Friday, August 5, 2011

Bike gear ratios

I'd been idly wondering for awhile now about two things:

1) How far my bike commute to and from work really is.
2) How the different gear combinations on my bike compare to each other.

So a week or so ago I worked it out:

Number of teeth on each of my front three gears: 22, 32, 42
Number of teeth on my back 8 gears: 11, 13, 15, 18, 21, 24, 28, 32
Gear ratios, in descending order:
3/8 3.8181818182
3/7 3.2307692308
2/8 2.9090909091
3/6 2.8
2/7 2.4615384615
3/5 2.3333333333
2/6 2.1333333333
3/4 2
1/8 2
2/5 1.7777777778
3/3 1.75
1/7 1.6923076923
2/4 1.5238095238
3/2 1.5
1/6 1.4666666667
2/3 1.3333333333
3/1 1.3125
1/5 1.2222222222
2/2 1.1428571429
1/4 1.0476190476
2/1 1
1/3 0.9166666667
1/2 0.7857142857
1/1 0.6875

So for all intents and purposes, shifting the front gear changes the effective ratio by about 2 "notches": 1 and 8 is about the same as 2 and 6 is about the same as 3 and 4.

Having worked that out, I measured the outer diameter of my bike tire - 82.5 inches - and worked out that if I leave it in 3/6 (which is around where I generally ride) and never backpedal, it takes about 69 turns of the crank to go a quarter mile:

5280 ft/mile * 12 in/ft / 82.5 inches/wheel = 768.0 wheels/mile
768.0 wheels/mile / 2.8 wheels/pedal = 274.3 pedals/mile
274.3 / 4 = 68.6 pedals in a quarter mile.

Then I rode home by my usual route, without changing gears and without backpedalling (which is surprisingly hard) and it comes out very close to three and a quarter miles. Which is pretty darn close to what Google Maps comes up with, even though it doesn't let me trace my actual route, which winds in and out of some back alleys and such.

I can't really imagine why I'd want to know this again later, but I haven't really got anywhere else to put it at the moment...

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