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In my question What is the largest achievable oxygen-atmosphere world?, my answer suggests an atmosphere of standard terrestrial air with a sea-level pressure of 20 ATM and platforms at an altitude of 25,250m above sea level.

This world is a water world, with a deep global sea. At the 1 ATM altitude, humans live on a number of suspended platforms. Surface gravity is 1g.

If an unprotected human was to fall from one of the platforms - or indeed from any other height between 5,000m and 31,000m, and didn't suffer from Nitrogen narcosis or Oxygen toxicity on the way down, would they be able to survive the fall into the ocean below? Would their potential survival depend upon maintaining a correct posture to minimise terminal velocity and to transition to a diving posture just before impact, or could they survive even if unconscious and falling in entirely the wrong postures? What physical condition might they be in after such a fall?

In other words, disregarding other environmental factors, would the terminal velocity of a fall through such an atmosphere be sufficiently low that a human might survive a fall into water?

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Entering water at high speed is serious business already before reaching terminal velocity.

At what height is it dangerous to jump into the water? Although risky, competitive high divers can enter the water from as high as 27 meters without injury, states Swim England. From this height, divers can reach speeds up to 60 miles per hour. However, serious injury is possible, even when jumping from much lower platforms. From a 10-meter platform, divers still hit the water at speeds of 36.6 miles per hour, according to an article published in the September/October 2017 issue of Current Sports Medicine Reports.

These speeds cause divers to hit the water with incredible force. While water may offer a softer landing than the hard ground, it still exerts a tremendous amount of force on divers' bodies, slowing their speeds by more than 50 percent in only a fraction of a second.

With proper form, the body can absorb the pressure from the impact. High divers typically enter feet first, allowing the feet and legs to absorb the impact. Many other divers enter with the hands and arms extended to protect the head and neck from impact. Even with correct form when entering the water, divers may experience overuse injuries in the joints, especially the wrist and shoulder. Moreover, the position which allows minimal terminal velocity is not the one considered proper form while entering water.

Note that those height are far from allowing reaching terminal velocity, and having a proper form after sky-falling for 20+ km is challenging.

Even considering the increased density of the atmosphere, let's not forget that the terminal velocity in inversely proportional to the square root of the density, so for example a 4 time denser atmosphere would only half the terminal velocity.

The square root of 20 is 4.47, and in the optimal position, human terminal velocity at 1g, 1 ATM is 200 KPH. In a head/foot down scenario, terminal velocity might be as much as 290 KPH at 1g, 1 ATM. That makes it an impact velocity of about 45 to 65 KPH at 1g 20 ATM. As divers can safely enter the water at up to 96 KPH with good form, it sounds survivable to me.

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    $\begingroup$ My two cents: at 1 atm, when you enter the water at high speed a lof ot the water moves outta the way in a huge splash, saving you from a lot of damage. At 20 atm though? The atmosphere will resist the splash much more, meaning less water moves to make way for you. That will hurt like hell. $\endgroup$ Nov 13 '21 at 6:17
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    $\begingroup$ The water won't have a greatly higher density due to its relative incompressability compared with air. The splash may not be as high, but I think it's pretty safe to say that the water will move out of the way almost as readily... and the terminal velocity is a lot lower than that of a reasonably diveable fall from 27m. $\endgroup$
    – Monty Wild
    Nov 13 '21 at 6:35
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    $\begingroup$ The real problem is going to be the temperature... at 15°C at 25km, the temperature at sea level is going to be around 141°C, though it won't be boiling because the boiling point will be around 210°C. It'll be like a pressure cooker down there. $\endgroup$
    – Monty Wild
    Nov 13 '21 at 6:39
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    $\begingroup$ @TheSquare-CubeLaw - The water splash is definitely better than a hard ground splash cthunk, but still not survivable in Earth atm terminal velocity of an unprotected human body - even the water can't move fast enough. That won't hurt at all, a human brain won't survive enough to register the pain. $\endgroup$ Nov 13 '21 at 7:38
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    $\begingroup$ @AdrianColomitchi, There are online calculators for the boiling point of water at any pressure. At 20 ATM, The BP of water is 210.47°C IIRC. It's based on the vapour pressure, I think. $\endgroup$
    – Monty Wild
    Nov 13 '21 at 8:20

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