Category Archives: Coincidences

Inferring Iranian Centrifuge Production Rates

_Warning: Mind-numbingly detailed and self-referential._

Someone requested a fuller explanation of one corner of “last week’s post on when Iran might achieve breakout capability”:, specifically the chart showing patterns of centrifuge installation at the Natanz Fuel Enrichment Plan (FEP) in Iran. So this is for anyone who didn’t quite grok the chart. It’s shown here with the original text that surrounded it:

So here, drawn from various IAEA reports, is the pace at which the Iranians have added centrifuge cascades at FEP:


What we can gather from this chart is a sense of the minimum rate of centrifuge production. No one can install more than they have. So the solid black line is a floor of about 18 cascades’ worth of machines per year, or one unit. (There are 164 machines in a cascade, so this means close to 3,000 machines/year.) The dashed extension of the line shows the implication of that floor: unless centrifuge production has (for some unknown reason) slowed considerably, a backlog of machines is building up, awaiting installation.

It’s like this. We’re assuming that the Iranians are still churning out new IR-1 centrifuges somewhere, working towards the 50,000 or so that are supposed to go in the Natanz FEP, eventually. We don’t know exactly how fast the machines can be produced, but breakout capability — the subject of the blog post — is sensitive to this question, so we need to come up with a reasonable range of possibilities. Just to be pessimistic, let’s assume that, in the future, they can installed and made operational more or less as soon as they are produced.

The approach explained here is really pretty simplistic, just one part of a “rough and ready” analysis of the larger issue of breakout capability. A more sophisticated analysis is probably possible for those interested in attempting it. Presently, at least, I’m not.

Anyhow, it went like so:

First was reconstructing from IAEA reports just how many cascades (linked groups of 164 centrifuges) were present in the Natanz FEP when the IAEA actually counted them. Those are the colored bars.

_(You can find all but the most current IAEA report on Iran at the “official site”: ACW may post first, but ISIS rolls up “everything in one spot”: [I could have saved myself a little time if I’d noticed that the Wisconsin Project had already compiled most of this info in a table and “posted it here”: Sigh.] As you can see, for simplicity’s sake, I collapsed a couple of categories of information into one.)_

Second was drawing a simple inference about the lowest possible rate of production for the period (February 2007 to February 2009) from the height and spacing of the bars. This is the solid black line. You will notice that introduction of centrifuges for the period actually peaks in May 2008. So I drew the line from February 2007 to May 2008. That’s the _minimum_ cumulative level of production that would explain the observed number of centrifuges present at the Natanz FEP — assuming, of course, that there wasn’t a big stockpile of centrifuges already sitting around somewhere. Probably there wasn’t, either. What little we know suggests that production wasn’t that rapid in the past. See the bottom of page 9/top of page 10 in “GOV/2004/60”:

In case the graphic has scrolled off your screen, here it is again.


_You’ll notice that the line kinks at May 2007. If it had been drawn straight from the top of February 2007 to May 2008, it would have sliced through May 2007, which clearly would have violated the assumptions set out above: such a cumulative level of production would not have sufficed to explain the observed number of centrifuges present at the Natanz FEP. Thus the kink. In hindsight, I should have just made the line perfectly straight, so it would intercept the y-axis a bit above the February 2007 bar. Gimme a break, it’s a blog post._

Third was extending the line to the right, in dashed form. This illustrates another assumption: that the pace of production over the entire 25-month period has been roughly constant, _at a minimum_. This would mean that the reason new machines were not introduced to the FEP after May 2008, whatever it was, wasn’t because the machines were unavailable. This interpretation is supported by the gradual ramp-up in operations that you can see in the colors of the bars.

Fourth was eyeballing an annual rate of centrifuge production. I came up with 18 cascades’ worth, which happens to be how many there are in a “unit” (or module) of cascades inside the Natanz FEP. Peering at it again, it looks closer to 19 cascades’ worth, but 1) we’re trying to come up with a low-end estimate, so let’s round down and 2) 18 is more convenient because of its relationship to the structure of the FEP.

Either way, that’s around 3,000 machines/yr, or 250 machines/mo. Minimum. To come up with a reasonable guess at a maximum figure, I simply doubled the minimum. Thus, my working estimate was that Iran produces enough machines to stock one to two new units (or 18 to 36 cascades) per year.

