The good folks at Information is Beautiful have an interesting post on nuclear weapons.
I’ll give you a few moments to hop over and catch the author’s error.
Did you find it?
That’s right: the area of a circle is not equal to its radius.
IiB went on Wikipedia and found the distance at which a Mark-53 nuclear bomb can send out an overpressure wave of 5 psi (roughly what it takes to knock down most buildings) and then took this distance, which Wikipedia calculates to be 14.9km (Personally I calculate a slightly different number), and treated it as if it were the area of destruction.
As most of you can figure out for yourselves, the area of a circle with a radius of 14.9 km isn’t 14.9 km^2– it’s just a shade under 700 km^2.
In fact, the area of destruction is likely to be much higher than this. Nuclear weapons have two prominent effects: prompt radiation and pressure. The pressure falls off with r-cubed, since it acts upon a volume. The prompt radiation (angry photons falling on your city and heating it up) falls off only with r-squared, since it is acting upon a surface. For large weapons, such as the B53, the radius of destruction due to the light of the bomb is greater than the radius due to pressure. At 10 calories per square centimeter, most burnable materials will ignite. Thus, the actual area of destruction, by my calculation, is at least 3,000 square kilometers– a factor of 200 different from the IiB’s figure.
With these numbers, the IiB’s point still stands– we cannot kill off the human race with our current stockpile of nuclear weapons. But his bolder contention, that nuclear weapons are incapable of taking out even a small fraction of our ecumene is wrong. If you detonated a B53 over London, there would be nothing left– the city would be engulfed in an all-consuming firestorm.
If the U.S. and Russia went to the mattresses, even though most of our nuclear weapons are not B-53 sized, we would annihilate each other. A Russian arsenal of 5000 nukes would not just take out a small chunk of our 300m citizens, it would be enough to drop one nuke on every single U.S. city with more than 4,300 citizens, from New York, New York to Sparta, Illinois, and kill the vast majority of the 175m citizens living there.
It’s important to fight misconceptions over nuclear weapons– humanity would survive a nuclear war. But let’s not kid ourselves– it would be a lot uglier than what IiB suggests.