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So I have some follow up questions from this thread:

Electric engine transmission

Basically, I am looking for a more precise mathematical statement that makes this true. Why is it that the electric motor can provide torque as necessary and the gas engine can't? What can we do to the gas engine to make it behave like an electric engine? I have only taken 2nd year analytical mechanics so keep that in mind.

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Electric motors can simply bring more electric energy, increase the electromagnetic fields, and produce a proportionally higher amount of work (or greater torque). Combustion motors may also have a greater output (or torque) but they must be larger motors. A combustion motor of a given size simply can't exceed a certain frequency in revolutions per minute because it would get overheated etc., and at this frequency, it can only suck, contain, and burn a certain amount of fuel. So the power of combustion motors is limited - XY horse powers; for electric motors, no real limit exists. –  Luboš Motl Apr 8 '11 at 20:33
    
""Why is it that the electric motor can provide torque as necessary and the gas engine can't? What can we do to the gas engine to make it behave like an electric engine?"" This is not true as stated. "the electric motor" is nonsense. There are dozens of very different electric motor types, differing a lot in torque. And: speaking that absolutely about torque without relation to rpm, is nonsense. –  Georg Apr 8 '11 at 22:06
    
@Georg: I think this is about "torque curves" the relationship between power, torque and revs for a gasoline engine is complicated, and occupies a lot of engineer time in the car world. The situation with electric motors is rather simpler. –  dmckee Apr 9 '11 at 1:43
    
@dmckee, right, the torque/revs relations (curves) are easier to understand, but nevertheless those are very different for different types of electric motors. In general, the question is not clear: ""..that makes this true."" Do You understand what is to be made true? –  Georg Apr 9 '11 at 10:54
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2 Answers

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Consider a simple DC motor with brushes and a permanent magnet stator.

If you simply turn it, it generates electricity, but when it's not turning, it doesn't.

If you apply power to it, like you connect a battery, the current in the armature creates a magnetic field that interacts with the stator's field, creating torque. If the motor is frozen so it cannot turn, that torque can be quite strong.

If the motor is allowed to turn, remember that it functions as a generator, pushing current back in the opposite direction to the battery's flow, so less current is flowing. If it turns fast enough, no current will flow, but it won't get up to that speed by itself. If somebody makes it turn even faster (i.e. negative torque), it can even charge the battery!

So that kind of motor gets maximum torque when it is stopped, and the torque falls off as it speeds up.

An internal combustion engine, on the other hand, only generates torque when the piston is on the power stroke, because it is being pushed by the expanding combustion gas. It can't get that combustion unless it also exhausts the old gas, brings in new air and fuel, and compresses it. If it's not turning, it can't really do those things.

It is possible for an internal combustion engine to accidentally start from a complete stop, if the piston happens to be in just the right part of its cycle and ignition happens to occur. This is a serious hazard in airplanes with that kind of engine, if the magneto happens to not be turned off, and somebody jiggles the propeller.

Some kinds of internal combustion engines generate more torque at low rpm than others. You can learn more about that elsewhere.

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You won't get the answer you're looking for here I'm afraid. This is because the limiting factors are unrelated. Ignoring any gearboxes etc the maximum torque of an electric motor is limited by the magnetic field it can create, in practical terms this means it's limited by the maximum current the windings will take before overheating.

A petrol/diesel engine is a relatively crude device, the maximum torque before stalling is related to the maximum force you can exert on each piston, this in turn is limited by the compression and the fuel/air ratio. For a given engine you can only drive the compression so high before the engine becomes un-runnable. High torque engines are principally made using the "bigger hammer" idea. ie. make a bigger one. More cylinders/more volume of gas at a given compression/ etc.

Hope that helps.

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