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

The zonal anti-aircraft missile defense systems, such as Patriot or С-300, have one significant drawback - an extremely low level of PV%. Destroying them is easier than you can imagine. And don't need a Кинжал.
 
Using the Sputnik program, calculate the speed and flight range of a hypothetical rocket depending on the launch conditions.

Initial data:
Starting mass 3800 kg, fuel mass 2300 kg, mass after fuel production 1500 kg
The thrust of the engine at the ground is 100 kN, in vacuum 120 kN
The specific impulse at the earth is 2551 m/s, in vacuum 2700 m/ s
The diameter of the rocket is 0.72 m

Start conditions: height 0 m, speed 0 m/s, pitch 54 degrees
Active section 0 – 55.2 sec, speed at the end of the active section 1783 m/s, 6419 km/h, M=6
Flight time 350 seconds / 5.83 minutes, speed at the time of arrival 1247 m / s, 4493 km / h, M=3.67
Trajectory length 462 km, flight range 383 km, maximum flight altitude 113 km at 192 seconds

MiG-31I
Start conditions: altitude 15,000 m, speed 650 m/s, 2340 km/h, M =2.2, pitch 44 degrees
Active section 0 – 52 sec, speed at the end of the active section 2785 m/s, 10026 km/h, M=9.44
Flight time 483 seconds / 8.05 minutes, speed at the time of arrival 1815 m / s, 6534 km / h, M = 5.34
Trajectory length 1121 km, flight range 980 km, maximum flight altitude 229 km at 249 seconds

The range of the carrier without external tanks is 1178 km, the complex is 1178 km + 980 km = 2158 km (no more)
The range of the carrier with external tanks is 1568 km, the complex is 1568 km + 980 km = 2548 km (no more)

Su-34M
Start conditions: altitude 10000 m, speed 265.5 m/s, 956 km/h, M=0.9, pitch 48 degrees
Active section 0 – 52 sec, speed at the end of the active section 2332 m/s, 8395 km/h, M=7.9
Flight time 423 seconds / 7.05 minutes, speed at the time of arrival 1579 m/s, 5684 km/h, M=4.64
The trajectory length is 793 km, the flight range is 683 km, the maximum flight altitude is 175 km at 222 seconds

The range of the carrier without external tanks is 1178 km, the complex is 1354 km + 683 km = 2037 km (no more)
The range of the carrier with external tanks is 1615 km, the complex is 1615 km + 683 km = 2298 km (no more)
 
Correct me if I'm wrong - I thought it was the MiG-25's mission to intercept Blackbirds. The MiG-31 was developed to counter cruise missile carrying B-52s.
I have the English edition of MiG - 1939-1989 (Docavia 1991 French edition, Airlife 1994 English edition) by Jacques Marmain and Rostislav Belyakov, on the Mig-25 they write (p.383):

On the MiG-31 (p.407):
The MiG-31 still had to deal with Blackbirds, the US didn't retire them until the 1990s.
 
Using the Sputnik program, calculate the speed and flight range of a hypothetical rocket depending on the launch conditions.

Initial data:
Starting mass 3800 kg, fuel mass 2300 kg, mass after fuel production 1500 kg
The thrust of the engine at the ground is 100 kN, in vacuum 120 kN
The specific impulse at the earth is 2551 m/s, in vacuum 2700 m/ s
The diameter of the rocket is 0.72 m

Start conditions: height 0 m, speed 0 m/s, pitch 54 degrees
Active section 0 – 55.2 sec, speed at the end of the active section 1783 m/s, 6419 km/h, M=6
Flight time 350 seconds / 5.83 minutes, speed at the time of arrival 1247 m / s, 4493 km / h, M=3.67
Trajectory length 462 km, flight range 383 km, maximum flight altitude 113 km at 192 seconds

