Tuesday, March 25, 2008

Time for A Little Math

I installed a bicycle computer to track mileage on my bike. I will live with the computer on the front of my bike from now through the conclusion of TransIowa. Due to the nature of the event, all navigation is in the form of turn-by-turn navigation at declared mileage points. There is no map.

How to calibrate:

Attempt One: Started with valve at the bottom of the wheel at a point on the ceramic tile in my basement. Sat on the bicycle and rolled what I thought were two complete revolutions of the wheel. Measured that distance as twice the circumference of my wheel. Divided this number by two to come up with 216, set the number and set off for work.

Results: I've got a pretty good feeling for cadence and speed. It felt like I was off quite a bit in speed. (Thought it could have been part of bazzaro world.) But when I got to work, I was off by about 2.5 miles over what I have concluded before as about 15 miles +/-. By the time I got home, I was off by about 4 miles over 30.

Attempt Two: Just turned the number ahead a couple of digits on the setting. (Figuring I was off by about 10%, I guessed and set the number at 218.)

Results Two: Still felt off. Stopped along the route to work and turned the number ahead to 220 and continued on my ride to work. Forgot to set the trip meeter, still felt slow... just enjoyed the ride to work.

Attempt Three: Before leaving work, set the number ahead to 221. Reset the trip meeter. Rode home trying to ride a straight line along a route that I would easily be able to map using the Internet when I got home. The results when I arrived back home were almost exactly what the map revealed.

While riding though, I figured out the fact that since I was riding a fixed gear bicycle, I could calculate the circumference of my wheel if I counted the crank revolutions over a long enough distance. So, I picked a point along a straight road and counted from curb to curb 155 complete crank revolutions.

Using a GIS utility that I have access through that allows one to measure pretty darn accurately I was able to determine that this distance was 2560 feet. So here's where we go:

41 teeth up front, 18 in the rear.

41/18 = 2 7/9 revolutions of the wheel per revolution of the cranks.

2.777777777777777777 (lots more sevens) * 155 = 353.055555555

2560*12 = 30,720 inches traveled

30720 / 353.05 = 87.0118 inches of circumference traveled per crank arm revolution.

87.0118 * 2.54 cm/inch = 221.0099 cm.

So, I confirmed my guess with a little math.


Jim Thill said...

Hmmm. I'd have guessed you'd get some comments on this one, at least about your devil-may-care attitude about significant digits in the decimal. Otherwise, clever!

Reflector Collector said...

I don't feel bad at all. My wife (may God bless her) listened patiently while I explained my exciting discovery.

Her eyes glazed over and she just smiled. Sometimes I appreciate the anonymity of the Internet.

Anonymous said...

My wife gets that same glazed look when I really get going about the bikes. Somehow, she does listen (while thinking other things, I'm sure) and will even engage in conversation if I speak of something bike related that she is interested in. My wife (and lots others) are amazing.

Pete said...

Here's how I calibrate: Put a dab of grease on the front wheel. Roll the wheel one full revolution so the grease makes two spots on the floor (best to use this method outside). Measure the distance between the two grease spots.

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