The matter of efficiency is simply stated.
The aerostat launch vehicle does not have to burn any fuel to achieve a high altitude.
Thus it may ascend above the thickest layers of atmosphere before it ever starts burning its engines.
This factor vitiates the drag due to air resistance,
which is where most of the fuel of the conventional lift vehicle is wasted.

As illustration, suppose the aerostat ascends to 60,000 feet before starting its engines.
(This is not an unreasonable figure: the altitude record for a free balloon is nearly twice that.)
It is above 90% of the atmosphere at that time, or in other words the air is only 1/10 as thick as at sea level.
The basic requirement to achieve orbit is a speed of about 20,000 miles/hour.
The less air gets in the way, the easier it is to attain that speed.
Since it also improves the total efficiency to use an air-breathing engine for part of that acceleration,
meaning the vehicle has to carry less oxidizer, the aerostat launch vehicle builds up much of its speed in the stratosphere.
This makes the angle of attack relatively low, keeping the vehicle in the zone which has enough oxygen to sustain the scramjet.
The tradeoff of a gradual ascent is remaining in the air resistance longer,
but this scheme easily bests carrying all the required oxidizer.

The efficiency comparison comes when the ground-launched rocket reaches the altitude at which the aerostat vehicle starts.
At that point, the Shuttle or whatever has already burned 80% of its propellant; the aerostat, zero.
The aerostat will need much less fuel to reach the same speed,
starting at a much higher altitude where the air is thinner.
Add to that advantage the weight of oxidizer saved by the use of the scramjet,
against that consumed by the pad-launched rocket.
In rocketry, saving weight is the name of the game.
Most rocket fuel is burned to push rocket fuel.
Any increment in efficiency is vastly multiplied in fuel savings.

It would be a good guess to suppose that the aerostat launch vehicle could achieve an efficiency advantage
between fourfold and tenfold over the metal rocket launched from the surface.
Without the drastic delta-vee (acceleration) required for a vertical launch,
the payload and passengers would not need to suffer such high gee forces to get to orbit.
This eases the design margins for all aspects of the flight, resulting in further weight savings.
Each pound shaved from the vehicle saves ten pounds of fuel, as a rule of thumb.

Having shown the soundness of the basic concept, the next step is to proceed
to more advanced speculation concerning refinements to the design.
Hydrogen has only 1/8 the mass of a corresponding volume of air, so hydrogen under moderate pressure,
say 100 psi (lb/sq in) at sea level, will still remain lighter than air.
This consideration almost invites consideration of a non-rigid envelope,
the traditional gas-bag blimp or elastomeric balloon concept but at greater pressure.
For the moment, we shunt aside the difficulties of supersonic flight in a nonrigid vehicle,
to consider only the pressure and buoyancy aspects of rising through the atmosphere in a pressurized vessel.
Pressurized hydrogen becomes heavier than air at a modest altitude.
This requires modification of the original scheme, of not igniting the engine until extreme altitude is reached.
Assuming a constant-volume envelope (not elastomeric), the lift can be calculated
to remain constant by burning off a certain proportion of the lifting gas during the ascent.
In other words, by the time the aerostat reaches a particular altitude,
enough lifting-gas hydrogen has been used as fuel for the ramjet to ensure the vehicle will have lift at that height.
The decrease in the density of the ambient atmosphere is balanced by a lower pressure in the envelope.
In this concept of the constant-volume nonrigid aerostat, the ascent is seamlessly integrated with acceleration.
Burning the lifting gas as fuel is a delightfully economical concept.

Regardless, the main fuel store must be in cryogenic liquid-hydrogen tanks.
Liquid oxygen will be needed as well, though a much smaller amount, due to the scramjet main propulsion.
("Scramjet" means supersonic combustion ramjet.)
With a favorable engine design, it may be possible to combine thr rocket engine and the scramjet engine,
so the same fuel-delivery system is used for both.
The proportion of rocket power to scramjet power could then be smoothly graded,
depending simply on how much supplemental oxidizer is introduced into the burn.
When the air becomes too thin to produce the ram effect, the inlet is closed off,
and the aerostat vehicle continues acceleration on purely rocket propulsion.
The inlet cloture, and oxygen injection, in short rocket power, is also used to start the ram.
A mere trickle of injected oxygen may also be used throughout the scramjet phase of operation,
for a torch inside the engine to maintain combustion, and eliminate the need for a flameholder structure.
The design principles of combining functionality, and smooth gradations of operational modes,
mark a sophisticated technology as opposed to one which is economically constrained to adopt the first design that works.

Whereaway?

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