Geoff FordenTarget: Dimona

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A recent London Times article reports that Israel is worried about Hamas using its artillery rockets to shell the Dimona reactor. I thought it would be interesting to calculate the probability of one of those rockets actually hitting the reactor containment vessel, which is 18 m is radius. Of course, if it was really an artillery rocket, it might have to hit it twice, once to penetrate the containment vessel and once to blow up the reactor. But that is a refinement we won’t go into right now.

Of course, we need to decide which rocket Hamas might actually use. The Times reports the Israelis are worried about the Fajr-3, which, according to, has a range of 45 km while Dimona is approximately 80 km away from the closest point to the Gaza Strip. So it’s probably not the Fajr-3. Perhaps they meant the Fajr-5, which has a range, according to, of 75 km. While Dimona is seemingly beyond the range of even the Fajr-5, there is considerable uncertainty in those sorts of quantities so it is at least possible.

If we use the 3000 m CEP for the Fajr-5, there is a 0.004% chance that its 90 kg warhead will hit the reactor containment vessel. (The only reference I found for the Fajr-5’s CEP was by Oliver Schmidt which lists it as 3000 m.) If, on the other hand, Hamas had managed to smuggle in Zalzel-2 guided missiles, which is said to have a CEP of 200 m, then there is a 0.3% chance of hitting the containment vessel with each rocket.


  1. kerbihan

    Cosmic ray is right. At issue here is whether or not Hamas could target Dimona. Geoffrey’s analysis is very useful and interesting. But I believe that he omits an important point: obviously Hamas could not do much damage to the plant by using Zelzal (not Zalzel, I believe) rockets. But merely striking in the vicinity of Dimona would be an important political victory, raising Hamas’s stature in the region.

  2. Mark Konrad (History)

    I agree that the Israeli claim of concern over a hit on their reactor is more a distraction than anything else. However I’m not sure that an HE warhead would need to penetrate the reactor itself to cause considerable damage. A lucky impact on a support building containing for instance electrical distribution and or control panels/cabinets could cause significant interruption of operation that would require immediate attention and repair.

  3. Yossi (History)

    The reactor’s power was upgraded at an early stage much beyond the original French design. The increased neutron flux is said to damage the steel pressure vessel and maybe the concrete dome. About 40 years later the structure is certainly weaker than a new similar facility and a rocket hit may cause unexpected damage.

  4. Josh

    The exercise is purely academic. No such missiles are at all likely to be in Gaza to start with: they are too big to go through tunnels from Egypt, which are dug with hand tools, and I’m not sure how the Iranians (the presumed suppliers) would get them into the Egyptian town of Rafah undetected in the first place.

    Where does this alleged concern arise, anyhow? A much better-documented Israeli concern about missiles and strategic facilities has to do with the West Bank and Ben Gurion International Airport.

    In general, though, the current conflict does show that unguided artillery rockets of decades-old design can have more real-world significance than the most sophisticated, destructive, and cutting-edge strategic weapons.

    A final thought. The tone of this discussion is unfortunate, and marks a decline from the usual high standards of ACW. Let’s see if we can’t improve it.

  5. Miles Pomper (History)

    Since we’re on this subject, I thought your readers would like to see the feature article ACT ran on this subject last year.

  6. Yossi (History)

    Miles Pomper, the ACT article you cite said:

    Israel’s supply of tritium, which is a radioactive isotope of hydrogen with a half-life of 12.5 years, would decrease, but that element could be produced in an accelerator.

    Well, there is now a 2mA accelerator that we are given thick hints will be used to produce Tritium. Another hint is that it’s already productive.

  7. Geoff Forden (History)

    I realize that by posting on a subject related to the current terrible events taking place in Gaza, I risked setting off a mini-war here at ACW. Now is a good time to remind readers that we are all here to shed light on topics not to simply generate heat. Perhaps someone could comment on Yossi’s contention that radiation damage to the reinforcing steel to the point that a single artillery rocket to do enough damage to the containment vessel that it would end in dispersing radioactive material? That certainly interests me. My own feeling at the start of this calculation was that it wouldnt but Im not sure how to go about proving it. (That is one of the reasons I said I didnt want to get into it in the original post.) What I would investigate would be the effect of having an air volume between the containment vessel and the reactor that might disperse the induced shock wave. Any thoughts on that?

  8. Jeffrey Lewis (History)

    Geoff is a soft-touch; I am not.

