Posts Tagged ‘Manhattan Project’


Silent Nagasaki

Friday, February 7th, 2014

Teaching and other work has bogged me down, as it sometimes does, but I’m working on a pretty fun post for next week. In the meantime, here is something I put together yesterday. This is unedited (in the sense that I didn’t edit it), “raw” footage of the loading of the Fat Man bomb into the Bockscar plane on the island of Tinian, August 9th, 1945. It also features footage of the bombing of Nagasaki itself. I got this from Los Alamos historian Alan Carr a while back. I’ve added YouTube annotations to it as well, calling out various things that are not always known.

You have probably seen snippets of this in documentaries and history shows before. But I find the original footage much more haunting. It was filmed without sound, so any sound you hear added to this kind of footage is an artifact of later editing. The silent footage, however, makes it feel more “real,” more “authentic.” It removes the Hollywood aspect of it. In that way, I find this sort of thing causes people to take the events in the footage more seriously as an historical event, rather than one episode in “World War II, the Movie.”

I posted it on Reddit as well, and while there was some share of nonsense in the ~700 comments that it accrued, there was also a lot of expression of empathy and revelation, and a lot of good questions being asked (e.g. Did the people loading Fat Man into the plane know what they were loading? Probably more than the people who loaded Little Boy did, because they knew what had happened at Hiroshima). So I think some learning has happened, and I think the fact that this has gotten +100,000 views in just a day is some sign that there is quite an audience out there for this sort of stripped-down history.

There is also Hiroshima footage, but it isn’t quite as good, on the whole. It is largely concerned with the crew of the plane taking off and arriving. Which is interesting, in a sense, but visually doesn’t mean much unless you know who everybody is.

There is a lot of Trinity test footage as well which I will upload and annotate in the future as well.

Until next week!


The trouble with airbursts

Friday, December 6th, 2013

Both the Little Boy and Fat Man atomic bombs were detonated high in the air above their target cities. That they did this was no accident — specialized circuitry, some invented just for the atomic bombs, was used so that the bombs could detect their height off of the ground and detonate at just the right moment. Little Boy detonated 1,968±50 feet above Hiroshima, Fat Man detonated 1,650±10 feet above Nagasaki. At least as early as the May 1945 Target Committee meeting at Los Alamos, “the criteria for determining height” of detonation had been agreed upon: the goal was to maximize the 5 psi (pounds-per-square-inch) overpressure blast radius of the bombs, with a knowledge that this was going to be a tricky thing since they weren’t really sure how explosively large the bombs would be, and a bomb either too big or too large would reduce the total range of the 5 psi radius. At the time, they estimated Little Boy would be between 5 and 15 kilotons, Fat Man between 0.7 and 5 kilotons — obviously this was pre-”Trinity,” which showed the Fat Man model could go at least up to 18-20 kilotons.

I was on the road quite a lot the last month, so I apologize about the radio silence for the past couple of weeks. But I’m happy to report to you that I managed to recently update the NUKEMAP’s effects code in a way I’ve been meaning to for a long while: you can now set arbitrary heights for detonations. I thought I would explain a little bit about how that works, and why that matters, in today’s post.

The 1962 edition of Glasstone and Dolan's The Effects of Nuclear Weapons and the Lovelace Foundation's "Nuclear Bomb Effects Computer."

The 1962 edition of Glasstone’s The Effects of Nuclear Weapons and the Lovelace Foundation’s “Nuclear Bomb Effects Computer.”

Why did it take me so long to add a burst height feature? (A feature that, to both me and many others alike, was obviously lacking.) Much of the NUKEMAP’s code is based on the calculations that went into making the famous Lovelace Foundation “Nuclear Bomb Effects Computer,” which itself were based on equations in Samuel Glasstone’s classic The Effects of Nuclear Weapons. This circular slide rule has some wonderful retro charm, and is a useful way of boiling down a lot of nuclear effects data into a simple analog “computer.” However, like most nuclear effects calculations, it wasn’t really designed with the kind of visualization that the NUKEMAP had in mind. For something like the NUKEMAP, one wants to be able to plug in a yield and a “desired” overpressure (such as 5 psi), and get a measurement of the ground range of the effect as a result. But this isn’t how the Lovelace Computer works. Instead, you put in your kilotonnage and the distance you want to know the overpressure at, and in return you get a maximum overpressure in the form of pounds-per-square-inch. In other words, instead of asking, “what’s the distance for 5 psi for a 15 kiloton surface burst?,” you are only allowed to ask, “if I was 2 miles from a 15 kiloton surface burst, what would the overpressure be?”

