Special Analysis: More Practical Math for the New American Century

The August 5, 2005, article, "Practical Math for the New American Century," published here at The Dark Wraith Forums provided readers with some elementary mathematical tools for calculating the destructive force of a nuclear device based upon its yield.

The possible use of nuclear devices has returned to the news with rumors of an impending airstrike to destroy Iran's uranium enrichment facilities to thwart its potential use of such enriched uranium to build nuclear weapons. Although top-level Iranian officials have denied that the uranium they are processing will be used for anything other than peaceful purposes, concerns in Washington and Israel have led some analysts to conclude that either Israel or the United States is planning to bomb the Iranian nuclear fuel production plants. According to the Defense Department, the sites where uranium enrichment is now underway are deep underground. They are essentially massive, hardened, underground bunkers protected by as much as 70 feet of concrete and steel overlain by another 50 feet of earth. To destroy them with conventional weapons alone would be impossible, so the presumption is that whoever carries out the attack would have to use nuclear bombs to effect the necessary level of damage.

CNN.com is reporting that Iran's highest leader, the Ayatollah Ali Khamenei, is concerned enough about the prospect of attack that he, himself, has spoken out, threatening to mount counter-attacks on U.S. interests and assets across the world should the United States be involved in or spearhead a strike against Iran. His concerns are perhaps enhanced by what appears to be an unwillingness even among U.S. President George W. Bush's critics to take a military strike against Iran off the table of possible responses to Tehran's alleged refusal to comply with United Nations demands that it halt its nuclear fuels production. In fact, the relatively popular U.S. Democratic Presidential candidate John Edwards, campaigning in Israel for the Democratic nomination, joined rivals John McCain and Mitt Romney at a public teleconference in suburban Tel Aviv to make clear his willingness to use force if discussions with Iran fail, hinting ominously, "[A]ll options must remain on table." Aljazeera described Edwards' speech supporting Israel as "shockingly bellicose," indicating that analysts in the Arab media believe Iran should not hope for a lessening of its fears of an attack merely because new voices from an American political party in opposition to the Bush Administration are entering public debate on Middle Eastern matters.

While some analyses are keyed to a U.S.-led attack on Iran, others predict that, in the absence of swift action by the Americans, the strike will be carried out by Israel, quite possibly supported by the United States. A recent post at the blog BlondeSense highlighted a March 2007 article in Vanity Fair by Craig Unger, who described in ominous terms rumors about a coming attack on Iran. In the comments to the post at BlondeSense, the role Israel would play was mentioned. Specifically, the range of bomb yields in the Israeli nuclear inventory was mentioned, with allusion being made to the Jewish State's blockbuster 400 kiloton devices and its enhanced radiation warheads.

In response, I offered a summary primer on the means by which Israel would destroy Iranian nuclear fuels production facilities in a nuclear attack. Below is an edited and expanded version of my comment, which will be followed by the application of some mathematical calculations to add a bit more of a technical, quantitative feel to what may come.

Israel will not use weapons in the 400 kiloton yield range. That would be something along the lines of nuclear overkill.

The ideal devices for use on Iran's nuclear fuels production facilities are in the one kiloton range, which is about one-fifteenth of the yield of the bomb the United States dropped on Hiroshima, Japan, and provides sufficient destructive force for the Iranian targets without the problem of overkill. Bombs with yields like this are quite likely in the Israeli arsenal, although they might very well be referenced as "enhanced radiation" devices, since that term is sometimes used rather loosely. In my article, "Practical Math for the New American Century" [linked previously], I explained that there are three principal sources of destructive power in a nuclear bomb: overpressure, heat, and radiation. As the yield of a device increases, the overpressure component comes to dominate the other two in terms of kill radius. Hence, with very low-yield weapons, the kill radius of the radiation globe will be considerably larger than that of the concussive force (or "wind," if you will). Thus, very low-yield weapons (around a kiloton or less) will be "hot radiation" bombs, doing destructive overpressure damage at a smaller scale than the thermal and radiative components. To some extent, these make for ideal "bunker busters" when used in combination with conventional bunker busters because the latter can be used to excavate a crater above a hardened underground facility, then the former can be dropped into the crater, which will focus overpressure and compromise the structural integrity of the targeted facility. The hot radiation serves to cause virtually instantaneous ignition of anything even remotely combustible within the building itself via the breaches created by the overpressure component, acting as it does to essentially "crack the can" so the intense heat can enter and start what is effectively a secondary fireball in the contained interior of the place. Everything gets destroyed, and it's not so much by the explosive force, although the whole ceiling might theoretically come down, but rather by the baking at temperatures above flashpoint for everything that's non-metallic. As far as the metal equipment, like the centrifuge components, is concerned, that will be in a thermal environment quite possibly hot enough to melt just about everything.

Given that the facility is all underground, the whole place becomes a tomb—a very hot, highly radioactive tomb, but a tomb, nonetheless.

