What's up with pointy time trial helmets?

Since several people were kind enough to comment favourably on my post about hills and weight, I thought I'd say just a little about aerodynamics, and in particular, time trial helmets.

There are many different ways that drag can be caused. However, for ease of discussion, we can classify by the nature of the mechanism that carries away the energy. Looked at that way, there are the following types of drag:

  1. Pressure drag
  2. Skin Friction drag
  3. Induced drag
  4. Wave drag

Induced drag is drag due to lifting surfaces. The energy goes into forming a wake behind the lifting surface which contains vorticity. Wave drag is roughly speaking the energy carried away by shock waves in a supersonic flow. Neither of these are applicable to cycling, since we don't have wings, and we don't move at near- or supersonic speeds. So we'll say no more about them — refer to any undergraduate aerodynamics text for more details.

Skin Friction drag is the drag due to tangential forces at the surface of the object. It is like the friction you feel when you rub your finger-tip over a table top. The amount of drag varies in a complex way depending on the details of the surface, and the nature of the flow. In general, the frictional drag will be the least for laminar flows and very smooth surfaces. If we hold the nature of the flow and of the surface constant, then the amount of drag depends on the wetted area — the amount of surface exposed to the flow.

Pressure drag (also known as Form drag) is the resultant force obtained when you integrate the pressure field over the surface. That means, for each tiny square of the surface, figure out what the pressure force on it is, and add up the forces, taking into account their direction. You might wonder why the pressure would vary over the surface. Bernoulli's equation (which is really just the conservation of energy cast in continuum mechanics terms) tells us that the static pressure exerted by a fluid against a surface is lower when the fluid is moving faster. (You may have heard this as an explanation of how an airplane flys. In fact, this is just one of the details, not the whole story. But that's a whole other rant.)

Now if you had a fluid with no viscosity at all, you would find that the resultant force would be identically zero. It turns out that the pressure lost as the air accelerates over the front of a body is fully recovered as the flow decelerates again at the back. Sadly, air does have viscosity, although it is low enough that it can be ignored for many purposes. We find that there is a net backwards force on a real object moving through real air, even if we subtract the skin friction out. There is an incomplete recovery of the pressure.

So if we want to minimize form drag, the problem becomes to get the best possible pressure recovery. One thing which inhibits full pressure recovery is flow separation. This is when the flow of fluid no longer conforms to the shape of the object, but instead leaves the surface. There is then an area of "stagnant" flow between the main stream and the object. One of the things that causes this is too rapid of a pressure recovery — and the thing that drives the pressure recovery is the shape of the body. If it is narrowing quickly as we go downstream, the pressure recovery will be rapid, and separation will be more likely. (This is why the classical aerofoil shape has a blunt, curved front part, and a flattish pointy back part.)

So finally, I think we begin to see what drives the shape of the time trial helmet. The point on the back is intended to ease the pressure gradient, to keep the flow attached to the surface, and reduce the pressure drag. But notice, by adding the point on the back, we substantially increase the wetted area, and so the skin friction drag. There are other practical limits to be considered. For instance, no matter how much the aero guys ask them not to, all cyclists put their heads down at some point during the time trial. This leaves the cone on the back of the helmet sticking straight up in the air, which is not ideal. (Incidentally, I speculate that this is why Armstrong's helmet from the pre-saftey-rule days had a two-dimensional trailing edge cut at a raked angle, instead of a simple cone. On the rare occasions that he would put his head down, it seemed to me like the trailing edge of the helmet was almost level, not protruding upwards much at all.) Furthermore, the helmet is shaped with the assumption that the flow comes from in front. But of course, out in the real world, there are cross-winds. Having to cope with flow that isn't perfectly aligned would tend to drive the cone length downwards, because the longer it is, the more of it there is to catch the crosswind. And finally, we have to consider weight, since the cyclist has to hold this up with his or her neck muscles, but with modern materials, that probably isn't much of a concern.

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Comments:

Terry, According to the 'Giro' helmet representative, on a recent 'Discovery Channel' special, Mr. Armstrong's new TT helmet is their best effort yet. A great depiction about NIKE ware employed by 'Team Discovery Channel' related to their specific aerodynamic or strength qualities. An excellent TT helmet 'physics' explanation by you!

Posted by William R. Walling on July 07, 2005 at 12:22 AM PDT #

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