    I have removed some of these comments that are off-topic. As a result, I have also removed some comments that were perfectly reasonable efforts to get us back on topic. No offense intended to those brave souls.

  9. Yossi (History)

    Having a functional computer only at work it seems I missed all the fun when I went home yesterday.

    I want to get a professional opinion from Dr. Forden, our missiles and rockets expert on the efficiency of Phalanx based systems intercepting artillery rockets and mortar shells. Is there anything wrong with such a request?

  10. dan (History)

    Having given an estimate of the odds of a Zelzal-2 hitting Dimona, it would only be fair if you could also give your estimate of the odds of such a missile being smuggled into Gaza via Egypt, which doesn’t have particularly good relations with the presumed supplier. Personally, I’d put the odds of this at zero.

    Bear in mind that this is a 3.5 metric tonne, 16 metre long beast that is launched from a large specialised vehicle.

    I guess it would be possible to dissasemble the TEL vehicle and then reassemble it, although I doubt that it would be possible to actually move the tyres through the Gaza tunnels.

  11. Geoff Forden (History)

    I gave an estimate for the Zelzal-2 hitting Dimona because I thought it was interesting to compare the difference between guided missiles and artillery rockets; not because I thought it was likely to happen. In fact, I heard on the radio that only components of the grad rockets are smuggled into Gaza. That implies that they are assembled by trained personnel but possibly not by personnel who could reassemble a guided missile. Aligning the guidance unit would certainly be more challenging than assembling a launch rail. Could the rocket grain be smuggled down one of those tunnels? I believe it could if the ends of the tunnel were properly prepared; perhaps even a complete missile. Im just not sure.

    As I understand it, Phalanx anti-missile system is very much a point defense system, perhaps with a range of 1 km (thats from memory, so if anyone knows different, I certainly wouldnt dispute them). That means that it would take a great many of them to defend even a single town. furthermore, Phalanxes shoot a near-continuous stream of bullets out—the radar system controls it like it is a continuous stream—and wears out the barrels very quickly. I think someone once told me they have to throw away the barrels after one minute of firing. I have serious doubts that it could handle barrage of artillery rockets. I wish there was some technical solution to this problem. At one time, the US and Israel were developing a high powered laser for just this situation but that relied on the HE being in direct contact with the nose cone. You can see how it would easily be defeated.

  12. Geoff Forden (History)

    Oh yes; I almost forgot. The Phalanx fires very dense bullets (depleted Uranium? Im not sure). Those have to land someplace. On the ocean its out of sight, out of mind but on land the cure might be worse than the original rocket threat.

  13. Yossi (History)

    Dr. Forden, thanks.

    ACW usually deals with nuclear weapons and ICBMs but having a very significant political weight, artillery rockets can’t be ignored.

    In Israel there was a long public debate on artillery rockets and mortar shells interception systems led by the Haaretz newspaper. The MoD was accused of refusing to employ or even test suitable systems and its claims they are unsuitable were met with widespread disbelief.

    Maybe an independent study or more info on US experience with such systems could settle the debate.

  14. Yossi (History)

    Wikipedia has interesting info on the system.

    Range is supposed to be 1-5 nautical miles, i.e. 9km max range. Covering a 40km front will take about 5 units. Mean time between jams or failures is in excess of 10,000 rounds, that with a 50-75 rounds/second firing rate is about 133-200 seconds of continuous firing. However it would run out of ammunition long before this limit is reached, say half a minute.

    The cost of barrel wear maintenance is certainly much less then the official solution, the Kipat Barzel missile which will cost more than $50,000 a piece. Kipat Barzel response time is about half a minute making it impossible to intercept short range projectiles with it.

    An Israeli expert said most shells will pass over the Gaza strip and land in the sea. I guess damage on the other side from a basically defensive weapon may be viewed as acceptable or even legitimate retaliation.

  15. Yossi (History)

    Sorry, I forgot something that seems important.

    The system employed by the US and UK in Iraq uses self destructing HE incendiary tracer ammunition that explode on impact with the target, or upon tracer burnout. This seems to solve the problem of collateral damage.

  16. Asterix

    It’s worth noting that reactor containments are routinely designed to take a substantial amount of abuse from without as well as within. For instance, it is often claimed that the D1G ball:

    was designed to take a direct hit from a fully loaded 747. This is clearly larger than the Dimona containment, but that’s because it’s got half a cruiser inside.

