Relax wrote:The problem with partial space towers, is that the cost of fuel is the miniscule part of the cost to LEO. The missile is the major cost, not the fuel. Fuel cost, by and large, is inconsequential. Now, if the number of launches dramatically increases and the number of rockets produced dramatically increases, dropping their price tag, then and only then will the price of fuel even make a small blip on the total $$$ to LEO.
Fuel cost is trivial, but the need to devote a large fraction of the rocket's dry mass to fuel tanks is not.
From some Usenet discussions (quite a few years ago):
Geoffrey A. Landis wrote: Some of the advantages of high-altitude launch:
(1) You start with a fraction of the potential energy needed to get to orbit.
Blair Patric Bromley wrote: If you could launch at 10000 ft above sea level, you could reduce your velocity change to get into orbit by approx. 250 m/s. However, you need about 8000 m/s to get into orbit. A 3% improvement.
Landis wrote: But three percent is a *tremendous* improvement. A RL-10A has an Isp of about 450 seconds; thus, exhaust velocity Ve is about 4400 km/sec. Structure & payload mass fraction is exp[deltaV/Ve]; a RL-10A powered vehicle could achieve a maxium amount of structure plus payload to 8 km/sec of 16.3%. Typically about 5% of this is actually payload. A 3% decrease in delta-V to orbit increases this to 17.3%. This increases the *payload* to 6% of the gross lift-off mass -- a 20% increase in payload.
Landis wrote: (2) You start at a lower atmospheric pressure.
a. reduced atmospheric drag loss
Which wasn't commented on by Bromley or by Pat, but is a significant effect, at *minimum* equal to the potential energy gain.
b. vehicle can be designed with less attention paid to aerodynamics. Lower aerodynamic design penalty means higher performance designs (ie., smaller fineness ratio allows more efficient tanks)
c. More optimum trajectory possible; you can curve toward horizontal thrust much faster since you start out closer to out of the atmosphere
d. Max-Q occurs at a much lower pressure; lower aerodynamic stress on the system means vehicle can be designed lighter.
Pat wrote: I think Max-Q is going to be at the same altitude or lower depending upon tank fineness.
Landis wrote: To the contrary. Max-Q is the product of air density, the square of velocity, and a vehicle-dependent factor which depends on mach number. For a given acceleration profile, Max-Q occurs at the same altitude *above the launch site* independent of how high the launch site is. That is, the actual value of dynamic pressure will decrease linearly with the initial pressure.
Landis wrote: a. Higher performance out of the rocket nozzle at launch
Bromley wrote: Atm. pressure is about 10 psia at 10000 ft.
This would result in approx. a 2% increase in exhaust velocity, which, under certain assumptions would result in roughly a 3% increase in payload mass fraction.
Landis wrote: How do you figure? A 2% increase in exhaust velocity gives a 2% increase in Isp, Structure & payload mass fraction is exp[deltaV/Ve], or roughly exp[0.98 * 1.82]. I calculate this as a 3.6% decrease in *total* mass-ratio. Using the same [structure+payload] mass, that comes to an 11.8% increase in *payload* mass.
Adding this to the potential energy gain [factor of 20% payload increase] and the drag gain [quick estimate says another factor of 20%] gives (going back to the rocket equation, instead of adding the increases separately) an increase in [structure plus payload] to 18.9% instead of 16.3%. That increases the payload by 52%.
http://yarchive.net/space/exotic/tower_launch.html[Yay -- promotion to the List!]