Balancing bicycles

Skate-bike overturns existing ideas on bicycle stability - Photo: Sam Rentmeester

Contrary to common belief the dynamic equilibrium of a bicycle does not critically depend on the gyro-effect of its wheels, nor on the trailing of its front wheel, so Delft researchers explain in Science.

Run next to your bike and let it go. Most bikes will continue straight ahead. Now give it a sideward smack. Such abuse is ruefully tolerated as the bike will steer itself back on the right track. Although the stability of bicycles has been studied for almost 150 years, a bit of a mystery still remains. Last week, TU Delft researchers, Dr Arend Schwab and Jordi Kooijman (Msc), together with American colleagues, added another sequel to the bicycle studies in Science.

It was commonly believed, they explain, that the gyroscopic effect of the wheels is essential for a bike’s balance, as is a certain amount of trailing (the point of contact of the front tire is some centimetres behind the steering axis). A clever experiment however has proven that neither aspect is essential for balancing the bike, although both aspects do generally help.

The mathematical model of a standard bicycle, as published by Schwab in 2007, has no less then 25 parameters. Researcher Jim Papadopoulos (University of Wisconsin) reduced that number to eight in what was, when built, a weird looking contraption. Delft researchers from the 3mE faculty then built that ‘bike’ to test its stability. Its design has no gyroscopic effect (each wheel is balanced by a similar wheel rotating the other way) and no trailing (the wheel touches ground in front of the steering axis). Hence, if the ‘bike’ is stable (which it is), apparently neither the gyroscope effect nor the trailing is essential for a bicycle’s balance.

So what is essential? Basically, as Professor Andy Ruina from Cornell University explains, it’s the ability to bring the bike’s wheels back underneath it. Schwab says the same thing but differently: a bicycle should steer towards its fall. Once a bike banks over (after a smack on the side), it is essential that the steering wheel falls even quicker than the rest of the bike. By steering into the fall the bicycle brings its wheels once again underneath it and restores the equilibrium.

bicycle.tudelft.nl/stablebicycle

J.D.G Kooijman, J.P. Meijgaard, Jim M. Papadopoulos, Andy Ruina, A.L. Schwab: A Bicycle Can Be Self-Stable Without Gyroscopic or Caster Effects, Science, 15 April 2011