Flyout Sim
(v1.00 - 30 July 2024)

(Page created 30 July 2024)

The Atmospheric Model is a combination of the 1976 US Standard Atmosphere with the MSISE-90 Model (Mean Solar Activity) (LINK) of Earth's Upper Atmosphere from 100 km to 900 km in 100 km increments. I tried using a simplified atmosphere model in beta versions; but found that they didn't accurately show the range(s) of endoatmospheric missiles such as PATRIOT.

The Gravity Model used for velocity vectors is a 1976 Standard Atmosphere gravity model that adjusts the gravitational force as altitude increases. All other calculations (thrust, etc) use the standard 9.80665 m/sec gravitational constant.

The Drag Curve is from Braeunig, and is his Sample Launch Vehicle Drag Coefficient. You can adjust it up or down via a multiplicative factor; especially if you're modelling something like SPRINT/HIBEX which is more in common with a rifle bullet than a missile.

To paraphrase Starship Troopers: "It's an ugly planet. A Bug planet." - there are serious limitations in this model; but because so much data is incomplete or unknown (try finding detailed specifications on THAAD); it all cancels out in the wash to create a somewhat useful general purpose model that lets you do educated guesses.

One of the things that becomes apparent is that ballistically, many air defense missiles can go much further than their official ranges and that operational limits -- flyout angle for SARH missiles, aerothermal heating, or just simply the radar horizon for communications -- quickly become the limiting factor.

- This uses data (IMG 1 / IMG 2) from ATK's Rocket Garden in Utah, as well as the Astronautix Page for the Mk 70 Booster Motor and the Astronautix Page on the MK30 Sustainer Motor used in the ER version.

- This uses data for the LEAP motor obtained from Orbital ATK's old 2016-era motor catalog (7.6 MB PDF) which has detailed information on the LEAP stage via their commercial (!!!) version of it (LEAP Motor Datasheet) as well as THIS paper; along with THIS paper. LEAP was designed as a minimum-cost, minimum-change to the existing SM-2, to the extent that the LEAP stage was 12.5 inches in diameter; so it could fit within the existing warhead space on SM-2. A significant amount of SM-2 motor data was obtained through THIS analysis by Chinese military officers.

- This utilizes detailed TSRM data found via the Internet Archive from Orbital ATK's old website (Description of Motor Pulses & Duration) as well as their old 2016-era motor catalog (7.6 MB PDF) which has detailed information on the TSRM via their commercial (!!!) version of it (ASAS-13-30V Datasheet). The datasheet for the military version (TSRM Datasheet), reveals that this version is significantly heavier. I believe the difference between the Civilian ASAS 13-30V (MR 4.553) and the Military TSRM (MR 2.791) is that NAVSHIPS imposed hard limits on how lightweight the motor cases could be, leading to TSRM being much heavier than ASAS 13-30V, despite both using graphite epoxy composite cases. There's also THIS thesis on SM-3 intercepts.

- Weight values used for Block IIA are based off two datapoints:

SM-3 Block I volumetric evaluation

• MK104 DTRM is 13.5" (342.9mm) diameter by 112" (2844.8mm) long; for a volume of 0.2626 m3, with a loaded mass of 1073 lbs (486.7046 kg) for a density of 1853.15 kg/m3.
• MK136 TSRM is 13.5" (342.9mm) diameter by 39.3" (998.22mm) long; for a volume of 0.0921m3, with a loaded mass of 305.1 lbs (138.4 kg) for a density of 1502.71 kg/m3.

SM-3 Block IIA Size Evaluation via measuring (SM-3 Blk IIA Artwork)

• New Second Stage Motor (NSSM): 533.4mm diameter by 2900mm length = 0.648 m3 = 1200.79 kg mass with 1853 kg/m3 density.
• New Third Stage Motor (NTSM): 533.4mm diameter by 850mm length = 0.1899m3 = 285.36 kg mass with 1502 kg/m3 density.

The two buttons (Upper & Lower) represent the lower/upper bounds of Mass Ratios (MRs) in the new 21" caliber motors for Block II. The only way Block II can meet even the lower 4.5 km/sec V_Bo claim is if the USN relaxed their safety standards on motor case designs under pressure from the Japanese (who footed most of the bill for Block II) to allow the use of more-representative ASAS motors with higher mass ratios than would be the norm for the USN, which was super conservative with the ASAS-derived TSRM on SM-3 Block I.

