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It's just my typical luck: I discover and recover the billion-dollars worth of gold on a sunken galleon on the same day my arch-nemesis decides to detonate a one Megaton hydrogen bomb right above my main surface ship. My arch-nemesis thankfully could not resist the temptation to gloat, so she let me know about it in advance, just to tell me of my doom.

My (perhaps not so brave) initial reaction was to rush to the submersible (all the gold still on it) and start diving without telling any of my surface crew. (I took Mr. Whiskers with me, of course). ... Hmm, on the upside, my labor costs for the mission are about to go waaay down.

Now I need to be moving horizontally as soon as possible (the arch-nemesis will surely send her minions after me). Unfortunately, I can only dive or move horizontally, not both (I know, terrible design, but wrong time to point it out) so I need to know how far I have to dive to be perfectly safe before I switch to the horizontal movement mode.

Is it possible to escape a hydrogen bomb by diving in a submarine? If so, how deep do I need to go?

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Is the nuke an air burst (above the water) or in the water? If air burst the shock wave will hit the surface of the water and mostly bounce, meaning less of a pressure wave under water. If the nuke is in the water then the pressure wave will be a lot bigger. For reference: en.wikipedia.org/wiki/Underwater_explosion – AndyD273 Feb 9 at 19:56
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Next time, call ahead if you are going to break a date...a woman scorned is a terrible thing, but a one megaton device? – Thucydides Feb 9 at 20:34
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@Thucydides, she also keyed my car – Serban Tanasa Feb 9 at 20:39
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Shouldn't you ask this on Physics? – the dark wanderer Feb 9 at 21:10
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@thedarkwanderer, I would but past experience suggests -5 votes within 5 minutes, followed by exile to WB. – Serban Tanasa Feb 9 at 21:18
up vote 22 down vote accepted

Depth may not be your friend, but number of layers is. When the shockwave hits the surface of the water, much of it is reflected, but some of the shockwave is transmitted. How much? It turns out they wrote a book about it:

As discussed by Henderson et al. (1990), when a blast wave first contacts a water sheet, a large portion of the incident energy is reflected back towards the source due to the impedance mismatch at the air-water interface. The remaining energy, which is transmitted through the water sheet, forms the observed weak shock wave and the resulting initial pressure rise. For the experimental conditions considered here, the initial blast overpressure is mitigated by as much as 80%. This indicates that a water sheet may be an effective emergency blast mitigant.

In this case, the explosive was 48.4g of PETN (page 14), but I don't have any reason to expect any one shockwave to behave differently from another.

So how far do you need to be? Well, they haven't written a book about that, but they did write a text file about it. I'm getting a little nervous just how much attention this problem has gotten...

 Blast effects of nuclear bomb (this is for an 80 col. printout)
 All distances to effect in miles.   Note: airburst distances in ( )
 Airburst for optimum damage for that effect, since the height of airburst
 changes these figures represent worst case.  See example for fixed height 
results.

MT        1psi      1.5       3         6         10        30 overpressure
0.2       4(7.5)    3(6)      2(3.4)    1.3(1.8)  1(1.2)    .55(.6)
0.6       6(11)     4.5(9)    2.8(5)    1.8(2.6)  1.4(1.7)  .8(.9)
1.0       7(13)     5.5(10.5) 3.3(6)    2.2(3.2)  1.6(2)    .95(1.05)
5         12(23)    9(18)     5.5(10)   3.7(5.5)  2.7(3.5)  1.6(1.8)
20        19(35)    14(28)    9(16)     6(8.5)    4.3(5.5)  2.5(3.4)
(Update note: the 5 & 20 Megaton bombs only existed in old Soviet Bear and 
Bison class bombers and have been replaced with more modern 1 Megaton bombs.
The old US Titan missiles with their 9 Megaton bombs were scraped during late
1987 and early 1988)

...