    I’d be surprised if the Israelis, being well within the range of hostile bombers, would not also build their containment similarly. The support buildings are much softer targets, but again, I doubt the Israelis built them out of corrugated aluminum.

  17. Andy (History)


    Rafael is currently fast-tracking the developing a system for Israel which uses guided missiles to destroy incoming rockets. It’s called “Iron Dome” and is supposed to be operational in 2010.

  18. lurker

    This could be a solution to such asymetrical threats.

    Counter-RAM: Skyshield 35 Ahead shoots down rockets, artillery and mortar rounds

    For stationary air defence missions such as protecting the forward operating bases of international peacekeepers or guarding critical infrastructure from terrorist attacks at home, the modularly designed, flexibly deployable Skyshield 35 offers excellent protection from medium- and low-altitude threats.

    The heart of the system consists of two state-of-the-art 35 mm revolver guns with a maximum rate of fire of 1,000 rounds per minute. Designed to fire Ahead ammunition, these guns can bring down even the smallest aerial target.

    A central sensor/C4I module with two independent 3D-search and target tracking systems (radar and electro-optical) is capable of controlling up to four fire control units. Aided by the latest fire control technology, the search-and-shoot sequence becomes a fully automated process, making it possible to detect, track and shoot down small RAM targets instantly and accurately. As an option, one or two additional guided missile launchers can be integrated into the system.


  19. AA

    I did a little research and it seems that the Phalanx/CIWS system based on the M61 Vulcan autocanon may be a solution for Kassam rockets and mortar shells.

    Main sources are Global Security and Wikipedia, see the “Qassam_rocket”, “Phalanx_CIWS”, “Counter-RAM” entries.

    * The Kassam rockets are homemade artillery rockets propelled by a mixture of sugar and the chemical fertilizer potassium nitrate. Diameter is 6-17cm, length 79-200cm, overall weight 5.5-200kg, explosive payload 0.5-10kg, range 3-10km. There is no guidance system and no stabilization spin. The alert to impact time is 15-45 seconds, suggesting a longer flight time. New models have ranges up to about 40km and their specifications are probably different from those given above.

    * The official solution is the developing Iron Dome missile system. Each interceptor is said to cost more than $50,000. Response time is said to be about half a minute, more than the flight time of the shorter range Kassams attacking the town of Shderot.

    * CIWS effective range is 1-5 nautical miles, i.e. max range is 9km. About 10 units would cover the 40km + 10km front nicely. Since each system costs 15M USD a full deployment is supposed to cost 150M USD.

    * Mean time between jams or failures is in excess of 10,000 rounds. With a firing rate of 50-75 rounds/second we get 133-200 seconds of continuous firing until maintenance.

    * Maximum burst size is said to be 1000 rounds, probably much more than is needed for interception. The magazine drum holds enough ammunition for 20s (Block 0), 31s (Block 1) and 20.6s (Block 1A and newer).

    * A land based version of CIWS was tested by the US as a Counter-Rocket, Artillery, Mortar (C-RAM) system. Global Security talking about C-RAM systems in general says tests showed a 60-70% shoot-down capability.

    * CIWS is the core of the C-RAM system selected by the US. It seems such systems are deployed by the US and UK in Iraq under a October 2005 Northrop Grumman $38 million contract at 8 forward operating bases. These bases include the Green Zone and Camp Victory in Baghdad and Logistics Support Area Anaconda in Balad. The British Army also uses such a system in southern Iraq

    * The C-RAM system uses High-Explosive Incendiary Tracer, Self-Destruct (HEIT-SD) ammunition that explode on impact with the target, or upon tracer burnout. This seems to solve the problem of collateral damage. Anyway, being a basically defensive system collateral damage may be viewed leniently or even considered acceptable retaliatory. An Israeli expert thinks that most shells will overshoot anyway and land in the sea.

    * The CIWS array may have to be used for only one interception every few days. The other side constantly offers a ceasefire and when these are in effect the Kassam/mortar firing rate drops to the said level, supposedly because of incomplete control over the launching crews.

