How does tire pressure affect distance traveled by a bicycle coasting to a stop?

[jbriggs444]

If you actually do the experiment, you will find that your initial assumption of, "with negligible air resistance" is a bad assumption. Unless you are moving very slowly, air resistance is the primary drag on a bicycle.

Once the force law is nailed down, there is a differential equation lurking here.

For purely linear drag (drag proportional to velocity), the time taken to come to a stop is infinite, but the distance taken to come to a stop should be finite -- the sum of a decaying geometric series.

[The time taken to halve the velocity is a constant and you never finish halving the velocity. But the distance traversed each time you halve the velocity is also halved]

For purely quadratic drag, both the time and distance taken to come to a stop should be infinite.

[The time taken to halve the velocity doubles each time you halve the velocity. So it still takes forever to slow down. This time the distance travelled for each halving is constant -- half the velocity for twice the time. So the total distance is infinite]

With a mix of linear drag and quadratic drag, there will be a rapid decay of velocity after which the linear drag will dominate. So an assumption of negligible air resistance after some point is not completely unreasonable [which point is already well understood by @phyzguy].

 

[berkeman]

No, I hunk it’s the sharpness of the bend as the tire rolls onto the flat area

Sorry, I'm a little slow on Jive. What's "hunk" in this context?