Examples of damage (from SURVIVING DOOMSDAY -Clayton, from tables in THE
EFFECTS OF NUCLEAR WEAPONS 1977 -Gladstone) 
0.5 psi Private airplanes damaged but flyable, windows have light damage 
1.0 psi Windows heavily damaged, wood frame houses lightly damaged 
1.75 psi Some, but not all, glass shards capable of penetrating abdominal wall.
2 psi Human body thrown hard enough to cause incapcitating injuries if standing
3 psi Human body thrown hard enough to cause 1% fatalities if standing up.
4 psi Forest road impassable due to fallen trees.
5 psi Wood frame house collapse, 1% of eardrums rupture (in the elderly) 
6 psi Human body thrown hard enough to cause 99% fatalities 

From this chart, 6 psi is enough for a 99% fatality rate. You're in a submersable, so that's 6psi in the air of the sub. The reflection off the surface means you need 5x that shockwave pressure (reciprocal of 80%), which is 30psi suggesting .95 miles of distance is needed. However, there's more to this, because you have two impedence mismatches. One from air to water, and one back from water to air. These effects stack, meaning you need 25x more pressure at the surface to affect you. Thus, you would need a 150psi shockwave hitting the water to reach the essential 6psi. If we look at the table, that pressure is remarkably hard to hit. Obviously the table doesn't go that far, but I'd be tempted to guess its around 0.1mi, or about 500 feet. As a point of comparison, Little Boy, the bomb dropped on Hiroshima, was detonated at 1,968 ± 50 feet. I won't play CONOPS games with nukes, but I'm guessing that by the time the shockwave hits the water's surface, it's gone far enough to be below the magic 150psi level.

How about radiation? Piece of cake. From our sister site:

We know from the nuclear power industry that spent fuel storage pools are pretty safe places to be around, radiation-wise. They're actually safe to swim in, to a point, because they're serviced routinely by human divers. They just can't get too close to the spent fuel.

We use these pools for short-term storage because water is a really good radiation shield. How good? Well, according to a report on the topic prepared for the DoE back in 1977, a layer of water 7 centimeters thick reduces the ionizing radiation (rays and particles) transmitted through it by half (the remainder is captured or moderated to non-ionizing energy levels, mainly heat).

Considering that you can hold your breath and dive to 700cm in a pinch, radiation is going to be a non issue for any submersible.

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Radiation might not be much of an issue anyway, due to the bomb being a hydrogen bomb. It does use a fission component, but that's probably smaller than a full-fledged fission bomb. Fusion won't release radiation. – cst1992 Feb 10 at 10:15
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I think you quoted wrong sister site : what-if.xkcd.com/29 – Euphoric Feb 10 at 11:51
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I doubt the submerisble would shrug off 6 PSI though. Surviving the blast is small comfort when you drown. – Fax Feb 10 at 12:31
    
Oh, a question if you don't mind: did they took into account the effects of the thermal layer? Thats important for sonar-stealth, because it does reflect sonic-waves (simplified), so will a thermal layer help bouncing off that shock-wave too? – Confused Merlin Feb 10 at 12:52
    
@ConfusedMerlin No, I did not take into account for that. The air-water boundaries were good for the 80% reduction in the experimental test they did. The temperature boundary would be more complicated, so I didn't look it up. – Cort Ammon Feb 10 at 14:37

The closer to the water that it is when it goes off the more energy is distributed to it. Air is a 'compressible' medium and so a body can deflect some of the pressure wave around itself. However water is not. Air allows for shrapnel and debris to travel and be dangerous projectiles. In water, it's reverse, the water significantly reduces the speed of projectiles and "radioactive particles" however it does transmit much more of the pressure wave directly.

It's like the difference between taking a long spring and pushing against someone to try and knock them over vs. taking a steel pole and pushing against them. The steel pole has a lot more direct transfer of the energy applied.

Quoted

If you stood outside of shrapnel range for an exploding hand grenade, you'd likely remain unharmed. If you stood at the same range to an underwater explosion, the pressure wave would probably kill you [source: Landsberg]. When the wave reached your skin, it would pass through you. After all, little of its power would be reflected because your body's density is similar to that of the water. The wave would hit the air-filled pockets of your body and instantly compress the gases there, possibly resulting in blocked blood vessels, ruptured lungs, torn internal tissues and even brain hemorrhaging. Waves hitting the surface of the water or the bottom of the pool would bounce back, inflicting even more damage. Explore the links on the next page to learn more about explosions, the human body and how to survive other dangerous encounters.

