UMLACA Maximum Range Analysis
This report attempts to establish, with a minimal level of rigor, the maximum range that can be assigned to the 330mm-class chemical rocket (the "unidentified munition linked to alleged chemical attacks [UMLACA]) used in the August 21, 2013 attacks on Ghouta, Syria. The report is based on public information including United Nations reports, NGO publications, amateur video & photography of the remains of the weapons, public weather data. In particular, this goal of this report is to determine whether this model of rocket could have been launched from the Syrian Army Republican Guard "base 104", approximately 9.5 km west of the impact sites.
In the early morning of August 21, 2013, the Ghouta residential suburb of Damascus, Syria was struck by a rocket attack that killed hundreds. Representatives of the Syrian Army and rebel forces were quick to blame one another for the attack, and international observer countries including France, the United Kingdom, Russia, and the United States made official but predictable statements blaming the "opposite side".
In mid-September, Human Rights Watch (HRW) and the United Nations (Sellström) released reports that confirmed the August 21st attack did make use of Sarin. Consistent with the UN Mission's charter, the Sellström report did not assign blame for the attacks. The report did, however, note the azimuth of the ballistic trajectories of two of the munitions used, including a UMLACA that impacted Ein Tarma. The Human Rights Watch, along with several news organizations, noted the the trajectory azimuths intersect deep in Syrian government-held territory, specifically the Republican Guard 104th Brigade military base.
However, this information is only meaningfully damning to the Syrian government if the UMLACA is capable of being fired approximately 9.5 km from the Republican Guard base to the impact site. Much of the flight path less than 8 km from the impact site is identified by Human Rights Watch as "contested" at the time of the launch (Lyons).
One organization to estimate the maximum range of the UMLACA is whoghouta.blogspot.com (sasa wawa). This analysis reported in a maximum plausible range of 3.5 km and concluded that the rockets could not have been launched from the Republican Guard base. This analysis was qualitatively reviewed, and in the opinion of this author the analysis contains a number important flaws. Some of the more significant errors include:
- 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.
- Using hobby rocketry engines as the basis of design. By extension, underestimating the propellant mass and specific impulse.
- Miscalculating the center of drag, severely underestimating the rocket's stability.
- Failure to consider wind direction, elevation above sea level, or air temperature.
Summary of available information
Information for this report was gleaned from publicly available information:
- Published photographs and diagrams based on those photographs, by Human Rights Watch.
- Field measurements and photographs taken by the United Nations Mission.
- Secondary sources of ballistic error such as Coriolis forces are ignored.
- Additional assumptions are listed in the relevant sections of this study.
UMLACA Physical Properties
The total impulse of the UMLACA rocket motor is limited by the propellant selected and the volume of propellant used. Since the purpose of this study is to evaluate whether a 9.5 km travel distance can be ruled out, each physical assumption is listed as a range between which the actual values for the UMLACA likely fall.
The total length of the UMLACA is about 2200 mm. Some portion of the nose section is filled with a bursting charge and detonator, so the maximum length of the solid fuel volume is assumed to be 2000 mm. The UN report implies that the motor section may be as short as 1340 mm, so a more pessimistic assumption incorporating a void space inside the weapon's warhead would be a fueled length of 1300 mm.
The external diameter of the UMLACA is 120 mm. Assuming a robust, wall thickness consistent with standard weight pipe, an internal diameter of 110 mm is used. This results in a volume range of between 0.0124 and 0.0190 m3.
The density of high-performance solid propellants varies between 1.6 and 1.86 kg/L (Zandbergen). Applying this value range to the fuel volume range, the rocket's propellant mass is found to be between 19.8 and 35.34 kg.
Specific and Total Impulse
The specific impulse of a rocket motor will have a profound effect on its performance. As a motor becomes more efficient, it can increase the final velocity of a rocket exponentially higher. This effect is more muted in a subsonic or transonic rocket than in an orbital or sounding launch vehicle, however. Military propellants have specific impulses in the range of 210 to 260 s (2060 – 2550 N*s/kg) (Zandbergen). Multiplying this range by the propellant mass gives us a total impulse for the UMLACA of 40800 to 90100 N*s.
