an instructor for more details.