Gear Inches calculator
#1
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Gear Inches calculator
I see a lot of posts regarding Gear Inches on this forum, and decided to develop a formula that can be used to calculate Gear Inches without the need to use an online calculator. Also, some rim sizes are not included in these online calculators. The formula is as follows:
GI = (CR / COG) x (BSD + 2 x TW) / 25.4
where:
GI = Gear Inches
CR = Number of chainring teeth
COG = Number of cog teeth
BSD = Bead Seat Diameter in millimeters, which is effectively the inner diameter of the tire when mounted on the rim
TW = Tire width in millimeters, which is also assumed to be the tire height
So, how does this compare with popular online gearing calculators, such as BikeCalc.com ?
Suppose we have a 700x23c tire. This fits a rim with a 622mm BSD. Let's say we are using a 46T chainring and a 17T cog. The Gear Inches per the formula is:
GI = (46 / 17) x (622 + 2 x 23) / 25.4 = 71.16 , whereas per BikeCalc.com it is 71.27 , which is a difference of 0.15 %. Interestingly, if I use 623mm for the BSD, then the results are the same. Anyways, this formula seems to give reasonable results. I you have a programmable calculator with a root solver, then you can set this up as a simple menu where you enter the known variables CR , COG , BSD and TW, and then solve for GI. Yeah, I know, pretty nerdy stuff, but hey I'm a nerd and proud of it !
Enjoy
GI = (CR / COG) x (BSD + 2 x TW) / 25.4
where:
GI = Gear Inches
CR = Number of chainring teeth
COG = Number of cog teeth
BSD = Bead Seat Diameter in millimeters, which is effectively the inner diameter of the tire when mounted on the rim
TW = Tire width in millimeters, which is also assumed to be the tire height
So, how does this compare with popular online gearing calculators, such as BikeCalc.com ?
Suppose we have a 700x23c tire. This fits a rim with a 622mm BSD. Let's say we are using a 46T chainring and a 17T cog. The Gear Inches per the formula is:
GI = (46 / 17) x (622 + 2 x 23) / 25.4 = 71.16 , whereas per BikeCalc.com it is 71.27 , which is a difference of 0.15 %. Interestingly, if I use 623mm for the BSD, then the results are the same. Anyways, this formula seems to give reasonable results. I you have a programmable calculator with a root solver, then you can set this up as a simple menu where you enter the known variables CR , COG , BSD and TW, and then solve for GI. Yeah, I know, pretty nerdy stuff, but hey I'm a nerd and proud of it !
Enjoy
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Oddly enough, 0.15% is probably less the uncertainty of how much your tire is squished by your weight.
You might be able to find out the formula that BikeCalc uses... many of these simple "calculator" pages are written in Javascript, so you can look at the page source and find the formula. You usually have to look past all of the code that's sending your personal data to a dozen different tracking sites.
What I do is measure the diameter of my wheel with a yardstick and multiply by the gear ratio.
You might be able to find out the formula that BikeCalc uses... many of these simple "calculator" pages are written in Javascript, so you can look at the page source and find the formula. You usually have to look past all of the code that's sending your personal data to a dozen different tracking sites.
What I do is measure the diameter of my wheel with a yardstick and multiply by the gear ratio.
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Close enough is Chain ring teeth divided by sprocket teeth, multiplied by the actual diameter of the wheel in inches.
My 700c x 25 measures around 27 inches across. If it squishes to 26.5 under my weight then that makes a difference of less than 2%.
My 700c x 25 measures around 27 inches across. If it squishes to 26.5 under my weight then that makes a difference of less than 2%.
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This is actually the true definition of Gear Inches. According to the formula, your rim + tire diameter should be about (622+2x25) / 25.4 = 26.5", so either you've got a rather tall tire or your measurement is a bit off.
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Last edited by TejanoTrackie; 05-31-21 at 06:32 PM.
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You might be able to find out the formula that BikeCalc uses... many of these simple "calculator" pages are written in Javascript, so you can look at the page source and find the formula. You usually have to look past all of the code that's sending your personal data to a dozen different tracking sites.
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Last edited by TejanoTrackie; 05-31-21 at 12:35 PM.
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Here is his explanation.
BikeCalc.com - How to calculate Bicycle Wheel Size
He uses the same formula.
Otto
BikeCalc.com - How to calculate Bicycle Wheel Size
He uses the same formula.
Otto
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Here is his explanation.
BikeCalc.com - How to calculate Bicycle Wheel Size
He uses the same formula.
BikeCalc.com - How to calculate Bicycle Wheel Size
He uses the same formula.