Here’s something interesting I found on the subject:
I’m an engineer in physics and I have made some calculations.
Note that many numbers are rounded. It won’t be exact, but the order of magnitude is as interesting as exact numbers here (and easier to calculate).
The submarine can be modeled as a cylinder with a length of 6.5 meters and a radius of 1 meter. It then has an area of A = 2pir^2 +2pirl = 2pi*(r^2 + rl) = 23*(1 + 6.5) = 6*7.5 = 45 m^2.
The water pressure at a depth of 3800 m is 380 kgcm^-2. The total pressure on the submarine’s hull is 380 kgcm^-2 * 45 * 10000 cm^2*m^-2 = 1.7 GN.
In the event of a total implosion of the pressure hull, this will rupture and the parts/shrapnel will fly into the center of the submarine at high speed. The submarine reportedly weighs 11,000 kg excluding ballast. Newton’s second law gives the acceleration of these parts during their one meter long “journey” towards the center of the submarine: F = ma -> a = F/m. a = 1.7e9 N / 1.1e4 kg = 1.55e5 ms^-2 (or 15500 G). We assume here that the implosion is symmetrical, which is not entirely true, but it will do as an approximation.
Implosion processes are much more complicated than explosion processes. The world’s first atomic bomb, “the Gadget”, which detonated in the Nevada desert on July 16, 1945, was of the implosion type, i.e. a plutonium core surrounded by a large amount of conventional explosives with the detonation directed inwards. With the resources of the time, it was impossible to calculate the progress, so it had to be tested practically with hundreds of tests.
The law of motion s = at^2/2 gives 2s/a = t^2. t = sqrt(21 m / 1.55e5 ms^-2) = 0.004 s (4 ms). This is a relief! The nervous system has a reaction time of at least 100 ms to react (and this only if you are prepared for what will happen, such as a sprinter in the starting blocks). In any case, the time is far too short for you to even have time to perceive that you are dying. So no anxiety.
Now we will calculate the speed that the fragments have when they hit each other in what was just before the center of the submarine: v = at -> 1.55e5 ms^-2 * 4e-3 s = 620 m/s .
The total kinetic energy is W_k = m*v^2/2 = 11000 kg * (620 ms^-1)^2/2 = 4.2e9 J (4.2 GJ), or coincidentally quite exactly equivalent to a detonation of one ton of TNT. This deflagration is indeed eleven times slower than the equivalent with TNT, but the deceleration during the collision is released as heat energy and is certainly enough to heat up the remains of the submarine to tens of thousands of degrees for a short while before they are cooled by the sea water. The water and blood in their body instantaneously boiled and super heated into a fine pink mist to then be squeezed out of the sub like a tube of toothpaste.
We can also calculate the power: P = W/t = 4.2e9 J / 4e-3 s = 1.1e12 W = 1.1 terawatts. That is roughly 200 times New York City’s entire electricity consumption during those 4 milliseconds.
We are thus dealing with a detonation of a ton of high explosive in a space as large as a minibus, which causes the internal dimensions of the submarine to shrink to one four-hundredth of its original size and with a temperature of tens of thousands of degrees, where the power is 200 times NYC’s electricity consumption for a brief moment.
Yes, good luck finding even the slightest trace of the five bodies there! The parts that have been found so far have, as far as I understand, been on the outside of the hull. It is possible that jewelry, metal keys, etc. may have survived the impact, but human tissue - not a chance. Any small pieces of tissue would drift away with the currents and soon be devoured by benthic animals. Even bones are quickly dissolved by the sea water or eaten by fish.
In 1977, a small passenger plane crashed into the water off Madeira (I was actually on Madeira when it happened!) and the wreckage lies at a depth of just over 100 meters. The wreck is complete and several passengers had managed to swim ashore. Twenty years later, dives on the wreck and in the cabin revealed that there was nothing left of the dead. You could only see clothes made of synthetic material lying neatly in the seats where the passengers once had been sitting. All the remains had disappeared without a trace. Of the 1,514 who died when the Titanic sank, 70 years later not a single body could be found either. Only pairs of shoes and boots lying next to each other.
PS I am now reading that sonar buoys in the North Atlantic belonging to the US submarine defense recorded what was probably the implosion. Such strong shock waves can travel very far in the ocean depths. It is also the reason why no more than one vessel at a time was allowed to be at the Titanic’s wreck site. An implosion of one craft would certainly knock out the other as well. Actually, it could be enough for a small external light fitting on the submarine to implode for the submarine to suffer severe damage.
See Also
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- - Single Phase Power
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- - ELI5: Human Progress
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