How to Figure Sprocket Speeds

Calculating sprocket speed for a bicycle or any other sprocket-dependent vehicle depends on the angular speed and the linear speed of the associated wheel. The angular speed is the rate the wheel turns measured in revolutions per second, or radians per second. The linear speed is often referred to as normal speed; it is measured in meters per second or miles per hour. Since the sprocket is attached to a wheel, its linear speed is the angular speed of the wheel multiplied by the radius of the sprocket.

Things You'll Need

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Instructions

    • 1

      Determine the linear speed of your bicycle or the sprocket-dependent vehicle in question. This is the speed for which you wish to determine the sprocket speed. For example, if you travel 50 meters in 5 seconds, your linear speed is 10 meters per second: 50/5 = 10.

    • 2

      Use the linear speed of the vehicle to determine the angular speed of the wheel associated with the sprocket. You do this by dividing the linear speed of the vehicle by the radius of the wheel (vehicle linear speed/radius of wheel = angular speed). For example, if the radius of the wheel is 0.20 meters, using the linear speed example above, the angular speed of the wheel is 50 radians per second: 10/0.20 = 50.

    • 3

      Determine the linear speed of the sprocket. The angular speed of the sprocket is the same as the angular speed of the wheel. You can determine the linear speed of the sprocket by multiplying the angular speed of the wheel by the radius of the sprocket (angular speed x radius of sprocket = linear speed). As an example, assume the radius of the sprocket is 0.05 m. Using the linear speed from the example above, the linear speed of the sprocket is 2.5 meters per second: 50 x 0.05 = 2.5.