I was thinking today about the variety of threats we face these days, ranging from minor ones like asteroid impacts to the most serious of all (secondhand cigarette smoke, of course), when I remembered that when I was at school somebody told me that the Soviet Union had a nuclear bomb that could destroy the whole of England (or maybe Great Britain) with one single blast.
And that really was the stuff of nightmares. But I always wondered whether it really could have been true. And so today, for the first time ever, I set out to investigate.
We know the amount of energy, E, that is released by nuclear weapons. We can also suppose that this energy expands in a spherical shock wave around the bomb as it explodes. The energy gets dispersed over the surface area A of this expanding sphere, which is 4πr2, where r is the radius of the sphere.
I then took a look at the 15 kiloton 63 TJ (TeraJoule) Hiroshima bomb, which was detonated 580 metres above ground level, and learned that the area of complete destruction extended in a circle of 1.6 km radius around ground zero (1.7 km from the bomb itself), with extreme to light damage extending as far as 5.6 km. I then calculated E/A, the energy per unit area of the sphere at a radius of 1.7 km and 5.6 km, and came up with figures of 1.7 x 106 J/m2 for complete destruction and 1.6 x 105 J/m2 for light damage.
I then took a look at the largest nuclear bomb ever exploded, the 50 megaton 210 PJ (Peta Joule) Soviet Tsar Bomba, which was detonated in October 1961 on the island of Novaya Zemlya, and estimated that the radius of the sphere of complete destruction was about 100 km, and the radius of severe to light damage was about 350 km.
And then I got a map of Britain, and drew a 100 km radius circle in the middle of it, and a 350 km radius circle around that (see right).
From this I concluded that Birmingham would have been completely destroyed, and London and Manchester severely damaged, with various degrees of damage over the whole of England and Wales, with only the west of Cornwall escaping. There might even have been light damage in Dublin and Edinburgh and Calais.
So the story I first heard 50 years ago looks like it was actually perfectly true: the Soviets had a single bomb that could have destroyed pretty much the whole of England.
I did the same calculations for the Chelyabinsk meteor that exploded with the energy of 30 Hiroshima bombs on 15 Feb 2013, at a height of about 30 km, and found E/A to be 1.72 x 105 J/m2, just above the threshold of light damage. Which was about right: the explosion shattered windows and collapsed one or two roofs.
Most of the nuclear warheads in ballistic missiles are of course much smaller than the Tsar Bomba (which was 8 metres long, and 2 metres in diameter, and weighed 27 metric tons), and release the energy in the range 500 – 1500 TJ. Using a mean value of 1000 TJ, I calculated that the radius of the area of complete destruction would be about 7 km, and the radius of the area of extreme to light damage would be about 22 km.
These were really just back-of-envelope calculations, but instructive all the same. The Wikipedia article on the Tsar Bomba gives an area of complete destruction with a 35 km radius, one third of my value. I checked my figures, and I can only suppose their numbers are calculated in a different way. But since the same article says that all buildings, both timber and brick, in a village 55 km from the test site were destroyed, it rather looks like 35 km was a bit of a low number.