Paper analyzing a Patriot PAC-2 ‘s probability of intercepting a Kh-47 M2 Kinzhal missile

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AndersJ

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The paper linked below analyses the performance of the Kh-47 M2 Kinzhal, and how likely it is that this type of missile can be intercepted by air defenses. However, in order to keep this post free of information that could be construed to be politically sensitive, the linked paper has been redacted so that only the parts focused on the technical analysis remain.

I did this paper because there have been so many rumors and speculation regarding the actual performance of this missile in the media and on different forums, most of which have been overly optimistic about the Kinzhal’s capabilities in my humble opinion.

Link to page with the paper in pdf format. On my homepage I also have a page with a description of the simulation model used.

Note that I in no way claim this paper to be the gospel truth, and this is just my assessment based on my simulations and the assumptions I outline in the paper.

Consequently, I would welcome any constructive input on it. However, please remember to keep it all related to the technical aspects in order to comply with the forum rules.
 
Do you know the expression “pull an owl onto a globe”? Try again.
It should be taken into account that the radius of the MiG-31 is ~ 700 km. The carrier speed at the moment of rocket launch is 2100 - 2300 km/h, the carrier flight altitude is ~ 15,000 meters.
A similar missile when launched from the ground has a flight range of at least 500 km. And it would be correct to call the rocket simply “Dagger” or "Kinzhal".
It is useful to compare the capabilities of the Iskander missile with the MGM-140 ATACMS missile and extrapolate the difference to the Kinzhal missile

Iskander, maximum 2100 m/s, in the target area 1400 m/s (M=4.2) calculated data
Kinzhal, maximum 4000 m/s, in the target area 2600 m/s (M=8) calculated data

ATACMS
a) graph of altitude versus missile flight range
b) graph of the speed versus flight time of the missile
 

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"It is useful to compare the capabilities of the Iskander missile with the MGM-140 ATACMS missile and extrapolate the difference to the Kinzhal missile"

Why? They aren't really comparable. Iskander pretty much masses double that of ATACMs.
 
paralay said:
Do you know the expression “pull an owl onto a globe”? Try again.
It should be taken into account that the radius of the MiG-31 is ~ 700 km. The carrier speed at the moment of rocket launch is 2100 - 2300 km/h, the carrier flight altitude is ~ 15,000 meters.
A similar missile when launched from the ground has a flight range of at least 500 km. And it would be correct to call the rocket simply “Dagger” or "Kinzhal".
It is useful to compare the capabilities of the Iskander missile with the MGM-140 ATACMS missile and extrapolate the difference to the Kinzhal missile

Iskander, maximum 2100 m/s, in the target area 1400 m/s (M=4.2) calculated data
Kinzhal, maximum 4000 m/s, in the target area 2600 m/s (M=8) calculated data

ATACMS
a) graph of altitude versus missile flight range
b) graph of the speed versus flight time of the missile
Click to expand...

No, I had to Google that Russian expression about the Owl, but when I understood what it meant and read your post the Anglo-Saxon expression “Pot calling kettle black” came to mind. Do you know it? Seems quite appropriate in this case I think.

First of all that first figure is quite hilarious: You really think a Mig-31 will be capable of flying at 2300 km/h at 15 km (i.e. M=2.2!) while lugging around a KInzhal? Assume the Mig gets up to speed in a straight line, what do you think will happen to the speed when the Mig-pilot applies g’s to pull up into the 45 degree climb? So lofting a Kinzhal from 15 km altitude at M=2.2 to an apogee altitude of 242 km? Really? I assume that figure “9” is referring to the Mach number? All those figures look wildly optimistic and more like something out of a propaganda poster than something realistic.

Try doing a sanity check assuming the very best solid fuel propellant out there and the amount of fuel you can stick in the Kinzhal missile cut-away you posted: In that scenario shown in that first picture: What missile weight is assumed? How much of that weight is assumed to be propellant? What is your estimate of the total impulse in Ns? What is the estimated burn time? What is the profile of the burn?
 
The invention relates to aerospace technology and can be used in the implementation of the air launch of launch vehicles (LV). The proposed method involves taking the aircraft from the PH to a horizontal trajectory in the plane of a given orbit of the object and accelerating the aircraft to supersonic speed. Then, within 10-20 seconds, the angle of inclination of the flight path is increased to 10-15 o. The separation of the PH from the aircraft is carried out at an altitude of 16-18 km at a speed of more than 2000 km / h.
Click to expand...

