Estimating the UMLACA Range

If this is your first time here, I recommend starting from the conclusion page.

Summary

In this page several methods are used to estimate the range of the rocket used in the chemical attack ("UMLACA"), resulting in a final estimate of 2.5 km. The methods:

1. The model design was entered into a rocket simulation software. Two engines were examined - one smaller than the real engine, and one larger. This resulted in a range of 2.0-2.5 km.
2. For verification, designs of four other rockets with known ranges were entered, giving results accurate within 20%. Additionally, the parameters of engines in the simulation were compared to known military rockets, and were shown to have the same efficiency.
3. Two videos of launches of a similar rocket model were analyzed, resulting in a range of 2.2-2.3 km.
4. A comparative analysis to another rocket of similar size, while not accurate enough to provide a range estimate, proves that the UMLACA could not have been launched from the Syrian army bases north of Damascus, as frequently claimed.
5. An analysis indicating rockets of this design are intended for short-range missions.
6. A full bottom-up analysis of the rocket, estimating its range at around 2.5 km.
7. A calculation placing an upper theoretical limit of 3.5 km if the rocket is assumed to be subsonic, as implied by its design.
8. Most importantly, this page has seen thousands of visits over several weeks, and no one has provided any evidence that contradicts this estimate (here or anywhere else). If you have it, please share.
9. Update - The same conclusion was later reached by two experts: Theodore Postol, a Professor at MIT (quoted in the Hersh report), and Richard Lloyd, a warhead technology consultant (quoted in the Brown Moses blog, and later in the NY Times). It was also later confirmed by the UN to be a "fair guess".

Method 1 - OpenRocket Simulation

Note: Method 5 below is considered a more reliable simulation. Feel free to skip this section.

Following the advice of Amund Hesbol, I used the OpenRocket simulation software to simulate the path of an UMLACA.

Here is my design:

I made the following selections:

1. All measurements according to the UN report.
2. 2mm steel for the material, which is my estimate based on the main body remains found in impact sites. The engine tube is much thicker, but when I tried 5mm the rocket lost control.
3. Added 60 kg weight to the body (the weight of sarin).
4. Added a plastic nose to improve aerodynamics (about 10% improvement to distance)
5. Motor (in gray): Cesaroni Technology Inc. 21062-03400-IM-P
6. 40 degree launch angle, which gave the maximal distance.

This resulted in a 100 kg rocket with the following trajectory:

So exactly 2 km.

It should be noted that the motor does not fill the entire tube (in length nor diameter). I tried stronger motors but they seemed to be too strong for the poor aerodynamic design and the rocket started to spin mid-air. Following the discussion with L.K. in the comments below, I realized I could optimize the fins to make the UMLACA stable even with a large engine. So I picked an oversized engine (Contrails Rocket 06300P) and optimized the fins, resulting in the following design:

The simulation now gave the rocket a distance of 2.5 km.

To assess the general accuracy of this simulation software, I ran simulations for 4 artillery rockets with known distances, including a Falagh-2 333 mm rocket, and got results that are accurate within 20%.

Update: Several people have raised the concern that the civilian engines in the simulation may be less powerful than military engines. Scarlet Pimpernel found some great information on the total impulse (the aggregate of force impacted by the engine over its burn time) and the propellant weight of 3 military rockets (different versions of Grad). They show the same efficiency as the civilian engines in the simulation, proving this is not a concern.

See the full discussion in the comments.

Rocket design files are available here.

Method 2 - Videos Analysis

In an anonymous comment below, I was referred to this video from December 2012 (Update: the video was removed, if anyone has a copy, please share):

It unmistakably shows a real UMLACA launch with a conventional warhead. It is described as a rocket shot from Mazzeh airport into Daraya (Update: Brown Moses managed to prove the source is Mazzeh airport). I took the following screenshots:

Since we have video and audio for both launch and impact, we can use the sound delay to estimate range. The sound delay for launch is 4 seconds and for the impact is 3 seconds, and speed of sound is 340 m/s. If we assume the rocket passes exactly above the camera, this comes out to 2.4 km, or 2.2-2.3 km if we assume a slight angle (as seems to be the case).

