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Old 02-15-09, 09:11 PM   #1
kamtsa
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Calculating gear inch for 406 wheel

When I enter the following to the Sheldon gear calculator:

Tire: "20 X 1.75 / 44-406 / BMX tire"
Chainring: 52T
Cassete: 11T

I get 88.3 gear inches.

I presume that the formula is: gear_inch = (52 / 11) x 18.68"

Where does the 18.68" constant comes from? Is it part of the specification of the rim and/or tire? 406mm is about 16" so is the extra 2.68" the contribution of the tire to the diameter?

(in my case, I plan to use Schwalbe Marathon Plus 20 x 1.35" (406)).

Thanks,

Kam
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Old 02-15-09, 09:28 PM   #2
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I have found an accurate enough value is to add twice the tyre width to the wheel bead seat diameter, so 406mm+2*34mm=474.6mm=18.68".
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Old 02-15-09, 10:22 PM   #3
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Usually I am a practical fellow not entering philosophical questions, but don't you guys think that is about time to start using gain ratios instead of gear inches. A bicycle moves forward thanks to a set of levers and the crank is the most important lever. A few millimeters change in the crank length changes the final amount of effort a ride makes for the same gear inches. Gain ratio takes into consideration effort and gear development no.

About your question, I doubt Sheldon Brown's calculator would not be right.
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Old 02-15-09, 11:39 PM   #4
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Seeing as I can't feel a 2.5 mm difference in crank length, I'm not too interested in gain ratio; though it should make a noticeable difference according to Mr Brown. 'Development' as per the Continental method, that's different.

Comparisons between one combination of chainwheel/cog ratios and another, they can be in inches, metres or anything else as long as I can understand the relative sizes.
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Old 02-16-09, 12:02 AM   #5
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Quote:
Originally Posted by caotropheus View Post
About your question, I doubt Sheldon Brown's calculator would not be right.
I hope that the knowledge how to compute gear ratio will outlive Sheldon's calculator ;-)

Kam
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Old 02-16-09, 12:39 AM   #6
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Originally Posted by LWaB View Post
Seeing as I can't feel a 2.5 mm difference in crank length, I'm not too interested in gain ratio; though it should make a noticeable difference according to Mr Brown.
I think that if your legs are either really long or really short or if you make a big jump in crank lengths you should feel the difference. I am not that tall 5"3' and 170mm cranks hurt my knees. And no, I am not a masher, I am a spinner that keeps a really high RPM.

One of my bikes has 165 mm cranks and another one has 145 mm cranks.

THERE IS A HUGE DIFFERENCE IN PEDALING DYNAMICS

There is significantly less torque since the moment arm is 20 mm shorter in the 145 mm cranks, but it is infinitely easier to spin since the pedaling circumference is
2 * pi * 145 = 911.06187 mm
and the 165 mm crank pedaling circle is
2 * pi * 165 = 1 036.72558 mm,

1036.7255 mm - 911.06187 mm = 125.66363 mm = 4.94738701 in

Almost a 5 inch difference in pedaling circumference!

In short, spinning is a lot easier for shorter cranks, but climbing is easier for longer cranks.

Anyways, to sort of reply to the original post, Sheldon's calculator doesn't have more tire sizes available for input, but it works well enough!

I hope we didn't confuse you with really technical jargon
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Old 02-16-09, 07:45 AM   #7
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I hope we didn't confuse you with really technical jargon
Just a bit of engineering. Since we are talking about engineering an since you started making your calculations in the metric system, I do not see the point on converting it to the imperial system. After all, the Americans in recognition for the help by the French in their struggle for independence, should at least adopt the metric system!

Oops, it seems that I have hijacked the thread again
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Old 02-16-09, 08:28 AM   #8
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Quote:
Originally Posted by caotropheus View Post
Usually I am a practical fellow not entering philosophical questions, but don't you guys think that is about time to start using gain ratios instead of gear inches. A bicycle moves forward thanks to a set of levers and the crank is the most important lever. A few millimeters change in the crank length changes the final amount of effort a ride makes for the same gear inches. Gain ratio takes into consideration effort and gear development no.
The problem I see with using gain ratios is that, unlike cog/wheel ratios, crank length also has biomechanical ramifications due to differences in bone size:


So although gear inches don't tell the whole story, at least they can be compared among different individuals without taking body measurements.
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Old 02-16-09, 08:58 AM   #9
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Quote:
Originally Posted by kamtsa View Post

Where does the 18.68" constant comes from? Is it part of the specification of the rim and/or tire? 406mm is about 16" so is the extra 2.68" the contribution of the tire to the diameter?