For surface bursts and a few low height (400 feet and under) airbursts, the Lovelace Foundation did, in a separate report, provide equations of the sort useful for the NUKEMAP, and the NUKEMAP’s code was originally based on these. But they didn’t allow for anything fancy with regards to arbitrary-height airbursts. They let one look for pressure information at “optimal” airburst heights, but did not let one actually set a specific airburst height. For awhile I thought this might just have been a strange oversight, but the more I dug into the issue, I realized this was probably because the physics of airbursts is hard.

Grim geometry: calculating the ground range of the 500 rem radiation exposure radius for a Hiroshima-sized nuclear weapon set off at the height of the Hiroshima bomb. Most objects roughly to scale.


There are three immediate effects of nuclear weapons that the NUKEMAP models: thermal radiation (heat), ionizing radiation (radioactivity), and overpressure (blast). Thermal and ionizing radiation pretty much travels in a straight line, so if you know the slant-line distance for a given effect, it’s no problem figuring out the ground distance at an arbitrary height through a simple application of the Pythagorean theorem, as shown above. The report the Lovelace Computer was based on allowed for the calculation of slant-line airburst distances for both of these, so that was a snap to implement. Somewhat interestingly, the ranges of the “interesting” thermal radiation categories (e.g. burns and burning) are so large that except with very high airbursts one often finds almost no difference between ground ranges computed using slant versus straight-line distances. Ionizing radiation, however, is relatively short in its effects, and so the height of the burst really does matter in practical terms for how much radiation the ground receives. This has a relevance to Hiroshima and Nagasaki that I will return to.

But this isn’t how the physics of blast pressure wrks. The reason is somewhat subtle but important for understanding nuclear weapons targeting decisions. The pressure wave that emerges from the nuclear fireball does not stop when it hits the ground. Rather, it reflects — bounces upward again — like so:

Reflection of the shockwave of a 20 kiloton nuclear explosion exploded at 1,770 foot altitude. Via Wikipedia.


You don’t have to take my word for it (or Wikipedia’s, for that matter) — you can actually see the reflection of the shockwave in some nuclear testing photography, like this photograph of Shot Grable, the “atomic cannon” test from 1953:

Shot Grable, Operation Upshot-Knothole — a 15 kiloton nuclear artillery shell detonated at an altitude of 524 feet.

Shot Grable, Operation Upshot-Knothole — a 15 kiloton nuclear artillery shell detonated at an altitude of 524 feet, with the reflection of the blast wave clearly visible under the fireball.

The initial blast wave is the “incident” or “primary” blast wave. The bounded wave in the “reflected” wave. When they touch, as shown in the Wikipedia diagram, they combine — which dramatically increases the overpressure at that location. So, referring the Wikipedia diagram again, by the time the primary shockwave was at the final radius of the diagram, it would have lost a considerable amount of energy. But when it merges with the reflected shockwave, it forms a single, vertical shock front known as the “Mach stem.” In the diagram above, that has an overpressure of 15 psi — enough to destroy pretty significant buildings. If the shockwave did not work in this fashion, the primary shockwave would itself be considerably less than 15 psi at that point.

So the overall point here is that blast reflection can dramatically increase the blast pressure of the bomb at the point where it occurs. But the location at this point varies depending on the height of the bomb detonation — so you can use the choice of bomb detonation altitude to maximize certain pressures in particular. So this is what the Target Committee was talking about in May 1945: they wanted to maximize the radius of the 5 psi overpressure range, and they recognized that this involved finding the correct detonation height and knowing the correct yield of the bomb. They knew about the reflection property and in fact referred to the Mach stem explicitly in their discussion. Why 5 psi? Because that is the overpressure used to destroy “soft” targets like the relatively flimsy houses used by Japanese civilians, which they had already realized would be much easier to destroy than German-style houses.