Per the Union of Concerned Scientists (LINK):

A primary rationale for the high-speed Block II interceptors is to enable “early intercept” — the capability to intercept the attacking missiles after their launcher burns out (post-“boost phase”) but before they are able to release countermeasures.

- Block IIB (aka "Next Generation AEGIS missile") was to be a follow-on missile specifically for AEGIS ASHORE facilities in "Phase IV" of the EPAA, entering service sometime in the 2020s; providing VBo in excess of 6 km/sec (Image). It was cancelled 2013, possibly due to USN resistance over a liquid propellant missile, which led to THIS concept using the 21" Block IIA stage instead of a new 27" Liquid Stage. Per a GAO report from 2013 (LINK):

"Navy has stated that the program may develop concepts with liquid propellants, but it has not made a final decision regarding whether it will overturn its 1988 ban on liquid propellants on ships and allow a sea-based SM-3 Block IIB to use liquid propellants."

SM-3 Block IIB Size Evaluation via measuring (SM-3 Blk IIB Artwork)

• 27-Inch Second Stage Motor (27SSM): 685.8mm diameter by 3270mm length = 1.2079 m3 = 2238.24 kg mass with 1853 kg/m3 density.
• 27-Inch Liquid Third Stage Motor (27LTSM): 685.8mm diameter by 1400mm length = 0.517 m3 = 646.43 kg mass with 1250 kg/m3 density (Storable Propellant; 300~ ISP); MR of 5?

- Looking at Astronautix and Wiki, it turns out the MIM-23B I-HAWK massed 638 kg at launch with a newer M112 motor which burned for 5 seconds and sustained for 21 seconds on a total motor mass of 395 kg (295 kg propellant) for a MR of 3.95 and a missile MR of 1.86

Thus, it makes it clear that the data plate at the ATK Rocket Garden in Promontory is for the MIM-23A HAWK version and its M22E7/E8 motor; the parameters as given by the data plate are:

• 14 in (0.3556 m) diameter
• 1,288 lb (584.227 kg) gross mass of which 849 lb (385.1 kg) is the TX-59 motor.
• Two pulse motor - 15,000 lbf (6,803 kgf) for 4.5 seconds; then 1,900 lbf (861.8 kgf) for 31 seconds.

- Known weights are from the ATK Rocket Garden in Promontory (S1 / S2 / S3) and S1/S2 Mass Ratios set to about the same as Minuteman, being of the same generation. Because S3 keeps the 1200 kg W71 warhead post-boost, S3 weight + MR have been adjusted to account for this. What's interesting is to compare SPARTAN (13.1T) to KEI (10.4T) and GBI (21.6T); to see how much land-based ABM has come since 1963, when SPARTAN's design was frozen.

Data on HIBEX is sketchy, but this is what we have from a 1990s DARPA retrospective:

• 3.6 ft (1.09728 m) diameter, 16 ft (4.8768 m) length
• 2,577 lb (1168.908 kg) gross mass of which 1,687 lb is propellant (MR 2.8955)
• 490,000 lbf (222,260 kgf) thrust for 1 second
• Burnout Velocity of 8,450 ft/sec (2,575.56 m/sec)
• Maximum Long Acceleration of 377G
• Maximum Normal Acceleration of 60G

Sprint was a two-stage missile massing 3447.302 kg at launch. Using THIS cutaway with a base diameter of 1341.12mm for scaling and volume calculations; we get:

• SPRINT STAGE I: 1340mm base diameter, 865mm upper diameter, 3225mm length = 3.12639 m3 - approx 2,661 kg with 851.3 kg/m3 density
• SPRINT STAGE II: 865mm base diameter, 167mm upper diameter, 3830mm length = 0.923047 m3 - approx 785 kg with 851.3 kg/m3 density
• TOTAL SPRINT SYSTEM: 4.049437 m3 total. With a 3.447 kg launch weight, we get 851.304 kg/m3 overall density.

