# Bicycle Mechanics - math question about gear ratio's

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View Full Version : math question about gear ratio's

MikeOK
01-14-03, 07:09 PM
Maybe some of you smart fellars out there can help me. I want to be able to calculate changes in gear ratios and wheel size. Maybe we can start like this (I am open to other suggestions too):

d= forward distance traveled with one revolution of the BB

w= tire size

f= front chainring

r= rear gear

I will be building a SS bike with 24" wheels, but I want to be able to select my rings by comparing them to my mtn bike, and I already know all the above variables for that bike. This way I will know how a certain combo will feel before buying the hardware.

TIA

Michel Gagnon
01-14-03, 07:19 PM
I suggest you visit http://www.sheldonbrown.com/gears

For "Gear Units" select either "Gear Inches" (U.S. notation) or "Meters Development" (European Notation). With either choice, Crank length isn't important

Regards,

Grendel
01-14-03, 07:20 PM
You can try the attached spreadsheet I put together to figure pedal cadence for given values of gears, wheel size and speed. This might help ya...

MikeOK
01-14-03, 08:42 PM
Thanks. I don't know why i didn't think of using excel, I think I can mod your file grendell, then use mgagnonlv's link to make sure I did it right...

Grendel
01-14-03, 09:07 PM
It took me a while to remember where I got all the numbers from -- I should comment my work better. Anyway, the part that might be a little confusing is the hidden column 'E'; the value in E4 is the number of rotations of the wheel at 1 mile per hour in one minute, since I was solving for RPM values (cadence, remember?). Basically what you are wanting to do is calculate wheel circumference (diameter * PI) then figure out how many times the wheel will turn for each rotation of the crank ((chainring tooth count) / (cassette sprocket tooth count)) and the rest kind of goes from there. I was trying to solve a different problem, kinda, but the math is pretty much the same.

MikeOK
01-14-03, 09:15 PM
Ahaa- column E, that's where you hid that. My brain is tired so I copied it onto my laptop, will look at it more tomorrow.

D*Alex
01-15-03, 08:15 AM
OK, let me nit-pick a bit here......

Firstly, using 26" as a true diameter for a 26" wheel is usually not true. As an example, take a "26 inch" MTB wheel, one with 1.95" tyres. In that case, the rim diameter is 559mm, and the profile height is 47mm, according to the ERTRO number on the sidewall. Using the usual method of estimating true diameter {rim diam + 2*profile**, you get 559mm+(2*47)=653mm. Dividing that by the conversion of 25.4 mm/inch, you get a diameter of 25.74", a 1.2% error. I have made a small change to your spreadsheet to reflect this.

Bandit
01-15-03, 11:21 AM
here's my highly sophisticated formula:

is it hard to pedal? choose and easier gear.

are you spinning too fast? choose a harder gear.

repeat.

John E
01-15-03, 09:09 PM
Originally posted by mgagnonlv
I suggest you visit http://www.sheldonbrown.com/gears

For "Gear Units" select either "Gear Inches" (U.S. notation) or "Meters Development" (European Notation). With either choice, Crank length isn't important

1) Yes, the U.S. and metric notations differ not only by unit conversions (2.54000 cm / inch, etc.), but also by the factor of pi built into the metric units, which do actually tell you how far you travel per pedal revolution. In contrast, the U.S. system tells you how your gearing compares to that of a fixed-gear penny-farthing bicycle with a drive wheel of a given diameter.

2) Although crank length has nothing to do with gear ratio and distance per pedal revolution, it directly affects how much force you must apply on the pedals, and how far your feet move per pedal revolution. This is why Sheldon likes the concept of "gain ratio," which incorporates crank length, wheel diameter, and gear tooth ratio.

50mileman
01-16-03, 01:41 PM
Mike - What is the intended purpose of this bike ? - 24" wheels -
probably MTB, offroad or on ?
If its a single speed, then you want to go 2:1 ratio for offroad, say a 34 front and 17 rear - depending if your a strong rider or not and the trails you will be riding - hilly or flat.