MiG-31I
Start conditions: altitude 15,000 m, speed 650 m/s, 2340 km/h, M =2.2, pitch 44 degrees
Active section 0 – 52 sec, speed at the end of the active section 2785 m/s, 10026 km/h, M=9.44
Flight time 483 seconds / 8.05 minutes, speed at the time of arrival 1815 m / s, 6534 km / h, M = 5.34
Trajectory length 1121 km, flight range 980 km, maximum flight altitude 229 km at 249 seconds

The range of the carrier without external tanks is 1178 km, the complex is 1178 km + 980 km = 2158 km (no more)
The range of the carrier with external tanks is 1568 km, the complex is 1568 km + 980 km = 2548 km (no more)

Su-34M
Start conditions: altitude 10000 m, speed 265.5 m/s, 956 km/h, M=0.9, pitch 48 degrees
Active section 0 – 52 sec, speed at the end of the active section 2332 m/s, 8395 km/h, M=7.9
Flight time 423 seconds / 7.05 minutes, speed at the time of arrival 1579 m/s, 5684 km/h, M=4.64
The trajectory length is 793 km, the flight range is 683 km, the maximum flight altitude is 175 km at 222 seconds

The range of the carrier without external tanks is 1178 km, the complex is 1354 km + 683 km = 2037 km (no more)
The range of the carrier with external tanks is 1615 km, the complex is 1615 km + 683 km = 2298 km (no more)

Thanks for that data paralay. Those are quite useful numbers and this Sputnik program seems quite useful I think. Is it publicly available and do you have a link to it? I don’t have the time to do a more thorough analysis of those results now since it is Friday evening after all, but all those numbers look quite reasonable after just a cursory glance.

Would it be possible for you to do a simulation of the scenario I did in the paper in the Sputnik program? I’m thinking about the launch at M=1 at 12 km with a 14 degree loft? I have assumed that the missile utilizes body lift during the flight after the apogee: Either 0.4 g’s and /or a maximum of 5 degrees alfa whichever is limiting. This gives a longer range (by using body lift), and I think it is better than just a ballistic trajectory in denser atmosphere. But if you can only do ballistic trajectories in Sputnik, then I can do that as well in my program. Would be interesting to compare results! :)
 
That figure from my paper may have been a bit misleading: Just taking a cursory glance at it, it looks like a launch at 45 degrees but it’s not: The x- and y-scales are different and with the same scales on both axes it looks like this:

View attachment 711335

Secondly, the 300 km attack profile in the paper is not to attain the longest range: It was an example of how an attack from a safe airspace and distance could be done with the shortest possible warning time for the defenders. And in this case a launch at a 14 degrees loft angle was enough. However, lofting the Kinzhal at 45 degrees would give it a much longer range than the ATACMS which I don’t dispute.

So the attack profile in my paper is more the one I assumed had been used for the missile that was purportedly shot down by the Ukrainians, and which according to them had been traveling at 1240 m/s at intercept. But for sure, the same target (let’s assume it was a Patriot battery) could have been attacked with an Iskander from the same range in a ballistic trajectory, but that would have given the defenders much more warning time.
I think having a shallow loft angle might give the defender a shorter radar horizon distance but not neccessary shorter warning time. Especially if we consider that thick air reduce air speed of the missile significantly. Besides, even if shallow loft does reduce time to impact, it negate the main advantage of Kinzhal which is hypersonic speed. Given that even hard kill active protection system on tank can react in fraction of a second, the reduced time to impact might not be as useful as moving at hypersonic speed


Then about the what classifies as a hypersonic missile: For sure, a lot of missiles may be able to be fitted under that heading, but I think it should be reserved for missiles flying fast at relatively low level for extended periods of time at speeds over M=5 with some sort of maneuvering capability and having a decent range as well. And in that case that rules out solid fueled ballistic type missiles IMHO. Because in order to get a decent range at hypersonic speeds other than in ballistic trajectories, you need to reserve all space inside the missile other than the payload for fuel, and not take up space and weight for the oxidizer as well.
I disagree with this assessment.
When talking about modern hypersonic weapons. There are two main types: scramjet missile such as Zircon, HAWC, HACM and boost glider vehicle such as Avangard, LRHW, DF-ZF. Scramjet missile are practically cruise missile that move at hypersonic speed. But boost glider are practically ballistic missile warhead that glide at lower altitude where their control surface still effective. And boost glider can retain their hypersonic speed for quite a while even without propulsion system.
D6388C89-6C2A-4313-8EAD-4522CA4E3A7F.jpeg
 
