air attack on US SAG

[CV32]

ORIGINAL: Warhorse64
From the latest version of the HCDB:
SM-2MR Block IIIB:  altitude VLow-VHigh, air range 60 nm, min range 3 nm, speed 1650 kts, air PH 70%
SM-2MR Block III:  altitude VLow-VHigh, air range 60 nm, min range 3 nm, speed 1650 kts, air PH 60%
SM-2MR Block IV:  altitude VLow-VHigh, air range 60 nm, min range 3 nm, speed 1650 kts, air PH 70%
RIM-162A ESSM:  altitude VLow-Medium, air range 30 nm, min range 0.5 nm, speed 2640 kts, air PH 65%

These figures are slowly being replaced by the more recent H4 data I mentioned above. [;)]

[Warhorse64]

Fair enough ... [:D]  We were posting simultaneously, and as soon as I finished, I saw your numbers, and thought "Oh, crud, what did I do wrong?!?" but they are as listed in HCDB-090128.

[CV32]

ORIGINAL: Warhorse64
Fair enough ... [:D]  We were posting simultaneously, and as soon as I finished, I saw your numbers, and thought "Oh, crud, what did I do wrong?!?" but they are as listed in HCDB-090128.

I figured that's what happened. No harm done. [:)] Its gonna take awhile to update the HCDB - its always a work in progress, ya know. [;)]

[VictorInThePacific]

Data on the relevant SAMs:

SM-2MR Block IIIB: min range 3.0 nm, max range 60 nm, ATA 7.0 (pH = 70), speed 1980 kt, altitude Vlow to Vhigh
SM-2MR Block IV: min range 3.0 nm, max range 81 nm, ATA 7.0 (pH = 70), speed 1980 kt, altitude Vlow to Vhigh

Based on this additional information, which increases the maximum range and speed values beyond what I was using, and seems to leave the fire per time values relatively unchanged, my initial assessment of this would be that there would be no way to saturate the Arleigh Burkes, so they would never be hit before all their SAMs were used up.

I will do a more detailed calculation later.

But I still don't understand the relationship between the rate of fire and the number of directors. Suppose there are 10 ASMs approaching. I shoot 2 each SAMs at the ASMs. That's 20, which is the ship control limit. But when the SAMs are about to impact, can only 3 be controlled?

I presume that a ship with both Standard missiles and Sea Sparrows will use the Sea Sparrows at short ranges and save the Standards for long ranges.

What is the ROF for the CV?

A comment on the hit probabilities:
With 2 SAMs targeted on one ASM, the chance of both missing is 30% x 30%, or about 10%. But if the first one hits, as I understand it, the second one gets to choose another target. So what I am going to do with this is, without any further calculation, treat the allocation of 2 SAMs per target as exactly one kill and leave it at that.

[VictorInThePacific]

The updated formation. All ship separations are 5 nm. This is good enough against nukes. A nuke hit will sink only one ship - but then so will one hit from a big ASM.

The formation is weak against subs, as discussed above, but subs are not being considered here, and the unused frigate and the deleted sub would be used in that case.

Against a surface attack from any direction, there will always be time to rotate the formation and move the flank DDs forward, or even to flee with the whole group. But any missile attack is being treated as equivalent to an air attack.

Due to the fact that an air attack can and will come in from any direction at the attacker's discretion (you divide the treasure; I choose the pile), the formation needs to be as symmetric as possible. Unfortunately, the 4 main ships all have quite different properties. But the Gridley is almost as capable as the cruiser (in terms of SAMs), so it will be placed opposite the cruiser, at the back of the formation. In terms of air defense, I almost rated the FF as a target only. Since the formation is so closely packed, all the SAMs except the RAMs can be used to protect each ship in the formation.

I'm not really sure what is the best direction from which to attack this formation. Both flanks are well defended by both of the best ships plus one of the weaker ones. Probably the best attack is from the back, but the second best ship is there. In any case, unless someone has a better suggestion, the attack is coming in from the back.

______________________________________________________________



______________________________________________________________

[VictorInThePacific]

Second version of the basic calculation.

I am using a range for the SM-2 of 60 nm, and a speed of about 2000 kn. Some of the SAMs have an 80 nm range, but I am simplifying the calculation by standardizing the ranges. These SAMs can engage targets at all altitudes. I am assuming that those ships with the Enhanced Sea Sparrows will use them as soon as they are in range instead of the Standard missiles. I am ignoring the differences in terms of speed, hit probability, and operational altitude.

