As the title says
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E=mc^2 tells you how much energy you’ll get from a given amount of mass. However the challenge in calculating the yield of a weapon is determining the efficiency. Not all of the mass in the core is going to react before it blows itself apart. To guess the efficiency and therefore the yield, you have to estimate how long adequate pressures can be maintained based on the types of explosive lenses you use to compress the core, as well as how fast the core material is disassembling itself before it can’t maintain the chain reaction. I won’t pretend to know the nitty gritty details but they used some serious computing power by 1940s standards to make their guesses on the first weapons.
They looked at the results.
We know that if we detonate a tonne of tnt we will get an explosion of a certain size – sit it on the ground and it will make a certain size of crater, and the blast wave will be of a certain pressure at a set distance from the detonation site.set it off underwater and you can again measure the pressure, the damage left behind, how much water is thrown in the air and so on.
If your test leaves a much bigger hole than expected, then you can compare your result to previous tests and work out a number.
Well, what you do is stand miles from the explosion and drop small pieces of paper and watch how they move in the air when the blast wave hits.
No, seriously, this is what Enrico Fermi did at the Trinity Test, the detonation of the world’s first nuclear bomb (the Gadget). He calculated it to be at least 10kt whereas the official results were 18kt so not bad for just dropping pieces of paper in the air.
There were a lot of ways they’d officially measure how powerful the blast was. One was by looking at how much radiation was given off by measuring the fallout. This only works if you get fallout, obviously. Another was how powerful the blast wave was. How bright the fireball was. How much the ground shakes (for, you know, explosions on or under the ground).
However, using each for the same explosion can give different results so…………………….
There are pretty straightforward physical “rules” for how the size of an explosion translates into how much damage is done, how big the fireball gets, how radioactive it gets, how tall the cloud goes, and so on. (All of these, except the radioactivity, apply to non-nuclear explosions as well.) So what they did was have lots of ways of measuring the effects of the blast: high-speed cameras that let you see how big the fireball was; airplanes that could measure the height of the mushroom cloud; blast-pressure sensors that could keep track of how powerful the blast wave was; and so on. Then they would work backwards from the data and their models to estimate the actual yield.
There are a few tricky things. These multiple methods didn’t always match up, both because nature is more complicated than simple equations (the humidity in the air, for example, can affect the blast distances, as can the temperature of the ground or water), because their measurements could have imprecisions to them, and because different nuclear weapon designs could output the energy in slightly different proportions (e.g., more as heat than blast, or more as radioactivity than blast). So sometimes they didn’t get it quite right, or came up with conflicting estimates — the radiochemical yield would be different from the thermal yield which could be different from the blast yield which could be different from the fireball size yield. They’d look at all of these and throw out the ones that looked sketchy and just decide on a number.
There has been a lot of work by the national labs over the last decade or so to digitize and re-analyze some of the high-speed photography taken of the tests with modern computers and physics models, and they’ve found that some of the tests were different yields than they expected (I think the max variation is 10%, which isn’t a whole lot, but could still matter for some types of calculations regarding the accuracy of weapons needed to destroy a given target).
Atomic tests were generally monitored with instruments to measure the yield. Here are a few ways it was measured:
1. Size of the fireball. The more powerful the bomb, the larger the fireball. Using a high speed movie camera, they could record the fireball and figure out how large it got.
2. Measure the wind/shockwave. Nuclear blasts put out a powerful wave of air pressure. If you measure the pressure at a known distance, you can figure out how powerful an explosion caused it.
3. Measure how much the ground shakes. Just like with the air, there is a pressure wave that travels through the ground. Using seismometers, the amount of ground shake can be used to calculate the size of the explosion. This can be done from very far away, and is used to calculate how large atomic tests done by other countries are (like the US monitoring North Korean nuclear tests).
4. Radiation measurements. Atomic bombs create a quick intense burst of radiation, then a cloud of radioactive particles (fallout). These can both be measured and used to estimate the nuclear yield.
Generally all four of these methods would be used, and by combining the estimates of all of them, you could get a fairly good idea of how large the blast was. It isn’t 100% precise, which is why you often see a fairly round number (10 kilotons instead of 9.734 kilotons).
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