This implies that you would need to be farther away from the blast than if you were on the surface of the water. That is also with the expectation that it was at least partially submerged when the warhead detonated.

Water doesn't compress well and the deeper you go the more pressure there is on the hull, now add a huge blast 'pushing' that water down even more, it will try to collapse all air pockets to help 'relieve' the pressure. Your little tin can would need to be extra strong. I would guess that being just a little way under the surface and traveling as fast and far away from ground zero would be your best chance of survival.

Going straight down, you are adding more water pressure putting your sub ever closer to its tolerances. and keeping you in direct line of the pressure wave. Going straight away just under the surface you change the angle of 'attack' very quickly as you run. if it blows above the surface the angle of reflection get easier for the water to deflect the farther you get away. If it blows under water you can more easily move with the water or might be deflected out of the water, like puss from a zit.

So my WAG is about 10ft down and tear out as fast as possible. Try to be a mile away or more if you can.

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Given that the bomb is detonating above the water's surface (see comments on the question) the pressure wave through the water is going to be minimal. Again, due to air's compressibility and water's lack thereof. – Draco18s Feb 9 at 20:42
    
@Draco18s yes, that was added later. But all it would do to my recommendation would reduce how far you need to be to be 'safe' – bowlturner Feb 9 at 20:44
    
True, it would. – Draco18s Feb 9 at 20:46
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@SerbanTanasa So I can't read. – bowlturner Feb 9 at 21:05
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Horizontal evasion has the advantage that hull pressure due to depth is minimized, so if the hull is breached the sub does not collapse like a tin can under an elephant, and hull failure is MUCH more survivable. Plus, you can still have a chance of getting to the surface to deploy your escape hydrofoil. – WhatRoughBeast Feb 9 at 21:22

You're probably not going to be able to escape by going down.

But this depends on what depth your ship was designed to withstand.

This paper gives equations to calculate the psi from a variable TNT equivalent bomb at a variable depth under the water (in feet, sorry) from the explosion on the surface.

$P = 0.7 * 2.16 \times 10^4 ({{W^{1/3}}\over{R}})^{1.13}$

Where $P$ is the overpressure in psi, the 0.7 coefficient is the attenuation due to being above the surface, $W$ is the charge weight in pounds, and $R$ is the range in feet.

The questions are derived empirically from this data: enter image description here

In your case, for a 1MT bomb, things don't look good. Your ship is probably able to go to at least 1,000 ft underwater (to collect the gold). In sea water that's about 460 psi. The overpressure from a 1MT surface detonation at 1,000 feet underwater is over 1,100 psi. So, unless your submersible has a pressure safety factor of over three times the operating depth, you're not likely to survive.

I don't know your planned depth, but I will estimate you have a safety factor of 20%. Given that information I can see that if you designed for 3,240 feet, and dove to that depth, the overpressure would just be inside your safety margins.

enter image description here

Note that the blue line only appears to be going back up because the additional overpressure has stopped diminishing faster than the growth of pressure at increasing depth.

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These tables seem to be for an underwater explosion. The OP indicated that the explosion is above the surface, which should help quite a bit! – Cort Ammon Feb 10 at 0:05
    
@CortAmmon Check the paper, it's for surface detonations. The pressure readings on the graph are, of course, underwater. – Samuel Feb 10 at 0:11
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Interesting. That leads to the question as to whether there are near field effects of a surface explosion that do not appear in an airburst, transmitting more of the shockwave downward. The airburst numbers I worked with yielded radically different results! – Cort Ammon Feb 10 at 0:17
    
Ah, I was looking for something like that; for whatever reason they only tested submarines with the underwater test at Bikini. The airdropped one only talked about surface ships. – Seeds Feb 11 at 18:59

One factor not discussed yet: Assuming you survive the blast and radiation, etc, what do you do next? Your ship is destroyed, and you're in a small short-range submersible miles from land. Even if the explosion was noticed by rescue parties (and odds are a 1 MT nuke would be noticed by somebody), they would naturally assume that nothing could possibly have survived. The ship would be in millions of pieces, it would be ages before anyone noticed that the wreckage of the submersible was not present in the debris. Also, you mentioned there were henchmen searching for you, and they would do whatever they could to hinder any potential rescue efforts.