I think having a shallow loft angle might give the defender a shorter radar horizon distance but not neccessary shorter warning time. Especially if we consider that thick air reduce air speed of the missile significantly. Besides, even if shallow loft does reduce time to impact, it negate the main advantage of Kinzhal which is hypersonic speed. Given that even hard kill active protection system on tank can react in fraction of a second, the reduced time to impact might not be as useful as moving at hypersonic speed

Ronny: I don’t claim to know how the Kinzhal should be used to greatest effect. In my paper I simply proposed a possible scenario for how the Kinzhals that have been fired recently MIGHT have been used and which could explain the purported 1240 m/s quoted at intercept. True, I have suggested some reasons for why such a low loft angle trajectory may have been used, but I’m not claiming this was how it was done or the reason for it. I have no idea what deliberations whoever planned those attacks made. In fact, I would very much like to hear how it was actually done if someone has been able to dig up that information. Regarding making an analogy between a Patriot and a tank protection system, I think those are quite different scenarios with totally different time constants involved, so not an analogy I would make.

I disagree with this assessment.
When talking about modern hypersonic weapons. There are two main types: scramjet missile such as Zircon, HAWC, HACM and boost glider vehicle such as Avangard, LRHW, DF-ZF. Scramjet missile are practically cruise missile that move at hypersonic speed. But boost glider are practically ballistic missile warhead that glide at lower altitude where their control surface still effective. And boost glider can retain their hypersonic speed for quite a while even without propulsion system.

Ronny: When you marked part of my reply in bold you conveniently left out the part above: “And in that case that rules out solid fueled ballistic type missiles IMHO”. So you’re making a bit of a strawman argument here. I have not said that boost gliders should be excluded from the hypersonic category. Maybe they belong there. I have no opinion on that. What I have objected to was that ballistic type solid fueled rockets like the Kinzhal should be called hypersonic missiles. Nothing else.
 
I think having a shallow loft angle might give the defender a shorter radar horizon distance but not neccessary shorter warning time. Especially if we consider that thick air reduce air speed of the missile significantly. Besides, even if shallow loft does reduce time to impact, it negate the main advantage of Kinzhal which is hypersonic speed. Given that even hard kill active protection system on tank can react in fraction of a second, the reduced time to impact might not be as useful as moving at hypersonic speed



I disagree with this assessment.
When talking about modern hypersonic weapons. There are two main types: scramjet missile such as Zircon, HAWC, HACM and boost glider vehicle such as Avangard, LRHW, DF-ZF. Scramjet missile are practically cruise missile that move at hypersonic speed. But boost glider are practically ballistic missile warhead that glide at lower altitude where their control surface still effective. And boost glider can retain their hypersonic speed for quite a while even without propulsion system.
View attachment 711435
Neither ATACMs or Kinzhal are boost gliders. Nor do boost gliders cruise in thick air. They stay up high and have a relatively high sectional density to minimize the effects of drag.
 

Thanks paralay. Apparently you got it running on your PC with no problems so there is that. However, I'm rather hesitant to run .exe stuff on my PC. Maybe I will try it out on an older PC to see how it behaves in quarantine. Not sure about that though. But since you have it up and running, how about trying out the M=1 at 12 km with 14 degrees loft to see what Sputnik says?
 