Способ запуска объектов на околоземную орбиту

Изобретение относится к аэрокосмической технике и может быть использовано при осуществлении воздушного старта ракет-носителей
findpatent.ru

437382.gif

437383.gif
 
The mass of the missile is 4000 kg
the mass of fuel is 2500 kg
the cruising altitude of the missile is 50 km

"9" is the duration of the hypersonic flight section - 9 minutes. But since the trajectory is quasi ballistic, see the ATACMS, then the passage time of this section is probably less than nine minutes
 
I'm not sure what are you arguing about. The main point of paper seems to be an assumption that on the terminal part of trajectory - where interception is supposed to took place, since PAC-102 is endoatmospheric only - the velocity of "Kinjal" would be low enough for the interception to be possible.
 
paralay said:
The mass of the missile is 4000 kg
the mass of fuel is 2500 kg
the cruising altitude of the missile is 50 km

"9" is the duration of the hypersonic flight section - 9 minutes. But since the trajectory is quasi ballistic, see the ATACMS, then the passage time of this section is probably less than nine minutes
paralay said:

Способ запуска объектов на околоземную орбиту

Изобретение относится к аэрокосмической технике и может быть использовано при осуществлении воздушного старта ракет-носителей
findpatent.ru

437382.gif

437383.gif
Click to expand...
Click to expand...
First of all that patent is hardly proof of anything: It’s simply a patent application for a payload launch concept utilizing an aircraft and the performance figures may have been taken straight out of Wikipedia.

Secondly, you still have not answered my questions about what is the total impulse in Ns in the figure showing an apogee of 242 km? What is the estimated burn time? What is the profile of the engine fuel burn?

Thirdly, where do you get the 4000 kg total missile weight from? What fuel are you assuming? What is the density of it? What is its specific impulse? What configuration is the Kinzhal? A single- or multiple stage unit with a separate warhead section? With what warhead and what’s the weight of it? What assumptions surround the 2500 kg “fuel” weight? What indicates that it’s the actual fuel weight and not the engine’s total weight including the housing and jet outlet? If it really is the fuel weight, then it has to be some pretty dense fuel to get all of 2500 kg into the volume shown in the cut-away. Some special Russian super-fuel perhaps?
 
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paralay said:
The speed of the KInzhal at the target is less than the speed of ATACMS (1.05 km/s)?
Click to expand...

No, no one is saying it is less, and the one which was shot down recently was doing slightly more, around 1250 m/s, not that that helped much since it still got intercepted. ;)
 
paralay said:
Do you know the expression “pull an owl onto a globe”? Try again.
It should be taken into account that the radius of the MiG-31 is ~ 700 km. The carrier speed at the moment of rocket launch is 2100 - 2300 km/h, the carrier flight altitude is ~ 15,000 meters.
A similar missile when launched from the ground has a flight range of at least 500 km. And it would be correct to call the rocket simply “Dagger” or "Kinzhal".
It is useful to compare the capabilities of the Iskander missile with the MGM-140 ATACMS missile and extrapolate the difference to the Kinzhal missile

Iskander, maximum 2100 m/s, in the target area 1400 m/s (M=4.2) calculated data
Kinzhal, maximum 4000 m/s, in the target area 2600 m/s (M=8) calculated data

ATACMS
a) graph of altitude versus missile flight range
b) graph of the speed versus flight time of the missile
Click to expand...

Just wondering where you get the ATACMS graphs from, and how to interpret it? Thanks .......
 
AndersJ said:
The paper linked below analyses the performance of the Kh-47 M2 Kinzhal, and how likely it is that this type of missile can be intercepted by air defenses. However, in order to keep this post free of information that could be construed to be politically sensitive, the linked paper has been redacted so that only the parts focused on the technical analysis remain.

I did this paper because there have been so many rumors and speculation regarding the actual performance of this missile in the media and on different forums, most of which have been overly optimistic about the Kinzhal’s capabilities in my humble opinion.

Link to page with the paper in pdf format. On my homepage I also have a page with a description of the simulation model used.

Note that I in no way claim this paper to be the gospel truth, and this is just my assessment based on my simulations and the assumptions I outline in the paper.

