Sunday, December 11, 2005

Math Question

This morning I posted this to the Fixed Gear List but I figured I'll put forth the question into the blogosphere as well:

Here's a math question for you. In my copy of "The Dancing Chain" by Berto, Shepherd and Henry (1st edition) on page 117 in a quote from a Cyclo catalog, a cyclist identified as C.A.P. recounts climbing a 1 in 4 hill in a 41 inch gear. Later on this page there is the comment:

"C.A.P.'s claim of riding up a 1 in 4 (25 percent) slope was a little optimistic. With a cyclist's entire weight on the pedal, the maximum rideable gear is seven times the slope denominator. On his low gear of 41, C.A.P. could, with maximum effort, have ridden up a slope of 1 in 6. For touring, an ideal gear is only twice the denominator. Thus a gear of 41 is comfortable to pedal up a slope of about 1 in 20 (5 percent.)"

Now this maximum rideable gear being seven times the slope denominator seems bogus. If I'm reading this right with a 70 inch gear I should only be able to climb a 1 in 10 (10% grade). Yet I've gone up 15% and even 18% climbs with a 70 inch gear. I'm not looking for a bunch of anecdotal "I've climbed hill X" stories but it does seem to me there is some kind of mathematical maximum which I think would have to factor in crank length, rider weight, gravity, the coefficient of friction (at some steep point tires will slip on the road) and maybe some other stuff. Any engineers with time to kill and fresh batteries in their 41GX want to take a shot at this?

BTW in general "The Dancing Chain" is a really cool book, even if it does focus on shifting and coasting and other things that clutter up the riding experience.

Kent Peterson
Issaquah WA USA

P.S. SHAMELESS PLUG: "Shiftless Bum" T-shirts with the No-Derailleur logo are available online at
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