Your submersible would eventually run out of fuel - they're not really built for long sea voyages. Even the process of diving and resurfacing requires energy to power the sub, and without the ship to provide recharging and refueling, your vehicle will soon be dead in the water. And I'm guessing you didn't have time to pack a water desalinater and few weeks worth of rations in there. Not to mention navigation equipment, so you might not even know what direction to go to find the nearest land. Air would also be a problem. You can't stay underwater forever, but surfacing to restock on air runs the risk of discovery by the villain's henchmen. Your most likely prognosis at this point would be a slow death by asphyxiation, thirst and/or starvation.

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I guess it will be a race between her minions and my remaining minions. – Serban Tanasa Feb 10 at 16:36
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@SerbanTanasa Yes, someone would definitely try to save you after you betrayed your crew. – Kiran Linsuain Feb 12 at 4:47
    
@KiranLinsuain the more practically-minded minions might consider the fact that Serban still has the gold in his sub, and now there are less heads to divide by. – Burki Feb 12 at 14:55

I'm thinking most surface ships are faster than submersibles, especially ones laden with gold. :)
The villain is unlikely to give one enough time to run on the surface, in either case.
I suspect one would not be able to submerge fast enough to get out of range either. A 1MT nuke at, or near the surface is going to vaporize a large amount of water, possibly just rendering it as Hydrogen and Oxygen plus all the other bits dissolved.

The radiation that isn't breaking down nearby matter into its component atoms is going to be winging through whatever medium you happen to have interposed, so assuming the primary and secondary shock waves do not crush/damage your submersible, you would definitely want to check your dosimeter to see what kind of lifespan you can expect on your organs, radiation lesions are supposed to be some of the most painful internal injuries.

You would want to be several kilometers away at the very least.

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Ouch, my liver just upvoted. – Serban Tanasa Feb 9 at 23:01
    
Water is actually pretty excellent at blocking radiation. A couple of feet should be enough. – DevSolar Feb 10 at 16:51
    
@DevSolar, the first couple of feet will likely get vaporized by the blast, alongside my employees, hehe – Serban Tanasa Feb 10 at 19:46
    
Water is excellent at blocking thermal neutrons, and adequate at blocking long wavelength EM, the shorter it gets, though, the more depth you need. Gammas are as short as it gets, you need like 40+ feet to keep from getting a sunburn. Spent fuel rods have nothing useful in common with a thermonuclear explosion. Spent fuel rods have very low activity, relatively, but compared to any weapon their activity is effectively zero. [rounded up] :) – Seeds Feb 11 at 18:54

Even if you escaped the explosion the chances of escaping radioactive isotopes is probably highly unlikely, but let's say you did. You technically would live slightly longer than those directly affected. Your chances of survival would depend how fast you can get medical treatment, if assuming such a treatment even exists. Radiation spreads faster than wildfire it can cover an entire block within seconds over several hundred km, you might even find taking an acid bath a more peaceful death than being affected by radiation. If it can affect air particles you can be assured the effects on water molecules can't really shield it. Though I would surmise a nuclear sub exploding would cause the body of water to become tainted for the next thousand years.

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Welcome to worldbuilding.SE Radioactive fallout from a land based explosion ends up concentrated at one level: ground level. In a water based explosion it would be spread throughout the water column, reducing its intensity significantly. I think if the water was ocean depth the tainting would be insignificant. Remember many nuclear bomb tests were carried out in the 1950s. – Level River St Feb 10 at 2:20
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Actually, water shields it quite well! – Charles Feb 10 at 4:31

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