soapbox racer physics

Aerodynamic considerations are often overlooked when building a first racer, in favour of things that are easier to see and quantify. Teams will often spend much time and money on tyres, bearings and brakes and treat the shape of the bodywork as little more than aesthetics. Spoilers, wings, external cameras, etc, will be added because they "look cool" without any thought to the effect they will have on the cartie's overall drag. But physics says that aerodynamic drag is the most significant factor at speeds over about 20mph.

I'm building a soapbox racer and I've read lots of stuff on the internet about what is the best kind of wheel. Now I'm hopelessly confused. Which is best - large diameter or small?

OK - this is complicated and there is no single right answer. It depends on what you want to achieve and what kind of course you will be racing on. There are several factors to consider;

• Rolling resistance
• Moment of inertia / mass
• Braking and cornering grip
• Aerodynamic drag
  

OK - so what about rolling resistance? Larger diameter wheels give lower rolling resistance right?

In theory yes, but it's not as simple as that. Rolling resistance comes from deformation of the rubber in the tyres, and (all other things being equal) smaller tyres are made proportionally "less round" than larger tyres so have higher rolling resistance. However, a bigger factor on rolling resistance is the tyre pressure, and if you can get high pressure tyres for your small wheel then you will be able to more than offset the effect of the smaller diameter.

Wider tyres have lower rolling resistance than narrow ones for the same reason - the deformation of the tyre is proportionally less for a wide tyre inflated to the same pressure. However, narrower tyres tend to support higher pressures, which can more than compensate for this. Aerodynamic drag is a bigger factor though. Wider wheels have more drag than an equivalent narrow wheel, and at high speeds that will more than cancel out any gains from lower rolling resistance.

Check out this page on tyre manufacturer Schwalbe's web site for further information on rolling resistance.

The force F acting to move a soapbox cartie down a slope of angle θ is m g sin(θ), where m is the mass of the cartie and g is the acceleration due to gravity.

OK - so which is better? As heavy as possible or as light as possible? I reckon it's got to be lighter = faster. Lower weight means less tyre deformation, less load on the bearings and so less rolling friction.