How rapidly would a manned capsule have to dive to simulate Martian gravity?

Question

This question is inspired by the following comment on Would colonising Antarctica be a good test for colonising Mars? :

This isn't a direct answer, but I think colonising underwater would be a better practice for colonizing Mars. Some problems are reversed in direction (you're trying to keep water out rather than air in), but the challenges are similar: you can't breathe outside and have to take precautions going in and out, reduced sunlight of similar length, isolation both physical and communication-wise (assuming there isn't an undersea cable), and unusual hazards.

Suppose we had a manned capsule that could dive into the depths of the ocean at a controllable rate. What acceleration would it need to maintain to simulate Martian gravity within the capsule?

If the capsule were diving to the deepest point in the ocean (roughly 7 miles or 11 km), how long would the inhabitants have in the simulated Martian gravity?

Suppose the capsule could also ascend at a controllable rate. If it turned around at the deepest point and ascended, how much additional time would this give in simulated Martian gravity before reaching the surface? I would think it would double the time, but I'm not sure.

Answer 1

Fluid resistance and with pressure and temperature changing viscosity of water would limit such tests to a rather short distance, depending on your acceptable margin of error. Unless you're able to constantly adjust buoyancy / rate of descent, and somehow overcome challenges of eventually hitting terminal velocity of your test apparatus in water.

Without it, and assuming ability to dynamically adjust buoyancy on descent, I get nearly exactly 60 seconds till the depth of 11 km at 6.096 m/s² (Earth sea-level gravity of 9.80665 m/s², minus Mars standard datum gravity of 3.711 m/s²), which is roughly how much of Earth's gravitational acceleration you need to remove to simulate that of Mars. Remember, we're still on Earth (well, slowly descending deeper into it, but 11 km isn't all that much compared to Earth's equatorial radius of ~ 6,378 km), so those 9.80665 m/s² didn't disappear.

Of course, your capsule would reach in 11 kilometers of free fall at Martian gravity over 366 m/s, which is above Mach 1 at mean sea-level Earth's standard atmosphere. So you'd have to employ some heavy drag reducing techniques, say a series of implosions in front of your capsule (on a parabolic trajectory) that would help if fall through it easier. I have no idea how to achieve that and keep capsule's acceleration more or less constant. Perhaps by installing a 11 km deep tube that had water evacuated and you replace it with some less dense (and inert, we don't want implosions at such depth!) gas. At such immense pressure (up to 1,100 atm), it would have to be quite a tube though.

For the ascent part though, you can't really do it. Your capsule's proper acceleration vector is negative to Earth's gravity, so all the forces combined within it don't partially cancel acceleration effect of Earth's gravity out, but add to it.