Of course, to trust sound delay we must ensure the audio and video are not out of sync. This is ruled out at time 0:04 when the sound of the camera movement is heard in sync.
These numbers also match well the distance from the center of Mazzeh to the center of Daraya.

It should be noted that while this does not indicate a maximum range, it does give an indication of the typical range.

Update: Brown Moses has found another video of a conventional UMLACA. Unlike the previous one, it does not show the launch so it's harder to use it for range estimation. However, the cameraman seems to be below the Apogee, as was the case in the first video, and the time delay from the impact site is 3.5 seconds - also similar. So this adds another indication that the typical range is around 2.5 km.

Update 2: HRI found another video of a conventional UMLACA launch.

This one was taken near the launcher so we can estimate the distance more accurately, and can more easily verify there is no sound delay. The delay between the flash and the sound is 5.5 seconds, which gives a range of 1.9 km.

Brown Moses tweeted to Amund Hesbol that the range for the lighter sarin warhead should be longer than the HE version seen in the video. This makes perfect sense, so I prepared a simulation for the HE version. Using TNT's density I reached a warhead weight of 170 kg (including the steel casing), which is 100 kg more than the sarin warhead. I then optimized the fins and nose as done for the sarin version, and got this:

This reached a range of a bit under 1700m, which is a ratio of 1.5 to the sarin version. So applying that to the 2.2-2.3 km range from the video, we get 3.2-3.4 km.

Three things to note about this calculation:

1. The software chose to place the fins at an extreme angle of 15 degrees, probably since this is the only way it would stabilize. Since we know the fins are not slanted in the real UMLACA, we can assume the designers managed to stabilize it some other way - and indeed it seems very stable in the video. If substantial energy is lost to spinning it would mean a lower ratio than 1.5.
2. The longer warhead also allows for a longer engine. If this was done, it would also result in a ratio lower than 1.5.
3. If the sarin version was a refilled WP warhead that wasn't redesigned for the lighter load, it may have lost some range to drag and instability.

This all makes me uncomfortable assigning a 3.5 km range to the sarin UMLACA, but since this is based on too much speculation, I will leave it as is.
Update: See Method 5 below, which invalidates this calculation. The sarin version does not have a longer range, since it also has a smaller motor.

Method 3 - Comparison to Falaq-2

For people who find the calculations here too complex or don’t trust the results, I thought of the following thought experiment:

Let’s compare the UMLACA to the Falaq-2 from Iran, chosen because its launcher was once speculated to be the inspiration for the UMLACA launcher:

1. They are roughly similar in length and diameter.
2. The Falaq-2 warhead is a bit heavier: 117 kg compared to around 90 kg for the sarin version of UMLACA (including the two large steel plates).
3. The Falaq-2 engine is much larger. To calculate its volume I’ll assume a length of 90cm (from the diagram), and 7mm width of the casing, resulting in an internal radius of 16 cm. So the volume is: Pi*0.16*0.16*0.9 = 72 liters (0.072 cubic meters).
4. Based on the UN report and photographs, the UMLACA’s engine volume would be Pi*0.055*0.055*1.34 = 12.7 liters. (18 liters if the engine extends into the warhead).

So, if the Falaq-2 range is 10.8 km, what would be its range if we were to shrink its motor by a factor of 5.6 (or 4) and ruin its aerodynamics? Of course hard to tell exactly, but it’s hard to imagine it being anywhere near 8-9.5 km, which is the distance to Syrian Army bases that are currently claimed to be the source.

Method 4 - Comparison to SLUFAE

Two prominent features of the UMLACA are the oversized warhead and non-aerodynamic design. There are very few rockets with similar design, with the most similar one being the US SLUFAE minefield-clearing rocket, described in this patent. In this related patent it is described as having a range of 700 meters.
While not something that can be used to directly estimate the UMLACA range, it indicates that rockets designed in this manner are intended for short-range missions. If anyone knows of a medium or long range rocket with a similar design, please share - so far none were found.