While we don't have any hard data on propellant loading for SPRINT, we can make assumptions off HIBEX, which was public with a MR of 2.89

- Based off THIS image and known mass of THAAD (662 kg) from this 2004 MDA Slide Deck:

• THAAD S1: THAAD Booster - 340mm diameter, 3400mm length = 0.308 m3 = 586.5 kg @ 1900 kg/m3 density.
• THAAD S2: Endoatmospheric Kill Vehicle + Hydrazine DACS - 370mm diameter, 75.5~ kg mass

Of note is that because THAAD is a dual role Exo/Endoatmospheric system; it can engage incoming targets very low; and does not have a hard descending altitude limit of 90 km (SM-3/EKV), but can pursue the target down to 30 km (or possibly lower); vastly extending it's defended footprint.

Speaking of defended footprint, the Report of the Defense Science Board/Policy Board Task Force on Theater Missile Defense (1996) says regarding THAAD:

"...potentially achievable defended footprints are being severely constrained (especially against longer-range TBMs) by ABM Treaty compliance findings that prohibit THAAD's use of external sensors."

- Based off known mass of PAC-2 (900 kg) from this 2004 MDA Slide Deck and various Russian websites and drawings (DWG #1 / DWG #2):

• TX-486 Motor: 11,000 kgf thrust, 11.5 sec burn time; single pulse. 406mm diameter & 3298 mm length = 0.426 m3 @ 1850 kg/m3 = 789.88 kg mass.
• Warhead: 70 kg (PAC-1) with 2 gram fragments or 90 kg (PAC-2) with 45 gram fragments.

If we assume that the TX-486 has a conservative MR of 2.4 (given that the motor casing is on display at ATK Rocket Garden in Promontory it has to be metallic); that makes it's burnout mass 329.1 kg; leading to an overall MIM-104 MR of 1.95.

- Based off known mass of PAC-3 (321 kg) and dimensions (5205mm length) from this 2004 MDA Slide Deck combined with this paper on its ERINT-1 Precedessor; we can just use ERINT-1 data for PAC-3 (255mm diameter, 304 kg launch mass, 140 kg burnout mass (2.171 MR for missile, about 5.9 for motor) and the use of a boost/sustain motor) because the mass difference is so small (just 20 kg).

- The MSE variant has a larger motor (290mm diameter, 2900m length = 0.191 m3 @ 1850 kg/m3 = 353.35 kg motor mass vs ERINT's 197.3 kg). Based off the known mass (420 kg) of MSE from the shipping container markings (TWITTER POST) this means that the non motor weight of MSE is 66.65 kg. If we assume the motor is slightly improved (MR 6.0), MSE's burnout mass is 118.89 kg (3.532 MR).

- Orbital's GBI uses the following stages (data from the 2016 OATK Catalog - 7.6 MB PDF)

- Lockheed Martin's alternative GBI used the following stages (data from the 2016 OATK Catalog - 7.6 MB PDF) and THIS page for Orbus.

• BV+ S1: ATK GEM 40 VN - 40 inch diameter - 265.3 ISP, 65 second burn, 28,886 lb mass (9.8 MR)
• BV+ S2 & S3: ATK Orbus 1A - 27.6 inch diameter, 293.27 ISP, 40 second burn, 1,050 lb mass (7.0 MR)
• BV+ S4: Raytheon EKV - 24 inch diameter, 64 kg mass

- Because KEI was cancelled long ago and relatively early in development, not much open source information is available on it -- mainly from:

• 2006 Report to Congress on BMD Programs, which contains THIS drawing
• 2006 KEI Datasheet, which contains THIS drawing
• KEI Affordability Paper
• THIS says: "Officials with the KEI program said the interceptor will have a first stage burn of about 35 seconds, and second-stage burn of about 24 seconds." ... "A KEI interceptor is bigger [than a SM-3], so the rough conversion ratio is that one KEI could fit where three SM-3s can be mounted now."
• Aviation Week v.169, Issues 8-12 says "The high-speed KEI, featuring a booster that provides two separate 30-sec burns..."

KEI was to have been a common land/sea based missile, designed from the start for use from USN warships as well. The main diameter of KEI was 40 inches (1016mm) and it would have been built off Advanced Solid Axial Stage (ASAS) technologies - high-strength graphite composite cases, high performance propellants and thrust vectoring nozzles - while the third stage would have been SM-3's MK136 TSRM. The kill vehicle would have been either Multiple Kill Vehicle (MKV) or a modified SM-3 EKV (with hypergolic propulsion for more divert capacity than SM-3).