For the NUKEMAP, this reflection made the modeling difficult. There are lots of models out there for calculating overpressure based on altitude, but they all do it similar to the Lovelace Foundation’s “Computer”: they tell you the maximum overpressure at a pre-specified point from ground zero. They don’t let you ask, “where would the 5 psi radius be for a blast of 15 kilotons and a height of 1,968 feet?” Which was inconvenient for me. The data is out there, though — just not in computational form. Graphs of pressure ranges plotted on axes of ground range and burst height are quite common in the nuclear literature, where they are sometimes known as “knee curves” because of the characteristic “bulge” in ground range produced by the aforementioned Mach reflection, the spot where the pressure range dramatically enlarges. Glasstone and Dolan’s 1977 Effects of Nuclear Weapons contains three of these graphs for pressure ranges between 10,000 and 1 psi. Here is the “low-pressure” graph showing the characteristic “knees”:

Glasstone and Dolan Fig 3-73c - Peak overpressures

Reading these is fairly straightforward once you understand what they show. If you want to maximize the 2 psi pressure range, find the point at which the “2 psi” curve is as far to the right as possible. Then look at the vertical axis to find what the corresponding height of burst is. Or, if you want to know what the pressure will be on the ground at a given distance from a bomb detonated at a given burst height, simply figure out which pressure regions that point is between on the graph. The graphs are always given for 1 kiloton bursts, but scaling from these to arbitrary detonations (with the caveat that very high and very low yields can sometimes be a little different) is pretty straightforward according to the scaling laws given in the text.

I searched high and low for a computational solution to the airburst question, without much luck. I had attempted to do polynomial curve fits on the graphs above, and just found them to be too irregular — the equations I was able to produce made huge errors, and splitting them up into sub-curves produced a mathematical mess. The only other computational solution I found was someone else who had done curve fits and also come up with equations that produced relatively large errors. I wasn’t happy with this. I discussed my frustrations with a few people (let me do a shout out to Edward Geist, currently a Stanton Fellow at the Rand Corporation, who has been doing his own modeling work regarding Soviet nuclear effects handbooks, and to Alex Montgomery at Reed College, both of whom were extremely helpful as people to talk to about this), and gradually came to the conclusion that there probably wasn’t an obvious analytical solution to this problem. So I did the next-best thing, which was to take samples of all of the curve values (less tedious than it sounds because of a little script I whipped up for the job) and just set up some tables of data that could then be sifted through very quickly by the computer. In other words, the way the NUKEMAP’s code works is pretty much the Javascript equivalent to consulting the graphs in Glasstone and Dolan’s book — it treats it as a simple interpolation problem between known values. Which turns out to give results which are no worse than those involved with using the book itself:

The NUKEMAP's overpressure data, graphed using R. Point samples are represented by circles, lines connect given pressure ranges. Color corresponds (logarithmically) with pressure ranges from 1 to 10,000 psi.

The NUKEMAP’s overpressure data, graphed using R. Point samples are represented by circles, lines connect given pressure ranges. Color corresponds (logarithmically) with pressure ranges from 1 to 10,000 psi. Unknown points on the graph are interpolated between known values.

The end result is that now the NUKEMAP can do arbitrary-burst height airbursts. In fact, the NUKEMAP pressure model goes all the way up to 10,000 psi — a pressure zone equivalent to being 4 miles under the ocean. Yow.

With this data in hand, and the NUKEMAP model, let’s go back to the Hiroshima and Nagasaki question. They knew about the Mach reflection, they knew about the height of the burst. It’s not clear that their assumptions for how this would work would line up exactly with those in Glasstone and Dolan, since those were modified according to actual empirical experience with airbursts in the kiloton range, something that they did not have on hand in 1945, even if they intuited much of the physics behind it. What can we say about their knowledge, and their choices, with regards to what they actually did with selecting the blast heights?