Gases escape a rocket nozzle in a predicable fashion. The fluid flow velocity through the nozzle throat is Mach 1, such that the total thrust generated by a rocket motor varies roughly proportionally to both the chamber pressure and throat area (Platzek). Unfortunately, no information appears to be publicly available documenting the precise the throat area of the rocket motor. The Human Rights Watch report contains one photograph of the rear of the motor and a tape measure, allowing estimation of the nozzle throat to be very roughly 50 mm. Assuming a chamber pressure of 7 MPa, this would equate with a maximum thrust of around 22 kN. Given the very large amount of uncertainty on this number, no conclusions can be drawn from this. It is simply noted that the estimated maximum possible thrust is within an order of magnitude of the thrust a designer would desire for this weapon.
A solid-fuel rocket has a practical maximum burn time – the regression rate of propellant is lowest in a solid grain geometry, but is still non-zero. Regression rates for typical high-performance propellants vary from 5 to 25 mm/s (Zandbergen), corresponding to a theoretical maximum burn time of 80 s to 400 s for a 2 meter, solid grain rocket motor. The longest total burn time considered in this study was 45 s, well within the realm of feasible achievability.
The amount of thrust a solid-fuel rocket provides over the course of its burn broadly customizable by changing the chemistry and structure of the rocket grain. For a rocket with no lift and poor drag characteristics such as the UMLACA, maximum range will be achieved with a short, high thrust initial impulse followed by a long, low thrust burn to sustain velocity at low transonic speed (~0.7M or 240 m/s). A thrust/time profile of this shape is both achievable and commonly found in military rockets (Platzek).
A rocket spends a significant amount of time in flight. In evaluating the maximum distance a rocket may travel, the velocity of the wind encountered must be considered. At 2:00 AM on the morning of the attack, the wind at Damascus International Airport was blowing from the WSW (about 248°) at a sustained speed of 6.9 miles per hour (3.1 m/s) and increasing (Weather Underground). Wind speed is typically higher a significant distance above the ground; for the purposes of this analysis the wind velocity is assumed to be an average of 4 m/s from 248° (37° from a pure tailwind from the rocket trajectory of 285°. Correspondingly, a rocket azimuth of 143° relative to a 4 m/s wind was used in the OpenRocket software trajectory models. For ~60 s long flights, this adds a few hundred meters to the range. If meteorological information shows that higher-altitude tailwinds were present, this could increase the maximum range by a high single-digit percentage.
Aerodynamic drag is proportional to the density of the fluid through which the projectile travels. The temperature in Damascus at 2:00 AM on the morning of the attack was about 73°F (22.7°C) – if a standard atmospheric temperature of 15° is assumed, drag will be overstated by about 2.8%. The elevation of the targeted area in Ghouta is about 760 meters above sea level – if sea level elevation is assumed, drag will be overstated by about 9.5%. Since the temperature profile of the atmosphere above Damascus is not known, trajectory models assumed a standard atmospheric temperature and a launch elevation of 760 m above sea level.
A projectile on a nominally parabolic trajectory will travel a greater distance if its impact location is of lower elevation than if it flies over a flat plain. The topography of northern Damascus is dominated by Mount Qasioun, a 1151 meter high peak. The areas of Ghouta targeted are lower, around 760 meters above sea level. Since the rocket attack was obviously not launched from the peak of Qasioun, the actual difference in elevation was less than 400 meters. This difference in elevation is not considered in these range calculations, since the actual launch elevation is not precisely alleged. This means that the maximum ranges shown are conservative by a small degree (probably 0.1-0.2 km) due to the relative elevations of the launch and impact sites.
Maximum Range Calculation
Physical Rocket Model
A model of the UMLACA and derivative UMLACA with a more aerodynamic nose cone were created in the Open Rocket program. Both models were modified from a model downloaded from the whoghouta.blogspot web site. The models are described in the two tables below; dimensions are in mm, roughnesses are in um, and masses are in kg (unless noted otherwise).