Scaling off these (#1, #2) drawings using 40 inch diameter, I get:

• KEI First Stage Motor (KFSM): 1016mm diameter by 5780~mm length = 4.686 m3 = 7029.04 kg mass with 1850 kg/m3 density.
• KEI Second Stage Motor (KSSM): 1016mm diameter by 2280~mm length = 1.848 m3 = 3419.66 kg mass with 1500 kg/m3 density.
• Total Mass of KFSM + KSSM: 10,448.71 kg (23,035 lbs). If you figure in 300 lb for TSRM + 30 lb for KV + 200 lb for nosecones/fairings = Total KEI Mass = 23,565 lb, close enough to meet the slide deck.

I believe KEI was ultimately killed over two factors:

• Disagreements between the US Army and US Navy over design safety margins. The only way KEI can meet the claimed 7 km/sec VBo's is if Mass Ratios equal to that demonstrated in commercial ASAS stages (4+ and above) are used. The USN likely reluctantly accepted 3~ and above Mass Ratios on SM-3 Block II due to the Japanese funding it - the Japanese (along with other East Asian Navies) have a more relaxed attitude towards warship safety - it's how they can build large combatants faster/cheaper than the USN. With no foreign involvement in KEI, the USN likely did not budge on safety standards, ultimately cancelling their plans to use KEI on CG(X). With the loss of USN support, KEI no longer had enough institutional support to survive the Obama Administration's cutbacks in Missile Defense.
• The fact that if you downloaded the 65 kg EKV and uploaded a 375~ kg Mk 21 RV (0.56 m diameter), you would get a ballistic missile that is a massive INF treaty violation. GBI itself is ICBM class, but I believe the Russians didn't contest counting GBI under ICBM launcher limits allowed under START because GBI is/was a kludged together launch vehicle using commercial motors. KEI would have been an all new, purpose designed road mobile system built to military standards. Since the Obama Administration didn't want to scrap INF, KEI had to die.

-- This is here to test ICBM flyout simulations using the code developed for ABM flyout simulations. It's very crude and raw at the moment; using publicly released data in THIS packet, combined with motor data released on target missiles, which used surplus M57A1 motors (Minuteman I/II Third Stages) and SR-19-AJ-1 motors (Minuteman II Second Stage).

More Threat Missiles will be added using data from THIS publication for future releases of this program; as well as USN Trident missiles using data from THIS publication.

These constraints keep the simulation "working"

Length of each Simulation Step (Seconds). Set to 1 for the majority of stuff here. Set to 0.1 for extremely high acceleration items such as SPRINT or HIBEX.

Drag Adjustment Scaler This adjusts the Drag Coefficient up or down by multiplying it. Used when you want to estimate something extremely streamlined (SPRINT/HIBEX).

Stop Constraints -- time and final terminal altitude
Only one can be active at any one time

Flyout Time (sec) Time since launch. Useful to see how far something would have flown in "x" amount of seconds and for generating flyout maps.

Launch Angle (degrees)

• VLS Launched = 90 degrees
• Air Launched = 2 degrees

Launch Altitude (km)

• 15 kiloft = 4.572 km
• 30 kiloft = 9.144 km
• 50 kiloft = 15.24 km
• 80 kiloft = 24.384 km

Launch Axial Velocity (m/sec)

• Mach 0.5 @ 25 kft = 154.915
• Mach 0.8 @ 25 kft = 247.864
• Mach 1.0 @ 25 kft = 309.83
• Mach 1.5 @ 25 kft = 464.745
• Mach 2 @ 50 kft = 590.4 m/s
• Mach 3 @ 80 kft = 885.6 m/s

Stage 1 -

Stage 2 -

Stage 3 -

Stage 4 -

Simulation Table Color Codes

Unpowered Coast

Stage 1 Booster Firing

Stage 1 Sustainer Firing

Stage 2 Booster Firing

Stage 2 Sustainer Firing

Stage 3 Booster Firing

Stage 3 Sustainer Firing

Stage 4 Booster Firing

Stage 4 Sustainer Firing