Method 5 - Full Bottom-Up Analysis

Since some people are still not convinced, I decided to do a full open calculation. Its importance is in providing detailed insight into the calculations and sensitivities, thus increasing our confidence in the accuracy of the result.

To keep a safe margin, we will assume a few ideal conditions:

1. The engine extends all the way into the warhead.This is calculated below to be 1.83 m.
2. Launch angle is optimized for distance.
3. Trajectory is perfect. The rocket does not lose energy to spin or wobbling.
4. Highly efficient rocket fuel with specific impulse of 2345 Ns/Kg (the highest I could find for an atrillery rocket).
5. Engine container width of only 2.5 mm, allowing for more propellant. Update: Brown Moses has pointed out this image which shows the engine has an additional casing. Together their width is 10 mm, and the propellant's diameter is 100 mm. The calculations below were updated to use this number.
6. Engine burn time of 3 seconds, as seems to be the case in the Liwa Al-Islam videos, and here.

The big question is the drag coefficient of the UMLACA. Some coefficients can be seen here and here: A long cylinder, like the UMLACA's warhead is 0.82. To this we should add some friction drag caused by the engine body and the drag of the fins. An exact estimate is relatively complicated, but according to this rocket design guide fins account for 20-40% of total drag (page 27), which would mean a coefficient well above 1. In comparison, a model rocket is estimated at 0.75, a bullet at 0.3, and a typical artillery rocket at 0.36-0.39 (subsonic; page 39 here). An interesting finding from this guide is that rectangular fins (like the UMLACA's) have higher drag.

Adding a nose cone to the UMLACA may somewhat reduce drag, but no remains of a nose cone were found in any of the impact sites, and the images captured by Brown Moses here don't seem to have one. 

The lack of a nose cone and the non-aerodynamic fin design are another indication that range was a low priority in the UMLACA's design process - probably since it was specially designed for the Syrian civil war, requiring large warheads at short ranges. It is however interesting to note that in the video of the experimental giant UMLACA a small cone was added (noticeable immediately after launch). In a screenshot from this video we can see it is very flat, so its effect on drag should not be significant. It also shows the sharp change in diameter behind the warhead - another indication of the low priority the engineers gave to drag and range.

So a realistic estimate of the drag coefficient would be over 0.9, and an optimistic one would be 0.75.

We can now estimate the range, by feeding all the assumptions and measurements into a simulation model. This simulation calculates for each second of flight the rocket's velocity and angle, by adding the acceleration caused by the engine (based on the amount of propellant burnt every second), and deducting the effects of gravity and drag (calculated using the drag equation). It is available here for public review.

A drag coefficient of 0.75 yields a range of 3.0 km, with the following trajectory:

A drag coefficient of 0.9 yields a range of 2.7 km, with the following trajectory:

If we use more realistic estimates of 1.0 drag coefficient, 2100 Ns/Kg impulse and 5% loss to inefficiencies, we reach a range of 2.3 km:

Update: We have received an analysis of the UMLACA's drag from a notable expert in rocket artillery. His estimate: "With a nose cone, the drag coefficient would be around 0.6-0.7, without a cone around 1.0-1.2. Please remember that the coefficient refers to the largest diameter of the cone, that is 350 mm, not 122 mm" (He used the 350 mm diameter reported elsewhere. The actual is calculated below at around 370 mm).
The expert may not provide an official response without his employer's approval, which we will try to obtain.
Using the lowest estimate of 0.6 with the optimistic specific impulse (2345) yields a range of 3.3 km, indicating that even with a nose cone, the rocket could not have been launched from regime-held territory.

It is interesting to note that in these simulations the rocket's velocity approaches the sound barrier. Since it is unlikely that the UMLACA was designed for supersonic speeds, these trajectories give us a theoretical upper limit on its range. In other words, any theory claiming a range beyond 3.5 km is based on highly unlikely assumptions (i.e. supersonic speed or very low drag). Specifically: The drag coefficient needed to bring the UMLACA's distance to the 9.6 km claimed by HRW is 0...