I am using a speed for the attacking missiles of about 1800 kn, and a flight altitude of medium. Radar range from a ship to a medium-altitude air unit is about 100 nm, so the SAMs will engage at their maximum range. (Actually, as they are launched to intercept, they may be launched while the attacking missiles are still more than 60 nm away.)

Start by shooting at a DD.

At 1800 nm / 3600 s, the attacking missiles need 120 s to move through 60 nm. I will assume that 2 SAMs will be fired at each ASM. So the target DD would fire 20 SAMs (the control limit) to start. The first engagement happens at 60 nm. That should wipe out 10 ASMs. 20 more SAMs are launched. The second engagement happens about 31.5 nm out and 57 s later. This will wipe out 10 more ASMs. 20 more SAMs are launched. The third engagement happens 16 nm out and 31 s later. 10 more ASMs are wiped out. 20 more SAMs are launched. The fourth engagement happens 8.5 nm out and 15 s later. 10 more ASMs are wiped out. The SAMs don't get another shot, because 30 s after the fourth engagement, the ASMs are only 1 nm away from the ship.

SAMs expended: 80. ASMs shot down: 40.

As predicted above, the DD actually runs out of SAMs before it gets hit; it isn't possible to saturate its launch capacity. It looks like it IS possible to saturate the CG, which will still have 25 or so missiles when it gets sunk. So perhaps the best attack actually starts from the front!

The 4 main ships should be able to get off 80 + 80 + 70 + 60 = 290 SAMs before the guns cut in. So the attacker needs to bring over 150 missiles to do any damage. The first 150 missiles can be ARMs, nukes, decoys, dud missiles, spitballs, whatever, they won't hit. That's 50 Backfires or 75 Badgers or the equivalent.

This still needs to be revised to include the CV and a few other details.

Stay tuned.

[CV32]

ORIGINAL: VictorInThePacific
But I still don't understand the relationship between the rate of fire and the number of directors. Suppose there are 10 ASMs approaching. I shoot 2 each SAMs at the ASMs. That's 20, which is the ship control limit. But when the SAMs are about to impact, can only 3 be controlled?

The 20x SM-2 limit is related to datalink channels, needed to keep the SM-2 going in the general direction of its target (the "basket"). The director is only needed to illuminate the target with a very narrow radar beam in the final few seconds of the engagement. As well, with CEC, the directors of other ships can be used to illuminate targets for other ships' missiles.

I presume that a ship with both Standard missiles and Sea Sparrows will use the Sea Sparrows at short ranges and save the Standards for long ranges. What is the ROF for the CV?

I think that's a safe assumption. ROF for both the Mk 29 GMLS (with ESSM) and the Mk 49 RAM launcher is 15.

A comment on the hit probabilities: With 2 SAMs targeted on one ASM, the chance of both missing is 30% x 30%, or about 10%. But if the first one hits, as I understand it, the second one gets to choose another target. So what I am going to do with this is, without any further calculation, treat the allocation of 2 SAMs per target as exactly one kill and leave it at that.

It would be interesting to investigate whether there is any real advantage to shooting two missiles at each target, given their high hit probability, or whether this method should be reserved for the most difficult targets.

Which brings to me another issue: I think its important not to forget that some attacking missiles make for more difficult targets than others, i.e. supersonic vs subsonic, high altitude vs sea skimming, stealthy vs not, etc. We need to determine what the Chinese attack can bring into the mix before we dive into calculations.

[Warhorse64]

ORIGINAL: CV32
Which brings to me another issue: I think its important not to forget that some attacking missiles make for more difficult targets than others, i.e. supersonic vs subsonic, high altitude vs sea skimming, stealthy vs not, etc. We need to determine what the Chinese attack can bring into the mix before we dive into calculations.

I would definitely agree with this. As an example, in HCE I find that the later model stealthy Harpoon missiles almost always get well inside 20 nm from their targets before being engaged, even though the radar horizon for a target at VLow from a Large ship is 26 nm, and the target usually has helo and/or AWACS cover.

[VictorInThePacific]

It would be interesting to investigate whether there is any real advantage to shooting two missiles at each target, given their high hit probability, or whether this method should be reserved for the most difficult targets.

Well, Brad, you're absolutely right. You should always shoot only one SAM at a target unless you have SAMs to spare. At that point, depending on how much time you have, you should or should not double up. And this is true regardless of whether the hit probability is high or low. As long as there is no secondary targeting, doubling (or more) up on a target leads to wasted SAMs each time you get a double (or more) hit.