  20. Azr@el (History)

    If Hamas were to opt for a symbolic strike against the Dimona nuclear weapons complex then the obvious delivery mechanism would be a UAV drone. Hizb-e-allah has demonstrated infiltration of Israeli controlled airspace with Iranian supplied UAVs. Iranian UAV’s are derived from tactical units deployed by both their army and revolutionary guards unit. These units all seem to designed for modular field assembly under rugged conditions. A few are designed to break down into man portable elements. In particular a version of Mohajer-5 disassembles into 4 backpack sized components, runs on standard commercial fuel, has a one way range of 120kms and a cruising speed of 200+kph. If the the sensor payload is stripped, there would be space for a rather large ~12-15 kilo shaped charge round.

    Food for thought.

  21. kme


    I’m interested in how you calculated those probabilities. I went looking for a good approximation to the cumulative density function for the bivariate normal distribution tailored for this kind of work (so simplified to a circular distribution and an area of integration centered around the mean) but couldn’t find one.

    In addition, can I suggest that it would be worth adding a calcuation along the lines of “if 100 rockets per day were fired at the target, a hit would be scored on average every N days” to put the probabilities into a real world perspective.

  22. Geoff Forden (History)

    Its only hard if you are looking for a closed form analytical equation. I used a Monte Carlo method to calculate it. (In general, I dont like to think more than I absolutely have to about the method of getting an answer.
    As for you second question, that is a very far one. Let me answer it slightly differently, however. For the Fajr-5 example, if you want to fire enough rockets to give yourself a 50% chance that one of them hits the reactor building, then you need to fire roughly 1,700 of them. You can calculate this from
    where Pt is the total chance that one rocket will hit out of the N, and p is the probabilities that I gave for single rockets.

  23. Gridlock (History)

    Doesn’t the use of White Phosphorous fall under the aegis (!) of this blog? Seeing how Palestinian civilians are being burned alive daily by the IDF’s use of this chemical weapon, care to calculate the odds of any given child being struck by a molten glob of toxic chemical?

    Not facetious, but a lot of the above discussion seems very suspect. ‘Imagine HAMAS had this rocket – wouldn’t reach. OK, let’s assume they have bigger, badder weapons with no evidence for and multiple evidence against! Does it work then?”

    I guess the question I’m hoping will get posted is whether the normalisation of using a banned chemical weapon against a civilian population is of more concern than an entirely theoretical question about whether the chance of weaponry HAMAS doesn’t even have hitting a reactor that oficially isn’t even a reactor is 0.004% or 0.007%.

  24. Geoff Forden (History)

    A sharp-eyed wonk reader, who would rather not be identified, points out that I should have said Fateh 110 and not Zelzal-2. Thanks!

  25. Yossi (History)

    What ACW readers think?

    Do the US C-RAM system provide a good solution to the Gaza Strip problem? See AA’s comment for details.

    It’s our opportunity to gain fame and help a lot of people!

  26. Yossi (History)

    Until comments to the contrary I declare AA’s solution as valid!

  27. Azr@el (History)

    Ad Gridlock,

    We live in an unjust world. A world where favored tribes are given free reign to drive unfavored tribes into destitution and semi-barbarism. Had western civilization in it’s guilt over the Holocaust not sanctioned and supported the disposition of the Palestinians would there be a Hamas? Would any of this suffering have to take place? The answer is no. But stuff happens and thus we are at this point where it doesn’t matter how badly the Israelis maul the dehumanized Palestinians, the free world will stand calmly by and blame the Palestinians for being so wretched. This will of course continue until some group decides to use nuclear weapons to bring about the decline of western civilization. Unfortunate, but in a way historically necessary.

  28. Austin Long (History)

    C-RAM is indeed currently deployed to Iraq- I lived just down the road from one at Camp Victory. I was always concerned about the potential fratricide by falling round/fragment question. Even if a 20mm round is detonated at tracer burnout there are going to be fragments or possible fire hazard. That said, I know of no incidents of that kind. As for effectiveness, I have no idea what success is being claimed but there were several successful rocket/mortar attacks on Victory while I was there so I would guess it is substantially less than 100%. Moreover, even a rocket that is hit may still have a warhead survive to impact if the target are is large enough i.e. a base or town rather than a moving ship.

  29. Yossi (History)

    Austin Long, thanks!

    My guess is that the C-RAM shell remains (or the duds) had overshoot Camp Victory and hit places far beyond the rocket/mortar launch point.

    Global Security says C-RAM in general has a 60-70% shoot-down capability. I’m not sure what this term means. Nothing hitting the protected zone?

    Do you know if the system was up all the time or have been improved since?

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