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I know earth's atmosphere is a show stopper for rail gun launch to orbit from Earth's surface.

The vacuum of the moon is often cited by lunar enthusiasts who point out lunar mass drivers could provide a lot of delta V.

But how about a rail up Olympus Mons? At $.02 kg/m^3$ Mars surface atmosphere is already rarefied. And at 22 km, Olympus Mons is a very tall mountain. At 3.5 km/s, Mars orbital velocity is a little less than half that of earth.

Is the air at the top of Olympus Mons thin enough to allow rail gun launches to orbit?

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I've been wondering this for years, not knowing how to approach the problem.

Then at a NasaSpaceFlight thread a poster who calls him(her?)self R7 told me about dynamic pressure, also known as q.

$q=.5*\rho*v^2$

q is measured in pascals. R7 told me the expression Max-Q is the maximum dynamic pressure a space craft endures during it's flight.

Page 109 of Introduction to Rocket Science and Engineering by Travis S. Taylor says the Shuttle's Max-Q was at an altitude of 11 km at a speed of 442 m/s. Max-Q was about 35,000 pascals.

What's the density of Martian air at the top of Olympus Mons? According to the Mars Fact Sheet the density of Mars surface atmosphere is $ .02 kg/m^3$ and the scale height is 11.1 km. Since Olympus Mons is 22 km high, it seems to me the the density at the mountain top would be $e^{-22/11.1}*.02kg/m^3$ where e is Euler's number, about 2.72. That gives a density of about $ .0028 kg/m^3 $. Mars orbital speed at 22 km altitude is about 3,540 m/s. Plugging these numbers into

$q=.5*\rho*v^2$

I get a dynamic pressure is about 17,268 pascals, or about half of the shuttle's Max-Q.

So at this point I believe Mars' atmosphere wouldn't be a showstopper for an Olympus Mons railgun.

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  • $\begingroup$ Dynamic pressure relates to the size of your structural problems (the acceleration loads in the mass driver will likely be a bigger concern than the aerodynamic loading at the muzzle). The other key parameter to consider is stagnation temperature, to assess the magnitude of your thermal problems. $\endgroup$ – Daniel Chisholm Feb 4 '15 at 12:12
  • $\begingroup$ @DanielChisholm Olympus Mons is about 600 km in diameter. Assuming a 300 km track, I get a little over 2 g's over 3 minutes to achieve 3.5 km/s. I followed the link but I still don't know what's meant by stagnation temperature. $\endgroup$ – HopDavid Feb 4 '15 at 23:29
  • $\begingroup$ You'll need to add another factor: the extra speed you need to compensate for atmospheric resistance on the way up. $\endgroup$ – Hobbes Feb 5 '15 at 13:53

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