Let's do rocket engineering from the beginning

There are schemes for gun-type spacelaunch systems which might have more reasonable accelerations, by spreading the acceleration out over a longer distance, but they tend to be electromagnetic systems, essentially a railgun or coilgun accelerating a payload which is levitated by magnets. For cargo launch, it's actually a pretty nifty idea, admittedly in a field with a ton of nifty ideas and a much smaller set of ones that make it into production. However, to make it survivable for human passengers, you need the acceleration to be a lot lower so that our blood and bones do not get into a violent disagreement and decide to divorce one another, and this means the designs get truly wacky.

We're talking about something in the neighbourhood of a gun "barrel" (really more like an electromagnetic rail) the length of the continental United States or at least a decent-sized country, curving upwards like a rollercoaster until it's poking up high in the upper atmosphere. The civilisation which has its shit together enough to do that can also probably build a space elevator, space fountain, space ferris wheel, a fleet of Skylons, or any number of simpler systems, although it's a fun concept.

The place where mass drivers tend to be more seriously considered as the obviously best solution is for launching cargo in low gravity environments, preferably with low atmospheres as well (atmospheric drag is a bitch). Designing a mass driver which could work for a moon base or a big asteroid, for example, is almost absurdly easy compared to designing one which could work on Earth.
 
A more pressing concern is how you survive being accelerated to 11km/s by a gun.

You don't :V
You really only should be using gun launch systems for bulk materials or some rather amazingly heavily build satellites. It isn't a tool for delicate cargo.

There are schemes for gun-type spacelaunch systems which might have more reasonable accelerations, by spreading the acceleration out over a longer distance, but they tend to be electromagnetic systems, essentially a railgun or coilgun accelerating a payload which is levitated by magnets. For cargo launch, it's actually a pretty nifty idea, admittedly in a field with a ton of nifty ideas and a much smaller set of ones that make it into production. However, to make it survivable for human passengers, you need the acceleration to be a lot lower so that our blood and bones do not get into a violent disagreement and decide to divorce one another, and this means the designs get truly wacky.

We're talking about something in the neighbourhood of a gun "barrel" (really more like an electromagnetic rail) the length of the continental United States or at least a decent-sized country, curving upwards like a rollercoaster until it's poking up high in the upper atmosphere. The civilisation which has its shit together enough to do that can also probably build a space elevator, space fountain, space ferris wheel, a fleet of Skylons, or any number of simpler systems, although it's a fun concept.

The place where mass drivers tend to be more seriously considered as the obviously best solution is for launching cargo in low gravity environments, preferably with low atmospheres as well (atmospheric drag is a bitch). Designing a mass driver which could work for a moon base or a big asteroid, for example, is almost absurdly easy compared to designing one which could work on Earth.

Now for completeness sake there are ways to lower the instantaneous acceleration of non-electric gun type launch systems. The use of multi-chamberesque systems similar to the V-3 cannon allows you to spread out that one hard punch into multiple still hard punches with the limit being the fact that each 'stage' you add to the gun increases the complexity of timing things and maintaining things massively. This is something that one of the scientists from SHARP wanted to actually build but it would cost billions and he never got the funding. Even call your project the Jules Verne Launcher can't save you from massive capital investments. It is honestly to complicated for the general tech level we are starting at.

There is also a even more kerbal system that could technically be slow enough you could put a human in it without them turning into paste. First you build a giant tube on a mountain or maybe sink it into the ocean like you do with your normal giant space gun. Then you you put thin, easily breakable seals along the length of the barrel at the correct intervals. After that you fill each section with different H2/O2 mixtures so that the speed of sound gets progressively higher the closer to the muzzle you get. Then you use a fucking railgun or light gas gun)to shoot a ram jet or even a scram jet down the barrel. The jet then huddles its way through this explosive mixture of fuel and oxygen, going faster and faster. Slamming into those flimsy partitions at higher and higher speeds while being kept in the sweet spot for mach speed till it flies out of the other end at 8 km/s. This is what is called a ram accelerator.
 
This isn't surprising as he thought that someone using rockets to get to the moon would be thought of by readers as to fanciful and unrealistic so he went with a gun. Even with the guncotton he talked so much about it simply wasn't possible to get the gasses up to the velocity needed.
The first description of a multi-stage rocket I'm aware of was published in the 17th century, and there are probably earlier ones too.

His audience was the general public. It wasn't the people who actually knew such things.
 
There are schemes for gun-type spacelaunch systems which might have more reasonable accelerations, by spreading the acceleration out over a longer distance, but they tend to be electromagnetic systems, essentially a railgun or coilgun accelerating a payload which is levitated by magnets. For cargo launch, it's actually a pretty nifty idea, admittedly in a field with a ton of nifty ideas and a much smaller set of ones that make it into production. However, to make it survivable for human passengers, you need the acceleration to be a lot lower so that our blood and bones do not get into a violent disagreement and decide to divorce one another, and this means the designs get truly wacky.

We're talking about something in the neighbourhood of a gun "barrel" (really more like an electromagnetic rail) the length of the continental United States or at least a decent-sized country, curving upwards like a rollercoaster until it's poking up high in the upper atmosphere. The civilisation which has its shit together enough to do that can also probably build a space elevator, space fountain, space ferris wheel, a fleet of Skylons, or any number of simpler systems, although it's a fun concept.

The place where mass drivers tend to be more seriously considered as the obviously best solution is for launching cargo in low gravity environments, preferably with low atmospheres as well (atmospheric drag is a bitch). Designing a mass driver which could work for a moon base or a big asteroid, for example, is almost absurdly easy compared to designing one which could work on Earth.

If your spacecraft is accelerating at 3 G, you only need a track that is 53 KM long to reach orbital velocity.

Length of the track is not the problem here. The problem is Earth's atmosphere, if you accelerate toward such velocities at near sea level it will pulverize most known things.
 
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If your spacecraft is accelerating at 3 G, you only need a track that is 53 KM long to reach orbital velocity.

Length of the track is not the problem here. The problem is Earth's atmosphere, if you accelerate toward such velocities at near sea level it will pulverize most known things.
What's coming out of the barrel at those velocities will quickly be turned into a molten slug of "whatever" or a cloud of ionized plasma by atmospheric friction within seconds if it even makes it out of the barrel intact.

There's a reason why we don't try such things.

It's not because the physics doesn't work (it does). It's because the materials and technology needed to do such things does not, and might never, exist.

If you do the static equilibrium equation for a rocket motor you can get thermal efficiencies of 90% or better if the exhaust consists of nothing but very hot Helium.

Umm ...

That's not doable outside the core of a main sequence star or shell of a star that's fusing heavier elements.
 
I was thinking about a what a hypothetical society from an Earth-like planet with a 10.6psia atmosphere, an approximately 23.2ft/s^2 surface gravity, and early 20's tech would have in terms of powerplants.

Theirs would look a lot like ours. A steam powerplant designed for about 8,750ft above sea level on Earth would work, without any modifications, at their sea level. One designed for our sea level would require only minor modifications to the pumps: place the pumps about 15' below where we do, add a low pressure stage on the suction side, or use pumps which don't require as much inlet pressure to work ... and even that might not be needed.
 
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