Consider a person making a turn on a bicycle. Assume the speed of the rider is such that the turn is purely facilitated by the tilt of the bike/rider, (compared to a slow, sharp turn where the rider must turn the front wheel to make the turn).

Is there a well-defined expression for the shape of the curve traced out by the wheels on the ground? (e.g. does the dynamical system require the rider to trace out a specific curve with the bike to not fall down in the turn?)

  • $\begingroup$ The front wheel of the bike must always turn to make a curve. It may not have to turn much (for whatever definition of "much" you prefer), but it has to be turned. $\endgroup$
    – TimWescott
    Nov 1, 2019 at 23:08

1 Answer 1


A turn on a bicycle is accomplished by steering the handle even though at times it is too small to be noticed.

leaning into the turn is required to counter the centripetal forces that would otherwise tumble the bicycle. if you don't lean, according to Newton's first law of motion your body wants to keep going straight while the force of the friction on the front tire wants to pool it from under you and the bike, so you will fall.

Even when you ride the bicycle while not holding the handles, the front wheel has steered just enough to keep the bicycle turning.

Riders who carry off-center loads on the basket maintain a bit of tilt even while they go straight to keep their balance.

  • $\begingroup$ You lean into the turn to counter centrifugal force with the centripetal force from the off center pull of gravity. $\endgroup$ Nov 2, 2019 at 0:41
  • $\begingroup$ Yes I agree, I realized this on my ride home from work. I can't turn without very slightly turning the front wheel. Even when riding without my hands on the bars I was slightly turning the wheel by moving my hips and upper body. $\endgroup$
    – Alex
    Nov 2, 2019 at 2:43

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