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In the early weeks of July, the conflict between Palestinians in Gaza and Israel flared up again, resulting in a new round of large-scale rocket attacks, launched by Hamas, operating from Gaza, against Israeli population centers. The last such large-scale rocket attacks occurred in November 2012.

Initially, the Israeli military responded to the rocket attacks with air strikes in Gaza, and with protective measures that include deployment of the Iron Dome rocket-defense system and a civil defense effort that includes an efficient system for early warning and sheltering of citizens. As of this writing, only one Israeli had died from Hamas fire, apparently from a mortar round (although that number increased with the Israeli invasion of the Gaza Strip begun late last week).

During the November 2012 conflict, a detailed review of a large number of photographs of Iron Dome interceptor contrails revealed that the rocket-defense system's success rate was very low—as low as 5 percent or, perhaps, even less. A variety of media outlets have attributed the low casualty number to the supposed effectiveness of the Iron Dome system, quoting Israeli officials as saying it has destroyed 90 percent of the Hamas rockets it targeted. But close study of photographic and video imagery of Iron Dome engagements with Hamas rockets—both in the current conflict and in the 2012 hostilities—shows that the low casualties in Israel from artillery rocket attacks can be ascribed to Israeli civil defense efforts, rather than the performance of the Iron Dome missile defense system.

The collection of data for Iron Dome's performance in July 2014 is still in progress. The data we have collected so far, however, indicates the performance of Iron Dome has not markedly improved.

Historical data on civil defense measures—including those taken to protect citizens from V-1 and V-2 rocket bombings of London during World War II—suggest that Israel’s low casualty rate from Hamas rockets is largely attributable to the country's well-developed early-warning and quick-sheltering system for citizens under imminent rocket attack. That is to say, Iron Dome appears to have had no measurable effect on improving the chances of Israelis escaping injury or death from Hamas artillery rocket attacks in Israel.

What performance characteristics make a rocket defense effective? To successfully intercept an artillery rocket of the type Hamas has been firing, an Iron Dome interceptor must destroy the warhead on the front end of the rocket. If the Iron Dome interceptor instead hits the back end of the target rocket, it will merely damage the expended rocket motor tube, basically an empty pipe, and have essentially no effect on the outcome of the engagement. The pieces of the rocket will still fall in the defended area; the warhead will almost certainly go on to the ground and explode.

Destroying an artillery rocket warhead is a considerably more demanding mission than damaging other parts of the targeted rocket—or, in the analagous situation of aircraft defense, successfully damaging an airplane, causing the failure of its mission.

Analysis of photographs of contrails left by Iron Dome interceptor missiles can show whether or not an attempted rocket intercept could have been successful. Such analysis focuses on two connected facts: To have a realistic chance of destroying an artillery rocket's warhead, an Iron Dome interceptor must approach the rocket from the front—in fact, almost directly head-on. And for all practical purposes, an Iron Dome interceptor has no chance of destroying the warhead if the interceptor engages the rocket from the side or from the back.

Photographs of Iron Dome contrails indicate that most of the system's interceptors have either been chasing Hamas rockets from behind or engaging those rockets from the side. In both such cases, geometry and the speed of the interceptors and rockets make it extremely unlikely the interceptor will destroy the rocket's warhead.

How an Iron Dome interceptor works. To understand why the Iron Dome interceptor must approach the artillery rocket from the front to be effective, it is necessary to understand the basics of how an Iron Dome interceptor is meant to function.

Figure 1 illustrates a theoretical front-on engagement by an Iron Dome interceptor against a Grad artillery rocket, a weapon initially produced by the Soviet Union in the 1960s, subsequently manufactured by many other countries, and now readily available to Hamas. The blue dashed line emanating from the forward section of the Iron Dome interceptor depicts the line-of-sight of its “laser fuse,” which creates a beam of light that reflects off the front-end of a targeted artillery rocket. Via its control system, the interceptor can then determine when the target rocket is in the process of passing the interceptor. The warhead in the Iron Dome interceptor is placed well behind the fuse assembly, a distance of roughly 3 feet from the laser-fuse aperture. This arrangement gives the fuse enough time to determine where the front of the target-rocket is, to estimate how long it will take for the front of the artillery rocket to pass parallel to the artillery rocket’s warhead, and to detonate the Iron Dome warhead at the moment when it is in position to cause the rocket's warhead also to explode.

