I agree with Pavel, and also think this is probably a concept to look at: The catapult has to be engineered as a pre-burningrocketburning rocket phase. Meaning, we could use the catapult to launch a rocket, capice? So, we may engineer the catapult to accelerate at the maximum rate a human body can stand (let's say, 5g), so that it reaches considerable velocity (say, 600km/h), way bellow the limit that would make things burn in the lower atmosphere.
In this visionary mind experiment, we could have a rocket ignition, where the rocket has inicialinitial velocity of 600km/h. The rocket would keep accelerating at 5g after the catapult line is over; using it's rockets (as currently). The nice thing is that the burning-rocket would start its trip at 600Km/h instead of 0km/h . I guess the main impact would be on the necessary amount of initial fuel (someone could estimate that, please?). You can cut of all the fuel necessary to reach 600km/h in a non-catapult launch. The whole ship would be lighter!
Considering our catapult works at acceleration = 5g = 5x10 m^2/s . Going from V_0 = zero , to V = 600km/h , demands 3.3seconds . Lets round it to 3.5s . Then, as next step we may think “who big should be the catapult line to allow this rocket lounchlaunch?“ , And the answer is not bad at all.
Guys, a robe to stand 5g and catapult a light rocket is not a problem (is it?)... I mean, even if a robe to "do the job" is the biggest problem you can imagine, I think this could be engineered to work.... for example, we could look for currently robes-specifications for catapulting foofightersfoo-fighters
About the "problem" of having rocket-motor failure during the catapultagge... guys, come on... If a rocket-engine explodes, it will be a tragic problem from both ground and catapult launch.
If a rocket fail to burn during catapulting, I agree it will be hard to stop the rocket. Probably we may lose the rocket. But we already have technology to eject crew (or any valuable-payload) (see the Abort Pad tests from NASA or SPACE-XSpaceX)
So, "rocket failure" should not be seem as a main strong argument against catapulting rockets (my view)...
Also, about extra structures needed to stand the catapulting... You know... maybe, we would not need to go to far to address this kind of problem. TodaysToday's launchers already stand >5g acceleration ... So, concerning this point, the current rockets are fine. Also, lets think for a moment... Where would we connect the robe? Well, we can simply apply the force in the same mechanic structure that holds the currently burningrocket-engineburning rocket engine pull . I mean... the currently burning engines already apply force enough for a >5g acceleration. So, we may apply the robe-force in the same place.