Even without the weight of the first stage, I'd imagine this would have to be a massive quantity of balloons. Lifting an adult human takes a house-sized amount of balloons. Fun to imagine dragging a stadium sized quantity of hydrogen balloons a mile up before detonating them with the engines, but likely impractical. Perhaps rockets could be launched from the top of a giant zeppelin once it reaches altitude? (~4 orders of magnitude larger than the Hindenberg)?
I've always been curious as to how effective a hydraulic lift could be at reducing necessary launch weight. A disproportionate amount of fuel is used at the beginning of the first stage when it is the heaviest, so seems like the benefit would be quadratic - Saturn V took 12 seconds to clear the tower. Would require major infrastructure, but if you could "throw" the rocket so it starts at a greater initial speed, seems like you could bend the rocket equation favorably. Perhaps even a giant underground potato-canon or railgun.
> I've always been curious as to how effective a hydraulic lift could be at reducing necessary launch weight.
I suppose you'd be able to approximate the effect by comparing the delta v needed to launch from a sea-level site (Cape Canaveral, Kourou, etc.) with that needed to launch from one of China's inland sites (e.g., Taiyuan, which sits at 1500m). I have no idea whether this data is publically available, though. I'd guess the bulk of your performance improvements would come from increased engine performance due to the lower ambient pressure (~0.83 atm according to Wolfram Alpha) rather than the increased altitude, since most of the energy is needed for horizontal acceleration [0]. The increased thrust would mean lower gravity losses, but I wouldn't be able to say how much.
A space plane is going to be more efficient. The idea is you fly the aircraft with jet engines (which use oxygen in the air) to their maximum altitude, and then switch over to rocket engines (which use oxygen in the fuel).
So far all demonstrations have been of rockets mounted under a jet engine powered aircraft, which then detaches at space launch. But I don't think there is any reason why you couldn't have a SSTO air/spacecraft, other than we don't have the propulsion technology yet - it works in KSP though :-)
