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If rocket engines can reach 70% efficiency, why don't we use them in cars?

Internal combustion engines get less and less efficient with higher speed just due to the kinetic energy equation (a unit of fuel produces a unit of velocity^2), while rocket engines have a constant efficiency (a unit of fuel produces a unit of velocity), ignoring fuel consumption.

This is a fundamental constaint, since an internal combustion engine necessarily pushes against the moving earth to propel the car, and a rocket engine effectively pushes against a gas that is stationary wrt the rocket.

So why not use a rocket engine in a car? Wouldn't it be more fuel-efficent?

reference for 70% figure: https://en.wikipedia.org/wiki/Propulsive_efficiency

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  • $\begingroup$ Perhaps because we aren't going for speed in a car? And rockets are unsafe? But it does seem like if all you were going for was ground speed a rocket would be fundamentally more suitable. $\endgroup$
    – Matt
    Aug 19, 2021 at 16:34
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    $\begingroup$ Scorching pedestrians would also be a negative. $\endgroup$
    – James
    Aug 19, 2021 at 16:44
  • $\begingroup$ @James cars already have exhaust, and rocket nozzles already cool gas by expansion $\endgroup$
    – Matt
    Aug 19, 2021 at 16:50
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    $\begingroup$ @Matt: You are totally correct. But I have been dieting on mechanical engineering for 30+ years, so my ass output isn't too shabby. :) $\endgroup$
    – James
    Aug 19, 2021 at 16:59
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    $\begingroup$ @Matt: I'm not trying to exasperate you, so sorry if it came across that way. Your question asked why we don't use rocket engines in cars, so I thought you wanted a list of reasons why a rocket engine is not appropriate. I provided one of those reasons... dangerous exhaust. $\endgroup$
    – James
    Aug 19, 2021 at 17:08

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I think you've misread the article. It says rocket engines can attain up to 70% $\eta_c$, which is only the cycle efficiency (how well it turns the energy of the fuel into mechanical energy). This is not the propulsive efficiency.

Unfortunately, for a rocket much of this mechanical energy is used to (wasted..) increase the KE of the exhaust rather than the rocket. As the article mentions, optimum efficiency is when the exhaust speed and rocket speed are matched. But this ends up being horrible for fuel consumption.

Being able to throw the mass of the earth or the atmosphere around makes regular propulsion much more efficient.

In one of your comments you linked to the question Velocity and kinetic energy, violating galilean relativity and said that the efficiency of a car drops with speed. I wouldn't agree with that statement. The question was specifically about interpreting energy in different frames.

If we stick to to just the frame where the ground is at rest (a very valid frame for travel on the earth), then the theoretical efficiency of your battery car approaches 1 as you eliminate drag. The energy of the battery can be given into KE of the vehicle almost entirely since the earth is so massive.

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  • $\begingroup$ Oh, thank you, this makes much more sense. So, the propulsive efficiency is substantially less than 1%? $\endgroup$
    – Matt
    Aug 19, 2021 at 17:06
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    $\begingroup$ The propulsive efficiency depends on the speed of the rocket and the speed of the exhaust. For a rocket moving at high speed, the efficiency may be very high. But for a rocket starting from rest, the efficiency is near zero. $\endgroup$
    – BowlOfRed
    Aug 19, 2021 at 17:08
  • $\begingroup$ Ah OK! Yep, this makes sense. I was confused by the statement about rockets: <a unit of fuel adds a unit of velocity, ignoring the rocket equation>. $\endgroup$
    – Matt
    Aug 19, 2021 at 17:09
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    $\begingroup$ That's correct. It's a constant relationship, but that doesn't mean (especially at low speeds) that it's an efficient relationship. One unit of velocity at a low speed would take a little bit of energy for a car. But it takes a huge amount of energy for the rocket. $\endgroup$
    – BowlOfRed
    Aug 19, 2021 at 17:13
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    $\begingroup$ Assuming it doesn't run out of fuel, yes. A rocket (at high speed) can exceed 100% efficiency. It does this by slowing down the fuel rather than speeding it up. But you have to have high-speed fuel to accomplish this (and you spent energy earlier to make that happen). $\endgroup$
    – BowlOfRed
    Aug 19, 2021 at 18:04

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