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In the red corner, a top of the line Main Battle Tank, you can have your pick, but let's say a tricked out M-1A2 'Abrams' with a full Nuclear-Bio-Chem Protection kit.

In the blue corner, a Nuclear Device. Let's start by assuming a standard Teller-Ulam design, say a W70 warhead set for about 15kt TNT equivalent yield, similar to the Hiroshima bomb.

As an initial set up, set the detonation point 50 meters above ground at about 500 meters from the tank. The tank is on, sealed, and facing towards the blast. There is a clear line of sight.

Would the crew survive? If not, what would be the minimum distance to give the tank crew some sort of fighting chance? If yes, how much closer can the detonation take place? Alternatively, could some modification be made to the tank to dramatically increase survivability against atomics?

Note: As the hard-science tag is meant to indicate, feel free to persuade me with numbers, if so inclined. Numbers are sexy, especially when it comes to nuclear attacks and radii of total and utter destruction! In part inspired by this story.

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    $\begingroup$ Why are you using a 2nd league player instead of one meant for this purpose? $\endgroup$
    – SF.
    Mar 20, 2015 at 5:29
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    $\begingroup$ Oh man, this question, despite its simplicity, is a beast to answer. I'm writing one up now... $\endgroup$
    – PipperChip
    Mar 20, 2015 at 8:21
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    $\begingroup$ Doesn't Teller Ulam imply a hydrogen bomb, which is orders of magnitude more powerful than the stated values? $\endgroup$
    – March Ho
    Mar 24, 2015 at 12:38
  • $\begingroup$ @MarchHo, it simply means a 2-stage, fission-fusion device - the yield in modern weapons can literally be dialed in. $\endgroup$ Mar 24, 2015 at 17:34
  • $\begingroup$ @SF. Because there was only ever one built. "Object" is the Soviet term for "Prototype". $\endgroup$
    – Schwern
    Apr 16, 2015 at 16:43

5 Answers 5

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The Assumptions

That "Abrams" tank is 50m below and 500m as measured on the ground. Pythagoras (at least his theorem) says that's about 502m away, so that is the number I am going to use as "the distance" from the nuclear explosion. This is considered a "surface burst" when surveying literature about nuclear explosions.

There is a clear line of sight. This is (somewhat) important to establish, because atmospheric conditions affect different aspects of the blast. John Walker was nice enough to make an interactive version of the United States Department of Defense's and Energy Research and Development Administration's 600-odd page report on nuclear weapons. Despite the date of the report (1977!), the science appears to be good, and I will be using this as a source to inform this answer.$^{1}$

The Energy the Tank Receives

A nuclear explosion appears to have two main destructive methods of "doing damage" to things around it. There are the mechanical shockwaves of the explosion and then the thermal radiation from it. It is estimated (from section 7.01) that around 70-80% of the energy released$^{2}$ from a nuclear weapon is thermal, and the remaining 20-30% is kinetic energy in the form of the blast wave. I'll be using the values of 75% thermal energy and 25% mechanical energy.

Thermal Energy

Several sections in chapter 7 deal with the energy delivered by a blast to targets at varying distances. Sections 7.07, 7.96, and 7.101 build upon each other and eventually yield an equation for the amount of thermal radiation received by a unit of area ($Q_{thermal}$) at a particular distance D is: $$Q_{thermal} = \frac{\tau E_{thermal}}{4 \pi D^2}$$

Using this equation and the table for section 7.101, $\tau = .18$. Tau represents the absorption of the atmosphere due to water and the density of air molecules at the surface. Adding a quick conversion factor for the explosion's thermal energy, we find that $Q_{thermal} = 2.675 \frac{J}{mm^2}$ (or $2.675 *10^6 \frac{J}{m^2}$)

Kinetic Energy

This comes in the form of the "blast wave" which the tank will need to cope with. The energy does not hit all at once; indeed, the blast wave hits and then the pressure gradually decreases until it becomes negative. At which point, the atmosphere rushes back in, and restores the pressure. The peak pressure and dynamic pressure discussed in chapter 3 are important values to consider for such a blast. Section 3.19 claims that most damage is caused by the blast wave hitting a target, and not be the subsequent phases of the blast wave. Although a tank designer would be concerned about this, I am going to simplify this a little and ignore the subsequent phases.

As this is a surface equation, we can take the advice from 3.34, and treat it as an air burst with double the energy. This is not always the case, and it is an oversimplification, but we would need much more information to determine exactly how much energy (and pressure) gets at the tank.

