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I have started to research about electrical motors and batteries.

I have learned physics in high school and I understand electricity. My question is whether an engine's power depends on its RPM or not. Let's say the specification says its 1V at 1 Amp, does it give me 1 watt at any operating RPM or a constant force, which gives 1 watt at maximal RPM? Maybe the resistance depends on RPM?

Because if it gives a constant force, the power is P=VF and I need gears if I want dynamic acceleration (like in cars, the acceleration starts high and is reduced with speed), and if the power is constant then the force starts high and is reduced, giving me optimal acceleration and force at any time. I think that its constant power, because electrical cars are single-speed (only one gear ratio). (contrary to internal combustion engines which its power varies by the RPM).

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There's a good solid guide to motor power curves here: http://lancet.mit.edu/motors/motors3.html

Basically there are two ends of a quadratic curve at which power is zero. At zero RPM, the motor is stalled and exerts maximum torque force (and will draw a large current, the "stall current" listed in the datasheet). It doesn't actually deliver any power to the load because it's not moving, therefore no work is done.

At the other end, there is no load on the motor and it spins freely at its maximum RPM. It doesn't deliver any power either, as there is no load.

There is a maximum power delivered at half of the no load speed, in the middle of the torque curve.

As you say, the ability to deliver high torque at zero and near-zero speed is extremely useful, and is why motors have been used for power conversion in diesel-electric trains for 50 years.

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  • \$\begingroup\$ From the graphs which I assume are true I understand that I will have relatively high torque at lower speeds, which will only decrease but "slow enough" so the power still goes up until it reaches the maximum. So, if I calibrate the gear correctly in a car or bicycle, I'd get enough force without having to make more than one ratio. Thanks! \$\endgroup\$
    – Mark Segal
    Commented Aug 5, 2013 at 10:32
  • \$\begingroup\$ Yes, absolutely. Putting the motor in the wheelhub directly coupled to the wheel is a popular option, possibly with planetary gears; but gears = maintenance, which it's good to eliminate. \$\endgroup\$
    – pjc50
    Commented Aug 5, 2013 at 10:41
  • \$\begingroup\$ Worth pointing out that at low speed, max torque, max current; and even at the peak power point (max rpm/2, stall current/2, efficiency = 50%) the motor won't last very long! It is dissipating a lot of your precious input power as heat... Some motors are designed to take such abuse in the short term (and some aren't!) but a more normal operating condition is 80-90% of no-load speed, 10-20% of stall current, and hopefully 80+% efficiency (less for small motors). Design for this region if you can. \$\endgroup\$
    – user16324
    Commented Aug 5, 2013 at 12:02
  • \$\begingroup\$ Ah - is there a better design guide for this? I hadn't realised efficiency was 50% at the maximum power point. \$\endgroup\$
    – pjc50
    Commented Aug 5, 2013 at 13:49
  • \$\begingroup\$ @BrianDrummond Really? An electrical motor isn't almost-100 efficient at every RPM? because this really screws up my plan of a super-bicycle... \$\endgroup\$
    – Mark Segal
    Commented Aug 5, 2013 at 15:43
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My question is whether an engine's power depends on its RPM or not

Input power = mechanical output power + losses

Mechanical output power = \$2\Pi N T\$

In other words output power is related to output RPM (N = revs per second) and output torque (T)

Ignoring the losses (which are usually less than 20%, think of motor output speed equating to the input voltage and output torque (load dependent) affecting current into the motor.

Just like V and I produce power so does N and T.

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  • \$\begingroup\$ I am obviously aware that P ~ VI ~ VF (where the second V means velocity, or RPMs). I am asking whether the torque is higher if the RPMs are lower, thus creating the same power, because its not true in gasoline engines, where the power depends heavily on the RPM (torque start low, reaches maximum and then slowly decreases over RPMs). \$\endgroup\$
    – Mark Segal
    Commented Aug 5, 2013 at 10:27

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