London 2012 Olympics: Fluid Technology for Cycling
Cycling is one of the fastest sports in the Olympics. With that speed comes an increased importance on aerodynamics. In cycling the aerodynamic design is focused on minimizing drag. However, as with swimming, there are carefully crafted rules that ensure there is only a narrow scope for aerodynamic optimization to gain a competitive advantage.
Power and Drag
The primary objective of a cyclist is to move efficiently and quickly. Factors that oppose that motion are:
- Friction between moving components in the bike, e.g., sprockets and chain, wheel bearings
- Friction between the tires and road
- Energy loss due to compression and expansion (heat) of the tires
- Mass of the bike and rider during acceleration (includes climbing)
However, by far the largest component sapping power from the cyclist is the drag force due to the movement of the cyclist through the air. Focusing on the drag force and ignoring other losses we see that the power (effort) required by a cyclist to maintain a given speed is:
P = D.v = 1/2.rho.v3.A.Cd
where P = power, D = drag force, v = speed, rho = air density, A = cross-sectional area, and Cd = drag coefficient.
This tells us that the power generated by the cyclist to match the drag force scales according to the combined cross-sectional area of the cyclist and the bike, the speed cubed, and the drag coefficient.
Right let's get to work then. First let's try to reduce the area the cyclist presents to the onset flow. Sitting upright is out. Try crouching down as close to the bike cross bar as possible - better! What about making the smallest cross-sectional area possible by having the cyclist lie on their back and place the pedals at the front of the bike? That would be a recumbent bicycle, the fastest form of bicycle - capable of over 80 mph (129 km/h), but that's not allowed under the UCI rules that govern the Olympic cycling events. The bike has to adhere to strict sizing constraints and most definitely has to be an upright design. Also since the hey day of Graham Obree and his Superman position, the cyclist's position on the bike has been mandated indirectly by handlebar and seat position constraints.
What about the drag coefficient? Clearly there needs to be a fairing shaped like an airfoil section (we know that will have low drag) that envelopes the entire bicycle and rider - another feature of the fastest recumbent bikes. Stop there, the rules dictate no fairings - the UCI are not making this easy! The UCI says you can shape the frame cross-section a little and you can do what you like with the wheels. Also you can wear skin suits to minimize parachute-like flapping clothes and streamlined helmets - no problems there says the UCI, helmets are also good for safety. I've also suggested that cyclists shouldn't shave their legs so they would benefit from the same effect that gives greater distance (reduced drag) to golf balls, but I haven't seen it widely adopted yet...
What about that speed cubed term in our power sapping equation? If you could somehow reduce the relative speed between you and the air then you can reduce the power required to maintain your speed. Reduced speed equals reduces drag, great, but now I'm last! OK, try this then, slip in behind another rider. Ah, slip streaming - of course! By exploiting the wake behind another rider, the following rider's speed relative to the air is reduced and therefore so too is the power required to remain there. However, make sure you check with the UCI first, because in some track cycling events, e.g., the individual pursuit, it's not possible to slip stream since the riders start on either side of the track. And in the individual time trial cyclists start at set intervals apart and if a rider catches another rider there's to be no slipstreaming by either rider, UCI says so.
Optimization within Constraints
Even within the UCI rules, cycling is still a rich environment for air flow modeling. It's a case of optimization within constraints, so engineers use Computational Fluid Dynamics (CFD) and wind tunnel testing to help determine a cyclist's position on the bike, the shapes of wheel rims, the best helmet design, and the bike tube profiles. It's just what they do!