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In the 1957 film Bombers B-52 an instructor says of the then-new B-52 Stratofortress:
“On a single mission one of these airplanes, just one, can carry greater destructive force than that of all the bombs dropped by the Allied Air Forces during the whole of World War II”.
Is there a sense in which this statement can possibly be true? At what I find, the B-52 could carry up to 32,000 kg of weapons, while “between 1939 and 1945, Allied planes dropped 3.4 million tons of bombs on Axis powers” (source), that is, five orders of magnitude more. Of course a part (how large?) of the B-52 payload could consist of nuclear devices: would this balance the account? Was that sentence just a hyperbole?
The B-52 was capable of carrying thermonuclear weapons. These were the second-generation of nuclear weapons with greatly increased destructive power over the original WW2 atomic bombs. By 1957, these weapons had yields measured in megatons compared to the tens of kilotons that the first atomic bombs produced.
For example, the Mark 39 nuclear bomb had a yield of 3.8 megatons and the B-52 was able to carry multiples of these (the B-52 in the Goldsboro incident was carrying two of them).
Taking the quoted 3.4 million tons of bombs as a starting point, this is the total weight of all types of bombs dropped by the Allies. So this includes the weight of the casing in addition to the weight of the explosive/incendiary payload. There were various explosive compounds used, some of which were weaker than TNT (e.g. Amatol) and some that were greater in power (e.g. RDX). So calculating the equivalent destructive power in terms of TNT isn't that easy.
As a simple comparison, if you take the quoted 3.4 million tons of bombs as a direct TNT equivalent, then a single Mark 39 was (theoretically) more powerful than those combined. If you add a second, third, fourth bomb… then it's even more so.
The heavier Mark 36 nuclear bomb was also in service in this time period and one variant of the weapon had a theoretical yield of up to 19 Megatons.