We are going to use a similar equation for the distribution of energy per unit area as the equation we used for thermal energy. We are going to remove tau and double the kinetic energy though, so the equation is: $$Q_{shock} = \frac{E_{kinetic}}{2 \pi D^2}$$

We calculate that to be about $9.909 \frac{J}{mm^2}$! That's more than three times more mechanical energy per unit area than thermal energy per unit area. This blast wave looks promising for a lot of destruction.

If we take the Kingerly-Bulmash equation to estimate the overpressure, we come to an overpressure of ~258.6 kPa. That is enough to "severely damage" cement buildings four times over.

The Ability of the Tank to Cope

This is a little difficult, because it is in the best interest of many tanks, tanks used to defend living solders on active duty, to not publish their material properties. Specifically, I looked for and failed to find properties of Chobham Armor, a type of depleted uranium armor.$^3$ What I do know is this; heavy armor variants involves a depleted uranium layer along with one, but likely more, layers of composite material.

So I do not become the focus of investigation of national entities (the rep here isn't worth it), I'm going to look at something I can find information about; uranium. With a bulk modulus of 100GPa, it can get very thin before it deforms due to the shockwave of our nuclear blast. Due to the fact that our tank isn't a box, and it has angles to it instead of flat walls, even the reflective pressure, which can spike up rapidly, may not be enough to deform the tank. Additionally, uranium is good at conducting heat, so our tank needs insulation from other sources to protect its occupants. Finally, uranium is good at absorbing the some deadly types of radiation, so it can offer protection there for the crew.

It should be noted that weaponized nuclear explosions generally do not cause items to become radioactive. As a matter of fact, you can visit ground zero at Nagasaki without radiation suits! The metal of the tanks should protect the inhabitants from most cancer-inducing radiation.

The blast wave itself would most certainly push the tank. Weighing in at about 69.54 tons, this isn't trivial. If I do a gross oversimplification and model the tank as a box with a 93 in high and 144 in wide, it has an area of around $8, 639, 982 mm^2$ (this is an overestimate). That's around 85 613 588 J of energy. Assuming this is all kinetic energy, and using $K=\frac{p^2}{2m}$ (solving for p), the tank gains 52 m/s in speed from the blast wave. Obviously, the tank's grip on the ground will determine how far it goes. We'll use the kinetic friction coefficient found here; .57. Through a series of calculations, I find the distance travelled by the tank is about 46 cm, over 9.3 terrifying seconds. This is because the tank is so massive and has such a good grip on the ground. (Once again, I should say that the 46 cm is from the initial blast, not the total blast wave, which may push it a little further.)

It seems the tank, under these conditions, will likely survive, but the occupants will not. All said, it appears that a nuke-proof tank needs a lot more to protect the inhabitants than a uranium shell. Something like Object 279 may do. I could not find or calculate exact details on the needed properties, though, but it is a place to start.

The Occupant Survival

The occupants in this blast need to worry about that shockwave and the heat. A proper nuke-proof tank needs to absorb the shockwave and the radiation. It must also do this before those things get to the crew.

You need a lot of stiff and soft material between you and a shockwave to prevent the shockwave from hurting you. Looking at bomb suits, you need foams and some other materials to protect you from the blast wave. The exact configurations of these things are beyond my expertise and the length we would like to see on SE sites.$^4$ I therefore will just say this: these foams could also help insulate you from the thermal energy of the blast.

If you play with the Kingerly-Bulmash equation, you will notice that a human can survive the blast wave from about 3km away. Obviously, a tank can get closer, but I do not know how much the tank wall impedes mechanical waves. Therefore, I know that the tank can be closer, but I cannot confidently say by how much.

At 3km away, you need to worry more about the radiation than the shock wave. Not knowing how much an Abrams tank absorbs radiation, I can only say that the tank will likely be a good spot (with its high-density armor) to avoid irradiation. Uranium is used, after all, in shielding radiography cameras. As uranium absorbs gamma and x-rays well, it will greatly help deter the negative effects of radiation in a nuclear blast. It is supposedly five times better at absorbing radiation (x-rays and gamma rays) than lead! In fact, some people are trying to figure out how to use depleted uranium in concrete to contain nuclear waste.


Footnotes

  1. This report, despite being dry and official, even has the occasional funny heading such as that in chapter 6: Underwater Shock: Bikini Experience
  2. This does not include the energy emitted from the atmosphere. As the radiation goes out from the device, it is partially absorbed and then re-released by air. This is due to the air becoming ionized or excited, and then falling down to its rest state.
  3. This is bad news for this question, but the publication of this information is worse news for the world in general.
  4. I may come back to this to provide a better answer.
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    $\begingroup$ @KSmarts I would think so. However, the properties of Chobham armor are guarded secrets, so I can only speculate. $\endgroup$
    – PipperChip
    Mar 20, 2015 at 19:46
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    $\begingroup$ @SerbanTanasa I think some leeway needs to be granted here because we cannot answer those questions without knowing the limits of modern tank armor, which is guarded (unavailable to the public) information. $\endgroup$
    – PipperChip
    Mar 21, 2015 at 17:31
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    $\begingroup$ 52 m/s 9.3s 0.46m these figures for the blast-induced motion of the vehicle can't all be true. $\endgroup$
    – Jasen
    Dec 29, 2016 at 8:28
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    $\begingroup$ @Burki It's the transmission of the wave into the tank. The tank doesn't move much, true, but it can still impart a lot of kinetic energy into the air (and people) inside it. Without some sort of damping the wave goes through the tank walls and kills the crew. I just cannot tell how much damping there is: there must be some because tanks survive enemy fire and muffle outside sounds, but I cannot tell how much. Ultimately, I err on the side of pessimism. $\endgroup$
    – PipperChip
    May 5, 2020 at 14:23
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    $\begingroup$ I don't believe it's valid to ignore radiation in this case. For most bombs it's ignored because if you pick up serious radiation you die from the blast anyway. With smaller bombs the situation is different, the radiation effects can outrange the blast (which was the intent of the neutron bomb!) Here we have substantial blast shielding but our armor contains lots of uranium. While U-238 won't support a chain reaction it does fission in the flux from a bomb. While I don't know what's going to happen here I can easily see it increasing the dose, not protecting the crew. $\endgroup$ Aug 18, 2020 at 0:21
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I am an instructor in the U.S. Army (active Guard) and was a tanker on M60A3's and M1A1's from 1982 through 2006 when I became a Paladin mechanic

It HAS been done, with a much less survivable "Centurion" British tank. The blast moved the tank a whole 5 feet. It was damaged and the sensors placed inside showed that the crew would have most likely been killed from the pressure wave. The M1A1 is much more survivable.

Another thing to note, the instantaneous radiation of the detonation is LESS lethal than the blast and heat, unless it is the legendary... NEUTRON BOMB! Then, the radiation is lethal to a distance greater the blast/heat.

The site I used for my source is below.

http://io9.gizmodo.com/the-atomic-tank-survived-a-nuclear-test-then-went-to-w-1542451635

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  • $\begingroup$ Not just the neutron bomb. Think of the Davy Crockett, a commonly-cited example of supposed military incompetence. The bang is very small, the radiation is deadly considerably farther than the other effects. At max yield the radiation is lethal beyond the flight range of the weapon. (It's not actually a suicide weapon, though--you dive into a foxhole while the weapon is in flight.) $\endgroup$ Aug 18, 2020 at 0:24
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Operating a M1A2 there are ICBM and Nuclear Protections from pressurizing the inside, sealing all hatches and hull to blowing out the inside of the tanks air of radiation.

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  • $\begingroup$ Welcome to Worldbuilding! This answers the question pretty definitively - do you have a link that contains more details about this (and would you be able to summarise more details in this answer)? Thanks! $\endgroup$ Jun 25, 2018 at 7:16
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They are pretty durable vehicles. Withstanding massive explosive forces at point blank range. But the question is what aspect of the blast are you talking about? The EMP from the blast. The air detonation wave? Ironically the Abrams M1A2 uses depleted uranium in it's armor matrix. Depleted uranium is used as a radiation shield so it may survive the blast, the emp and the ensuing fall out. Tanks have already survived nuclear blasts, an M4 sherman was modified with lead coating for the Trinity test. enter image description here

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They would likely not survive. Even IF they had some magical lead shielding which would protect them from some forms of radiation coming from the blast they still would die because their lead armor wouldn't protect them neutron radiation. The only way they could survive FOR AWHILE is to have some kind of layered shield protection of multiple substances. Something that could at first deflect the non neutron radiation like the lead then some other material to absorb the gamma radiation from neutron absorption which would occur and finally some more lead to protect from the gamma radiation. FYI, This tank would be incredibly heavy. As PipperChip told you even once you protect your crew and tank from radiation you now need to protect them from the blastwave. All in all this is not cost effective for the protection of less than 5 men.

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  • $\begingroup$ A number of tank models can be equipped with a snorkel and go underwater (not sure how deep, honestly). That might be your neutron protection. And why one tank? What about a batallion of fifty? $\endgroup$
    – Karl
    Sep 24, 2016 at 18:53

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