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Well, scaling seems to be my pet issue. I recently wrote something not entirely well reasoned in a comment at Paul Breed’s. (For some reason Chrome complains about blogrolling.com malware there so continue if you’re sure you’re safe.)
So let’s make it better. (A word of caution though, I’m quite sleep deprived now.)
For those who like to jump into conclusions, it’s going to be like this all over again.

Assume a pressure fed rocket first stage has a certain propellant chemistry, tank and thus chamber pressure and must operate in the atmosphere, hence has a certain exit pressure (0.1 MPa or 1 bar or 15 psi is the optimal). Then it has certain thrust per nozzle area.

Now, the rocket needs thrust to lift off. If we assume a constantly scalable shape, its mass will be base area times length times density.

Since the maximum fittable nozzle exit plane also depends on the base area, we find that for a certain area, the rocket can only have so much mass – or that the rocket has a maximum density times length parameter. If we assume the propellants have been picked early on, density is set and the rocket only has a height constraint.  Each pressure and propellant chemistry basically has a “characteristic length” that can’t be exceeded. Otherwise it can’t lift off.

The higher the exhaust velocity, the smaller the nozzle, so raising chamber pressure reduces the needed nozzle size per thrust and the rocket can be lengthened.

For small rockets, I’d hunch that they have little length and thus they don’t really have to worry about this. They can be as thin (and thus long) as practical, to try to avoid drag losses.

For upper stages, the thrust to weight needed is less and the weight even less so it’s even less of a problem – except that the expansion ratios can be huge since there’s no back pressure anymore. Still, with small rockets, pretty huge expansions might be possible without having much problems because the second stage is very small (=also short) anyway and thus there’s little mass per nozzle exit plane area.

On really tall rockets like Saturn V, the thrust per base area has to be huge, hence it had to have those base extensions for the corner engines (note how the N-1 had a conical shape with a wider base, the engines had a bit higher pressure but the upper stages were kerosene – these cancel out a bit but the base of the rocket had some empty space) . Similarly with STS, putting so much thurst on the tiny orbiter’s tail required high chamber pressures and some tail shaping

I don’t have any numbers handy, but if we assume a 10 m tall 1000 kg/m^3 density (water) rocket, then it has 10,000 kg per m^2 or the thrust required for a 20 m/s² acceleration is 200,000 N/m^2. This is easily achievable. With an exhaust velocity of 2000 m/s, the mass flow needs to be 100 kg/(s*m²) to produce that thrust. Again with the exhaust velocity that mass flow means a density of 0.05 kg/m^3. Air’s density is 1.2 kg/m^3 at 300 K, so that’s 20 times less dense which means hotter, the density is like hot air at 6000 K. Though the molecules might be mostly lighter OH instead of N2 and O2, making that rocket exhaust at 3000 K for the density. Rocket exhaust isn’t that hot – it’s cooler and denser and thus more thrust per unit area.

For a second stage we can look at the pressure fed AJ-10 from Delta 2: 1.7 meters diameter (certainly constrained), 40 kN of thrust. For a T/W of 1, density of 1000 kg/m^3, we get 4 tonnes and 1.7 meters of depth. Quite a stubby stage with a roughly spherical tank! Isp is 321 s. The real Delta II second stage weighs 7 tons and the payload is some too, but reusable rockets won’t have such high performance first stages (nevermind solids!), so they might need more T/W.

Oh, BTW, I assume three stages to orbit for pressure feds though I haven’t looked it that closely.  Mass ratios and ISP:s I’ve only hunched.

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..is despicable.

They take clearly too little water.
They take it clearly too slowly.

They idle far too much at the beginning.
They idle far too much at the end.

They do not offer fast forward capability like mechanical machines did.
They do not show their current status like mechanical machines did.
They’re often broken like mechanical machines were.

They make it unclear which programs have pre-wash and which don’t.
They make everything else pretty unclear too, like what a particular button does.

An ideal washing machine:
Large intake hose (or two if it is a model that takes warm water too where district heating or wood heating is available). When the user presses start, the machine starts taking water at full speed at that precise microsecond, unless it is gauging the weight of the laundry.
Laundry weighing will be done in a few spins, after which water intake commences with no delay.
A display shows the state of the machine. At least the following states are displayable: pre-wash, wash, rinse, spin.
A fast forward mechanism moves the machine to the next state.
A stop mechanism stops the machine in any state.
After the laundry is spun, the machine can spin slowly and reverse a few times to unstick the clothes from the drum walls, but this can be stopped and the laundry removed from the drum immediately.
The spin is braked so it doesn’t take minutes to coast down.
The temperature of the wash can be changed even if the program or wash has already started without having to reset or flush.
The spin cycle can be enabled or disabled even if the program or spin has already started without having to reset or flush.
Extra water can be enabled in the middle of the program.
etc etc.

All this was possible with seventies mechanical logic industrial washing machines. Note that almost all of it is pure logic whose cost is pretty much exactly zero once you’ve developed it, and other things like large hoses are trivial improvements.

If you will use this specification when designing a washing machine, then send me a machine: I will test it and say what improvements still have to be made.

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