The Hiroshima yield has been calculated as about 15 kilotons, and the Nagasaki yield was about 21 kilotons. According to the Glasstone and Dolan model, to optimize the 5 psi pressure range for each, you’d want a burst height of ~2,500 feet for Little Boy and ~2,800 feet for Fat Man. Those are significantly higher altitudes than the actual detonation heights of 1,968 and 1,650 feet. The Target Committee meeting shows that they were assuming that 2,400 feet was the correct height for a 15 kiloton bomb — which is about right. Which means either than the detonating circuitry fired late (not impossible though I haven’t seen it mentioned), or they changed their blast range criteria (for a 15 kiloton bomb, 1,940 feet maximizes the 9 psi radius rather than the 5 psi radius), or that they were being very conservative about the yields (a 1,960 feet burst height corresponds with maximizing the 5 psi radius of a 7 kiloton burst, whereas 1,700 feet corresponds to a 5 kiloton burst). My guess is that the latter was what was going on — they were being very conservative about the yield.

The net result is that at both Hiroshima and Nagasaki, you had lower burst heights than were optimal. The effect on the ground is that while the 5 psi blast radius didn’t go quite as far out as it might have ideally, the range of radiation effects and radiation around Ground Zero was significantly increased, and the maximum overpressures around Ground Zero were substantially higher. Overall, it is interesting to see that they were apparently, even after Trinity, still being pretty un-optimistic regarding the explosive yields of the bombs, calibrating their burst heights to half or even one quarter of what the actual blasts were. For a “soft” targets, like Hiroshima and Nagasaki, this doesn’t matter too much, as long as the fireball is above the altitude which produces local fallout, but for a “hard” target, where the goal is to put a lot of pressure in one spot, this would be a serious miscalculation.


Liminal 1946: A Year in Flux

Friday, November 8th, 2013


Washington Post - January 1, 1946



































How many people worked on the Manhattan Project?

Friday, November 1st, 2013

Everyone knows the Manhattan Project was big. But how big was it? There are lots of ways to try and convey the bigness. The size of the buildings and sites, for example. Or the cost — $2 billion 1945 USD, which doesn’t sound that big, even when converted to modern numbers (e.g. around $30 billion 2012 USD, depending on the inflator you use), since we’re used to billions being tossed around like they are nothing these days. But consider that the USA spent about $300 billion on World War II as a whole — so that means that the atomic bombs made up for a little under 1% of the cost of the entire war. Kind of impressive, but even then, it’s hard to wrap one’s head around something like “the cost of World War II.”

General Groves speaks to a group of Oak Ridge service personnel in August 1945. From the DOE. There are lots of great Oak Ridge photos from the 1940s in this Flickr set.


Another approach is to talk about how many people were involved. There are a number of various estimates floating around. Instead of focusing on those, I want to jump directly to the source: a once-secret postwar report on Manhattan Project personnel practices that includes some raw numbers on hiring.1

This report has two very interesting graphs in it. The first is this one, showing total employment by month, broken into the various important Manhattan Project categories:

Manhattan Project contractor employment by month

Let’s just take a moment to marvel at this. They went from pretty much just talking about a bomb, in theory, on paper, in late 1942, and had a project with 125,310 active employees at its peak, 22 months later. That’s a huge ramp-up.

I like this graph because it helps you see, very plainly, the progress of the project. You can see that Oak Ridge (CEW) and Hanford (HEW) construction both got rolling pretty quickly but took about a year to hit their maximums, and that all construction peaked in early 1944. At which point, operations became the main issue — running the plants. It’s interesting to compare how many more people were required for Oak Ridge operations than Hanford operations, and that the “Santa Fe Operations” — Los Alamos, et al. — barely registers on the graph. A couple thousand people at most.

You can also see how rapidly that curve starts to drop off in September 1945 — over 10,000 people left at the end of the war, a significant chunk of them being Oak Ridge operations personnel. There is then a long slumping decline until late 1946, when you start to get an up-tick. This maps on pretty well with what we know about the history of the Manhattan Project in the period before the Atomic Energy Commission took over: Groves’ hard-built empire decayed under the uncertainty of the postwar and the dithering of Congress.