The timing of this sequence of events is critical to performance. The Iron Dome interceptor must account not only for the location of the target-rocket’s warhead, but also for the high crossing speed of the Iron Dome interceptor and the artillery rocket; for any off-parallel orientation of the Iron Dome interceptor relative to the artillery rocket; for the distance between the interceptor and rocket when the interceptor's explosive warhead goes off; and for the speed of the shrapnel fragments shooting from the warhead.

Figure 2 shows how the fragments from the Iron Dome warhead would move, under the assumption that the crossing speed of the Iron Dome interceptor and artillery rocket—that is, their speed relative to one another—is about 1,200 meters per second. The explosive in the Iron Dome warhead projects fragments at about 2,100 meters per second, perpendicular to the direction the interceptor is traveling. According to standard physics calculations (suggested by the red and yellow vector diagram at the lower right of the figure), the net direction of the cloud of fragments, as experienced by a theoretical observer sitting on the artillery rocket, is shown by the pale blue arrow passing through both the Iron Dome warhead and the artillery rocket’s warhead.

Figure 3 provides a slightly more vivid and detailed view of the outcome, if an Iron Dome interceptor works as intended. There is, however, only a limited range of possible outcomes that provide a high likelihood of success. Beyond that range, the possibility of success diminishes drastically.

The many ways that Iron Dome can miss. Because of the uncertainties in the exact crossing speed and geometry of two high-speed missiles, even a perfectly operating Iron Dome fuse may fail to place lethal fragments onto an artillery rocket’s warhead. In addition, unless the distance between the Iron Dome warhead and the warhead of an artillery rocket is small (roughly a meter or so), there will be a greatly diminished chance that a fragment from the Iron Dome warhead will hit, penetrate, and cause the detonation of the artillery-rocket warhead.

So a front-on engagement does not guarantee that an Iron Dome interceptor will destroy the warhead on the artillery rocket. A front-on engagement geometry merely indicates that an Iron Dome interceptor has a greater-than-zero chance of destroying the target-artillery rocket warhead.

The consequences of a failure in fuse timing—in what was almost certainly an engagement between an Iron Dome interceptor and the artillery rocket—are shown in Figure 4 and Figure 4A.

The photo in Figure 4A shows the magnified front-end of the rocket; holes can be seen in the expended and empty rocket motor casing immediately behind the warhead. In this case, it is nearly certain that the artillery rocket was engaged by an Iron Dome interceptor properly approaching the artillery rocket, front-on. Unfortunately, it seems the timing commands from the fuse resulted in fragments from the exploding Iron Dome warhead hitting the artillery rocket after the warhead had passed. The relatively low density of holes in the artillery rocket’s after-body suggests that the encounter also had a relatively high miss distance—possibly several meters. And as can be seen in Figure 4, there is significant damage in the area where the rocket fell—damage almost certainly caused by the detonation of the rocket's small warhead when it hit the ground. This photograph illustrates that even when the Iron Dome interceptor is in a proper front-on trajectory, it can still fail to destroy the warhead of a target-artillery rocket.

Figures 5, 6, 7, and 8 are detailed diagrams that indicate how an Iron Dome interceptor would perform if it engaged an artillery rocket from directions other than head-on. They show why the kill rate for an Iron Dome interceptor will be very low when the interceptor does not attack its target almost directly head on.

As Figure 5 shows, even a moderately skewed approach to the targeted rocket will result in a drastically reduced chance that fragments from an Iron Dome warhead could be sprayed onto the rocket's warhead. Such small but crucial off-frontal errors could result from faults in the master guidance and control system of the Iron Dome interceptor.