In the aforementioned "Practical Math for the New American Century," I derived the equations for the kill zones of the three types of destructive power of a nuclear device. Again, they are as follows, with associated lethality thresholds indicated:

• blast: 4.6 pounds per square inch of overpressure;
• thermal radiation: 8 Calories per cm² (creating 3rd degree burns);
• nuclear radiation: 500 rem.

The equations of kill radii (in kilometers) associated with "optimal height" detonation are such:

• kill radius of blast = (Y_r)^0.41
• kill radius of thermal radiation = (Y_r)^0.33
• kill radius of nuclear radiation = (Y_r)^0.19,

where Y_r is the "yield relative" to a 2.5 kiloton device. Hence, we would use as the yield relative for a one kiloton nuclear bomb,

Y_r = 1÷2.5 = 0.4,

meaning that a one kiloton nuclear bomb has 40 percent of the yield of the baseline 2.5 kiloton weapon.

Before proceeding, it must be acknowledged that the equations above would be somewhat off for one kiloton devices detonated at ground or below-ground levels, since, as noted, the equations assume "optimal height" bursts. A little more specifically, if a nuclear device explodes in a crater already formed by a conventional bunker-buster bomb, the overpressure directly beneath the blast will be somewhat higher, as will the thermal component. The radiation globe will be contained laterally by the walls of the previously formed crater, forcing what would otherwise be a spherical shell in an airburst to deform into more of a fountain-like plume emanating from the crater. This effect, of course, will be observed with the blast wave and with the thermal shell, too; but the blast will be particularly affected since underneath the explosion presumably is a 70-foot thick stratum of concrete protecting the facility under attack. This hard surface will reflect a considerable amount of the overpressure upward. The hope, of course, is that, in so doing, the structural integrity of the concrete will suffer catastrophic failure or compromise clear through to the open chamber underneath, thereby allowing the fireball and some of the radiation to enter and do crippling damage.

These considerations having been noted, below are the calculations of the kill zones for the three destructive forces of a one kiloton nuclear device:

• kill radius of blast = (0.4)^0.41 = .69 km = 2264 ft
• kill radius of thermal radiation = (0.4)^0.33= .74 km = 2428 ft
• kill radius of nuclear radiation = (0.4)^0.19 = .84 km = 2756 ft

Readers will notice that, unlike with a large-yield nuclear bomb, whose wide-ranging destructive power is caused principally by the blast wave, fatal heat and radiation from a low-yield nuclear device cover a wider area than does the blast wave. This is why low-yield devices are sometimes generically referred to as "enhanced radiation" devices or "dirty bombs": their largest kill zone is the one caused by the radiation from them.

Addressing the immediate problem of destroying an underground nuclear facility, then, using a low-yield nuclear bomb is not to the purpose of "blowing up" the place; it is, instead, to the purpose of blasting it open so it can then be torched and irradiated.

In a little more graphic, if wholly expository, detail, here's what should happen. A conventional bunker-buster device is detonated on the earth above the facility to form a crater, probably no more than 20 to 50 feet deep, into which the nuclear bomb is then dropped. When the nuclear device detonates, the blast wave will immediately create a spherical shell of wind, but that shell will be instantly deformed by the walls of the crater and the earth and concrete beneath, which will act as reflectors to create a complex set of waves inside and over the crater. A considerable amount of force will be exerted downward, of course, excavating earth above the concrete and then damaging the concrete, itself. The reflected pneumatic pressure will pump upward, but will encounter the echoing blast waves around and above it as they are moving back and forth and up. Those waves will cause some of the energy that had been reflected upward from the initial pounding on the concrete to reflect back downward, again hitting the already breaking concrete, further compromising it. Ideally, the concrete—reinforced as it is with steel girders—will be breaking away, with the chunks, pieces, and dust getting swept up in the "mushroom cloud" billowing out of the hole in the ground. The thermal energy of the nuclear explosion will be glazing the concrete, making it more brittle, and melting the steel girders.

All of this should happen in a period of considerably less than a second. The jackhammer effect of the overpressure, along with the heat being delivered to the concrete, might not create a catastrophic collapse of the entire ceiling of the underground bunker, but it should be more than sufficient to open a gaping hole through which the thermal energy can enter at a temperature of several thousand degrees, more than enough to burn anything of importance inside the chamber. Overpressure echoes will be pushing in, too, feeding the ball of fire roaring through the interior of the building. Radiation in the form of subatomic particles, ions, and isotopes of various kinds will deliver a thin plasma wave coursing through the raging wind and hellish fire.

The effect of all this should be utter destruction of equipment and people in the underground facility. The walls will cave under the blast and heat; the glass, metal, and wiring will all melt; and any humans unlucky enough to be anywhere inside will be baked to ash. The irradiation will ensure that whatever remains of the bunker is unapproachable for years, if not decades.

And whatever aspirations Iran had to produce nuclear fuel for peaceful or other purposes will be at an end.



The Dark Wraith trusts that readers have benefited from this educational article.