The first rule when it comes down to gearing (as i've put on almost every page to do with motors and speed) is to ensure you gear for track speed. You do not want to gear the loco higher than necessary as the motors will run hot and will drop significantly in speed.

If you are going up a hill or pulling a large load and your car starts to sruggle we go down a gear and increase the revs, this is exactly the same principle we need to apply to a motor, the higher the revs the better. Yes pulling a good load will cause the motor to slow down but it will be constantly dropping into higher and higher torque speeds resulting in a point where equilibrium is found and the motor is giving what it needs to keep the speed up, it also means when the motor is not having to pull hard it is back up to full speed doing very little work therefore dropping the current required.

As a good (normally very accurate) rule of thumb a motor with a no load speed of 3000RPM with an 8t sprocket on it geared to as big a sprocket on the axle as possible results in a speed (MPH) of the metric pitch of the chain used. For example using 8mm chain results in 8MPH, using 3/8" (10mm near enough) results in 10MPH and using 1/2" (12.7mm) results in 12.7MPH.
Unfortunately i've not found a good relationship to use with gears due to the large gap in the number of teeth available on the axle mounted gears.

Now onto the mathematics for working it out.

MPH = speed wanted
KPH = speed wanted
D= diameter of tread on wheel

    MPH x 1056  
3.142 x D(inches)       = Axle RPM

KPH x 16,667
3.142 x D(mm)           = Axle RPM

To convert MPH to KPH simply multiply MPH by 0.621
To convert KPH to MPH simply multiply KPH by 1.61

Now we need to work out the ratio.

Motor no load speed
      axle rpm              = ratio

Divide the sprocket/gear you wish to mount to the axle by the ratio to get the sprocket/gear size you need on the motor.

Occasionally you will need a double reduction, we recommend where possible to go for about 1.5 or 2:1 from the motor to a layshaft.

Please note that where possible you should avoid choosing sprockets with a common factor such as 2:1 or 3:1, this results in what we call hunting tooth where the same teeth end up wearing on the same section of chain resulting in a surface that gets more wear than others. Just moving up or down by 1 tooth size can drastically change the amount of wear.

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