When entering the details of the HE version of the UMLACA (170 kg mass, 2.23 m engine), we get a range that is longer by about 100 m. This means the positive effect of a larger engine exceeds the negative effect of having a larger mass.

Next let's examine a White Phosphorus UMLACA, which is probably what the sarin rockets were originally designed for. White Phosphorus has a high density of 1.823, compared to 1.09 for sarin, which results in a 40 kg heavier warhead. Surprisingly, its range is similar to the sarin version. This is possible since the rocket's mass affects its trajectory in two ways: It resists the engine's force during acceleration, and resists the drag force in deceleration. It is therefore possible in some cases to add weight to a rocket and extend its range (imagine a paper ball being launched from a cannon). This may indicate that the UMLACA was indeed originally designed for the heavier White Phosphorus warhead.

So 3.5 km is our theoretical limit, and 2.5 km is a realistic estimate.

Response to Analysis at Brown Moses

The Brown Moses blog published an UMLACA range analysis by John Minthorne, a mechanical engineer, reaching estimates of 3.3 to 15 km.

First thing - Awesome. The goal of this blog is to reach a conclusion through open discussion, and having another professional analysis adds great value. I hope this will start a fruitful discussion that will together help reach a consensus. I will do my best to be open and not get attached to my previous statements, and hope John will do the same.

Let's start with John's critique of my analysis:

1. "Assuming very short burn times (and wrongly stating that such an assumption is conservative). Drag increases as a function of more than the square of the velocity, and as a result the thrust of the rocket motor over time is a crucial consideration."
   Response: Not sure to which analysis this relates, but the most recent analysis (method 5 above) uses a burn time of 3 seconds, which is what is seen in the Liwa Al-Islam videos (also here). Claiming that the UMLACA has an optimal thrust curve is highly doubtful when the rocket is obviously not optimized for range (e.g. high diameter, thick steel body, discontinuity in shape, non-aerodynamic fins). However, for calculating an upper theoretical limit, I don't mind assuming this is the case. So far a few experiments I did with thrust curves hardly affected range, and in the OpenRocket models provided by John, the effect seems to be about 5%. This is probably since longer burn times also mean longer flight times, which result in more gravity impact.
2. "Using hobby rocketry engines as the basis of design. By extension, underestimating the propellant mass and specific impulse."
   Response: This was shown to be incorrect. In the discussion below with Scarlet Pimpernell three Grad rockets were shown to have a specific impulse that is similar or lower than the OpenRocket engines.
3. "Miscalculating the center of drag, severely underestimating the rocket's stability."
   Response: I assume this relates to Method 1 above. I haven't checked yet but agree that this could be the case. However, Method 5 assumes an optimal trajectory with no loss to instabilities and reaches a similar range.
4. "Failure to consider wind direction, elevation above sea level, or air temperature."
   Response: Wind and temperature were indeed ignored since they have negligible effect. Elevation was incorrectly ignored in Method 1, but this was corrected in Method 5. 

Next, here are my comments to John's analysis:

