The Syrian Qassam Part IV: The Lions of Allah Sham Freedom Missile Accuracy and Final Assessment

Accuracy Continued and Final Assessment

For simplicity, let’s start by targeting only the section of the Army Chief of Staff building seen ablaze in Part III, which may be measured in Google Earth at around 45 x 17.5 m.

To also include hits collapsing the outer façade of the building, let’s look at what range the blast of an 8 kg TNT warhead may destroy concrete, which generally requires 10 - 15 psi of blast overpressure.

 The relationship between warhead size and lethal radius may be expressed as follows:

 R_L = D x W^1/3

Where RL is the lethal radius of the warhead, W is the size of the warhead in kilograms, and D is the lethal radius for a 1 kg TNT warhead (for 15 psi, approximately 3 meters). Thus, R_L = 3 * 8^1/3, or 6 meters. 

We can therefore add 12 meters to the effective length and width of the target, arriving at 57 x 29.5 m, which covers an area of 1,681.5 m². 

Finally, for targeting, let’s convert the building area to a circle of equal area, yielding a radius of about 23.13 m.

To determine the probability of a direct hit, or single shot kill (SSK) probability, we may consider the following formula, taken from "Missile Accuracy (CEP)," an excerpt from "Statistical Snacks":

p_ssk  = 1 – e ( -0.41 · R² / CEP² )           

Plugging in (1) missile CEP and (2) target radius, we arrive at:

p_ssk = 1 – e ( -0.41 · 23.13²/ 100²) = 0.0217 = ~2.2%

So, even if we generously assume the respectable 100 m CEP of an Iranian Fateh A110, the Sham Freedom missile SSK probability against a facility-sized target is little more than 2%, a far cry from the claimed 80%. 

To achieve that kind of SSK probability against the same target, the Sham Freedom missile would require a CEP of ~11.5 m –on par with some of the most advanced guided artillery rocket systems in the world.

So how many Sham Freedom missiles would it take to strike the Army Chief of Staff building?

Now we may evaluate the utility of a 500 unit Sham Freedom missile arsenal against facility sized targets.

To begin, the probability of missing the Chief of Staff building with a single Sham Freedom missile is 1 – 0.0217 = 0.978 = 97.8%. 

The probability of a miss occurring say ten times in a row is .978 to the tenth, or 0.8, with a hit occurring 1 - 0.8 = 0.2, or 20% of the time.

And if we launch more?


A salvo of half the reported Lions of Allah arsenal, or 250 Sham Freedom missiles, will achieve a strike against the section of the Army Chief of Staff building measured previously with a probability of 1 - (.978¹⁰⁰) = 0.89%.  To strike the Chief of Staff building with an acceptable 75% probability, the Lions of Allah would need about 62 missiles.

Here’s the fine print:

Previously, we selected the extraordinarily generous CEP of a guided Iranian Fateh A110. If we consider a more plausible, yet still optimistic CEP of around 500 m, which would be about the same as a Russian 9K52 Luna artillery rocket, the Lions of Allah would need to launch about 1,580 Sham Freedom missiles to achieve a single strike against the Chief of Staff building with ~75% probability. If we bump up the CEP to the neighborhood of a North Korean Hwasong 6, at around 1,000 m, the Lions of Allah would need to fire around 6,335 Sham Freedom missiles to hit the Chief of Staff building just once, 75% of the time.

Ultimately, I doubt the Sham Freedom missile boasts a CEP any less than the Qassam II rocket, universally known as an inaccurate terror weapon at best.  

III. Final Performance Assessment: Claims Evaluation and Actual Utility

For a recap, here's our evaluation of the source claims:

•   Range: Tentatively confirmed at approximately 7 km with an 8 kg payload, given a relatively efficient rocket motor. For a sanity check, the similar sized, locally manufactured Palestinian Qassam II rocket has a range of 10 km with a 5 kg warhead.  A simulation using only a 5 kg warhead extends the Sham Freedom missile range to ~8,500 m. 

•   Quantity: The Lions of Allah may certainly have 500 units. But such a capability means little if the intended targets are relatively small facilities. However, a 500 unit arsenal may be more useful in other roles, as will be explored below.

•   Accuracy: If the unqualified accuracy of "80%" was referring to SSK probability for a facility sized target, then that's almost certainly disproved. And frankly, calculations were not required. A quick sanity check with a Qassam II will tell that locally manufactured, unguided missiles are only good for terror, propaganda, and perhaps indiscriminate area coverage.


Does that mean that unguided rockets like the Sham Freedom missile are useless to the Syrian opposition? Not at all.


First, they serve as a useful propaganda and terror tool, especially during the early to mid-stages of the Syrian civil war, when more sophisticated, conventionally manufactured SSM were hard to come by. That a rag-tag opposition brigade could assemble the expertise, material, and safe haven to produce relatively advanced locally manufactured arms like the Sham Freedom missile is impressive, especially if delivered in quantity on regime-held positions and neighborhoods, even if inaccurately. 


Second, this analysis considered a facility sized target. But if the Lions of Allah brigade instead used Sham Freedom missiles en masse, similar to a Russian truck-mounted Katyusha battery, they may be more useful. Indeed, what look like locally manufactured truck-mounted Katyusha batteries have been snapped in Syria:

These kind of truck-mounted, mass-barrage systems are very effective for raining long-range death quickly. A salvo could be launched in minutes, with the missile crew evacuating the launch site immediately.

In the second shot, we see the "Islam 3" missile. Sources claim a "60 km range" and "85% accuracy." These capabilities may be evaluated using methods described in Parts I - IV of this post. However, if the Islam 3 is deployed as truck-mounted rocket artillery, it may  provide a more effective, tactically useable system, as opposed to single launches that do not achieve the kind of barrage density necessary to make up for lack of missile accuracy.