Ronny: When you marked part of my reply in bold you conveniently left out the part above: “And in that case that rules out solid fueled ballistic type missiles IMHO”. So you’re making a bit of a strawman argument here. I have not said that boost gliders should be excluded from the hypersonic category. Maybe they belong there. I have no opinion on that. What I have objected to was that ballistic type solid fueled rockets like the Kinzhal should be called hypersonic missiles. Nothing else.
I think you misunderstood the reason I talked about boost glider weapons. I know you didn't excluded them from the list of hypersonic weapons. But I talked about them because they have very similar working principle with a ballistic missiles, especially in boost phase.
Take for example: Avangard glider vehicle used the common ICBM like Topol-M as booster. In other words, Hypersonic boost glider vehicle are basically special kind of RV that instead of following a normal ballistic arc as normal RV, they sort of glide at much lower altitude where the air is thicker. So that they can maneuver. However, because they glide at much lower altitude compared to a normal RV, they also decelerate much quicker. My point is that: if a hypersonic glider can hold hypersonic speed for long enough to be consider a hypersonic weapon, then a ballistic missile will absolutely fit that criteria too, because they can hold speed for longer (due to thinner air).
Anyway, this is how a hypersonic glider decelerate when it glide
Hypersonic missile.PNG

 
Neither ATACMs or Kinzhal are boost gliders. Nor do boost gliders cruise in thick air. They stay up high and have a relatively high sectional density to minimize the effects of drag.
I mean comparatively, a boost glider cruise in thicker air than a ballistic missile warhead of the same size
Like this ( yes I know ATACMs and Kinzhal don't fly as high as ICBM but I think you got my point)
BR9OB.png
 
Now, I seem to remember fatigue problems with Saberjets release heavy ordinance and flipping back home.

That's a pretty big missile...any scuttlebutt about structural issues?
 
BRGV cruised for almost 5000nm at around 30km.
I don't deny that HGV can fly far, just that they will decelerate more than ballistic missile because ballistic missile fly higher (sort of in space without air resistance)
 
I don't deny that HGV can fly far, just that they will decelerate more than ballistic missile because ballistic missile fly higher (sort of in space without air resistance)
Of course but still, 5000nm gliding from 100,000ft ain't bad.
 
Figured it out or help?

I get an error message when I try to run the Sputnik software on my old quarantined computer and I don't plan on running it on anything else. But at the risk of repeating myself (third time I think? ;)), since you have it up and running, why don't you run the M=1 at 12 km with 14 degrees loft scenario to see what Sputnik says?
 

OK thanks for those results. However, I think you need to change something in the test setup: The short range (only 182 km) is probably due to the missile in Sputnik strangely only reaching 15 km altitude. In my setup I reach circa 35 km altitude. The missile is supposed to keep the boost angle of 14 degrees in the burn phase but it only reaches 15 km after 53 s in Sputnik as far as I can see. As a sanity check, if the missile is doing an average of 2000 m/s for 53 s at an angle of 14 deg then it should add 26 km altitude so it should be at roughly 12+26=37 km before beginning ballistic trajectory. From there it is reasonable that it goes more than 300 km.

Kinzhal in Sputnik 14 deg loft.jpg
 
Deleted post was wrong: the 7000 I mentioned there was km/h, not m/s. I have a missile model with less fuel weight and lower ISP than you are assuming in Sputnik and in my model the speed tops out at slightly under 2000 m/s at engine burn-out.
 
it is necessary to select the pitch angle

Yes, and I saw you set it at 14 deg which is fine, but in order to reach any decent range the control system in the missile needs to keep it at the loft angle for the entire duration of the burn, otherwise gravity will take over and the missile will soon be going horizontal again. This is what I think is happening in the Sputnik numbers you posted: The missile only reaches an altitude of 15 km and flies a little over 180 km before it hits the ground. If it instead keeps 14 deg during the 50 s burn, it should reach 35 km altitude and go over 300 km.
 
Yep. The MiG-31 was however still expected to shoot down SR-71 if needed, and MiG-31 pilots were more confident in MiG-31 to do it over MiG-25 due to the better avionics and missiles.
 