1. Propellant Mass - Here I believe I found a major oversight. John assumes that all of the engine's volume is filled with fuel. This is never the case. A large part of the volume is composed of voids designed to control the thrust curve (see examples here and on page 35 here).
   By comparing the propellant mass of the largest engines in OpenRocket to their volume, I found the average portion of volume used is 0.62 (assuming 2.5 mm casing and after filtering engines with special thrust curves that can be below 0.5), with the highest being 0.69. I assumed 0.65 in Method 5, but will gladly update it based on reliable evidence.
   Just to prove the UMLACA is not filled to capacity: Typical burn speeds of propellants ("regression rates") are below 10 mm/sec. This would mean that if the UMLACA was filled to capacity, its engine would take over 3 minutes to burn (and would probably never take off).
   Another small correction: The UN report gives a rocket length of 2.04 m (1.34 + 0.7), from which the booster charge and nozzle should be deducted. I estimated 1.8m for the engine length, and 1.9m in the optimistic scenario.
2. Specific Impulse - 2550 Ns/kg is an extreme example. The analysis of the three Grad rockets mentioned above shows a range of 1937-2272, and the largest engines in OpenRocket and ThrustCurve are 1966-2272.
   Together with the overestimation of the propellant's mass above, this results in a Total Impulse value of 90000 Ns, which is twice my most optimistic estimate of 46000.
3. Environmental Considerations - Generally agree. Small correction: Elevation in Zamalka is 700m, not 760.
4. OpenRocket model - A few minor corrections: (a) According to the UN, warhead diameter is 360mm and not 350mm. (b) Body tube length is 1.34m and not 1.55m. (c) Sarin weight is 60kg and not 50kg (56 liters). (d) The warhead's inner tube is missing. (e) The two thick steel plates on both sides of the warhead are missing (around 10mm?). (f) The thick steel blast plate is missing (over 70mm). Images here.
5. Fin Layout - I like the idea of adding the ring to the fins' area.
6. Drag - This is the most important part of the calculation. First, as shown above there are good reasons to assume no nose cone is used: (a) There doesn't seem to be one in the videos we have, (b) no remains were found in any impact site, despite minor damage to all other parts, and (c) other features of the UMLACA were not optimized for range (high diameter, thick steel body, discontinuity in shape, non-aerodynamic fins) so there is no reason to assume this was done for the nose cone.
   Even if we do assume a nose cone, OpenRocket's drag coefficient estimate of 0.21 is wrong. As mentioned above, a typical aerodynamic artillery rocket is 0.36-0.39. A coefficient of 0.21 would imply an outstanding (and maybe impossible) aerodynamic design, which is definitely not the case here.
   Update: Amund Hesbol has communicated with Sampo Niskanen, OpenRocket's developer, who explained OpenRocket was not designed to simulate rockets with a non-standard design like the UMLACA, and therefore the drag calculations "may be way off".
   Since there seems to be a bug in the drag calculation module, I suggest we use the spreadsheet in Method 5 above from now on, instead of OpenRocket. It also allows more visibility into the calculations.

Additionally, the analysis has the following shortcomings:

1. No sanity checks are given for the assumptions made in the simulation. For the results to be trusted, they should be applied to known artillery rockets (e.g. as I did for Falaq-2) and show that they give the true results. John - would be great if you can prepare a few.
2. It ignores the two videos we have, in which the UMLACA flies less than 2.5 km, despite its trajectory not being exceptionally shallow or high (as evident by the rocket's apparent velocity and sound level).
3. It fails to explain how a rocket with a significantly smaller engine and worse aerodynamics than the Falaq-2 manages to travel a longer distance (15 km compared to 10.8).

Summary: John Minthorne's analysis overestimates the engine's total impulse by a factor of 2, and the drag coefficient by a factor of around 4. Once corrected, range estimates should be similar to all other analyses.

Once again, I'm excited that this discussion is happening. John has improved on my analysis in several points, and I hope that he too will incorporate the feedback I provided, leading to an overall better and more reliable result.

Update:

In the comments to his post John responded to my review. My response:

Gravity drag is less significant for a blunt-nosed rocket with a Cd of around 1. Any thrust that would accelerate a more streamlined body to above ~M0.8 is wasted on the extremely high drag forces. For lower Cd's, the length of the thrust curve does indeed become a less significant of factor.
Response: For the sake of argument, I'm fine with assuming an optimal thrust curve. However, the Liwa Al Islam video and this new video clearly show a burn time of 3 seconds, as typical to artillery rockets.

The fins did not seem bad to me.
Response: Page 20 of this guide discusses fin shapes, with rectangular being the least efficient. I assume the UMLACA uses rectangular fins since they’re the easiest to produce, indicating range was never a goal.

260 s is a high but plausible specific impulse for a solid rocket. Using literature to identify performance criteria is a more robust means of analysis than comparing with a single model of rocket or comparing with specific impulses of a few hobby rockets.