(in my case, I plan to use Schwalbe Marathon Plus 20 x 1.35" (406)).

Thanks,

Kam
Jur has it right, you take the 406 mm diameter of the rim and add twice the diameter of the tire to get the overall diameter. I generally just use the spec diameter of the tire. That's worked pretty well for me. Schwalb has a page on tire dimensions. At the top of their table they have some 406 mm tire examples. Take the 40-406 as an example. I would calculate the diameter as 2*40+406=486 mm. The tire circumference is given in the table as ~1530 mm. That tire circumference corresponds to a diameter of 487 mm. So, for the kind of accuracy that I require (not much) just using the specified tire diameter works pretty well.

To get back to inches divide by 25.4 in/mm

Speedo
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Old 02-16-09, 09:03 AM   #10
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Quote:
Originally Posted by LWaB View Post
Seeing as I can't feel a 2.5 mm difference in crank length, I'm not too interested in gain ratio;
+1

I go back and forth between bikes with 170 mm and 175 mm crank arms. The bikes are different, so I notice a difference between bikes, but I really can't feel anything different in the crank motion.

Quote:
Originally Posted by parcoju View Post
In short, spinning is a lot easier for shorter cranks, but climbing is easier for longer cranks.
Part of every ride I'm spinning and part of every ride I'm climbing! What's a guy to do?

Speedo
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Old 02-16-09, 09:05 AM   #11
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I get 94.5 in?
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Old 02-16-09, 09:11 AM   #12
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Originally Posted by caotropheus View Post
After all, the Americans in recognition for the help by the French in their struggle for independence, should at least adopt the metric system!
Amen to the metric system. But, in the end, it's just a number and, with experience, you get to understand what that number means to you. So, for example, I know that I really don't need a high gear any higher than about 103 inches. I know that with an unloaded bike I can climb the steepest steep hills comfortably with a 22 inch low, and that lower doesn't help. I could express these numbers in mm, m, or furlongs, or I could use development or gain, as long as I understand what they mean to me.

I kind of like the gear inches. Sort of archaic and quirky.

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Old 02-16-09, 10:28 AM   #13
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Originally Posted by caotropheus View Post
Just a bit of engineering. Since we are talking about engineering an since you started making your calculations in the metric system, I do not see the point on converting it to the imperial system. After all, the Americans in recognition for the help by the French in their struggle for independence, should at least adopt the metric system!

Oops, it seems that I have hijacked the thread again
I'm all for metric/SI, but some things in cycling are still in inches: 1" and 1-1/8" steerer diameters, BB shell threads in TPI, ... And I still think in psi for tire pressures rather than bar, atmospheres or kpascal; and chain wear limits in fractions of inches.
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Old 02-17-09, 11:53 PM   #14
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Gain ratios are fine and dandy, but i've been used to thinking in terms of gear inches that I'd rather keep to what I know. Besides, all my cranks are the same length, so it wouldn't matter to me.
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Old 02-18-09, 07:14 AM   #15
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I get 94.5 in?
You, Sir, are a man among boys.
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Old 02-18-09, 08:49 AM   #16
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Originally Posted by Speedo View Post
I go back and forth between bikes with 170 mm and 175 mm crank arms. The bikes are different, so I notice a difference between bikes, but I really can't feel anything different in the crank motion.
I can't tell the difference between 170's and 175's either, because they both fit me the same: too big!

Seriously, you're talking about a 3% difference in crank size. That's almost nothing. Try alternating between 180's, 170's, 155's and 140's for a while; not only will you feel a difference, but you will quickly learn which is the best size for you.
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Old 02-18-09, 05:13 PM   #17
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I rather like the gear inch system; the reason being is that you can get a fair idea of how a bike will perform regardless of the wheel size. I currently have a Dahon MU SL and should be getting my new Brompton in a couple of weeks, but I already know how the gears will compare between the two bikes.
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Old 02-25-09, 04:10 PM   #18
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I can't tell the difference between 170's and 175's either, because they both fit me the same: too big!

Seriously, you're talking about a 3% difference in crank size. That's almost nothing. Try alternating between 180's, 170's, 155's and 140's for a while; not only will you feel a difference, but you will quickly learn which is the best size for you.
I have, somewhere between 167.5 mm and 175 mm works for me. 180 and 177.5 cranks hurt my joints (don't know why) and shorter cranks slow me down. YMMV
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