# Diagonal ice tunneling rover to reach a safe pressure in Mars?

Is the ice on Mars deep enough to bore down into it to sustain around 10 PSI (69 kPa) air pressure? The device I have in mind is a rover with a reactor that melts through the ice slowly to create a stable tunnel.

• Your question is unclear to me. Do you mean to ask if the ice goes down far enough that atmospheric pressure reaches 10psi (as @Starship has answered)? Or do you mean to ask if the ice is thick enough to have the strength to contain a 10psi pressurised atmosphere within it? Commented Jul 22 at 3:31
• What is the significance of diagonal? Commented Jul 23 at 12:49
• We've addressed this over on Worldbuilding but I'm not finding it right now. The rock collapses in on itself before you're deep enough. Commented Jul 23 at 21:06

There are two ways to interpret this question. In the techniques that I'm familiar with, where ice is melted by a probe to bore a hole, the melted water is allowed to refreeze into ice behind the probe. If we make that assumption, then the answer is...

"Yes, it is". Because ice is solid, a pipe made of ice can contain a gas inside it. The amount of force trying to break the ice apart is the internal pressure of the gas times the cross-sectional area of the gas. The amount of force holding the ice-pipe together is the cross-sectional area of the pipe times the tensile strength of the ice. For the pipe to not burst open, the following must be true (with some engineering margin):

$$P\times d_{inner} < \sigma_{ice} \times (d_{outer}-d_{inner})$$ where $$P$$ is the difference between the internal pressure and the external pressure, $$d$$ is diameter, and $$\sigma_{ice}$$ is the tensile strength of the ice.

The minimum thickness of the pipe wall is thus proportional to the inner diameter of the pipe. So if you bore a sufficiently small hole, you will not need much ice around that hole to contain the pressure of the gas inside the hole - assuming that you cap the end of the hole.

But if you are asking if you can get enough pressure by simply digging a deep enough open hole, then the answer is...

No. To work out how deep a hole you would need, you'll need to plug some Mars values into the Barometric Formula, or you can find a chart of pressure versus altitude and extrapolate. 10 PSI is 68947.6Pa, if you use the chart method, you can extrapolate to estimate how deep a hole you would need to dig.

It looks like you would need a hole roughly 60 km deep. The ice on Mars is estimated to be about 2 km thick on average. The ice is definitely not thick enough to melt or dig an open hole and have the air pressure at the bottom reach 10 PSI.

Short Answer:No, not by a long shot

How deep you would need to dig to reach 10 PSI (69 kPa)?

According to a formula provided by Karl Brace (source), "each extra 1000 feet (roughly 305 meters) of elevation multiplies the pressure by 0.979." Since Earth (14.7 PSI) is roughly 170 times higher pressure than Mars, 10 PSI (69 kPa) is roughly 116 times higher pressure than Mars. 0.979 to the power of -224 is also roughly 116. Multiplying 224 by 1000 will give 224,000 feet (68 km), which seems like a pretty good rough estimate.

Is the ice on Mars 224,000 feet (68 km) deep?

No. According to NASA, the South Pole (the region with the greatest average ice thickness) is about 3km deep in ice (source). This is only about 4.3% of the 224,000 feet (68 km) so unlikely. As well, NASA has also said that the "icy layers" are 3.7 km deep (source), which is only 5.4% of the way.