# Thread: Crunching numbers for fun...

1. ## Crunching numbers for fun...

So I'm sitting around fairly bored today, and got to thinking about all the different kinds of numbers SSers routinely talk about. Gear inches, ratios, tooth counts. We are all really quite mathematically inclined, or suffering from a kind of mass obsession.

In either case, I like numbers as much as any other (maybe more) and cooked up this take on ratios. Nothing new here, but seeing it line up this way so neatly was fairly interesting.

For 26x2.00 with 175mm cranks:

175mm * 2 = 350mm (13.78") crank diameter

2pi175 = 1099mm (43.26") crank circumference

Development for 1 complete turn of the cranks 1099mm (43.26") at a ratio of:

1.0:1 = 2.2m (87")
1.5:1 = 3.2m (126")
2.0:1 = 4.2m (166")

So, a gear that let 1" of crank movement = 2" of development would be a 1:1 ratio.

A 22/22 gear (1:1) would yield about 2 inches of development for each 1" of pedal movement. Development/Crank ratio = 2:1

A 30/20 gear (1.5:1) would yield about 3 inches of development for each 1" of pedal movement. Development/Crank ratio = 3:1

A 32/16 gear (2:1) would yield about 4 inches of development for each 1" of pedal movement. Development/Crank ratio = 4:1

And so forth. The fact that a vast majority of single speed mountain bikes are geared in ratios that fall between 1.5:1 and 2:1 is mathematically interesting, as the maximum and minimum represent a range of only 1" of development per inch of pedal travel. This works out to a maximum delta of about 40" of total development. This really underscores the sensitivity and narrow power range involved in the biomechanics of human powered machinery.

Anyhow... that's how sad it gets sitting around in my office. Only another 2 hours before they let me out to ride.

2. now calculate what it would be with 165 mm cranks

3. Nah... I'll let someone else have the dubious honor of deriving all the different crank lengths, or writing a little java code to do it.

The interesting bit was that 175s on 26" wheels quietly became sort of an industry standard. Whether this is because of the economics of manufacturing or because the underlying mathematics just somehow made it 'work' is up for debate.

Granted, I did a little rounding, but not in an unequitable way. For the machine to have evolved such that the gear ratio we all know and love has a 2:1 relationship to development is just neat.

4. Been done already, why reinvent the wheel (gear calculator)?

5. Originally Posted by slocaus
Been done already, why reinvent the wheel (gear calculator)?
Beat me to it...

6. Originally Posted by slocaus
Been done already, why reinvent the wheel (gear calculator)?
thanks very much

7. Originally Posted by pinkrobe
Beat me to it...

next step:
http://eehouse.org/fixin/fixmeup.php

8. Hmmmm.... Since when is a 40t x 20t gear any different than a 32t x 16t? One weighs less, the other might last longer... Did you mean 30t x 20t?

9. Nothing ever changes... everyone wants to talk about gear inches and chainstay lengths... the practical stuff. Next thing you know, everyone on the forum will be posting their ratios.

Sorry, I was simply observing a relationship that exists between the movement of the cranks, gearing, and development when these variables are within the 'naturally arrived at' or at least fairly common values. It demonstrates a certain principle defying the random distribution of statistical variables... ie, that there is an underlying phenomena which results in the set being distributed as it is.

FWIW, I don't see how a gear calculator, no matter how good, or even hosted by a cycling icon (Sheldon, RIP), can make this point.

That is all.

10. Originally Posted by ATBScott
Hmmmm.... Since when is a 40t x 20t gear any different than a 32t x 16t? One weighs less, the other might last longer... Did you mean 30t x 20t?
oops... I did indeed. Fixed.

11. Originally Posted by sunset1123
Sorry, I was simply observing a relationship that exists between the movement of the cranks, gearing, and development when these variables are within the 'naturally arrived at' or at least fairly common values. It demonstrates a certain principle defying the random distribution of statistical variables... ie, that there is an underlying phenomena which results in the set being distributed as it is.
My bad, I did not think as I read to see the real point you were making. I just thought you were bored and wanted to look at gearing development and crank length. You did make a real interesting observation - probably a result of the fact that we are only able to produce about a quarter horsepower, at best, for very short periods. Thanks for the post, even if we were too thick to get it the first time.

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