Like it says, rough and ready.

Now, could that minimum figure actually be 3,000 machines/yr too high? Is it possible that the Iranians actually ran out of some key ingredient after May 2008? (Rotor juice? Ball grooves? Handles for the bellows?) Let’s not count on it. The latest report, “GOV/2009/8”:, observes that

Installation work at Units A25, A27 and A28, including the installation of pipes and cables, is also continuing.

Hmm. Maybe that range should have been _one to three_ new units.

For your reference, here again is the link to “Jeff Lewis’s near-simultaneous post with a near-identical graphic”: What’s fascinating is that we independently produced these illustrations to make two different points. Seriously, “what’s the chance”:

Hopefully that clarifies things. Yes, it’s pretty long for a footnote to a blog entry.

You’ve suffered enough. Enjoy the “musical bonus”:




This wasn’t planned.

Stuff Happens

Much remains to be explained about the remarkable encounter between two nuclear ballistic missile submarines in the Atlantic in early February. The whole affair really puts the Foxtrot* in “WTF”:

One angle probably not worth fixating on is the idea, mooted in the “comments at ACW”:, that this was no coincidence. There’s just no plausible reason to operate SSBNs intentionally in proximity to one another.

But meant another way, perhaps it was no coincidence. It’s easy to “underestimate”: “probabilities”: for at least a couple of reasons.

First, the “role of iteration”: If the chance of a bad event per patrol is one umpteenth, the chance of a bad event per umpty-ump patrols may be a good bit higher. (It’s the complement of the chance-of-no-bad-event-per-single-instance raised to the power of the number of instances.) We tend to overlook this.

The implications of this point for the chance of general nuclear war are left as an exercise for the reader. Happy spreadsheeting, and sleep well.

Second, the “assumption of independence”: It’s simplicity itself to do calculations such as the one above, but it assumes that each instance is not influenced by any other instance. They’re all mutually independent. But whether it’s satellites or sous-marins, there routinely seem to be reasons — physical, technical, geographic, etc. — to operate in similar or overlapping patterns. In short, there are dependencies between events. This, too, is easy to overlook. Among other things, it makes the math a great deal harder.

The implications of this point for credit default swaps are left as an exercise for the reader should be lost on no one by now.

All of which is a way of saying that the “shut-mouthedness of the French and British navies”: about this event is no indication of anything more sinister than the wholly reasonable desire to preserve secrecy about their SSBN patrol areas. Based on what’s been published so far, you can already make some educated guesses about the general vicinity of this event, which ought to be enough to make anybody a little uneasy.

It helps to recall why the boat goes under the water in the first place: so you can’t see where it goes.

*Yes, I realize that neither of these boats has much in common with a “Foxtrot”: except that they all go under the water.

What’s The Chance? Ctd.

Yes, it’s the “theme”: of the “week”:

According to the “BBC’s defense correspondent”:, the undersea collision of HMS Vanguard and Le Triomphant was not too likely:

“This is clearly a one-in-a-million chance when you think about how big the Atlantic is,” she said.

Now, clearly that’s a figure of speech rather than a considered estimate. And perhaps it’s one of those probabilities that’s altogether too easy to lowball. As a source explains later in the same item, submarines like to hang around and spend time together:

Nuclear engineer John Large told the BBC that navies often used the same “nesting grounds”.

“Both navies want quiet areas, deep areas, roughly the same distance from their home ports. So you find these station grounds have got quite a few submarines, not only French and Royal Navy but also from Russia and the United States.”


Here it is, your “musical bonus”:

What’s The Chance?

Econo-blogger extraordinaire Felix Salmon writes:

“Low-Probability Disaster of the Day, Exosphere Edition”:

From “Andy Pazstor”:

Pentagon brass, satellite industry executives and NASA leaders for years have publicly expressed concern about the dangers of orbital debris. But the odds of a direct hit between satellites were considered so small as to be basically unthinkable.

Is there a way of distinguishing, ex post, between (a) the ex ante probabilities having been wrong, and (b) the collision having been genuinely improbable? I’m going with (a).

