Thread: Rocket engine Carnot efficiency paradox

I read that rocket engine (or rocket itself) could practically acheive 70 percent of absolute efficiency.http://en.wikipedia.org/wiki/Rocket#Energy_efficiency
If I no make mistake a rocket produce very hot exhaust gases
which have practically the same temperature as fuel combustion.
Lets say we have the following example:
Rockets are flying on low altitude and doing some job,for example deliever freights.
On trajectory of their flights are installed Stirling engines (on towers) which capture
very hot exhaust of rockets and convert it into usefull work.If those Stirling engines
work close to ideal Carnot cycle their efficiency will be over 70% if hot sink temperature (rocket exhaust) will be 1300 K.
70%+70%=140% of total system efficiency.
Is there some mistake or nature`s law violation?

Total energy in = x

total used by jet = 0.7x

total captured by towers (assuming all waste heat is captured) = 0.3x

tower efficency at 70%.

therefore total work by towers = 0.7*(0.3x)
= 0.21x

therefore total useful energy output = 0.21+0.7 = 0.91

=91% efficency

basically your misunderstanding was that the 70% of the towers applied to all the energy obtained from the jet

I don`t understand how rocket could use 0.7 of X.
Exhaust gases which it produces should be very hot, almost the same as fuel combustion temperature.It means rocket almost use no heat converted to mechanical energy.Yet it moves very efficiently. Number 70% efficiency I took from wikipedia article.Common sense tells that rocket efficiency should always stay very low,otherwise we could use those very hot gases and power very efficient Carnot engine and obtain perpetium mobile.Efficiency of Carnot engine is somewhat proportional to difference between combustion and exhaust temperature.Does rocket engine obey Carnot law?

70 percent is a quite high efficiency.
The normal Watt engine can only achieve a efficiency about 35%.
I think any way can improve the efficiency (even only 5%) of Watt engine will gain a Nobel prize.

let alone your calculation procedure is not right. If your want to reuse the hot exhaust gases, firstly you need to slow down them, this will also cause the rocket slow down. That's not valuable.

70 percent is a quite high efficiency.
The normal Watt engine can only achieve a efficiency about 35%.
I think any way can improve the efficiency (even only 5%) of Watt engine will gain a Nobel prize.

If you mean my example with Stirling,it`s quite possible. Even ceramic Otto cycle engines working on gasoline(?) acheive over 70% efficiency.Stirling believed to be more efficient then Otto cycle.Usual engine with 35% efficiency is made from easy meltable materials and loose 35% of energy in cooling system.Read more about ceramic engines.

let alone your calculation procedure is not right. If your want to reuse the hot exhaust gases, firstly you need to slow down them, this will also cause the rocket slow down. That's not valuable.

Could you comment it in detail? I don`t think that rocket bothers what will happen to
exhaust gases after they left it.Those gases might be slowed down by nature processes such as wind and air friction.Or might be used to power some Stirling engine.Trajectory of a rocket not necessarly should be even straight.When exaust gases of it is captured by Stirling engine and slowed down it may already have moved to the right or to the left, towards another Stirling engine.Could you explain how it could slow down a rocket? :?

Originally Posted by Stanley514

If you mean my example with Stirling,it`s quite possible. Even ceramic Otto cycle engines working on gasoline(?) acheive over 70% efficiency.Stirling believed to be more efficient then Otto cycle.Usual engine with 35% efficiency is made from easy meltable materials and loose 35% of energy in cooling system.Read more about ceramic engines.

Seems I didn't mention the data in a more understanding way. Okay, since rocket engine is technically different from Watt engines, its much more efficient, this is all I mean. Don't bother with the data I mention.(BTW, even for the ceramic engines, 70% seems to be only a theoretical data)

I don`t think that rocket bothers what will happen to
exhaust gases after they left it.

Eh, (FOR only one engine) if the rocket do not bother with the exhaust gases, how can the energy be transfered back to the rocket?
To reuse the energy in the exhaust gases, whatever you used to make so, this procedure is time dependent, the longer time the more energy you reused, right?
so to make the reuse time longer, the possible way is to slow down the speed of the exhaust gases, right?
And, according to the law of conservation of momentum, if the exhaust gases slow down, the rocket itself will also slow down.


