Power/torque ratio vs acceleration

Let there an object with determined mass which needs to be moved with a motor (lets say electrical). We have two available motors, which have exactly the same power (and other characteristics), but different torque / rated speed. Which motor will accelerate the object faster, motor with high torque, but low rated speed, or motor with low torque, but high rated speed? There is no transmission.

Depends on the transmission and rotating masses. With ideal transmissions and identical rotating masses, both will achieve the exact same acceleration of the "object". If there's no transmission, then the question is what the power output of the motors look like as a function of speed.

• There is no transmission. – jurij Dec 24 '16 at 22:01
• See updated answer. The answer is still "it depends". – Pirx Dec 24 '16 at 22:04
• Lets assume both motors have completely flat torque curve ... all torque is available from 0 rpm to rated speed. – jurij Dec 24 '16 at 22:06
• You need to distinguish between rated power and actual power output. If you have constant torque, you will have zero power at the start, linearly increasing with speed. It also means that the higher-torque motor will output more power at any instant than the lower-torque motor. Your question then trivially becomes: If I have two motors, one putting out more power than the other, which one will accelerate a vehicle faster? Well, duh... – Pirx Dec 24 '16 at 22:10
• I see, but given a period long enough, both motors will move with the same speed, due to identical power, correct? – jurij Dec 24 '16 at 22:14

In theory since: $$a = {P \over mv}$$ with: $$a = acceleration$$ $$P = power$$ $$m = mass$$ $$v = velocity$$ then only power matters and both motors would be equal.

In practice it also depends on how you apply the motors torque to the object, or practically how your transmission works. With an ideal CVT transmission you could keep the engines at peak power and the above equations would apply.

Lets assume both motors have completely flat torque curve ... all torque is available from 0 rpm to rated speed.

Ok, let's also assume a 1:1 transmission to a wheel pushing the object.

In this case, since:

$$power = torque * rpm$$

and both engine have same power then the engine with higher torque will have a lower final rated speed (rpm)

In this condition the higher torque motor will accelerate the object faster, but only up to the maximum rpm which will be lower than the faster motor with less torque.

The motor with high torque, because it holds for the torque $M = I a$ with angular acceleration $a$ and moment of inertia $I$.

• Thanks!. Does that also mean, that motor with high torque will reach its rated speed faster? – jurij Dec 24 '16 at 22:00