This is where we get the number one usually sees cited for the Manhattan Project: 125,000 or so employees at its peak. Which is impressive… but also kind of misleading. Why? Because peak employment is not cumulative employment. That is, the number of people who work at any given company today are not the number of people who have worked there over the course of its lifetime. Obvious enough, but if one is wondering how many people did it take to make the atomic bomb, one wants to know the cumulative employment, not the number on hand at any one time, right?

Digging around a bit more in the aforementioned personnel statistics of the Manhattan Project (a thrilling read, I assure you), I found this rather amazing graph of the total number of hires and terminations by the project:

Manhattan District Contractors Hires and Terminations through 31 December 1946

Now that number on the left, the total hires, is a pretty big one — over 600,000 total. Unlike the other graph, I don’t have the exact figure for this, but it looks to be around 610,000. That’s a huge number. Why would the numbers be at such odds? Because at the big sites — Oak Ridge and Hanford — there was a pretty high rate of turnover, as the “terminations” bar indicates: over 560,000 people left their jobs on the Manhattan Project by December 1946.

Some of this, of course, is because the job was done and they went home — once the construction was done, you didn’t need as many people working on construction anymore. But it’s also because even during the war, there was a considerable amount of people either quitting or getting fired. People left their jobs all the time, at all times during the war. As the report indicates, the reasons and rates varied by site. For construction at Hanford, they had an average monthly turnover rate of 20%, with a ratio of resignations to discharges set at 3 to 1. Of those who resigned, 26% did so because of illness, 19% were to move to another location (which could be a lot of things), 13% cited poor working conditions, 13% said there was an illness in the family, 14% had got another job somewhere else, 7% cited the poor living conditions, 6% got drafted or otherwise joined the military, and 2% complained about wages. Of those who were discharged, about a quarter of the time it was because they were an “unsatisfactory worker,” and the rest of the time it was because of chronic absenteeism. For construction at Oak Ridge, the average turnover rate was 17%, with mostly the same reasons given, though the resignations to discharge ratio was 2 to 1. (More people, by percentage, complained about the living conditions at Oak Ridge than at Hanford.) For the operations at Oak Ridge, the turnover rate was 6.6%, with a resignations to discharge ration of 1.3 to 1 — of those who left, a little over 40% did so because they were fired.

A 1944 "Stay on the job" rally at J.A. Jones Construction Co. in Oak Ridge. The workers seem a little unimpressed. Source.

A 1944 “Stay on the job” rally at J.A. Jones Construction Co. in Oak Ridge. The workers seem a little unimpressed. Source.

Of course, these numbers run through the entire tenure of the Manhattan Engineer District. When most people want to know how many people it took to make the bomb, they want to know up until August 1945 or so. I don’t have exact numbers on this. However, if we take the data from the report and the graphs, and assume an average monthly turnover rate of about 17% for the entire project, we end up with about the right number total.2 Subtracting all of the people added after August 1945, we get around 485,000 total people required to make the bombs during World War II. Given how much of that employment was front-loaded (again, with a peak in June 1944), I don’t think it’s too far off to assume that probably half a million people were employed to make the bomb. Which, to put that in perspective, means that during World War II, approximately 0.4% of all Americans worked on the bomb project — about one out of every 250 people in the country at the time.

Which is pretty impressive. By contrast, I’ve seen estimates that said that the Soviets used about 600,000 people total to make their atomic bomb. Which is not too different a number, actually — a bit less impressive than one might think if one is only comparing it to the peak of the Manhattan Project. The Soviets had around 170 million people at the time, so it works out to be a pretty similar percentage of the total population as the American project. Of course, one suspects that fewer of the Soviet workers were able to quit because they didn’t like the wage and working conditions. Though I’m sure they had their own form of grim “turnover.”

  1. Manhattan District History, Book I – General, Volume 8 – Personnel (dated 19 February 1946 but with numbers that suggest later additions were made. []
  2. If you want to play with the data yourself, I’ve uploaded it here as a CSV file. Some of it is extrapolated from the top graph. []

Little boxes of doom

Wednesday, October 23rd, 2013









