Gear ratio is the speed of a gear multiplied by the number of cogs, or teeth, in that gear as compared to the speed and number of cogs of a second gear driven by the first one. It does not matter how many gears are in between the drive gear and the last one. Gear ratio can also be expressed using the number of cogs of each of these gears in relation to one another.
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Things you need
- Intermeshed gears
Determine the speed in rounds per minute (rpm) of the gear that drives the assembly, or gear 1. For the purposes of this calculation, you can designate the rpm as S1. As an example, let us say that gear 1 has a speed of 100rpm. Therefore, S1=100. Also, count the number of cogs in this gear as well. Designate that number as C1 for the purposes of the equation. As an example, it has 30 cogs. Therefore, C1=30.
Determine the speed in rpm of the last gear on the train driven by the driver gear, or gear 2. Designate this speed as S2. For our example, say that gear 2 rotates at 75rpm. Therefore, S2=75. Now, count the cogs on this last gear and designate that number as C2. For the example, say it has 40 cogs. So C2=40.
Use the algebraic gear ratio equation to determine the gear ratio. The equation is S1 x C1 = S2 x C2. Substituting our example numbers in the equation we have 100 x 30 = 74 x 40. Multiplying this, we see that each side of the equation is equal to 3000.
Use the equation for determining unknown quantities. For example, you do not know the rpm of gear 2, but you do know it has 60 cogs. Substitute the known values into the equation and solve for S2. Therefore, 100 x 30 = S2 x 60, and S2 is equal to 50rpm.
Express the gear ratio another way using the number of cogs in each gear relevant to the ratio. Therefore, in the first example, C1=30 and C2=40. Write it mathematically as C1/C2. Therefore, 30/40=3/4, and the gear ratio is 3 to 4. In our second example, the gear ratio can be written as 30/60, which is equal to ½. The gear ratio is 1 to 2.
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