Thursday, April 10, 2008

Advice for you

If you want to avoid pedal strike on your fixed gear (which I'm sure that you, sensible reader, most certainly do) one thing to take into account is your gear ratio.

Imagine a stretch of curb with an obstacle positioned briefly alongside it (this could be anything: a speed bump, an old lady with a walker, or perhaps a small infant (and really, aren't all infants small).)

Imagine further that the gap between the curb and the obstacle is wide enough to fit the bicycle tires but not wide enough to guarantee that your pedal won't hit the curb. --A certain percentage of your pedal arc will be too wide to fit in the gap.

Assume that the position of the pedals when you arrive at the gap is a uniform random variable (meaning all positions will be equally likely.) Then, whatever your gear ratio, the percentage of your pedal arc that is too wide for the gap will be the probability that your pedal is hitting the curb at any given time.

This is admittedly not all that profound and smacks of pretentious washed-up-math-major posturing. Which is what it is. The crucial insight comes, however, when you realize that if your gear inches are less than the length of the curb/obstacle gap, then your pedal is guaranteed to strike the curb. --You cannot get through the gap without making more than one complete revolution of the pedals, and part of your pedal revolution is too wide to get through.

Therefore, fixed-gear cyclists arriving at gaps between curbs and small infants (or whatever) can maximize the probability of successfully navigating such gaps by making their gear ratio as high as possible. For example, with an infinitely high gear ratio, one could potentially navigate between an infinitely long curb and infinitely long old lady and her walker.

...Just something to keep in mind while you're shopping for girl pants or listening to Sufjan Stevens.


Fatbot said...

I will imagine it.

one Les car said...

good point, I ride a 52x14 and cruise through turns with no pedal stike all the time

patrick said...

i just avoid ever turning.