Response: Page 36 of this rocket artillery guide gives a specific impulse range of 210-250s (2060-2452), and one example of 239s (2345). We should not use theoretical limits of propellant fuels - only those that we actually know were used in rocket artillery. Additionally, Zandbergen gives a range of 240-260s for the highest grade fuel, but also a density range of 1660 to 1855. There is no reason to assume that fuel that reaches the highest impulse also has the highest density. When calculating a theoretical upper limit, it's ok to take a combination of high assumptions, but they should be plausible as a whole. I suggest using 239s (the highest we have so far) and a density of 1750, when calculating an upper limit.

Unfortunately Sasa Wawa's spreadsheet treats Cd as a constant, which is not valid for speeds above M0.7. This is not problematic at subsonic velocities, but is a problem when comparing results with a supersonic projectile such as the Grad.

We appear to agree that the rocket is effectively stable.

Response: I agree. I will stop comparing to Grad's Cd, thanks for correcting. Small correction: According to the graph on page 41 here of a typical artillery rocket, Cd only takes off at 0.8-0.85M, not 0.7M.
By the way, it shows the subsonic Cd of an aerodynamic rocket as 0.36-0.39, which again makes the 0.21 estimate for the UMLACA highly implausible.

For ~60 second flight times, ignoring wind will generate over 5% error.
Response: Agree. If we ever get to 60 seconds, we can take wind into account. But I doubt this will be the case once we agree on the other parameters.

Technically, purely end-burning rockets do exist though I agree that the UMLACA is not an example. I did consider the volume ratio and ignored it as insignificant, but I should have noted and justified this assumption. Please note that hobby rockets have much lower volume fractions than heavier rockets; Zandbergen suggests a Kv of 0.8-0.95. More specifically, a dual-thrust configuration such as I proposed can have excellent volume fractions; see Himanshu Shekhar's Burn-back Equations for High Volumetric Loading Single-grain Dual-thrust Rocket Propellant Configuration for a more involved analysis. For the curves I proposed (roughly 5:1 boost:sustain thrust ratio), a Kv of 0.95 is appropriate. While 10mm/s is a quite typical regression rate, as I alluded in my report the rate can be varied by around an order or magnitude. It is indeed quite plausible to design a rocket of the dimensions described, with a volume fraction near unity and a burn time on the order of 30 seconds.
Response: Page 35 of the artillery rocket guide states that most engines are star shaped, with the alternative being multiple tubes. The theoretical discussion is interesting, but our goal is finding the maximum plausible range for the UMLACA - not the range that the world's best rocket scientists could get it if they worked on it for years. Claiming that the Syrian Army designed a rocket where the body has a discontinuity in diameter, yet somehow decided to maximize range by using a grain structure and propellant that were never used in the history of rocket artillery, is not constructive to our goal.
If we want to claim volume use above 0.7, we should be able to show at least one artillery rocket where that is the case.

Also, I could not find where Zandbergen suggests 0.8-0.95. John – could you please quote it?

Another contributor suggested that all military rockets have multiple, tubular grains; this is demonstrably false.
Response: Agree, the guide states the star shape is more popular.

The dimensions were based largely on the HRW report. The UN report goes out of its way to point out the dimensions are approximate.
Response: Good point. So let's do our own calculations:

Body length is 136 cm:

Plus 6 cm here:

The warhead's internal tube is 67 cm (I estimate 2 cm loss due to the measuring method), plus 2 cm of the steel plate:

of which at least 7 cm is lost to blast plate. Let’s assume 8 cm.

The booster charge is after the blast plate, so no need to deduct it (which means the warhead length is actually 75-80 cm).

So total length of engine: 136 + 6 + 67 + 2 - 8 = 2.03 m

Which is very similar to John's initial estimate. However, we need to take the nozzle into account. I couldn’t find the exact measurements, but a quick review found that nozzles have a length-diameter ratio of around 2.5. So for a 100 mm internal diameter, this would indicate a nozzle length of 250 mm. This estimate is verified in these diagrams of Grad rockets, which have a slightly larger diameter and nozzle lengths of 280-285 mm. 