Considering the example of 70% hit probability, if you fire 20 SAMs at 20 different targets, you will on average hit 14 times. If you fire these 20 SAMs 2 each at 10 targets, you will on average destroy only 9 targets. I seem to recall reading somewhere that the method Harpoon actually uses is to fire 2 (usually) SAMs per target, but to reallocate SAMs within the target subgroup where there would have been a double kill. For those 10 ASMs, the 20 SAMs get a double kill about 50% of the time, and a double miss about 10% of the time. The "unused" 5 SAMs then all go for the lone surviving ASM, which has only a .24% chance of surviving the second round. That's why I have assigned exactly 10 kills to my 20 SAMs in the calculation earlier in the thread.

If there are 52 attacking missiles, and their flight time was such that the SAMs get to shoot 4 times, the optimum method would be to target 1 SAM per ASM on the first 3 rounds, killing 42 and leaving 10. Double up on the last round, killing 9. The guns can get the last one. The method used earlier in the thread would only get 40 ASMs, so the ship would wind up very dead.

However, if I am shooting AAMs at airplanes, I like to double, triple, or even quadruple up. I am certain that the pilot of the target airplane is going to do his utmost to outmaneuver the AAM. Probably he can outmaneuver one AAM, regardless of the stated hit probability. Maybe he can outmaneuver two. Can he outmaneuver 3? Four? I think it is a lot harder to outmaneuver 4 coming in all at once than sequentially. (I have no idea if this actually has an effect, but it certainly feels like it is the right approach.)

[VictorInThePacific]

Which brings to me another issue: I think its important not to forget that some attacking missiles make for more difficult targets than others, i.e. supersonic vs subsonic, high altitude vs sea skimming, stealthy vs not, etc.

So far, I have completely ignored this. I am using only the basic hit probability. I expect that there are percent modifiers, but I have no idea what those might be. I am also assuming that the ASMs are acquired early enough by the ship that the SAM is only limited by its fuel range or the ship's radar range.

I do have anecdotal evidence from Harpoon that (fast) Grumbles kill more (slow) Harpoons than early Standards kill Kitchens, so it looks like the relative speed is used by Harpoon to modify the hit probability.

[VictorInThePacific]

So far, the calculation has assumed that the ASMs come in at medium altitude at 1800 kn, and are engaged as far away as 60 nm.


What about sea skimmers?

The radar range from a ship to VL altitude is only about 25 nm. For ease of calculation, let's take the range at which the ship's radar acquires the ASM to be 20 nm. This is only 1/3 of the range used above, which means less SAMs would get launched. So a batch of sea-skimmers has a much better chance of getting through?

Not necessarily. The data I have seen shows that the sea-skimmers tend to travel much more slowly than the higher-altitude long-range cruise missiles, about 600 kn, to be precise. Thus the time of flight for these missiles is the same as in the earlier calculation. But because the SAMs still travel at the same speed, the engagements actually take place relatively further out compared to the earlier calculation. And this means that the SAMs may actually get to launch one more time, whereas in the earlier calculation, the ASMs were already within the SAM minimum range when the fifth SAM launch was ready.

What about the Sunburns that the Chinese have recently acquired? Those weapons might definitely cause a problem, so we will need to make sure that the ships that carry them don't get close enough to launch. We need to sink them at long range or run away from them, or perhaps keep in mind that China can't actually field very many of these weapons (4 x 8 ?), which is not enough to cause a real problem for this scenario.


What about an SSGN getting real close?

Well, that's definitely a problem, because it will have fast missiles, and if they are launched from 20 nm (or even 5 nm) out, they could cause a lot of damage. I'm not even going to attempt to address this one, except to say that one sub only carries about 20 missiles, and how many of these subs have got close, anyway?


What about relativistic weapons?

Max speed: 2,900km/s
(http://sinodefence.com/airforce/weapon/kh29.asp)

That's 3,000,000 m/s = 1% of the speed of light. That is going to cut through any defence system like a Swiss army knife through Swiss cheese. Hopefully the Chinese don't have too many of these. [&o]


Other Chinese weapons

I looked here:

http://sinodefence.com/weapons/missile/anti-ship.asp
http://sinodefence.com/weapons/missile/ ... urface.asp

and found nothing better than what is already being considered, except the YJ-91 ARM, which is listed as traveling at about 3,000 kn. This is MUCH faster than the previously considered weapons, and accordingly much more dangerous. However, Wikipedia gives the speed of this weapon as about 2,000 kn (http://en.wikipedia.org/wiki/YJ-91), and Jane's (http://www.janes.com/extracts/extract/j ... sa010.html) gives its speed as even less than the 1800 kn I have used above. Which figure is correct? In any case, it doesn't matter. The only thing that matters is what is available in Harpoon, because that is what we are talking about here.

