## Tuesday, August 02, 2011

### Diffusers and rake

A recent column by Mark Hughes (Autosport, July 21, p21), and a subsequent explanation Mark elicited from McLaren technical director Paddy Lowe (Autosport, July 28, p41), provide some extra illumination on the overall aerodynamic concept pursued in Formula 1 by Red Bull since 2010, and followed to some extent by other teams this year.

Both articles explain that the basic idea has been to run a car with a significant degree of rake, so that the front ride-height is lower than the rear. The effect of this is twofold: the front-wing generates greater downforce due to ground effect, and the rear diffuser also acquires the potential to generate greater downforce.

Maximising the downforce of the diffuser is, however, a subtle issue. The downforce generated by a diffuser is a function of two variables: (i) the angle of the diffuser, and (ii) the height above the ground. Generally speaking, the peak downforce of the diffuser increases with the angle of the diffuser. Then, for a fixed diffuser angle, the downforce generated will increase according to an exponential curve as the height reduces, until a first critical point is reached (see diagram above, taken from Ground Effect Aerodynamics of Race Cars, Zhang, Toet and Zerihan, Applied Mechanics Reviews, January 2006, Vol 59, pp33-49). As the height is reduced further, the downforce will increase again, but according to a linear slope, until a second critical point is reached, after which the downforce falls off a cliff.

Without running any rake, the diffuser is limited by regulation to a shallower angle than seen in years gone by. By increasing the rake, the effective angle of the diffuser is increased, thereby increasing the potential peak downforce. However, increasing the rake also has the effect of increasing the height of the diffuser.

So, how does one combat the detrimental effect of increasing the height of the diffuser? Well, the key, I think, is to understand exactly how a reduction in height increases the downforce generated by a diffuser. The crucial point is that the edges of the diffuser generate a pair of counter-rotating vortices, and the magnitude of the downforce generated is determined by the strength of these vortices. The downforce increases exponentially as the height is reduced, because the strength of these vortices is increasing. The first critical point corresponds to the height at which the vortex strength begins to decrease, and the second critical point corresponds to the height at which the vortices breakdown.

So, to pose the question again, how do we mitigate the downforce-reducing effect of an increase in diffuser height? Simple, one merely uses the exhaust gases to boost the strength of the side-edge vortices to levels otherwise seen at lower heights.

In fact, this is to simplify the issue, because the exhaust gases playing on the sides of the diffuser have two effects: (i) to strengthen the side-edge vortices inside the diffuser, and (ii) to act as air curtains, preventing the ingress of turbulent air created by the rotating rear wheels.

So, with exhaust-blown diffusers to be banned from next year, the trick will be to find other ways of boosting the strength of those side-edge vortices. Do so, and you'll still be able to run your car with a significant degree of rake.