Granted, there is no comparison between a Mig-31 and a JA-37 Viggen when it comes to climb, ceiling and speed, but a Viggen Squadron in Sweden supposedly has a letter of congratulations from the USAF for having locked up an SR-71 over the Baltic. However, many SR-71’s flew the same repetitive pattern passing in the small international airspace corridor between the Swedish islands of Öland and Gotland, so there was usually plenty of time to set up an intercept. And one day, they sent up a Viggen in a ballistic climb and timed it so that the Viggen at the apex would have a short window of opportunity to lock up the Blackbird for a head-on shot which they apparently managed. But this was of course simply because they knew exactly when and where that Blackbird would be. If the SR-71 instead of the narrow corridor had a bit more room to manoeuvre they would never have pulled it off.

So this begs the question: Just how is this theoretical intercept profile for a MIg-31 “shooting down” a SR-71 supposed to look like? What is the loadout in terms missiles assumed? What speeds are the Mig-31 and SR-71 supposed to be at? I assume it’s a more or less head-on engagement envisioned since I have a hard time seeing a Mig-31 doing a take-off, climb, and then accelerate and catch the SR-71 in a tail chase? So what was the way the Soviets envisioned doing this?
 
Granted, there is no comparison between a Mig-31 and a JA-37 Viggen when it comes to climb, ceiling and speed, but a Viggen Squadron in Sweden supposedly has a letter of congratulations from the USAF for having locked up an SR-71 over the Baltic. However, many SR-71’s flew the same repetitive pattern passing in the small international airspace corridor between the Swedish islands of Öland and Gotland, so there was usually plenty of time to set up an intercept. And one day, they sent up a Viggen in a ballistic climb and timed it so that the Viggen at the apex would have a short window of opportunity to lock up the Blackbird for a head-on shot which they apparently managed. But this was of course simply because they knew exactly when and when that Blackbird would be where. If the SR-71 instead of the narrow corridor had a bit more room to manoeuvre they would never have pulled it off.

So this begs the question: Just how is this theoretical intercept profile for a MIg-31 “shooting down” a SR-71 supposed to look like? What is the loadout in terms missiles assumed? What speeds are the Mig-31 and SR-71 supposed to be at? I assume it’s a more or less head-on engagement envisioned since I have a hard time seeing a Mig-31 doing a take-off, climb, and then accelerate and catch the SR-71 in a tail chase? So what was the way the Soviets envisioned doing this?
Like when F-15 pilots bragged about "shooting down" a Blackbird during a canned run. Then the Blackbird pilots changed it up and the Eagle pilots were left standing there with their dicks in their hands.
 
Like when F-15 pilots bragged about "shooting down" a Blackbird during a canned run. Then the Blackbird pilots changed it up and the Eagle pilots were left standing there with their dicks in their hands.

So you're saying it never happened? I mean that a Viggen locked-up an SR-71?
 
An earlier thread on a hypothetical/projected Military Concorde also covered the SR-71 / Viggen matter.
There's a link to an AviationGeekClub story in it:
That story gets much of its data from Lockheed Blackbird: Beyond the secret missions by Paul Crickmore.
SR-71s were intercepted by JA-37s in the eighties, because
- the SR-71s were flying very predictable patterns
- JA-37s carried better electronics than the Soviet fighters of the day, compensating for their lower performance compared to the MiG-25

In the AviationGeekClub there's also this:
Almost every time the SR-71 was about to leave the Baltic, a lone MiG-25 Foxbat belonging to the 787th IAP at Finow-Eberwalde in the German Democratic Republic was scrambled. […] Arriving at its exit point, the “Baltic Express” was flying at about 22km and the lone MiG would reach about 19km in a left turn before rolling out and always completing its stern attack 3km behind its target. We were always impressed by this precision; it was always 22km and 3 km behind the SR-71. [this would seem to suggest that these were the parameters necessary for its weapons system to effect a successful intercept if the order to fire was ever given.] This is interesting, since US Air Force intelligence specialists and SR-71 crewmembers believed that the only possibility of an interceptor successful engaging a Blackbird would be head on, a position given further credence by the fact that the DEF systems designed to tackle an airborne threat operating within the X-band (DEF A2) was forward-facing]. When the SR-71 detachment at Mildenhall was deactivated, the 787th IAP re-equipped with new MiG-29 Fulcrum, but even after the withdrawal, we believe that at least three Foxbats remained behind at Finow-Eberswalde, just in case the “Baltic Express” returned!”
 