Consequently, I would welcome any constructive input on it. However, please remember to keep it all related to the technical aspects in order to comply with the forum rules.
Click to expand...
nice, thank you
 
paralay said:
Do you know the expression “pull an owl onto a globe”? Try again.
It should be taken into account that the radius of the MiG-31 is ~ 700 km. The carrier speed at the moment of rocket launch is 2100 - 2300 km/h, the carrier flight altitude is ~ 15,000 meters.
A similar missile when launched from the ground has a flight range of at least 500 km. And it would be correct to call the rocket simply “Dagger” or "Kinzhal".
It is useful to compare the capabilities of the Iskander missile with the MGM-140 ATACMS missile and extrapolate the difference to the Kinzhal missile

Iskander, maximum 2100 m/s, in the target area 1400 m/s (M=4.2) calculated data
Kinzhal, maximum 4000 m/s, in the target area 2600 m/s (M=8) calculated data

ATACMS
a) graph of altitude versus missile flight range
b) graph of the speed versus flight time of the missile
Click to expand...
The discussion about the DF-21 has mentioned that RVs from ICBMs end up slowing down to about Mach 1.5 (~500m/s) at impact due to the thick air at low altitudes, even when they're doing Mach 8-15 at 160kft/50km.

Now, that same discussion also says that the RVs don't slow down out of the plasma sheath until about 16,000ft/5000m, which for a Kinzhal is deep in the terminal dive onto a stationary target. For the DF-21, though, that means that any guidance sensors on the RV are blind until about then, which is why it's being mentioned.

The Kinzhal RV is not powered, so every maneuver it makes in the atmosphere slows it down. If it goes out of the atmosphere, it's limited in maneuverability (and pictures of the Kinzhal do not suggest a reaction control system for exoatmospheric flight, any maneuvers would have to happen in boost before leaving the atmosphere or after reentry). After the May 16 2023 attacks on Kyiv, Ukrainian Patriot SAM operators were interviewed and stated that the missile was doing about 1240m/s, mach 3.6, which is within the capabilities of MIM-104s (PAC-2s?) to intercept.

Just means you need (lots) more launchers spread out over the area because each launcher has a (much) smaller protection footprint. Other papers about HGVs have talked about a 7 mile/12km defensive footprint, defensive missiles need to be within 12km of whatever they're supposed to protect!
 
paralay said:
take any modern fuel from the textbook, you won't make a big mistake
Click to expand...

So then it should be quite easy for you to answer the question I already asked you: What are the fuel properties: What is the specific impulse in s and the density in kg/m***3? And which is “the textbook” these numbers come from?
 
Scott Kenny said:
The discussion about the DF-21 has mentioned that RVs from ICBMs end up slowing down to about Mach 1.5 (~500m/s) at impact due to the thick air at low altitudes, even when they're doing Mach 8-15 at 160kft/50km.

Now, that same discussion also says that the RVs don't slow down out of the plasma sheath until about 16,000ft/5000m, which for a Kinzhal is deep in the terminal dive onto a stationary target. For the DF-21, though, that means that any guidance sensors on the RV are blind until about then, which is why it's being mentioned.

The Kinzhal RV is not powered, so every maneuver it makes in the atmosphere slows it down. If it goes out of the atmosphere, it's limited in maneuverability (and pictures of the Kinzhal do not suggest a reaction control system for exoatmospheric flight, any maneuvers would have to happen in boost before leaving the atmosphere or after reentry). After the May 16 2023 attacks on Kyiv, Ukrainian Patriot SAM operators were interviewed and stated that the missile was doing about 1240m/s, mach 3.6, which is within the capabilities of MIM-104s (PAC-2s?) to intercept.

Just means you need (lots) more launchers spread out over the area because each launcher has a (much) smaller protection footprint. Other papers about HGVs have talked about a 7 mile/12km defensive footprint, defensive missiles need to be within 12km of whatever they're supposed to protect!
Click to expand...

Yes, and the 1240 m/s figure at intercept is totally in line with the figure I have in my simulation in the paper I posted. And with the kind of attack profile one could assume, this would be the speed of the Kinzhal missile the Patriot battery had to contend with and which seems to be well within its operability parameters.

In addition, it is rumored that a Patriot battery was damaged by falling debris from the intercept, which then also implies it was suitably positioned to make the intercept.

