What's the maximum depth that materials science could allow a submersible to dive to?

Factual Questions
1

Not wanting to hijack the ongoing Titanic-submarine thread, so an offshoot:

Suppose for a moment that the ocean’s depths were far deeper than they currently are - say, 200,000-feet oceans (we’ll ignore the other ramifications of that and just examine the depth):

We’ve made submersibles capable of going to 30,000 feet, as the manned descents to the bottom of the Mariana Trench proved. At what point would materials, and metallurgy, reach its limit and a submersible would reach its max limit?

Is a 60,000-foot-diving-without-imploding submersible possible?

2

A related question would be - what’s the maximum pressure water can be under? Depth = mass of water, more or less, so at what point does the sheer weight of all that water turn it into… Something else? Like, at some point, fusion would happen and you’d be “diving” into a plasma, right?

Edit to answer my own question: Surprisingly, someone seems to have done the math on this! You’d need stellar quantities, a water-star 13 times larger than Jupiter to start fusion. So Velocity’s deep dives are nowhere near this kind of theoretical ultimate limit.

3

60,000 feet is 25,980 PSI. if I did the math right.
I used 2 different calculations and it appears to be correct.

1 foot of water depth = 0.433 psi

Greatest ocean depth is 36,200 feet or 15,674 PSI.

4

You won’t get any fusion until you’re on something the size of a brown dwarf or bigger, so a quick googling says somewhere north of 200 million feet. For comparison, Earth is approximately a mere 42 million feet in diameter.

5

We can build some pretty strong containers. Depending on what you want to go inside the deep sea sub plays a role. It could have a thick hull and small interior space that was very cramped for people. It could have internal bracing. It could have the interior air pressure increased to match the outside pressure more closely. But all of those methods make it less suitable for people onboard.

6

Structural steel has a maximum compressive strength of about 25,000 psi (according to Mr. Google), so I would say a 60,000 submersible is probably possible, but it’s going to take some serious material science and engineering to give the submersible enough of a safety factor to allow a human to sit inside of it.

I suspect that a 200,000 ft submersible is well beyond our capabilities at the moment.

7

How far away are carbon nanotube material of any size? That seems like the only material within reach that might be able to handle more than 60,000 deep.

I’ve seen estimates that it may be able to handle 500,000 PSI. I’ll look for a cite.

Can you build with Tungsten? That can handle 500,000 PSI.

8

Are you looking at the strength of the material in tension, or compression?

The problem with compression is that the minute you have a any kind of flaw in your surface it creates a stress riser that will wreck your day.

Lots of materials are very strong in tension (carbon fiber), but lousy in compression.

9

Not if the material has sufficient plasticity, like steel. A hollow sphere with incredibly thick walls would do fine in the hypothetical 60,000 foot deep trench. How deep I don’t know but if we are assuming the ocean is made out of liquid water there should be a maximum possible temperature to consider at some point.

10

At about 500,000 PSI, water becomes solid, a form known as Ice VII at any temperature below room temperature.

The ocean floor on Europa is suspected to be composed of Ice VII, but not because the pressure is that high, but because it’s likely very cold. Becaue Europa is small, even though the oceans are 100-200 km deep the equivalent on Earth would be a dive to about 13-26 km, which is within the range of deep diving tech today. However, we’d have to figure out how to do it with much less weight.

11

Here is the formula you need:

https://www.piping-designer.com/index.php/disciplines/mechanical/stationary-equipment/vessel/3097-hoop-stress-buckling-load-external-pressure-or-vacuum

12

That would be about 350 km of water at Earth’s gravity, if I’ve done the calculations right. A big if.

13

A diamond sphere, with a 2 m crew sphere on the inside and 2 m walls, would be able to survive a pressure of around 600,000 atm, or 9 Mpsi. In that case, the thick-walled pressure vessel equations hold, but since the crew space radius is fairly small compared to the total radius, most of the terms drop out and you end up with the compressive strength of the material. Which is about 60 GPa for diamond (though it could be higher if you’re careful with the crystal orientation).

The sphere would sink in water. But that’s ok; you can use the same trick as the vessels that went to the Mariana Trench did and add flotation devices. The Trieste used a container of gasoline. Whether that continues to work further down depends on the compressibility, but I suspect it would be ok; water tends to be more compressible than hydrocarbons. And there are other solutions (new vessels use syntactic foams, though I don’t know what their limit is).

Anyway, it looks like you can go as far down as you want in water before it turns to solid. You can go down further if you are diving in a sea of hydrocarbons, or even just liquid hydrogen. Diamond will still do well, but the buoyancy problem is trickier. I wouldn’t try it.

But that’s just normal material science. Dumb materials. Active structures, on the other hand, can have virtually unlimited strength. Consider a cylinder divided into rings. Each ring has a set of masses inside it, revolving around the perimeter. They’ll exert a centrifugal force against the outside. And they can be made to revolve as quickly as necessary. They still need to be braced against the outside, but what this means is that your wall thickness is limited, which means you can scale up the whole vessel as much as necessary.

A cylinder would need to have its endcaps braced. That could be done with a linear accelerator, where masses “bounce” back and forth between the caps, exchanging momentum to counter the crushing forces. Or, you could build the vessel like a torus, with rings along the major and minor radii.

Sure, there are some engineering challenges here, but you asked about theoretical limits…

14

I like the cut of your jib, Sir!

Although embarking and debarking might be a tad challenging until one invents the Star Trek transporter.

15

If you can make perfect diamond spheres, then you can probably just make it in two halves, with atomically flat mating surfaces. Just get in one half and push the two pieces together. They should bond quite nicely.

To get out, just smash it open along one of the planes. Should cleave as easily as a gemstone. Just throw it out after that. I mean, it’s just carbon. Shouldn’t cost more than the equivalent volume of coal.

16

Once we’ve perfected direct molecular assembly that will work great. Until that time it’s … problematic as the kids say.

That’s about 109m3 of diamond. Which weighs about 385K kg. Which is less than I expected. With carbon’s atomic weight of 12, we’re looking at about 32M moles of carbon. So about 1.8E31 carbon atoms.

Your molecular assembly machine had better work fast.

17

nevermind edit window closing

18

Nitpick

Nitpick:

Based on the chart linked below, it seems that at moderate temperature and increasing pressure you will probably first hit Ice VI at around 145,000 PSI, so if zimaane calcs are correct and linear, maximum depth is a bit over 100 km

Meanwhile if you are on Europa with lower pressure but extremely low temperature you are probably getting ice XI.

Vonnegut fans might be interested to know that ice IX does exist :scream:, but relieved that it only exists at very low temps and high pressures. :relieved:

19

It’s even more relieving to know that actual ice IX and Vonnegut’s ice IX have very different properties. The real one is much better behaved.

20

Granfalloons also exist, but I tend to think they are far less well behaved.