Tuesday, September 11, 2012

What keeps a moving bike from falling over?

Alberto Contador in the bunch, Tour de France 2010 stage 20
Photo credit: http://www.cyclingweekly.co.uk/news/latest/492803/contador-wins-2010-tour-de-france-as-cavendish-takes-final-stage.html

There are a number of mechanisms that can contribute to a bicycle’s stability. They all have one thing in common: Whenever the bike tilts, they turn the bike toward the direction of lean, returning the center of mass (of the rider and bike) over the wheels, hence restoring balance. So, even if we think we're going in a straight line, we’re constantly tilting right then turning right or tilting left and turning left [1].

Two important means of stabilization are:

Image credit:  http://hyperphysics.phy-astr.gsu.edu/hbase/amom.html
1)    Conservation of the angular momentum generated by the bike’s wheels. Angular momentum, which every spinning object possesses, is a vector quantity, meaning it has both magnitude and direction. “Conservation” here means that, absent any outside forces, the angular momentum of the system (the bicycle in this case) will remain constant. The magnitude of the angular momentum is a function of the mass of the spinning object, how the mass is distributed and the rotational velocity. The direction of this vector is by convention taken to be parallel to the axis of rotation. If the bike tilts left, for example, conservation of angular momentum requires the bike turn left (that is, trace a counter-clockwise path)*, hence keeping the system’s center of mass over the wheels.

Image credit:  http://www.wired.com/wiredscience/2011/04/moving-bicycle-physics/
2)    The “caster” effect, which is similar to the caster in a shopping cart, where the wheel trails the pivot axis of the caster when the cart moves forward. The steering axis of a typical bike, when extended as an imaginary line, intersects the ground in front of where the bike tire meets the ground (figure on left). This leads to a torque that turns the wheel left when the bike leans left, hence keeping the bike stable. This torque can be felt on the handlebars even when the bike is steered straight. Lean right on the bike and tilt the frame left. You’ll notice you have to apply a clockwise torque on the handlebars to keep the bike going straight [3].

Researchers discovered that neither of the above mechanisms is universally necessary for bike stabilization, however [3]. Without these two, a third means can stabilize the bike if the front wheel assembly possesses a lower center of gravity than the rear portion of the frame. In the event of tilt, then, the front wheel will fall more quickly than the rest of the bike, allowing the bike to turn in the direction of the lean.

* By convention, the direction of the angular momentum is determined by the so-called right-hand screw law. If you cup your right hand such that the fingers are curled in the direction of the wheel rotation, your extended right thumb should be pointing left, parallel to the ground. If your bike tilts left, this vector angles down toward the ground. But, conservation of angular momentum requires that some other vector must point upward to compensate. To that end, the bike turns left, going in a counter-clockwise direction—note the screw for this rotation points upward, as required.

[2] DEH Jones, The stability of the bicycle, Phys. Today, April 1970, p. 34
[3] JDK Kooijman et al., Science 15, April 2011, Vol. 332, No. 6027, pp. 339-342, http://www.sciencemag.org/content/332/6027/339.full