Toward the end of 2010, I was reading this article by Rena Marie
Pacella, “[NASA Engineers Propose Combining a Rail Gun and a Scramjet
to Fire Spacecraft Into Orbit][0]”. The idea is that you use a
two-mile-long ground-mounted 180MW maglev linear motor (not a rail
gun) to accelerate an aircraft at 3 G to Mach 1.5; the aircraft then
accelerates to Mach 4 with turbojets and then, with a scramjet, up to
Mach 10 at 200 000 feet altitude, at which point a rocket orbiter
stage breaks off and goes into orbit.
In SI units, that’s a 3200-meter maglev track, acceleration of 30
m/s/s up to 500 m/s (thus taking 17 s, although the article merely
claims “under 60 seconds” --- maybe the acceleration gets smaller
toward the end of the track), and 61 km altitude. Mach 4 and Mach 10
vary somewhat with temperature, but at ground-level temperatures, Mach
10 is 3300 m/s. You need about [7000m/s][1] to get into orbit.
(A little calculating says that accelerating at 30 m/s/s up to 500 m/s
in 17 s will require the integral of 30 m/s * t dt from t=0 to t=17,
whose indefinite integral is 15m/s t², which is 4335 m, so somebody’s
fudging some numbers.)
My understanding is that you can’t just use a gun (chemical, railgun,
maglev track, or anything else) at ground level to shoot things into
orbit because of air resistance. Your projectile would have to start
out going much faster than orbital velocity and be braked on its way
up through the atmosphere down to orbital velocity. There’s about ten
tons of air above every square meter of ground, all of which would
have to be accelerated to orbital velocity or above — and with the
tangential direction you need to get into orbit, considerably
more. But it gets worse. Such high velocities adiabatically produce a
lot of heat that gets lost as radiation — so not only do you have to
provide the energy to accelerate the air, you also have to provide the
energy to keep it hot as it’s radiating energy away.
The alternative, to accelerate as you go, requires that you carry the
fuel with you on the way up. But [the specific orbital energy of low
earth orbit is about 32 MJ/kg][1], because staying in orbit requires
that you be going about 7000 m/s horizontally, and that’s dismayingly
large compared to the [energy densities of chemical fuel systems][3].
The consequence is that you have to spend most of your fuel
accelerating other fuel, and only a tiny amount of it accelerating
your “payload”.
So, that’s the reason for the Rube Goldberg contraptions we’ve used so
far to get things into space, and new ones like this. The big
advantage of this approach is that the fuel for the maglev track can
stay on the ground, and the scramjet doesn’t have to carry oxygen with
it to burn its hydrogen fuel. Hydrogen burns with about 140 MJ/kg,
but you need about 8kg of oxygen to burn 1kg of hydrogen, so if you
have to carry it with you, your energy density drops to 15 MJ/kg. The
scramjet avoids this problem by harvesting oxygen from the atmosphere,
and it and the railgun can contribute about a quarter of the energy
you need to get into orbit. You still have to supply the other
three-quarters the old-fashioned way, with rocket fuel.
But can you do better?
The troposphere extends up to about 8-18km, and the stratosphere up to
about 50km. You can lift small loads to 90km fairly easily with a
weather balloon, basically at the mesopause, the boundary between the
mesosphere and the thermosphere. At that height, the pressure is
about [0.2 pascals][2], much smaller than the 100 kPa at sea level.
This implies that about 99.9998% of the atmosphere is below this
altitude.
So perhaps you could launch a huge dirigible to the mesopause carrying
a maglev track, and use the maglev track to launch things directly
into orbit.
If your dirigible has a 100km track and you want to launch things at a
speed of 7km/s, we have (assuming constant acceleration)
a/2 t² = 100km, at = 7km/s
:. a = 7km/s/t
:. 7km/s/t t² = 100km
:. 7/s t = 100
:. t = 100 s/7 = 14.3 seconds
:. a = 490 m/s/s = 50 G
At the muzzle end of the track, you’d be dumping about 3.4 MW/kg into
your projectile and accelerating it at 50 G.
On the plus side, I think virtually all of your energy could end up as
orbital kinetic energy. 32 MJ costs about 90¢ at $0.10/kWh. 90¢/kg is
substantially less than the current price of lifting things into
orbit. Even if your launcher were only 10% efficient, the energy
would cost US$9/kg, which is still far less. Rockets, on the other
hand, dump the vast majority of their energy into the atmosphere.
On the other hand, the capital cost of the dirigible could be high.
The *Hindenburg*, the largest dirigible ever built, was only 245
meters long. We’re talking about a dirigible 400 times as long as
*Hindenburg*, one which could probably only be constructed in the
mesosphere; I think the troposphere and stratosphere are too windy.
[0]:
http://www.popsci.com/technology/article/2010-11/nasa-engineers-propose-combining-rail-gun-and-scramjet-fire-spacecraft-orbit
"Popular Science, 2010-12-17"
[1]: http://en.wikipedia.org/wiki/Orbital_speed#Earth_orbits
[2]:
http://www.grc.nasa.gov/WWW/k-12/Numbers/Math/Mathematical_Thinking/designing_a_high_altitude.htm
[3]: http://en.wikipedia.org/wiki/Energy_density#True_energy_densities
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