Kilotons per kilogram
December 23rd, 2013
Nuclear weapons can be made to have pretty
much as much of a bang as one wants to make them, but
with increased explosive yield comes an increased weapon weight. We always talk vaguely about being able to make H-bombs to arbitrarily high yields, but recently I've been mulling over this fact somewhat
quantitatively. I gave a talk last month at the History of Science Society Meeting on
US interest in 50-100 MT bombs around the time of the Limited Test Ban Treaty, and while working on this paper I got
slightly obsessed with what is known as
the yield-to-weight ratio.
Little Boy — a big bang compared to a conventional bomb, but still a very crude nuclear bomb.
What makes nuclear weapons impressive and terrible is that their default yield-to-weight ratio — that is, the amount of
bang per mass, usually expressed in terms of
kilotons per kilogram (kt/kg) — is much,
much higher than conventional explosives. Take TNT for example. A ton of TNT weighs, well, a
ton. By definition. So that's 0.001 kilotons per 1,000 kilograms; or 0.000001 kt/kg. By comparison, even a crude weapon like the Little Boy bomb that was dropped on Hiroshima was about 15 kilotons in a 4,400 kg package: 0.003 kt/kg. That means that the Little Boy bomb had an energy density
three orders of magnitude higher than a regular TNT bomb would. Now, TNT isn't the be-all and end-all of conventional explosives, but no conventional explosive gets
that much boom for its buck compared to a nuke.
The Little Boy yield is
much lower than the hypothetical energy density of uranium-235. For every kilogram of uranium-235 that completely fissions, it releases about 17 kt/kg. That means that less than a kilogram of uranium-235 fissioned in the Little Boy bomb to release its 15 kilotons of energy. Knowing that there was 64 kg of uranium in the bomb, that means that something like 1.3% of the uranium in the weapon actually underwent fission.
So right off the bat, one could intuit that this is something that could probably be improved upon.
Fat Man — a lot better use of fissile material than Little Boy, but no more efficient in terms of yield-to-weight.
The Fat Man bomb had a
much better use of fissile material than Little Boy. Its yield wasn't that much better (around 20 kilotons), but it managed to squeeze that (literally) out of only 6.2 kilograms of plutonium-239. Pu-239 releases around 19 kilotons per kilogram that completely fissions, so that means that around 15% of the Fat Man core (a little under 1 kg of plutonium) underwent fission. But the bomb itself still weighed 4,700 kg, making its yield-to-weight ratio a mere 0.004 kt/kg.
Why, despite the improve efficiency and more advanced design of Fat Man, was the yield ratio almost identical to Little Boy? Because in order to get that 1 kg of fissioning, it required a
very heavy apparatus. The explosive lenses weighed something like 2,400 kilograms just by themselves. The depleted uranium tamper that held the core together and reflected neutrons added another 120 kilograms. The aluminum sphere that held the whole apparatus together weighed 520 kilograms. The ballistic case (a necessary thing for any actual weapon!) weighed another 1,400 kg or so. All of these things were necessary to make the bomb either work, or be a droppable bomb.
So it's unsurprising to learn that improving yield-to-weight ratios was a high order of business in the postwar nuclear program. Thermonuclear fusion ups the ante quite a bit. Lithium-deuteride (LiD), the most common and usable fusion fuel, yields 50 kilotons for every kilogram that undergoes fusion — so fusion is nearly 3 times more energetic per weight than fission.
So the more fusion you add to a weapon, the better the yield-to-weight ratio, excepting for the fact that all fusion weapons require a fission primary and usually also have very heavy tampers.
I took all of the reported American nuclear weapon weights and yields from
Carey Sublette's always-useful website, put them into the statistical analysis program
R, and created this semi-crazy-looking graph of American yield-to-weight ratios:
The horizontal (x) axis is the yield in kilotons (on a logarithmic scale), the vertical (y) axis is the weight in kilograms (also on a log scale). In choosing which of the weights and yields to use, I've always picked the lowest listed weights and the highest listed yields — because I'm interested in the optimal state of the art. The individual scatter points represent models of weapons. The size of each point represents how many of them were produced; the color of them represents when they were first deployed. Those with crosses over them are still in the stockpile. The diagonal lines indicate specific yield-to-weight ratio regions.
A few points of interest here. You can see Little Boy (Mk-1), Fat Man (Mk-3), and the postwar Fat Man improvements (Mk-4 — same weight, bigger yield) at the upper left, between 0.01 kt/kg and 0.001 kt/kg. This is a nice benchmark for fairly inefficient fission weapons. At upper right, you can see the cluster of the first H-bomb designs (TX-16, EC-17, Mk-17, EC-24, Mk-24) — high yield (hence far to the right), but very heavy (hence very high). Again, a good benchmark for first generation high-yield thermonuclear weapons.
What a chart like this lets you do, then, is start to think in a really visual and somewhat quantitative way about the sophistication of late nuclear weapon designs. You can see quite readily, for example, that radical reductions in weight, like the sort required to make small tactical nuclear weapons, generally results in a real decrease in efficiency. Those are the weapons in the lower left corner, pretty much the only weapons in the Little Boy/Fat Man efficiency range (or worse). One can also see that there are a few general trends in design development over time if one looks at how the colors trend.
First there is a movement down and to the right (less weight, more yield — improved fission bombs); there is also a movement sharply up and to the right (high weight, very high yield — thermonuclear weapons) which then moves down and to the left again (high yield, lower weight — improved thermonuclear weapons). There is also the splinter of low-weight, low-yield tactical weapons as well that jots off to the lower left. In the middle-right is what appears to be a sophisticated "
sweet spot," the place where all US weapons currently in the stockpile end up, in the 0.1-3 kt/kg range, especially the 2-3 kt/kg range:
http://blog.nuclearsecrecy.com/2013/12/23/kilotons-per-kilogram/
, a very sane and relevant point that Kim cannot damage his country for something non-existent. But I would that if he didn't test the full fledge TND, he is very close ...
