At 2 gee and 7 km I get 500 m/s. So the exit velocity is about Mach 2. Drag losses at 5 km height would still be substantial. I wonder if the laser can even keep the speed up…

Then there’s the problem that you are probably limited to small payloads - because of the tunnel and maglev and laser size and because of the laser launch scalability - ie you need thrust and thus base area proportional to vehicle mass - so max vehicle depth is constrained.

And of course being limited to one inclination sucks too (unless you are at the equator and launch to the equator) - if you want to launch to rendezvous (and you want if you only can launch small things) you can only do it once per day - and even then the phase will suck a lot of time meaning rendezvous will take long.
This could perhaps somewhat be ameliorated by picking magic orbits which have resonances in a way that the phase is always the same when passing the launch site. At least that’s my hunch, haven’t thought of it so closely.

And in the end you need rockets on the payload anyway to manage the orbit.

Also if you launch once per day, and the launch mass is 1 ton, you only end up with 30 t to orbit per month. That’s not a huge mass.

I think it’s too complicated and limiting for marginal gain.

Iain, I remember reading your steam rocket article. It is fascinating how much things that can be judged as little by delta vee can help anyway in the early gravity and drag loss dominated part of the flight.

Steam rockets have a couple of problems that have popped to my mind:

The first is that pressure vessels are dangerous even when not filled with anything that can detonate or burn. Actually a steam/hot high pressure water pressure vessel is probably much more dangerous than a kerosene or liquid oxygen one - in case of a rupture the water flash boils and the volume multiplies by a huge amount.
Steam has killed lots of people in the past because of exploding boilers.
The thing would be under constant high pressure when filled/heated so you would have to have very big safety margins on the pressure vessel, all the rocket valves - as well as possibly the fill and storage systems.

The second problem is the old complaint - that if you altitude optimize the main stage nozzle and only start it up when high enough, you now have more failure modes and different vehicle configurations than without the steam.
There is a significant number of times when in a launch attempt, the liquid main propulsion has been started, and then shut down again since there has been a problem. But if you use a steam rocket and only start up your main stage at 30 km altitude, if you have a problem with that, you are done. Also, if you only start the main stage at altitude, the steam rockets will have to have gimballing or throttling capability which increases complexity.
The solution to this is of course to go Ariane style - make the nozzle such that it just runs without flow separation at sea level, but still has pretty high exhaust velocity at altitude. But the benefits are probably not as good then. (Or then you can use staged combustion high pressure engines like the shuttle.)

How about a hot water rocket instead? It has really sucky Ve (300 m/s), but it’s really, really cheap.

300 m/s doesn’t sound like much, but it’s about all you’d get from a winged launch vehicle, and at least a few folks think it worth quite a lot of hassle (Airlaunch LLC, Rutan, Orbital Sciences).

I estimate that a LEO booster (such as the Falcon 1), fitted with a hot water rocket, with it’s tanks lengthened and a high-altitude rocket nozzle fitted, will deliver 2.4x the payload that the original LEO booster delivered.

The cost of the hot water rocket will be so low that it will be dominated by the development cost of ensuring the booster operates correctly as a second stage.

The other nice thing about a hot water rocket is that you can build it really big. There are scaling problems, but they don’t show up until the thing boosts something the size of the Saturn V.