So everything adds up I think: The Patriot did the intercept, and the Kinzhal's performance is simply hyped and inflated by some sources. In fact, it does not seem to be a Wunderwaffe at all, but limited by physics just like the rest of us. ;)

Another interesting piece in the puzzle is that in an official statement by the US Department of Defense the Pentagon spokesman Air Force Brig. Gen. Pat Ryder has confirmed that a Kinzhal has indeed been shot down:

Key part from the linked interview:

Q: I just wanted to double check -- you -- you did confirm -- you did confirm that a Patriot downed this Kinzhal missile ...

GEN. RYDER: Correct.

Q: ... did I hear that right?

GEN. RYDER: Correct.
 
AndersJ said:
So everything adds up I think: The Patriot did the intercept, and the Kinzhal's performance is simply hyped and inflated by some sources. In fact, it does not seem to be a Wunderwaffe at all, but limited by physics just like the rest of us. ;)
Click to expand...
I've also seen no verifiable evidence that Kinzhal is equipped with a detachable RV. There may be some drawings floating around that claims this, but that isn't proof of anything, really. Its penetrating warhead stays attached to the missile body during terminal phase, based on the Kinzhal that crashed into Stavropol. It's an air launched short range quasi ballistic missile, and nothing more. You can't say that, or you have IRA and Glavset shills screeching at you, though.

Russian Hypersonic Missile Accidentally Fell on Own Territory: Report

A Russian hypersonic missile meant to strike Ukraine reportedly fell from a MiG-31 aircraft and struck inside Russia.
www.thedefensepost.com
 
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zjz said:
Just wondering where you get the ATACMS graphs from, and how to interpret it? Thanks .......
Click to expand...
The S-300 and S-400 have failed to intercept even one ATACMS so far. I doubt they have any actual data on ATACMS, or they would be swatting them out of the sky like clay pigeons.
 
activeaero said:
I've also seen no verifiable evidence that Kinzhal is equipped with a detachable RV. There may be some drawings floating around that claims this, but that isn't proof of anything, really. Its penetrating warhead stays attached to the missile body during terminal phase, based on the Kinzhal that crashed into Stavropol. It's an air launched short range quasi ballistic missile, and nothing more. You can't say that, or you have IRA and Glavset shills screeching at you, though.

Russian Hypersonic Missile Accidentally Fell on Own Territory: Report

A Russian hypersonic missile meant to strike Ukraine reportedly fell from a MiG-31 aircraft and struck inside Russia.
www.thedefensepost.com
Click to expand...

Thanks for the info. I was also wondering about the drawing showing a second stage Kinzhal missile section with RV but I have not seen any firm evidence for it either. In addition, as you say, the only type we have photos of (as far as I know) is with the penetrator type warhead and where the missile stays in one piece until it hits its target. In addition, concerning the veracity of claims for wonder weapons, maskirovka is just a part of the landscape these days, and sometimes it’s subtle and difficult to detect, but mostly it just sticks out like a sore thumb! ;)
 
I have a suggestion, let's play officers of the General Staff?
Combat mission: to destroy the air defense complex of the city of Kiev located at the airfield. How will you do it?

activeaero said:
Why can't the S-300/400 intercept ATACMS?
Click to expand...
Russian air defense shoots down these missiles regularly, In October, 6 missiles were shot down

AndersJ said:
So then it should be quite easy for you to answer the question I already asked you: What are the fuel properties: What is the specific impulse in s and the density in kg/m***3? And which is “the textbook” these numbers come from?
Click to expand...
Y.S.Pavlyuk "Ballistic missile design", 1996 / Ю.С. Павлюк "Баллистическое проектирование ракет" 1996 год
 

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paralay said:
5981930_original.jpg
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So what is this picture supposed to prove? Launching payloads from aircraft has been done for ages. First of all that underslung missile is huge in itself and will cause a lot of drag simply on its own. Then there is the effect this will have on the supersonic wave drag which will be monumental due to the area-ruling which will go out of the window with that thing under the belly. So first of all, no way that aircraft will reach 2300 km/h at 15 km in horizontal flight with that thing hanging under it. Secondly, if the pilot tries to pull up into a 45 degree launch attitude he will loose even more speed due to the induced drag!

