# Gearing

#### Scott.D.Lang

##### Member
Im trying to figure out how to figure out gearing if you have 6 gears from crank to wheels. Also need to know what raito Id need for 24" wheels to run the same type of speeds as 26" wheel.

Ahead of time I want to thank who ever can help me.

Scott

#### TheNecromancer13

##### Member

I assume that by having 6 gears you mean 3 stage gear reduction. To calculate gear reduction, take the first gear from each stage of the gear reduction (drive gears, usually smaller), and multiply all the tooth counts. For example, let's say you have a first stage with a 11t driving a 24t, a second stage with a 10t driving a 30t, and a third stage with a 12t driving a 20t (I just made up these tooth counts on the spot, I have no idea if they would actually make a good ratio). So you'd do 11 x 10 x 12 = 1,320. Now, you take the second gear from each stage (driven gears, usually larger unless over driving) and multiply their tooth counts. So you'd do 24 x 30 x 20 = 14,400. That gives you a ratio of 1,320:14,400. Those numbers are a bit big, so then you reduce it by dividing 14,400 by 1,320. So 14,400 / 1,320 = 10.91. So you'd have a gear ratio of 10.91:1. The formula is (a1 x a2 x a3) / (b1 x b2 x b3). If the drive and driven gears in any particular stage are the same size, you can leave that stage out of the equation, because their ratio would be 1:1 and doesn't change anything.

On to your second question: To figure out how much faster you need to turn a 24" wheel to go the same speed as a 26" wheel, you just need to find the circumference of each wheel. So, 26 x 3.14 = 81.64, and 24 x 3.14 = 75.36. Now you need to figure out how many times 75.36 fits into 81.64. So 81.64 / 75.36 = 1.08. So you will need the wheel to spin 1.08 times faster to achieve the same speed. To figure out what ratio you need when compared to 26" wheels, divide the ratio you used on the 26" bike by 10.91. I'll use my most recent predator bike as an example this time. It has a gear ratio of 13.1:1. So 13.1 / 1.08 = 12.13. So if I were to build a bike with 24" wheels to go the same speed as my predator bike, I would need an overall ratio of 12.13.

You can also calculate theoretical top speeds if you know the wheel circumference, gear ratio, and maximum engine rpm by dividing the engine rpm by the gear ratio, multiplying by the wheel circumference, multiplying by 60, dividing by 12, and dividing by 5280. That will give you the top speed in mph. So if I had an engine that can turn 7000 rpm on a bike with 24" wheels, and a 15:1 ratio, I'd do 7000 / 15 = 466.67, then do 466.67 x 75.36" = 35,168.25. Then I'd do 35,168.25 x 60 = 2,110,096. Then divide by 12 to convert inches to feet: 2,110,096 / 12 = 175,841.26. And finally divide by 5280 to convert feet to miles: 175,841.26 / 5280 = 33.3 mph.

Hope this helps!

#### MotorBicycleRacing

##### Well-Known Member
No need to calculate anything! http://jimsitton.net/ratiocalc/

Just right click on the file gearratio.exe and select "save link as" and put it somewhere you can find it again. Once it's saved, double click on the gearratio.exe file and it will run.

The program allows for up to three ratios in series. If you have fewer just leave the unused ratios set to 1:1.

The program will also calculate speed based on
engine RPM,
drive ratio,and
wheel diameter.

Be sure to measure the outside diameter of your wheel for accurate results.

#### TheNecromancer13

##### Member
I wish this program would work on my new bike, but the engine has built in 2 stage gear reduction, and then I have 2 more stages outside of the engine cause I was too cheap (read: way over budget) to buy a bunch of sprockets and used what I had on hand. Also being able to put in numbers into a program is one thing, but understanding why it works is another.

#### MotorBicycleRacing

##### Well-Known Member
I wish this program would work on my new bike, but the engine has built in 2 stage gear reduction, and then I have 2 more stages outside of the engine
If you have more than 3 ratios combine some of them into one of the ratio boxes.

Also being able to put in numbers into a program is one thing, but understanding why it works is another.
Knowing the math behind the calculator is not necessary to figure
out what gearing your bike needs.

#### TheNecromancer13

##### Member
If you have more than 3 ratios combine some of them into one of the ratio boxes.

Knowing the math behind the calculator is not necessary to figure
out what gearing your bike needs.
Yes, but knowing the math is a plus.