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20180703 023047
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A one kiloton nuclear detonation produces 4.19e12 joules of energy. One kilometer away from the detonation point defines a sphere with a surface areaof about 12,600,000 square meters (the increase in surface area with the radius of the sphere is another way of stating the Inverse Square law). Dividing reveals that at this range the energy density is approximately 300 kilojoules per square meter. Under ideal conditions this would be enough energy to vaporize 25 grams or 10 cubic centimeters of aluminum (in reality it won't be this much due to conduction and other factors).

1e8 watts per square centimeter for about a microsecond will melt part of the surface of a sheet of aluminum. 1e9 W/cm2 for a microsecond will vaporize the surface, and 1e11 W/cm2 for a microsecond will cause enough vaporization to create impulsive shock damage (i.e., the surface layer of the material is vaporized at a rate exceeding the speed of sound). The one kiloton bomb at one kilometer only does about 3.3e7 W/cm2 for a microsecond.

One megaton at one kilometer will do 3.3e10 W/cm2, enough to vaporize but not quite enough for impulsive shock. At 100 meters our one meg bomb will do 3.3e12 W/cm2, or about 33 times more energy than is required for impulsive shock. The maximum range for impulsive shock is about 570 meters.

Luke Campbell wonders if 1e11 W/cm2 is a bit high as the minimum irradiation to create impulsive shock damage. With lasers in the visible light and infrared range, 1e9 W/cm2 to 1e10 W/cm2 is enough. But he allows that matters might be different for x-rays and gamma rays due to their extra penetration.

As to the effects of impulsive damage, Luke Campbell had this to say:

First, consider a uniform slab of material subject to uniform irradiation sufficient to cause an impulsive shock. A thin layer will be vaporized and a planar shock will propagate into the material. Assuming that the shock is not too intense (i.e., not enough heat is dumped into the slab to vaporize or melt it) there will be no material damage because of the planar symmetry. However, as the shock reaches the back side of the slab, it will be reflected. This will set up stresses on the rear surface, which tends to cause pieces of the rear surface to break off and fly away at velocities close to the shock wave velocity (somewhat reduced, of course, due to the binding energy of all those chemical bonds you need to break in order to spall off that piece). This spallation can cause significant problems to objects that don't have anything separating them from the hull. Modern combat vehicles take pains to protect against spallation for just this reason (using an inner layer of Kevlar or some such).

Now, if the material or irradiance is non-uniform, there will be stresses set up inside the hull material. If these exceed the strength of the material, the hull will deform or crack. This can cause crumpling, rupturing, denting (really big dents), or shattering depending on the material and the shock intensity.

For a sufficiently intense shock, shock heating will melt or vaporize the hull material, with obvious catastrophic results. At higher intensities, the speed of radiation diffusion of the nuke x-rays can exceed the shock speed, and the x-rays will vaporize the hull before the shock can even start. Roughly speaking, any parts of the hull within the diameter of an atmospheric fireball will be subject to this effect.

In any event, visually you would see a bright flash from the surface material that is heated to incandescence. The flash would be sudden, only if the shock is so intense as to cause significant heating would you see any extra light for more than one frame of the animation (if the hull material is heated, you can show it glowing cherry red or yellow hot or what have you). The nuke itself would create a similar instant flash. There would probably be something of an afterglow from the vaporized remains of the nuke and delivery system, but it will be expanding in a spherical cloud so quickly I doubt you would be able to see it. Shocks in rigid materials tend to travel at something like 10 km/s, shock induced damage would likewise be immediate. Slower effects could occur as the air pressure inside blasts apart the weakened hull or blows out the shattered chunks, or as transient waves propagate through the ship's structure, or when structural elements are loaded so as to shatter normally rather than through the shock. Escaping air could cause faintly visible jets as moisture condenses/freezes out - these would form streamers shooting away from the spacecraft at close to the speed of sound in air - NO billowing clouds.

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