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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)

It is not clear from that video what angle the camera is pitched at. The clouds floating in the background post launch seem arranged vertical with regards to the viewing angle. I would not make any assumptions of launch angle from that film.
 
Ronny: When you marked part of my reply in bold you conveniently left out the part above: “And in that case that rules out solid fueled ballistic type missiles IMHO”. So you’re making a bit of a strawman argument here. I have not said that boost gliders should be excluded from the hypersonic category. Maybe they belong there. I have no opinion on that. What I have objected to was that ballistic type solid fueled rockets like the Kinzhal should be called hypersonic missiles. Nothing else.

I have long thought there should be a name for a third category of hypersonic missiles that includes aeroballistic missiles with no optimized glider that achieve hypersonic speeds at burnout but might fall out of that regime later in flight (as HGVs likely do as well, at their range limits or in their decent to a target). Hypersonic coasters (as opposed to gliders)? I don't know, but someone should coin a phrase to split out platforms like Iskander, Kinzal, SM-6 blk 1b, etc from boosters that deploy a true glide body.
 
I have long thought there should be a name for a third category of hypersonic missiles that includes aeroballistic missiles with no optimized glider that achieve hypersonic speeds at burnout but might fall out of that regime later in flight (as HGVs likely do as well, at their range limits or in their decent to a target). Hypersonic coasters (as opposed to gliders)? I don't know, but someone should coin a phrase to split out platforms like Iskander, Kinzal, SM-6 blk 1b, etc from boosters that deploy a true glide body.

For sure, there could be other appropriate naming categories as well. However, what I was objecting to was the creative way in which the Russians have tried to associate the Kinzhal with modern hypersonic cruise missiles, that's all.

It is not clear from that video what angle the camera is pitched at. The clouds floating in the background post launch seem arranged vertical with regards to the viewing angle. I would not make any assumptions of launch angle from that film.

No, but looking at those clouds it sure does look like a vertical launch which could make sense I suppose since they could then probably use much the same guidance system as for the Iskander which of course would assume it was being launched vertically. And the added effects of a higher launch altitude, an initial speed and then much less air resistance in the boost would of course add a lot of range.

So maybe I'm expecting too much of the Kinzhal guidance system in my paper, i.e. that there is some level of flexibility in the launch parameters. ;)
 
Here is a link to a collection of PPI films from SwAF GCI.

The whole video as such is well worth watching, and there are some interesting sequences showing the effects of ground returns entering the radar side lobes, jamming and chaff etc., so if you master Swedish then there is a lot of nice information in this video ;-)

But in the context of this discussion, there are tracks of both the SR-71 and Mig-31 in it:

About 27:50 into the video, the SR-71 makes its appearance close to the small circle (over the Danish island Bornholm) in the lower part of the screen and then goes up the middle of the Baltic until it makes a turn back west with the apex at around 28:00 when it begins going south and passes between Öland and Gotland on a southward course.

Interesting to note is that the low RCS of the SR-71 makes it flicker on and off on the track which is not the case with the other returns from more conventional aircraft also caught in this sequence.

The sequence with the Mig-25 begins around 29:05 and can be seen as the inverted U-track in the middle lower part of the video.
 
I have long thought there should be a name for a third category of hypersonic missiles that includes aeroballistic missiles with no optimized glider that achieve hypersonic speeds at burnout but might fall out of that regime later in flight (as HGVs likely do as well, at their range limits or in their decent to a target). Hypersonic coasters (as opposed to gliders)? I don't know, but someone should coin a phrase to split out platforms like Iskander, Kinzal, SM-6 blk 1b, etc from boosters that deploy a true glide body.
Those are usually called "Re-entry Bodies" (RBs or occasionally RBAs, Re-entry Body Assemblies) or "Re-entry Vehicles" (RVs).
 

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