The exhaust, mostly.
Correct. And compressible fluids that possess heat can do pressure-volume work. This is the basic principle of a thermodynamic engine. Those fluids want to expand, and when they do, they can be harnessed to do mechanical work. That's how most engines work.
For a time, it'll also be heating up the hardware (chamber, nozzle) - until those reach steady state.
Correct, and well spotted. The heat that goes into raising the temperature of the rocket hardware is effectively unrecoverable and therefore a true loss. That's not true for all heat in the system.
Show that we can't.
Show that you get to. We've got a working fluid in a thermodynamic engine that possesses heat. You don't get to just ignore it. That's why the basic thrust equation doesn't.
F =
ṁ ⋅ ve +
(pe - p0) ⋅ AThe
blue term is what we get from the kinetic energy of the exhaust that we created in the de Laval nozzle, which takes a part of the energy of combustion. The rest of the energy of combustion that remains as heat in the working fluid (irrespective of its kinetic energy) is slightly reduced by transferring heat to the chamber, but then lives on as static pressure in the exhaust at the exit plane. That's the
maroon term.
It isn't negligible, even at steady state. The energy efficiency calculations for rocket motors do tend to focus on the kinetic energy part. But a significant portion of a rocket's thrust in a vacuum is pressure thrust. The pressure-thrust term is often zero at launches in atmosphere because we can design a nozzle that produces static exit plane pressure that's equal to the ambient. No pressure difference means no pressure-volume work. But no such nozzle can exist in a vacuum. The contribution of the pressure term increases in vacuum.
Now in free flight in a vacuum, the plume can expand in all directions freely once it leaves the nozzle. That doesn't eliminate the effect altogether, but it does limit how much the expansion in the direction of the rocket can be harnessed to perform pressure-volume. What would happen if that expansion were limited in certain directions by relatively immovable objects? What would happen to the pressure-volume work capacity in the direction of the thing that
can move? What if the mechanical arrangement of rocket and surroundings briefly created a kind of cylinder with the spacecraft as a kind of piston?
Pre-Steady-State, from what I've seen, is WORSE efficiency than Steady-State...
No, no, no. You've fallen back into confusing the different kinds of mechanisms that produce thrust. Remember how you were confusing chamber pressure with ambient pressure?
So make this proof 1 step at a time.
What do you think I'm doing?
But as a good engineer would, START by showing the top level approach that you plan to take here.
The top level approach begins with the energy balance equation and understanding how the various terms apply.
Instead of saying "there are other things" - great say what they are.
What do you think I'm doing? The other thing is heat—but heat contained in a working fluid. I'm leading you carefully to an understanding of why you don't get to ignore it as you did. If you were to set aside all your silly posturing for a minute and pay attention, you might actually figure it out on your own.
