How to Calculate Speed Ratio

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A gear consists of toothed wheels attached to shafts. It creates a mechanical advantage in a range of applications, for example a cyclist uses gears to intensify the power output of his pushing on the pedals. Gears have many properties, one of which is the speed ratio, often known as gear ratio. This is the ratio of the turning speed of the input gear to that of the output gear, in other words, how many time the input gear has to revolve to make the output gear revolve once.

TL;DR (Too Long; Didn't Read)

A gear is made up of toothed wheels ("teeth") connected to shafts. To calculate speed ratio, otherwise known as gear ratio, you divide the number of teeth of the input gear by the number of teeth of the output gear.

Speed Ratio Definition

A gear train consists of more than one gear connected to each other, and their teeth interlock. When a machine has two gears of different sizes, the smaller gear turns faster than the larger gear. When the first gear (the driver or input gear) turns, the second gear (the driven or ouput gear) turns in response. The difference between the speeds of the two gears is called the speed ratio or gear ratio.

Speed Ratio Calculation

The ratio is determined by the number of teeth on each gear wheel. Calculate the speed ratio of two gears by dividing the angular velocity of the output gear (represented numerically by the number of teeth) by the angular velocity of the input gear (represented numerically by the number of teeth).

Speed Ratio Example

Say you have an input gear with 10 teeth and an output gear with 20 teeth. You find the speed ratio by working out:

\frac{20}{10}=2

This pair of gears has a speed ratio of 2, or 2/1. In other words, the input gear revolves twice to make the output gear revolve once.

Calculating Speed Output

If you know the speed ratio and the speed input, you can calculate the speed output using the formula output speed = input speed ÷ speed ratio. For example, if you have a speed ratio of 3, and the input gear revolves at 180 rpm, work out :

\frac{180}{3}=60

The output speed is 60 rpm. You can reverse this formula to work out speed input if you know the speed output and the speed ratio. For example, if you have a speed ratio of 4, and the output gear revolves at 40 rpm, work out:

40\times 4 = 160

The input speed is 160 rpm.

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