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# Converting gear inches to MPH???

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# Converting gear inches to MPH???

09-06-08, 01:49 PM
#1
MAK
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Converting gear inches to MPH???

Is there a chart that takes gear inches, multiplies by stroke count and converts to MPH?

I just bought a fixie/SS that has a 48x18 drivetrain. That equates to 72". If I multiply 72 times strokes per minute that gives me inches per minute. Divide that by 12 to make it feet per minute and multiply by 60 to get feet per hour. I then divide by 5280 and that should give me miles per hour. At 80 rpm, my math says 5.45 mph. That can't be right. I know it's got to be faster than that. Where is my math error?

For example:

72" x 80 rpm= 5760" per minute
5760"/12"=480' per minute
480' x 60 minutes=28800' per hour
28,800'/5280'=5.4545 mph

At 120 rpm it comes to 8.18 mph. To average 15 mph I need to cranking at 220 rpm? I must be missing something. Would someone please educate me.
09-06-08, 02:03 PM
#2
Nikephoros
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09-06-08, 02:28 PM
#3
StephenH
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Gear Inches

One of the three comprehensive systems for numbering the gear values for bicycle gears. It is the equivalent diameter of the drive wheel on a high-wheel bicycle. When chain-drive "safety" bikes came in, the same system was used, multiplying the drive wheel diameter by the sprocket ratio. It is very easy to calculate: the diameter of the drive wheel, times the size of the front sprocket divided by the size of the rear sprocket. (From Sheldon Brown's site)

The key being here that it is the diameter, not the circumference of the wheel. So you need a Pi factor in there somewhere.
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09-06-08, 03:25 PM
#4
UncleStu
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For goodness sake, listen to StephenH. You are working with a *diameter* of 27" to get your figure of 72 GI. For the distance, you need to convert that to circumference by multiplying by Pi, ~3.14159...(Remember Pi? Remember where it comes from? Hint Hint)

Short version- your only real mistake was in not converting wheel-tire diameter to circumference by multiplying by Pi.

For your purposes 3.14 will be fine. Want more accuracy? Adding more digits to the right of the decimal point will help almost none at all. If your really want more accuracy- you need to determine the "static loaded rolling radius" of your drive wheel. Do this by inflating your tires to riding pressure, at riding temperature. Then sit on your bike, with whatever gear & accessories you normally have, with bike held upright on level hard floor, & have someone measure from the floor to the rear wheel's axis of rotation- ie, the center of the axle. Multiply that measurement x 2 x Pi & that's about as close as you can get to your true loaded rolling diameter. I'd be surprised if it's exactly 13.5"(27/2) from the floor to the axle centerline when loaded.

Last edited by UncleStu; 09-06-08 at 06:11 PM.
09-06-08, 03:34 PM
#5
MMACH 5
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http://sheldonbrown.com/gears/

See how your figures match up to the Gear Calculator results.
09-06-08, 05:42 PM
#6
wmodavis
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Sheldon is the guru! I re-iterate go to http://www.sheldonbrown.com/gears/ and digest all links from there and you'll know more then you ever wanted to in about it.
09-06-08, 06:21 PM
#7
UncleStu
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A little something extra:
For MAK- To convert from cadence(crank RPM) to speed in MPH, with 72 Gear Inches: multiply cadence by 0.2141992. Such as: RPM x 0.2141992 = speed in miles/hr. This is only good for 72 gear inches.

For something more generally useful: If you know Gear Inches(GI) and cadence(RPM), multiply by (Pi/1056), which is ~0.0029749. So: GI x RPM x 0.0029749 = speed in miles/hr.
09-06-08, 09:42 PM
#8
MAK
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Thank you to all that responded. You were all extremely helpful.
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