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I'm trying to understand power and torque relationship in terms of cars.

Let's assume we have a four tracks with a load that needs a total of 1000N to move.

  1. First one has 1000 Nm and 1000W

  2. Second one has 1000 Nm and 2000W -> (Q1) Is my understanding correct, that no.2 will move the load on the same distance 2x faster than no.1?

  3. Third one has whooping 5000W but only 500Nm -> (Q2) Is my understanding correct, that it won't even move?

  4. Fourth one has 2000 Nm and 1000W -> (Q3) Will it move the load in same time as no.1 or no.2? If no.1, will it cost less fuel (energy)?

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  • $\begingroup$ Why does the load "need a total of 1000N to move"? To overcome static friction? If the load is connected to wheels and friction can be ignored - which it otherwise kind of is in this question - then any amount of torque will move the load, and small amounts will move it more slowly. $\endgroup$
    – AXensen
    Commented Mar 22, 2023 at 11:31
  • $\begingroup$ Typically we think of a cars' torque and horsepower as being the maximum torque and the maximum power the engine can output, and they're relevant in different situations. At low RPM, with the gas all the way down, the power of the engine is much lower than the reported "horsepower." In the highest gear on the highway, the torque is much lower than the reported torque. $\endgroup$
    – AXensen
    Commented Mar 22, 2023 at 11:35
  • $\begingroup$ @AndrewChristensen Yes, I was assuming friction, or any other opposing force $\endgroup$
    – Cansisti
    Commented Mar 22, 2023 at 11:45
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    $\begingroup$ Torque is not a useful quantity for the car, but for the engine only. Power on the other hand equally applies to the whole car as its invariant along the driveline. $\endgroup$ Commented Mar 22, 2023 at 12:18
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    $\begingroup$ I have a sneaking suspicion this question originates from a science teacher who is encouraging an incomplete understanding of what power and torque actually are. This question is kind of unanswerable without more information about what exact situation is being described. $\endgroup$
    – AXensen
    Commented Mar 22, 2023 at 12:31

1 Answer 1

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Power and torque transmitted on a shaft or to a wheel are not unrelated variables:

$\frac{P}{T}=f$

Here $f$ is the revolution frequency. Power, torque and frequency are expressed in W, Nm and Hz respectively. You can change from rpm to Hz dividing by 60.

Basically your examples are operating at different velocities, hence the confusion.

Note that there are mechanisms that allows changing the power/torque ratio, acting on the revolution frequency, the simplest being a gear.

In general, if we are in a case where the resisting force is independent of the velocity (such as going uphill or pulling a sled) some torque is required to overcome the force (and no more if the velocity is constant), then the power defines how fast you are going. If you adjust your gearing so that the torque at the wheel is just right, then the velocity will be maximized according to the power available. If instead the force depends on the velocity (such as air friction), then to sustain higher speeds you will not only need more power, but also more torque. In situations where acceleration is involved, part of the torque is spent for that as well.

The torque at the engine is of little use in the initial characterization of the dynamic of a vehicle. Instead (neglecting losses) power is much more relevant, being invariant from the engine to the wheels.

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  • $\begingroup$ This clarifies some things, I wasn't thinking about gearing at all. Would it all be relevant, if we assume that there is no gearbox, and the trucks are stuck with only one ratio? $\endgroup$
    – Cansisti
    Commented Mar 22, 2023 at 13:30

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