Is a railgun up Olympus Mons possible?

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?

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.

• 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. Feb 4 '15 at 12:12
• @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. Feb 4 '15 at 23:29
• You'll need to add another factor: the extra speed you need to compensate for atmospheric resistance on the way up. Feb 5 '15 at 13:53