Calculating the torque required for a particular application can be done in a number of ways. If you are driving a pump or similar piece of equipment it may be as simple as contacting the manufacturer or consulting the datasheet to see what they recommend for that particular application.
Let’s imagine you are building a new motor assisted bike and know key information such as the required bike speed, the mass that needs to be moved and the diameter of the wheel that is going to be turning you can then calculate the motor torque from this.
For simplicity lets assume the speed required from the bike is 20km/h, the total mass of bike and rider will be 100kg and the wheel diameter is 600mm. Removing factors such as wind resistance, rolling resistance (friction from the road or bike lane) and inefficiencies of bearings etc. we can then begin to calculate what is required.
With a direct drive system the total wheel diameter can be calculated simply using ∏r
Therefore total wheel diameter is ∏x300mm =942mm
In order to then calculate the required revolutions per minute (rpm) we can need in an hour we can therefore start by dividing the distance required in that time by 60 (60 minutes in an hour) to get the distance required in a minute.
20000/60 = 333.3m a minute or 5.6m/s
We can then take this distance of 333.3m in a minute and divide it by the distance covered by one rotation of the wheel.
333.3/0.942 = 353.8 rpm
Assuming we need to accelerate up to top speed (20km/h) in 10 seconds, we can therefore calculate the acceleration required in metres per second as:
Where V=final required speed (m/second), U=starting speed (in this case 0), A =acceleration and T=time. As we are starting from 0rpm we can remove U from the equation. To calculate acceleration we can therefore rearrange this formula as;
We then need to calculate the force required, for which the equation is Force =Mass x Acceleration (F=MA). As the force required is in newtons we need to convert the weight we have (100kg) to mass. To do this we times the weight we have by the Earth’s gravitational constant of 9.81m/s2. Therefore:
We can now calculate the force required:
In order to turn this into torque we must therefore multiply by the distance to the pivot:
549.4 x 0.3m
With a direct drive motor in place the torque calculation would therefore be the distance from the pivot (0.3m)x