How to calculate the destruction caused by a bomb explosion

By MUNGAI KIHANYA

The Sunday Nation

Nairobi,

23 July 2006

Last week’s article about the destructive power of bombs stated that the explosion of an average nuclear bomb would cause severe damage to all houses within a 5km radius. Farther, if all the 12,000 warheads were dropped and detonated at the same place, the explosion would destroy everything within a 70km radius. Now that did not seem to add up and it prompted reader George T to ask “was that a typo, or did you actually state 70km? It seems too small”

That was not a mistake. The destruction caused by a bomb is not related to the explosive power in a linear manner. That is, if you double the power, you will not get double the destruction. Suppose you dropped an average (300-kiloton) nuclear warhead on a target. It will destroy all structures in a 5km radius. If now a second explosive was detonated at the same site, what additional destruction would it cause?

The first 5km are already flattened by the initial bomb. The second explosive will therefore only bring down the structures outside the 5-km boundary that had suffered minor damage – you can’t kill something that is already dead! But quite clearly, the destruction will not be extended by another 5km – it will be less.

The actual mathematical relation (developed from explosion tests) is this: the radius of destruction is proportional to the cube-root of a bomb’s explosive power. Thus if the power is increased by a factor of two (from, say 300kt to 600kt) the range of destruction will go up by about 26 percent (from, say, 5km to only 6.3km).

How do we arrive at that? Well, the cube root of two (explosive power was doubled) is about 1.26 (check 1.26 x 1.26 x 1.26 in your calculator). Thus the affected region increases by a factor of 1.26 or 26 percent. Now, a 5km radius is equivalent to 79 square km and 6.3km is equal to 125sq.km. Thus the area destroyed increases by abut 72 percent.

Alternatively, if two 300-kt bombs were dropped at two separate sites, each would clear a 5km radius at its target. The two explosions would affect a combined area of about 158sq.km (79 x 2). It now becomes clear why the total destruction caused by all the worlds’ nuclear weapons would be much greater if they were dropped at different places.

Finally, you may want to know the range of destruction of the largest bomb ever made – the Russian “Ivan”. At 50 megatons, it is 167 times as powerful as a standard nuclear warhead. The cube-root of 167 is 5.5, thus Ivan would clear a radius of “only” 28km (5.5 x 5).

Unfortunately, Ivan is not a very useful military weapon; it weighs about 24 metric tonnes and that makes it difficult to deploy. Thus it is just a museum piece that was intended to tell the west “mine is bigger than your” during the cold war!