Edit: Spelling.
 
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paralay said:
Y.S.Pavlyuk "Ballistic missile design", 1996 / Ю.С. Павлюк "Баллистическое проектирование ракет" 1996 год
Click to expand...

My Russian I kind of sketchy, but I understand that the first column in that table is the specific density so no problem there. However, where is the specific impulse (Either stated in s or Ns/kg)? Or how is that table supposed to be used to calculate the impulse?
 
The debutant of Asian Aerospace 2006, KazKosmos company from Kazakhstan, for the first time publicly presented a promising Ishim aircraft and rocket launch complex, created on the basis of the MiG-31D aircraft. According to the company's materials, Ishim is designed for the operational launch of a large number of small satellites into various orbits. According to KAZKOSMOS experts, in the XXI century it will be necessary to launch and maintain various groupings of small satellites in orbit, the optimal means for which can be a complex based on the MiG-31D aircraft.

The complex includes two aircraft carriers, designated MiG-31I, a three-stage launch vehicle suspended between the engine nacelles, as well as an air command and measurement complex based on the Il-76MD aircraft. The take-off weight of the MiG-31I aircraft with a launch vehicle is 50 tons, the flight range to the launch point is 600 km, the height of the launch point is from 15 to 18 km, the speed at the launch point is 2120-2230 km/h.
Click to expand...

AndersJ said:
if the pilot tries to pull up into a 45 degree launch attitude he will loose even more speed due to the induced drag!
Click to expand...
It doesn't turn 45 degrees

View: https://youtu.be/abWKmsjv2n0

The specific impulse is measured in meters per second, the penultimate column (2400, 2300, 2440, 2460)
 
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paralay said:
It doesn't turn 45 degrees

View: https://youtu.be/abWKmsjv2n0

The specific impulse is measured in meters per second, the penultimate column (2400, 2300, 2440, 2460)
Click to expand...

Well if the Kinzhal is launched horizontally like in that video it will not reach very far: Either it will hit the ground shortly due to no ballistic trajectory and flying in dense air, or it will expend a lot of energy to transition to a 45 degree climb in order to reach a ballistic trajectory and less dense air. Either way is uneconomical and not as good as the lofting launch mode I proposed in the paper where the Mig launches it at a roughly 14 degree angle which is what is needed to get the +300 km range in that example. For the longest range, the Mig should of course pull up into a 45 degree climb before launch.

Then about the specific impulse: I suspected it was the column with those numbers (2400, 2300, 2440, 2460) and then those fuels are worse than the best western (which I calculated with!) which are in the order of 252*9.81=2472 m/s.
 
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AndersJ said:
Then about the specific impulse: I suspected it was the column with those numbers (2400, 2300, 2440, 2460) and then those fuels are worse than the best western (which I calculated with!) which are in the order of 252*9.81=2472 m/s.
Click to expand...
Not a secret book of 1996 ;)
 
paralay said:
Not a secret book of 1996 ;)
Click to expand...

No, but this was what you came up with when you said "take any modern fuel from the textbook, you won't make a big mistake"! So we have now established that I have actually been too optimistic about the fuel for the KInzhal and that it is actually not as good as I have assumed in the simulations! :D
 
activeaero said:
Can I see the ATACMS intercepted by the S-300/S-400?
Click to expand...

Появились кадры обломков сбитой в зоне СВО американской ракеты ATACMS

Добавить Известия в избранное. В распоряжении «Известий» 17 октября появились эксклюзивные кадры обломков сбитой дальнобойной американской ракеты ATACMS — эти боеприпасы США поставили Вооруженным силам Украины (ВСУ). Ракета была сбита системами противовоздушной обороны (ПВО) РФ вчера на одном из...
iz-ru.turbopages.org
 
paralay said:

Появились кадры обломков сбитой в зоне СВО американской ракеты ATACMS

Добавить Известия в избранное. В распоряжении «Известий» 17 октября появились эксклюзивные кадры обломков сбитой дальнобойной американской ракеты ATACMS — эти боеприпасы США поставили Вооруженным силам Украины (ВСУ). Ракета была сбита системами противовоздушной обороны (ПВО) РФ вчера на одном из...
iz-ru.turbopages.org
Click to expand...
Seriously? You're really going to go with this? You've been a member of this forum since '06, and you seem to be somewhat intelligent. So, you know what the M39 Block 1 ATACMS is, and how it functions. The M39 spins in its terminal phase, and releases its payload of M74 bomblets. The M39 ATACMS missile body (propulsion and control sections) stay intact, and impact the ground intact.
View: https://www.youtube.com/watch?v=shl_4JgQAI4


Almost exactly as the cluster variants of the Iskander, and Tochka-U do.

