|Quoting CygnusChicago (Reply 25):|
Not sure how you get the 7% reduction. If you consider a standard equitorial LEO launch, you need about 30,000 fps to get into orbit, and that includes the gravity and drag penalty. If you launch at Mach 0.85 at a 25 degree inclination, you gain about 1,500 fps delta-V over vertical ground launch, (...)
The basic amount of reaction mass (for a rocket that's fuel plus oxidizer) to achieve a given delta-V is given by the general rocket equation (also known as the Tsiolkovsky rocket equation, http://en.wikipedia.org/wiki/Rocket_equation
In short, for a vehicle mass of 1, the required reaction mass is M=(e**(delta-v/Ve)-1). Where Ve is the exhaust velocity. Note that the nature of the reaction mass does not matter, just its velocity. You can be throwing rocks, ions or superheated steam out the back end at 5000m/s, and it's all the same.
This is basically the rocket version of the Breguet range equation.
Anyway, The better liquid bi-propellants (for example, LOX/LH) manage a Ve of about 5000m/s, or about 16,400 ft/s. Using that, to get 30,000ft/s of delta-V, requires about 5.5 units of reaction mass. So if your single stage vehicle ended up weighing 100,000lbs at burn out, it would weigh 650,000lbs at the start, 550,000lbs being reaction mass (aka fuel and oxidizer). Reducing the delta-V requirement to 28,500ft/s, reduces that to about 4.9 units of reaction mass, or a starting vehicle mass of 590,000lbs (490,000lbs of fuel), or a reduction in fuel/oxidizer requirements of about 10.5%. And that assumes that there are no secondary benefits (for example, lighter structures) from reducing the fuel load.
The point is that reaction mass requirements are exponential as the desired delta-V increases relative to the exhaust velocity, and delta-V's greater than about three times the exhaust velocity are basically impractical (at three times you've got 95% of the starting mass of the vehicle being fuel, at four times, it's well over 98%, at five times, it's 99.4%). You're only hope is to reduce the final vehicle mass or increase the exhaust velocity. The first is the reason for staging, and the second is why ion drives are so attractive - the exhaust velocity is very, very high. Unfortunately, staging is still problematic, as each lower stage tends to grow substantially relative to the one above it, and exhaust velocities have stagnated at about the 5000m/s mark for engines that generate the significant amounts of instantaneous thrust required for a launch from earth.