(FOR more engines)what is the direction relationship of the speed of exhaust gases and your second engine?
Are these engines all in one line?
If i have a engine B with twice length compared to the shorter one engine A, and i make a "engine team" with two A to let the second A reuse the exhaust gases of the first A, is this 'team' more efficient than engine B?

To reuse the energy in the exhaust gases, whatever you used to make so, this procedure is time dependent, the longer time the more energy you reused, right?

I can`t really get in it.

Maybe I mistaken something,but probably you need to read about basic principles of rocket operation.Rocket drive force doesn`t suppose to depend on what will happen to exhaust gases.It is based only on reaction force which is somewhat similar to inertia.Rocket engine will have the same efficiency in outer space, on air and underwater if you will carry fuel oxidant in the first case and eliminate forward friction it two other.Do you think that when space rocket is starting from the Earth and exhause gases will strike the Earth surface and slow down it will prevent roket from flying?I would be very glad to read about this law. Rocket not necessarly even depend on comustion.For example you may shoot back some particles with help of rail gun and it will provide you reaction force.Those particle may fall down on earth later or continue motion forever in outer space,it will not influence rocket.I cannot get in your other exampes either.
All examples I provide are clearly theoretical,I dont suppose to argue about trajectory of rocket which might be straight or curved.
Rockets may deliver exause gases in short inpulses and each impulse is getting exactly into hot sink of Stirling engine.Theoretically it could be 99 % captured and reused.Rocket may make a turn eache time after it delievered pulse of ehaust gases and before Stirling captured it.This is just exampe to understand wether slowing down exhaust gases could slow down a rocket.I don`t see how could it be.

Hi, Stanley514

Actually, I'm quite attracted by your thoughts.
Maybe because my major is more practical.
The only question bother me is 'how to'.

our focus point is different.

Originally Posted by Stanley514

I don`t understand how rocket could use 0.7 of X.
Exhaust gases which it produces should be very hot, almost the same as fuel combustion temperature.It means rocket almost use no heat converted to mechanical energy.Yet it moves very efficiently. Number 70% efficiency I took from wikipedia article.Common sense tells that rocket efficiency should always stay very low,otherwise we could use those very hot gases and power very efficient Carnot engine and obtain perpetium mobile.Efficiency of Carnot engine is somewhat proportional to difference between combustion and exhaust temperature.Does rocket engine obey Carnot law?

the rocket is 70% efficent....

this means that if you combust fuel and produce x Joules
then 70% of x will be used to propel the rocket forward...
70% of x = 0.7x

learn maths then move onto rocket science

The combustion chamber of a rocket is indeed very hot - the hotter the better. The exhaust leaving the expansion bell is much colder. When gases expand and do mechanical work, they cool down. The "mechanical work" is pushing the exhaust stream to very high speed. The exhaust leaving the rocket bell is still quite hot, but much cooler than the gas in the combustion chamber at the top of the bell.

If you let the air out of a tire through the valve, it comes out cold. It is expanding, pushing atmosphere aside, and cooling. On the other hand, when you pump air into the tire, the pump gets hot - heat is forced out of the air while it is compressed. The magic words are "adiabatic expansion".

So yes, rockets are very "efficient" in the mechanical sense, otherwise they would melt in fractions of a second. I hope the 70% number is correct, that is what I came here looking for. I expect it is higher for high-expansion rocket bells in vacuum, because those expand the gas even more, and it comes out even colder. In the deep cold and high vacuum of space, very high efficiencies are theoretically possible, but friction and turbulence and other things means that the expanded gas comes out warmer than we would like.

Also, most of what we are pushing with the rocket engine is fuel to burn later, so overall, the fuel-energy to payload-energy conversion is awful, fractions of a percent for payload headed to the moon or Mars. So the 70% may be valid as far as waste heat is concerned, but not the real whole-system efficiency.

Oh come on, it's not rocket scien...D'oh!