Kramatorsk station attack: What we know so far

Some 50 people are said to have been killed in Kramatorsk, Ukraine and Russia are blaming each other.
www.bbc.com

Those ATACMS missile bodies show no signs of being intercepted by Russian AA/SAM. Where is the damage from the blast fragmentation warheads that would be used to intercept the M39 ATACMS? There's zero damage to the M39 ATACMS missile bodies from fragments you would expect in a successful intercept, is there? All I see is slight damage to the control section from impacting the ground after successfully dispensing its payload of M74 bomblets. The Russian MoD reported to TASS that it was an S-400 that intercepted the two ATACMS, though, they wouldn't show any proof, or name the location in which the intercepts occurred. Why wouldn't they name the location, or show proof? Well, I think the answer is because they didn't intercept anything, and those ATACMS destroyed 3 S-400 systems in Luhansk.

S-400: Ukraine Overwhelms 'World's Best' Defense Systems; Reports Say At-Least 3 Launchers Destroyed

Ukraine launched a new attack on the Kerch Strait connecting Crimea and the Russian mainland, reportedly damaging a warship while firing eight Storm Shadow air-launched cruise missiles (ALCMs). Before that, towards the end of October, reports also claimed Ukraine destroyed four S-400 systems...
www.eurasiantimes.com

Three Russian S-400 reportedly destroyed as Moscow says ATACMS "thwarted"

On Wednesday, the Russian Ministry of Defense said it had destroyed two of Ukraine's ATACMS "over the past 24 hours."
www.newsweek.com
Debris from a Ukrainian ATACMS strike on Bilorichenskyi, Luhansk Oblast. Also pictured is the fire it caused last night.
by u/tractoroperator77 in UkraineWarVideoReport
View: https://www.reddit.com/r/UkraineWarVideoReport/comments/17gtem7/debris_from_a_ukrainian_atacms_strike_on/

View: https://twitter.com/JayinKyiv/status/1717579727743901914

Донбас➔Оперативний

‼️ З'явилися вранішні кадри прильоту біля с. Білореченський Луганської області. Орки написали, що зірвався газогін. Але на відео чітко видно, що це приліт і саме туди, куди і треба... Донбас Оперативний ✍️ Підписатись Запропонувати новину
t.me


In essence, you've proven that the S-400 is actually incapable of intercepting ATACMS. LMAO. Please just stop; this is getting ridiculous.
 
Scott Kenny said:
? Huh? Specific Impulse is measured in seconds, not in meters per second.
Click to expand...

Yes, this is the unit I'm used to as well but apparently the Russians prefer using m/s. But by dividing with g you get it in s:

So (2400, 2300, 2440, 2460) in m/s becomes (245, 234, 249, 251) in seconds.

But since I apparently have been too optimistic about Russian solid fuel technology and assumed 252 s, paralay's attempt to lecture me on how to avoid "mistakes" kind of backfired a bit. ;)
 
AndersJ said:
Yes, this is the unit I'm used to as well but apparently the Russians prefer using m/s. But by dividing with g you get it in s:

So (2400, 2300, 2440, 2460) in m/s becomes (245, 234, 249, 251) in seconds.

But since I apparently have been too optimistic about Russian solid fuel technology and assumed 252 s, paralay's attempt to lecture me on how to avoid "mistakes" kind of backfired a bit. ;)
Click to expand...
Yeah, I expect the mods to delete my post for some odd reason, even though there was nothing wrong with the 4 posts they deleted, and nothing wrong with my post above. So, watch out, they'll probably delete yours too. Kind of ridiculous that you basically have to be a lobotomized yes man to post on here.
 
paralay said:
Do you want to teach Russians the science of building rockets? are you serious?
Click to expand...
I learned my rocket science from John D. Clark. You know, the guy who wrote Ignition! back in 1971 or so.

He measures Specific Impulse in seconds. So does NASA and the USAF. And the ESA.
 
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