Figures 6, 7, and 8 show interceptor engagements that approach the targeted artillery rocket from the side or from the back. Careful inspection of the geometry of the fuse sensing beam and the spray pattern of the fragments from an Iron Dome warhead reveals two very serious problems with these kinds of engagements: First, even if the fuse detects the artillery rocket in these angles of approach, it has no way of determining where the warhead is on the rocket. Second, even if the fuse detonates the Iron Dome warhead, by chance, at a time when fragments might be sprayed in the direction of the rocket warhead, in almost all circumstances the result will be a very low density of fragments arriving at the artillery rocket warhead location. Given the small number of fragments that can be dispersed by the Iron Dome warhead, this translates into a very high chance that no fragment will hit the warhead.

Making a successful interception even more problematic, the projected target area of the rocket warhead is very small, viewed from the front or back, rather than from the side. Also, when an Iron Dome interceptor approaches from these side and rear angles, fragments from its warhead are very likely to hit the metal surfaces of a target rocket at low grazing angles, with fragments tending to bounce off the shell of the rocket body or warhead casing. In sum, then, for engagement geometries that are not front-on, the probability that an Iron Dome interceptor will destroy the warhead of an engaged target-artillery rocket will be, for all practical purposes, nearly zero.

Understanding Iron Dome contrails. If artillery rockets are fired at their maximum range, they can be expected to fall at angles of 60 to 65 degrees relative to horizontal in their descent to a target; they will fall at angles well above 65 degrees when fired at less than maximum range.

The very steep descent of artillery rockets is important to keep in mind when attempting to visualize what is happening when viewing the photographs that show only the smoke contrails of Iron Dome interceptors attempting to engage artillery rockets. When Iron Dome interceptors explode in the sky, but have contrails showing they have crossed the expected rocket trajectory in a side-on geometry or chased the artillery rocket from behind, it can be said, with a high degree of certainty, that no intercept could have occurred—assuming of course, an artillery rocket was even being engaged.

Figures 9, 10, and 11 are photographs taken during the artillery rocket attacks in November 2012. They show contrails in the sky that indicate Iron Dome interceptors were attempting to engage target-artillery rockets from behind or from the side. The geometries of the engagement are easily established; the artillery rockets are falling at high elevation angles relative to the ground, and the contrails show Iron Dome interceptors clearly approaching from above or sidelong to any reasonable estimate of a rocket's descent path.

The photographs in Figures 12 and 13 show intercept attempts in July 2014 that are nearly side-on, and hence, have essentially a zero chance of destroying target rockets, if they are present.

Observations colleagues and I made in November 2012 found no more than 20 percent of Iron Dome contrails indicating an engagement geometry that was front-on to the targeted rocket. At that time we estimated the probability of destroying a SCUD warhead in a front-on engagement might be between 30 and 60 percent, meaning that if all other engagements affectively resulted in a zero probability of interception, then the overall intercept rate would be between 6 and 12 percent. Given that less than 20 percent of the engagements we were able to get data on were actually front-on, our best estimate was that the intercept performance of Iron Dome was likely 5 percent or less.

Daytime visual photographs of Iron Dome debris clouds can show, in many cases, the evidence of a successful intercept, i.e., the destruction of the targeted artillery rocket warhead. Since the Israeli government has been claiming a very high intercept rate—near 90 percent—it should be expected that visual evidence of hits would be common. But we have found only one example of photographic evidence in which it is clear that such a head-on success occurred.

Figure 14 shows photographic evidence of the destruction of a rocket warhead by an Iron Dome interceptor. In this photograph, the Iron Dome missile is clearly on a trajectory that engages the falling artillery rocket head-on. The large white arrows at the top and bottom of the photograph show the relative directions of the rising Iron Dome interceptor and the falling artillery rocket. An inspection of the debris cloud shows that it is asymmetrical—indicating that two explosions have occurred nearly simultaneously.

This debris cloud formation is essentially the result of fragments from the Iron Dome warhead hitting the warhead of the artillery rocket and detonating it. The explosive process that led to this observable debris cloud took less than one half of a millisecond, or essentially instantaneously from the perspective of an observer or with regard to the frame rate of a standard video camera, which would take a picture roughly every 30 to 40 milliseconds.

This photograph is the only successful engagement I have found during very extensive searches of voluminous photographic and video evidence of Iron Dome interceptor activity.