This is a really meaty question, actually. It’s not, as one might suppose, a deterministic problem, as there is a human element involved in steering active satellites away from anticipated collisions. (Expect some hard questions to be asked about how this collision came about.) It’s just the sort of complex and continuously occurring situation that “nuclear deterrence wonks often think about”:, in fact.

So if one were to assess the probability of a sat-sat collision beyond a first approximation, it would probably involve interrogating experts to get their probability estimates. And no, you really could not know if their probabilities for this or any other specific question were right or wrong. But you can establish, “after the fact”:, which experts provide accurate probabilities, and which don’t. What is more, with creativity and good preparation, you can even get a pretty solid idea of who is accurate and who isn’t “well before the fact”: All without resorting to “black magic”:

One thing you probably shouldn’t do is to try to judge the accuracy of past predictions by what happens now, “post-Iridium-Cosmos”: This event presumably reduces the odds of the next sat-sat collision, since operators will be more vigilant for a good while. There’s that slippery human element again.

Then again, sat-sat collisions are the least of our worries. The real threat is sat-debris collisions. Not only are these relatively common — David Wright identifies “seven such incidents since 1991”: — but we should expect the fresh debris generated by Tuesday’s debacle to accelerate the trend.

For The Record

A side note. “Andy Pasztor’s WSJ article”: contains a startling inaccuracy:

Industry officials say Iridium has identified the Russian craft as a Cosmos series satellite launched in 1993, weighing more than a ton and including an onboard nuclear reactor. That couldn’t be independently verified. Experts have said the chance of radioactive debris surviving a fall through the atmosphere and reaching inhabited areas is very small.

Rest assured, there was no nuclear reactor on board. Although “such a thing has been contemplated”:, so far as I’m aware, it’s never been done, and at least in my naive estimate, the practicalities seem daunting. That is presumably why this claim “couldn’t be independently verified” — which maybe means that it shouldn’t have been published, either.

(And let’s not even get into “Project Orion”:

What Pazstor’s confused source probably was thinking of was a “radioisotope thermoelectric generator”: (or RTG), used to power deep space probes, the occasional satellite, or, in Russia, “various other things that require power, but people don’t routinely visit”: (RTGs have also provided Iran’s nuclear research agency with “an embarrassingly lame excuse for experimental Po-210 production”: Long story short, a pellet of plutonium (or other radioisotope) gives off heat, which is used to generate electricity.

But, as it happens, this wasn’t the case, either. Pavel Podvig has “flagged”: the dead bird as a “Strela-2M”: comsat, which apparently involved chemical batteries of some type.

Hey, live and learn.


“Apollo-Soyuz”: it ain’t.

For those who haven’t heard, the _Washington Post_ “sums it up”: thusly:

The Pentagon and NASA are scrambling to assess the risk to spacecraft and the international space station from hundreds of pieces of debris created in the collision Tuesday of two satellites 491 miles above Siberia. NASA’s initial estimate is that the space station faces a “very small” but “elevated” risk of being struck.

The situation is unprecedented. Scraps of spacecraft and other orbital junk have crashed together previously, but this was the first incident involving two intact satellites. One was an Iridium satellite launched in 1997 and used for the company’s satellite telephone network; the other, a Russian Cosmos satellite launched in 1993, had been non-operational for a decade, NASA and Pentagon officials said.

“Geoff Forden told you so”: He “did”:! So did “David Wright”:, “a whole bunch of guys from NASA”:, and probably lots of others besides. It’s funny how low-probability events have a way of becoming high-probability events if enough time passes. Which it does, pretty gosh-darn consistently.

Iridium says “the following”:

In a statement, the company said that it had “lost an operational satellite” on Tuesday, apparently after it collided with “a nonoperational” Russian satellite.

“Although this event has minimal impact on Iridium’s service,” the statement added, “the company is taking immediate action to address the loss.” The company’s hand-held phones can be used anywhere around the globe to give users voice and data communications.

Inquiring minds want to know what, ahem, “impact”: this will have on a Sirius XM buyout. What with the heightened risk of a space debris chain reaction in low earth orbit.

I kid. But seriously, folks, could we avoid using “impact” in a metaphorical sense here?

Oh, and one other thing. Could we rethink this whole ASAT war business now? What do you say?

Get your musical bonus “here”: