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Background info:

  • The explosion is a simultaneous detonation only.

  • Assume starting level is ~500 feet above sea level.

  • By Mantle, I mean the outer edge. The explosion doesn't necessarily need to reach the very core (and would be exponentially greater I believe) but must expose the outer mantle to the air.

  • How big of a crater would such an explosion make, supposing the optimal placement and shaping was used in the explosion?

  • Assume the geological makeup is similar to Earth's, and the area is mostly bedrock.

  • The mantle is the same size as the Earth's, as is the total size of the planet (it's an alternate dimension setting).

  • The bombs are each approximately fifteen (15) megatons each (Castle Bravos).

Thanks in advance!

EDIT: Added the megaton specification.

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    $\begingroup$ Bombs are very far from ideal digging machines. It would help if you indicated how the process is supposed to work -- should the rock be vaporized, blown to pieces and the debris carried away by slave in wheelbarrows, ... $\endgroup$ – AlexP Jun 8 '17 at 3:44
  • $\begingroup$ Welcome to Worldbuilding! $\endgroup$ – JDługosz Jun 8 '17 at 8:37
  • $\begingroup$ Does simultaneous detonation mean that all of the bombs detonate at once and that they have to detonate on the surface? I'm wondering if that is even possible using conventional bombs (conventional nuclear bombs that is). You might need something trickier. $\endgroup$ – DRF Jun 8 '17 at 15:16
  • $\begingroup$ enough to wipe out all complex life on the planet if you tried. the bigger the boom the less effective it is at penetration, the pulverized rock itself acts as a barrier limiting how much can be thrown out. For comparison the Vredefort impact crater has a diameter of more than 300km but had a maximum depth of only about 24km onlinelibrary.wiley.com/doi/10.1111/j.1945-5100.2003.tb00265.x/… $\endgroup$ – John Jun 9 '17 at 4:25
  • $\begingroup$ @John, yeah I was going to say, sounds like an extinction level event! $\endgroup$ – Len Jan 30 '18 at 0:35
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Let's make some gross simplifications, just to get a figure:

  • each bomb digs a semisphere of 250 feet radius (as Redstoner stated)
  • to prevent collapsing of the hole, you need to dig also laterally, not only vertically. Let's say an angle of 45 degrees prevents collapse of the walls.
  • the "erosion capability" of the bomb stays the same, regardless of the type of rock
  • debris are all vaporized and outside the vaporized area rocks are stable despite the explosion

To dig 262 kfeet in the ground, you also need to expand laterally of the same amount, to keep the 45 degrees. This would make a cone having volume 5E+16 cubic feet.

Since each bomb would consume 3E+7 cubic feet, it would take about 1.7 billion bombs.

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    $\begingroup$ Will the falling ejecta just rain back down in the pit? After a while, I see this as being a problem. $\endgroup$ – JDługosz Jun 8 '17 at 8:37
  • $\begingroup$ The Castle Bravo bomb made a crater 75m deep... and nearly 2000m wide. I don't think you have to worry about expanding it laterally to prevent from collapsing. Specially, since the heat automatically makes a wall of molten compressed rock. $\endgroup$ – Rekesoft Jun 8 '17 at 8:40
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    $\begingroup$ @Rekesoft: Rock is heavy. At the bottom of a 100 meters deep well the lateral hydrostatic pressure is about 40 to 50 atmospheres: 50 kilograms-force pressing sideways on each square centimeters of the wall, or 500 tons-force per square meter. The wall will collapse. If you look how roads are built, whenever they pass under the level of the surrounding terraing the sides are cut at 45 degress so that the retaining walls have a chance of resisting. $\endgroup$ – AlexP Jun 8 '17 at 10:29
  • $\begingroup$ @AlexP Redstone calculations yield 1050 bombs needed. L.Dutch says it's 1.7 billion. That's quite a difference, and basically he's making the assumption that every bomb carved a semisphere of 250 radius. A crater 6,500 feet wide per 250 feet deep is nothing like a sphere. What I'm saying is the bombs are providing enough inclination of the walls to prevent collapsing. Like, about 98º. Of course, as you dig deeper underground the hole walls will become much more inclinated, but I'm guessing the actual number of bombs would be closer to Redstone's calculus, even if an order of magnitude greater. $\endgroup$ – Rekesoft Jun 8 '17 at 11:48
  • $\begingroup$ You overlooked a part of the question: "The explosion is a simultaneous detonation only." This means that you can't chain one explosion after another to dig; it's one big boom. Presumably, one is then limited to the maximum digging depth of one bomb. So the answer is: dig within 250 ft. of the mantle and use one bomb. $\endgroup$ – Frostfyre Jun 8 '17 at 12:24
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The Castle Bravo originally blew 250 feet in the ground. If the planet you are talking about has the same geological dimensions as Earth, exposing the outer mantle would need digging down to about 26,2457 feet in the ground.

After doing some math, I think it would take approximately 1049/1050, or precisely 1049.180328 Castle Bravo sized bombs to expose the outer core of the planet's mantle. Also it would be really helpful to identify how the process would work.

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  • $\begingroup$ Welcome to WorldBuilding! If you have a moment please take the tour and visit the help center to learn more about the site. Have fun! $\endgroup$ – Secespitus Jun 8 '17 at 5:49
  • $\begingroup$ As you did down, will subsequent explosions fling the debris far enough to clear the hole? $\endgroup$ – JDługosz Jun 8 '17 at 8:36
  • $\begingroup$ The Wikipedia entry on the Mantle; "A thin crust, the upper part of the lithosphere, surrounds the mantle and is about 5 to 75 km (3.1 to 46.6 mi) thick." I think you are assuming evacuating a hole down to the shallower depth for the crust. $\endgroup$ – a4android Jun 9 '17 at 2:39

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