Any designer tasked with extending the range of the UMLACA would immediately consider improvements to the rocket's drag. With a Cd of about 1.0, the rocket's drag is several times the value to which it could be reduced with relatively superficial modifications. The nearly blunt front of the rocket generates about 80% of the subsonic total drag.
The UN and HRW reports both sketch the UMLACA with a completely blunt end, but the least is known about the front portion of the rocket because it is damaged upon use by the bursting charge and subsequent impact with the ground. The front plate includes six threaded holes which could be used to attach a light-weight aerodynamic nose cone. As such, the possibility that rockets fitted with nose cones were used on August 21 cannot be ruled out. Since addition of an aerodynamic nose dramatically changes the maximum range of the UMLACA, maximum ranges were established both with and without the aerodynamic nose cone.
Rocket Motor Design
Six hypothetical rocket motors were evaluated, three per drag condition of the UMLACA. All utilized an initial boost phase to accelerate the rocket to about 0.7M (240 m/s), followed by a lower sustainer thrust to maintain flight speed. Two used total impulses of 40800 N*s, the lower end of the estimated motor impulse. The remaining motors used the higher end of the estimated impulse, about 90100 N*s. The full .eng data for each motor can be found here.
For convenience, this study matched the "whoghouta" blog's selection of Open Rocket as the software to simulate the UMLACA trajectory. The UMLACA is several times larger than a typical large single-stage hobby rocket, and its characteristic geometry likely challenges the software in ways that were not the focus of its development.
Simplification of Fin Layout
The Open Rocket software does not support modelling of a circumferential band around the perimeter of the tail fins. This band is parallel to the air stream, generating significant drag as well as contributing to the stability of the rocket. To model the ring's contribution to drag and efficiency, the fin height was increased from the actual dimension of 95 mm to 135.6 mm, replicating the total fin material area of 0.179 m2.
In addition, the enclosed nature of the air stream through the fin assembly may create directional flow effects more pronounced than a more simple fin arrangement. Study of the airflow through this fin assembly is an excellent candidate for further study of the UMLACA's aerodynamics.
Transonic and Supersonic Drag Performance
The UMLACA is likely but not certainly an exclusively subsonic weapon. The coefficient of drag of an object in a fluid flow stream is not constant; it changes with velocity. At about M0.8 the Cd beins to increase, peaking locally at M1.0 and dropping to an intermediate value for low supersonic values (Heinrich). The Open Rocket software attempts to model these changes in Cd, but for a rocket with such an unusual shape as the UMLACA it is likely that the modelled transonic behaviour is not fully accurate.
For the UMLACA without drag-reducing features, the maximum distance travelled was about 6.5 km, for the UMLACA4 motor curve at a launch angle of 43° from vertical. Maximum distance travelled using a 41 kN*s motor was about 3.3 km.
If the UMLACA weapons used in the August 21st attacked had aerodynamic nose cones, their maximum range could be in excess of 15 km. With a range of 15 km, the UMLACA5 motor curve did not produce the greatest travel distance but its lower average thrust kept the more streamlined rocket at transonic speed (increasing confidence that the simulation is accurate).
- The rocket with a blunt nose has mediocre drag characteristics. A designer seeking to maximize the weapon's range could add a nose cone to the weapon, which would greatly reduce the drag coefficient and increase the range. The presence of threaded holes on the front plate of the rocket could be an indication that this was, in fact, done.
- The rocket is aerodynamically stable and unlikely to tumble or excessively oscillate in flight.
- The publicly available information on the UMLACA (particularly the chemical variant) leaves a large margin of doubt as to the rocket's range and flight characteristics.
- On the basis of the publicly available information referenced in this report, an attack from the Republican Guard 104th Brigade base cannot be ruled out as implausible.
- The maximum range of the UMLACA is probably between 3.3 km and 6.5 km, increasing to 15 km if a nose cone were installed.