Originally Posted by
Lazyass
For those who don't know, a 17T cog is the best to run if you don't have brakes.
Umm... okay.
From
Sheldon Brown:
" 
f you make a habit of doing "skip stops" you will wear your rear tire out considerably faster than if you use your front brake. This problem is exacerbated by certain gear ratios, because you may tend to repeatedly skid on the same section of the tire.Riders who plan to do a lot of skip stops should consider the ratio when selecting their chainring and rear sprocket. The mathematics of this is actually fairly simple:- Simplify the gear ratio to the smallest equivalent whole number ratio. Let's call it p/q.
- if the numerator, p, of the reduced gear ratio is even then the number of skid patches is q. Skid patches are evenly spaced around the tire if there is more than one.
- If you are an ambidextrous skidder, and the numerator is odd, the number of possible skid patches will be doubled. The skid patches with one foot forward fall halfway in between those with the other foot forward.
Examples:
48/12 simplifies to 4/1, so there will be only 1 skid patch
45/15 simplifies to 3/1 so there will only be 1 skid patch, or 2 if you are an ambidextrous skidder.
42/15 simplifies to 14/5, so there will be 5 skid patches.
44/16 simplifies to 11/4, so there will be 4 skid patches, or 8 if you are an ambidextrous skidder.
43/15 can't be further simplified, so there will be 15 skid patches, or 30 if you are an ambidextrous skidder.
Explanation: let's look at 45/15, or 3/1. The rear wheel turns exactly 3 times for each turn of the cranks -- so, if the same foot is forward, the same place on the rear tire is always down. 1/2 turn of the cranks places the other foot forward, and turns the rear wheel 1 1/2 times. Then, the opposite place on the tire is down. Similarly for higher numbers, if the numerator of the reduced fraction is even, skid patches will be in the same places with either crank forward, but if the numerator is odd, the number of skid patches with each crank forward will be odd, and skid patches will interleave. John Allen's Excel spreadsheet calculates the number of skid patches for any sprocket combination."
In other words, the size of cog isn't what counts, but the ratio of chainring to cog.