The image below shows that the nozzle protrudes a length of around half diameter, leaving 200 mm inside the body. This means the propellant length is 1.83 m, which is what we should use from now on.

Update: Brown Moses pointed out this image which clearly shows the propellant diameter is 100 mm:

Amund Hesbol prepared this video illustrating the engine and external tube, as seen in the image above.

Update: Here is another video by Amund which shows the dispersion mechanism. It is illustrative only - actual liquid dispersion would be sideways. More details in the comments.

My impression is that none of these mass or dimensional adjustments (save external diameter, which appears to be within the margin for measurement error) have a significant impact on ballistics. Would you agree?

Response: The 10% shorter engine length is definitely significant. The missing steel parts would affect mass significantly, but possibly not range. The radius of the steel plate is seen below as 18.5 cm. This is nearly a 12% difference in area., which may have significant effect on drag. The reduction of propellant diameter to 100 mm should have a dramatic effect on range.

For reasons listed above, the spreadsheet is not accurate for velocities above Mach 0.7
Response: As shown above, significant changes only happen at around Mach 0.8-0.85, which we currently assume the UMLACA does not reach, so the spreadsheet is valid.

John then discusses drag calculations in length, ending in a conclusion that without a wind tunnel or wind tunnel simulation, it's hard to reach an accurate result. I agree and don't see a point in discussing each item in detail, but I would like to respond to the following claim:

I think a subsonic Cd of less than 0.25 is plausible for the munition with nose cone.
...The Falaq-2 is a different rocket. It travels at supersonic speed and has a heavier payload. There is no reason to think that two very different vehicles must have ranges proportional to any superficial characteristic such as launch mass. As discussed above, the UMLACA with a nose cone may have subsonic drag performance comparable to a rocket with more "streamlined" appearance.
...It probably is possible to select a thrust curve that propels the Falaq-2 more than 10.8 km. The designers probably did not do this for other reasons, such as time-on-target and accuracy. This does not mean that it is implausible that a modified Falaq-2 could hit a target 15 km away.

Response: The claim here is that the UMLACA can indeed take the same payload farther with an engine that is 4 times smaller, but this is because the Falaq-2 engineers didn't optimize for range. This statement is extremely problematic. Even if the Falaq-2 had other considerations, there must have been someone in the history of rocket artillery who wanted a design that can take a 100 kg warhead to 15 km with such a small engine. Why did no one do it before? Why do all artillery rockets have exactly the same design? It should be clear that if the UMLACA's Cd was 0.25, we would have seen this design everywhere. 

We have above an example of a standard rocket with a subsonic Cd of 0.36-0.39. The UMLACA's design is dramatically different than the norm, with features that are obviously not optimized for range. It's Cd must be much much higher than 0.39.
Update: According to the expert opinion we just obtained, the lowest Cd we can reach with a nose cone is 0.6. More details in method 5 above.

So to sum up the next steps:

1. Unless we have evidence that there was ever an artillery rocket that had a specific impulse above 239 s, propellant density above 1750, and propellant volume ratio above 0.7, these should be the parameters we use. It's perfectly fine to build an optimistic scenario, but it can't be based on the UMLACA engineers making breakthroughs in rocket science.
2. Propellant length should be changed to 1.83 m, warhead diameter to 360-370 mm, propellant diameter to 100 mm, and extra mass added according to the missing steel parts.
3. Getting a reliable estimate of the UMLACA's drag coefficient. Anyone who can help with this - feel free to jump in.
4. OpenRocket can be used for simulations without a nose cone, but the spreadsheet is preferable. Once we have an estimate of the UMLACA's Cd with a nose cone, we can enter it to the spreadsheet for a reliable range estimate.

John - would be great if you update your estimates for the version without a nose cone. And once again, thank you very much for your contributions.

Conclusion: The UMLACA used to attack Zamalka has a range of around 2.5 km.