Science Forums 2

modest · 04-29-2009

Quote:

Originally Posted by Titas Aduksus

OK,

If I were to be given the task of colonizing Mars with the facilities and technologies of today I think it would go something like this, (with acknowledgement to Bob Newhart)...

I would plan the building of a shaft sunk into the ground at such a shallow angle below the horizon, and continue this shaft until it re-emerged that at it's deepest point the collected atmosphere within the tunnel would be close to 1 earth atmosphere.

At this depth a large cavern could be excavated to house the neccessary life support systems for both plant and human habitation

This is an interesting idea. We could figure the depth such a tunnel would need to reach on Mars to attain 1 earth atmosphere's pressure. The equation for atmospheric pressure at height is given by:

$p=p_0 e^{(-h/H_S)}$

where p is pressure, $p_0$ is pressure on the surface, h is height above / below the surface, and $H_S$ is the so called "scale height" equal to $R_gT/g$ . On mars the values are:

$p_0$ = 7 mb
$H_S$ = 10.6 km
-source

To solve for pressure as a function of h we rearrange:

$p=p_0 e^{(-h/H_S)}$

$a = e^b \Leftrightarrow b = \ln(a)$

$\frac{-h}{H_S}=\ln{\left(\frac{p}{p_0}\right)}$

$h = - \ln{\left(\frac{p}{p_0}\right)}H_S$

And now to solve for 1013 mb (earth's atmospheric pressure at sea level)

$h = - \ln{\left(\frac{1013}{7}\right)}10.6$

$h = - 52.73 \ km$

So, in order to have a pressure on mars equivalent to earth we would need to dig a hole 52.73 kilometers deep. The deepest mine shaft on earth is 3.5km and the deepest we've been able to drill (a small hole) is 15 km. Therefore, there's probably a good argument to be made that making a ~50 km hole on Mars would have seemingly insurmountable practical problems. Rather than saying it's completely impossible, I would just say that making an airlock system for a shallow tunnel would be easier.

It also might be interesting to know how long this tunnel would be if it is constructed how Titas explains:

Quote:

Originally Posted by Titas Aduksus

I would plan the building of a shaft sunk into the ground at such a shallow angle below the horizon, and continue this shaft until it re-emerged that at it's deepest point the collected atmosphere within the tunnel would be close to 1 earth atmosphere.

Knowing the radius of mars is 3390 km and the maximum depth of the tunnel would be 52.73,

The length of OE is AO-DE or 3390-52.73 = 3337.27. As $a^2+b^2=c^2$ , the total length of the tunnel would be,

$l = 2 * \sqrt{3390^2 - 3337.27^2} = 1191 km$

And, again, the longest tunnel on earth (which isn't yet complete) is the Gotthard Base railway tunnel at 57 kilometers. The one on mars would be 20 times as long as anything we've done on Earth.

It's an interesting idea to think about, but I think there would be easier ways to build a settlement on mars.

~modest

Science Forums 2

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