## Things I Think About When I’m Really Bored

By admin, September 7, 2006 6:48 pm

by Stephen Herrick

Ever wonder how many pedal strokes you would have to turn if you rode 100 miles? (Come on, admit it, you think about it all the time…) Well, if you’re on a bike that shifts gears and can coast down hills, then you would need a wheel rotation sensor to count it out for you, or the best you could do would be to estimate. However, if you’re riding a fixed gear bike, then you can actually calculate the answer pretty accurately. You’ll need to do some conversions, and you’ll need to understand something about gear ratios and gear inches, also called virtual wheel size.

Your gear ratio compares the relative sizes of your front chain ring and rear cassette, and is easily calculated by dividing the number of teeth on your front cog by the number of teeth on your rear cog. Since the chain ring is attached to the crank set, and since the rear wheel is spinning at the same speed as the cassette when you are not coasting, then the ratio of pedal strokes to wheel rotations will be the same as the gear ratio. In other words, if a roadie is in her big 52 ring in front, and in her 13 ring on the rear cassette, then 52 divided by 13 = 4, so her wheels will be rotating exactly 4 times for each pedal stroke.

To understand chain inches and virtual wheel size, picture an old penny-farthing; the antique bike where the rider was perched up on top of a large wheel with the pedals mounted directly on the hub of the wheel. These wheels grew to about 60” in diameter, or about 15 and ¾ feet in circumference. Each pedal stroke turned the wheel around once, and so the distance that the bike traveled forward was exactly the circumference of the wheel. Calculating chain inches/virtual wheel size of a bike with cogs and chain is like trying to figure out how big the wheel on a penny-farthing would have to be in order to move you the same distance forward with each stroke. Figure out your gear ratio, (teeth in the front divided by teeth in the back,) and multiply that by the diameter of your tire in inches. So if the roadie in her 52 / 14 was on a standard tire with a diameter of 27.6 inches, then her virtual wheel size would be (52 divided by 14), times 27.6 inches, which equals 110.4 inches, or a little over 9 feet high! Her distance forward per pedal stroke would be the same as the circumference of the wheel, (Diameter X Pi = Circumference) so 110.4 inches X 3.14 = 346.7 inches, or 28 feet, 11 inches.

Okay, back to the fixie and his century. Let’s say he’s using a pretty standard set up for a fixed gear bike with a 42 front chain ring, and a 17 back cog. 42 divided by 17 equals a gear ratio of 2.47 wheel revolutions per pedal stroke.

Now take the gear ratio of 2.47 and multiply it by the circumference of the tire, and you’ll get how far the bike moves with each stroke. A standard 700 mm diameter road tire converts to a circumference of about 7.2 feet.

2.47 times 7.2 feet = 17.82 feet. That’s how far forward a fixie goes with each stroke.

Using 5,280 feet in one mile, divided by 17.82 feet per pedal stroke = 296.29 pedal strokes (revolutions) per mile. Multiply that by 100 miles and you get:

29,629 turns of the cranks to ride a fixed gear bike for 100 miles!

Summary:
Gear Ratio = Front Cog divided by Rear Cog
Chain Inches, or Virtual Wheel Size = Gear Ratio X Wheel Diameter in inches
Distance Traveled per Single Pedal Revolution = Gear Ratio X Wheel Circumference
Pedal Revolutions per Mile = 5280 feet/mile divided by DT/SPR (in feet)

If you like this kind of thing, and you want to see what the numbers would be like on your bike, follow this link to a great web site for calculating just about any gear set up.

http://www.jbarrm.com/cycal/cycal.html

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