How do you power a rocket engine?

Basically, it would already work if you left out the diverging part. However, the exhaust has still excess pressure. You want to make it do work while expanding to ambient pressure, so you provide a ring around the throat where the exhaust pressure pushes against to direct the exhaust momentum vector for every part of the exhaust plume to be as close to retrograde as possible. Sideways momentum is wasted momentum.

To actually get it to push against your ring, the diameter can't increase too fast, because the sideways flow velocity of the exhaust inside your bell needs to be subsonic. So you first increase steeply, because it's still high pressure and thus hot and thus has a high speed-of-sound, and gradually reduce how fast you increase (gradually reducing the taper).

Eventually you have expanded it to a pressure equalling ambient pressure, and won't get more thrust from further expansion (doing more also causes flow separation at the edge where ambient air pushes the plume radially inwards and separates it from the inside surface of the bell. The supersonic shock effects can break your bell if you're not careful.).

Also at low pressure you get little thrust per additional nozzle area, while the low temperature requires a low taper that requires a lot of surface for the additional nozzle area. That is why even vacuum engines don't go down to extremely low exhaust pressure.

IIRC you can only ever double your momentum with an expanding nozzle, even in the asymptotic limit of an infinite bell in perfect vacuum and compared to a knife edge throat.

Fundamentally, rocket nozzles are weird open-cycle heat engines subject to the Carnot limit. Thrust times (exhaust) velocity is power, and the chamber (combustion) temperature your hot side. If your exhaust has a different molecular mix than the atmosphere, there is some additional energy to theoretically gain from there. Otherwise, you should have IIUC reached outside temperature when you reach outside pressure. Or maybe you would need to expand to outside temperature regardless of pressure to scratch at Carnot-efficiency...

The conversation is about GPS for the general public and google maps.

Those things emerged for the general public circa 2010.

So 1970 to 2010 that's 40 years not 20. Also those who paid the lionshare of that were of course not young but in their 50 or 60, because that's the demographic which pays more taxes.

Highly unlikely they got to see it.

That's the reason why every person talking about space should know that the state goes out for them to take money from people's pockets.

A brief stint into an insurance company, pension fund, Sovreign wealth fund or hedge funds would render them much more pragmatic about costs and tradeoffs.

Nice writeup! Former chemist here. Helium is indeed poorly soluble in most liquids. It's actually used to sparge (purge by bubbling through) solvents to drive out other dissolved gasses.

This is because Helium has very weak intermolecular forces due to its electronic symmetry. For that same reason, it's also as close to an ideal gas, giving you the most pressure/volume bang for your mass buck (only hydrogen is better, and that's bad for oxidizer tanks for obvious reasons).

But this also limits the ability to cryogenically condense helium, which would improve storage density. But you really don't need much in turbopump fed engines.

That's why I was asking for an ELI5 explanation. I know that the equation holds and that compressibility turns everything upside down, I just haven't been able to figure out an intuitive explanation.

I have this idea that in supersonic flow, a pressure wave can't move backwards against the flow, right? Which would mean that any single molecule inside the flow has no way of knowing what's in front of it (because the information simply can't get there), but it feels the pressure of the molecules behind it, so it accelerates towards the void.

The "Fanno flow" article on Wikipedia says that "... For a flow with an upstream Mach number greater than 1.0 in a sufficiently long enough duct, deceleration occurs and the flow can become choked ... Conversely, the Mach number of a supersonic flow will decrease until the flow is choked.", which means that supersonic flow behaves differently in a diverging nozzle than in a simple straight pipe. This is the part that I don't understand. Is the friction inside the nozzle somehow inhibited by the walls of the nozzle gradually moving out of the flow's way or something?

I've planted many seeds to grow trees I'll never sit under. As did many many many others before me. This is the true nature of this world.

Perhaps you might reconsider your limiting beliefs before reality catches up with you. Maybe not. At least you might still yet have fun on roads and highways you didn't pay for. Schools you didn't build. Parks your money never constructed.

I cannot imagine being so limited and short-sighted. But, as they say, You be you.