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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

Qmechanic
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Matt
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  • 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. – Matt Aug 19 '21 at 16:34
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    Scorching pedestrians would also be a negative. – James Aug 19 '21 at 16:44
  • @James cars already have exhaust, and rocket nozzles already cool gas by expansion – Matt Aug 19 '21 at 16:50
  • I imagine the biggest issue besides safety is the cost, it would make buying cars only something for those with massive amounts of disposable income. – Triatticus Aug 19 '21 at 16:51
  • @Triatticus I'm asking -- why don't we use an engine with an open piston, rather than an engine with a closed piston that pushes against the ground. Do you guys actually understand that the efficiency of a car drops with speed? https://physics.stackexchange.com/questions/658234/velocity-and-kinetic-energy-violating-galilean-relativity I am also suprised that rockets have comparable efficiency to cars, but that is what wikipedia says! – Matt Aug 19 '21 at 16:53
  • @Matt: If the output of your rocket nozzle is equivalent to the exhaust pipe on the average automobile, then your acceleration and top speed will be an issue. – James Aug 19 '21 at 16:56
  • @James you are just pulling this out of your ass, you are not engaging with the content of the question – Matt Aug 19 '21 at 16:57
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    @Matt: You are totally correct. But I have been dieting on mechanical engineering for 30+ years, so my ass output isn't too shabby. :) – James Aug 19 '21 at 16:59
  • The point is that (1) car fuel efficiency scales with the inverse velocity -- i.e. the efficiency of a car is 100X worse at 100km/h, but a rocket efficiency is constant (2) a rocket actually gets comparable efficiency to a car, apparently. – Matt Aug 19 '21 at 16:59
  • @Matt aggressive comments will usually attract negative attention, there isn't any need for that here. – Triatticus Aug 19 '21 at 17:00
  • OK @Triatticus -- but do you get what the question is getting at? apparently cars legitimately use 100X as much fuel to go 100km/h => 101km/h as 0km/h => 1km/h. This isn't true for rockets. – Matt Aug 19 '21 at 17:01
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    @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. – James Aug 19 '21 at 17:08
  • @James haha not at all. I think we got the answer -- it's that rocket engines have almost zero efficiency at low speeds And the statement about car KE efficiency just isn't true. The whole question is based on my misconception – Matt Aug 19 '21 at 17:11

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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.

BowlOfRed
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  • Oh, thank you, this makes much more sense. So, the propulsive efficiency is substantially less than 1%? – Matt Aug 19 '21 at 17:06
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    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. – BowlOfRed Aug 19 '21 at 17:08
  • 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>. – Matt Aug 19 '21 at 17:09
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    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. – BowlOfRed Aug 19 '21 at 17:13
  • Thanks @BowlOfRed . I'm confused again. If the rocket adds velocity linearly with fuel, isn't its velocity eventually going to overtake the sqrt relationship (fuel and velocity squared) which should be optimal via energy conservation? – Matt Aug 19 '21 at 17:56
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    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). – BowlOfRed Aug 19 '21 at 18:04
  • thank you so much. This has been keeping me up at night! – Matt Aug 19 '21 at 18:06