It's said that people never publish negative results. Well, in response to a comment on the previous post, here's mine.
Most every engineer who has looked at a rocket launch has been appalled at the horrible efficiency of a rocket coming off the pad. At the moment of launch, the rocket is using as much propellant per second as it can, throwing away nearly all that energy in gravity losses, and getting very little velocity with the rest. Almost anything can convert propellant energy into projectile velocity more efficiently than a rocket just off the launch pad.
One of the best things, it turns out, is a cannon. A cannon with reasonable muzzle velocity uses the earth or the cannon as the reaction mass, where a rocket just uses the propellant itself. More mass means more efficiency. So many folks have wondered, why not use a cannon to launch a rocket?
It's been done, of course. Back in the 1960s, and 1970s, and finally 1980s, Gerald Bull looked into using cannons to launch rockets. I've looked at Gerald Bull's work. His is a sad story -- the guy got so taken by the promise of his research that he eventually let his ethics slide. When the U.S. military cancelled his funding, he started doing work for nearly anyone who would pay for his research. Near the end, he was doing work for Saddam Hussein, at which point he was assassinated, maybe by Israel, but maybe not.
But nevermind about Mr. Bull, what about gun launch?
Cannons convert propellant energy into projectile kinetic energy well when the muzzle velocities are well below the Ve for the propellant combination -- around 2000 m/s for solid propellants, and 3000 m/s for liquids (liquids have better oxidizers, see wikipedia). Most guns have muzzle velocities much smaller than that, so you see very good payload/propellant ratios, as my commenter "fred" stated. (Fred should check his numbers, though. A 1000 m/s rifle round has a payload/propellant ratio closer to 2 than 100.)
Low-energy gun launch has been done too. An MX missile launch from a silo starts by blowing the missile 100 feet out of the silo with compressed air, and then air-starting the rocket. This is done to make the silo cheaper, not to give the missile any substantial delta-V. One could conceivably boost a satellite launcher this way as well, but the delta-V is probably limited to 100 m/s or so, which isn't enough to help the rocket much. And it's certainly less safe than starting a set of liquid-fuelled engines while bolted down, checking for correct operation, then releasing.
High-energy gun launch only makes sense for bulk payloads like fuel. High value payloads like comsats and people are never going to take the accelerations from any cannon anyone can afford to build. But still, one wonders, maybe just for bulk loads....
Guns really get expensive when muzzle velocities approach Ve. Essentially, the propellant gases run out of energy by the time they expand enough to act on the base of the projectile. To even get close to Ve, the gun has to accelerate a good fraction of the propellant before it burns, and now we're talking about a rocket inside a gun barrel. And we enter the realm of rocket-like payload/propellant ratios, but with a very nasty twist.
Lots of propellant isn't a problem by itself (the propellant is cheap). The problem is processing all that propellant. More propellant requires more stuff (plumbing, pumps, thrust chambers, or gun barrel) to contain and process it. Launch guns process all the propellant in a very short period of time (tenths of a second), which means they need two orders of magnitude more stuff than a rocket to process the same amount of propellant. Sure, it's simple stuff (a gun barrel), but there is just too much of it.
A few years ago I thought I'd had a clever idea here. Since a gun doesn't have to contain the blast for very long, I figured you might be able to build a thin barrel and then immerse it in the mud at the bottom of a lake (or any other high density fluid). When the gun fires, the barrel attempts to explode, but to do that it has to move the mud out of the way. This is inertial confinement: the mud can't move away fast enough, so instead it compresses. The gun propellant deflagration turns into a pressure wave in the mud, which can be arranged not to crush the barrel after the barrel pressure returns to normal. You get to make a big cheap gun, that is horribly difficult to point at different things, and so pretty much worthless as a weapon. Sounded good to me.
I wrote some simulators, and faced the following choice: after gun launch, would the projectile have one stage or two? (I assumed liquid propellants. Bull used multiple-stage solid propellant rockets.)
If the projectile is a single stage, then you need a muzzle velocity of at least 2500 m/s. That's fast enough that the round inside the gun ends up looking like a big solid rocket -- one that burns it's fuel in a fraction of a second. Since solid fuels burn at centimeters per second, you end up with a highly perforated fuel grain and a very nasty ignition problem (all that surface area has to simultaneously jump a thousand degrees C in a few milliseconds). Also, this fuel grain itself has to survive hundreds or thousands of Gs of acceleration, and to do that you end up using carbon fibers as the fuel rather than HTPB or something more standard (and higher energy).
Then comes the brutal comparison. If you were going to do all that work to put the rocket in the gun barrel, how does it compare to just having an ordinary solid rocket first stage? Answer: the ordinary stage has way lower capital costs, isn't much bigger, and doesn't subject the payload and avionics to brutal accelerations.
Okay, so what about a medium-energy gun lauch of a two-stage rocket? Starting with 1000 m/s or so really does help the payload quite a bit. But the massive acceleration requires building that rocket to be very sturdy, so most of the payload ends up being structure. And a two-stage liquid-fuelled rocket can get to orbit just fine without a gun launch to start, while being so much simpler.
In short, rockets may seem horrible coming right off the pad, but they don't spend much time at low speeds. They get up to canon-muzzle-velocity-like speeds in 30 to 50 seconds, and then they get to keep using that engine hardware to go a whole lot faster.
The best optimization yet found for the first 30 seconds of flight is strap-on solid rocket motors: they're cheap, fairly reliable, small, and require few changes to the support infrastructure. If the rocket has some delta-V margin and positive acceleration even if the strap-ons fail to ignite, then failure of one of the strap-ons can be survivable.