It could be argued that the details that can be seen in this photograph are sufficiently subtle that they might not be observable in all engagements. This argument is probably correct. All the same, it seems extremely unlikely that the Iron Dome system would be intercepting 90 percent of the artillery rockets it engaged, but result in only one photo among hundreds as evidence of a successful intercept.

It is absolutely clear: There is no evidence in the public record to show that Iron Dome is performing at an intercept rate of nearly 90 percent.

If Iron Dome doesn't work well, why are Israeli casualties from rocket attacks so low? Israel has a vast system of shelters, arranged so citizens can easily find protection within tens of seconds or less of warning. The Israeli rocket attack warning system is sophisticated; Figure 15 shows warning times published by the Israelis for artillery rockets of varying ranges. Figure 16 shows the screen of a mobile phone warning system that issues an audible alert of an impending artillery rocket impact. This particular phone application is called “red alert.”

The app's message indicates the general area where an artillery rocket impact is expected; depending on the location of individuals receiving the warning message, they know whether or not to take shelter.

During the World War II bombing of London by Germany's V-1 and V-2 rockets, seconds of early warning resulted in reductions in casualties and deaths by a factor of two or more, even when the people under attack did nothing more than take expedient measures like falling to the ground before a rocket impact.

In the World War II bombings in London, the warheads were much larger than those used by Hamas, carrying about 2,000 pounds of explosives; in the Gulf War of 1991, SCUD warheads were also much larger, about 500 pounds each. In the case of the recent artillery rocket attacks against Israel, the overwhelming number of artillery rocket warheads are in the 10- to 20-pound range. These small warhead sizes make early warning and protective sheltering even more effective, because the smaller warheads are very unlikely to penetrate or destroy a shelter.

These two factors—the small size of the warheads, and the warning and sheltering system—go far toward explaining why there has been only one Israeli death from rocket and mortar attacks. The one Israeli death attributable to the current conflict as of the writing of this article occurred on July 15; a man was hit by shrapnel from an exploding mortar shell near the Israeli border with Gaza, and his death was clearly the result of two unfortunate circumstances: The man was not in a shelter, and he had no warning of the arriving mortar shell.

Another example of the hazards of not taking shelter occurred in November 2012. Three people were out on a terrace; one of them was hoping to observe the Iron Dome system intercepting incoming artillery rockets. An artillery rocket hit the terrace, killing all three people. Had these people followed the simple procedure of taking shelter, they would be alive today.

A need for Israeli transparency. I do not know precisely why Iron Dome interceptors are not engaging most artillery rockets using the proper front-on geometry. It is clear that the Iron Dome radar tracking and guidance system is not working as it should work; it is initially sending Iron Dome missiles to intercept points that then result in interceptors not being able to achieve the right engagement geometries when they start the process of homing on targeted artillery rockets. Photographs from November 2012 show such problems, and pictures from July of this year indicate that Iron Dome interceptors are still behaving erratically, resulting in continued low intercept rates.

If Iron Dome is in fact working at the high levels of performance being claimed, there is systematic data that the Israeli government could present to document the success.

The Israeli government publishes insurance claim data that occur during different time periods. This data would very clearly show a reduction in ground damage in the areas defended by Iron Dome. This could not be otherwise, given the large number of successful intercepts being claimed by the Israelis and the significant reduction in damage that would occur from destroying artillery rocket warheads that would otherwise explode on the ground, or in or near buildings.

This is not to say that there would still not be significant insurance claims in areas successfully defended by Iron Dome. A successful intercept can at the very best destroy the explosive warhead carried by the artillery rocket. It cannot destroy the pieces of debris from the artillery rocket itself. This debris will fall whether or not an artillery rocket has been intercepted. Nonetheless, the major contributor to significant damage is the exploding warhead on the artillery rocket. The Israelis have not provided any evidence of a reduction in ground damage that would surely have to accompany the amazing success rates that they have claimed for Iron Dome.

In the absence of Israeli data backing claims of Iron Dome efficiency, and based on the unambiguous evidence I have reviewed, a conclusion seems clear: The Israeli government is not telling the truth about Iron Dome to its own population, or to the United States, which has provided the Israeli government with the bulk of the funding needed to design and build the much-heralded but apparently ineffective rocket-defense system.