Unfortunately, I cannot access the game anymore, so someone else will have to provide the data. Does the Chinese arsenal include any ASM that travels faster than 1800 kn?

[VictorInThePacific]

As an example, in HCE I find that the later model stealthy Harpoon missiles almost always get well inside 20 nm from their targets before being engaged, even though the radar horizon for a target at VLow from a Large ship is 26 nm, and the target usually has helo and/or AWACS cover.

I cannot say for sure, because the uncertainties may be quite large, but this may have a very simple explanation.

If we take the speed of the sea-skimmer to be 600 kn (an approximate figure purely from my memory), then this missile travels 10 nm per min, or 5 nm per 30 s detection chance, so if you miss the first detection, the missile is already at 20 nm before you get another chance.

[Warhorse64]

Sea skimmers: The PRC hangs 4 C803s on a Badger, they do about 1000 knots and are sea skimmers. And there's always the possibility they'll turn up with something really nasty from the Russian arsenal, like the AS-22/Kh-41 Moskit, a 1650-knot sea skimmer ... [X(]

[CV32]

ORIGINAL: VictorInThePacific
Max speed: 2,900km/s
(http://sinodefence.com/airforce/weapon/kh29.asp)
That's 3,000,000 m/s = 1% of the speed of light. That is going to cut through any defence system like a Swiss army knife through Swiss cheese. Hopefully the Chinese don't have too many of these.

Hehe, pretty sure thats a nasty typo, VitP. [:D] The Kh-29 is a short ranged weapon (about 7.6 nm with the longest ranged variant), and Harpoon assigns a speed of 791 kt.

[VictorInThePacific]

ORIGINAL: Warhorse64

Sea skimmers: The PRC hangs 4 C803s on a Badger, they do about 1000 knots and are sea skimmers. And there's always the possibility they'll turn up with something really nasty from the Russian arsenal, like the AS-22/Kh-41 Moskit, a 1650-knot sea skimmer ... [X(]

The C-803 would be significantly more powerful than what I have already considered. Off the top of my head, it would degrade the defenses by one batch of SAMs. However, I understand that this missile only goes to Mach 1.6 during its "attack phase". It becomes critical to know exactly what that means, because the main thing we need to know is how long does the ASM spend within range of the SAMs.

I have mentioned the Sunburn above and feel that it is not much of a problem.

[Warhorse64]

Fast PRC ASMs:

On the JH-7A, 2 * Kh-31A Krypton, range 27.5 nm, speed 1940 kts.
On the Su-30MK2, 4 * Kh-31P Krypton ARM, range 55 nm, speed 1940 kts, or 4 * Kh-31A.
On the H-6M, 4 * C803 (YJ-83), range 135 nm, speed 990 kts.

There are a number of other PRC aircraft with ASM loadouts, but the missiles are all subsonic.

[VictorInThePacific]

Fast PRC ASMs:

On the JH-7A, 2 * Kh-31A Krypton, range 27.5 nm, speed 1940 kts.
On the Su-30MK2, 4 * Kh-31P Krypton ARM, range 55 nm, speed 1940 kts, or 4 * Kh-31A.
On the H-6M, 4 * C803 (YJ-83), range 135 nm, speed 990 kts.

There are a number of other PRC aircraft with ASM loadouts, but the missiles are all subsonic.

Thanks, Warhorse, for providing this information.

Regarding the Kh-31P: This missile is slightly faster than what I have been considering. However, the speed difference (10%) is small enough so that the SAMs will still get off 4 shots, so there will be no effect on the 1-ship calculation.

Regarding the Kh-31A: The problem with this missile is getting a live plane to launch range. I will be discussing this in an upcoming post. People should be able to guess what the technique will be.

Regarding the YJ-83: I have somewhat different data. Everybody knows that Wikipedia is the only source of true data in the world and this is what they say about that missile:

"Speed: subsonic for most of the flight, Mach 1.3 @ 30 km away from target, Mach 1.7 @ 20 km away from target, Mach 2 @ 8 km away from target"

(http://en.wikipedia.org/wiki/C-803)

Most of the information I have seen on this missile is similar to the above.

In knots, that's 600 kn out to 16 nm, 880 kn until 11 nm, 1100 kn out to 4.5 nm, and then 1300 kn.

This variable speed will give me a headache. Still, I will recalculate based on these figures. It will be the 25-3 nm range that matters.

I will also work out what the CV can do, and then what the group as a whole can do, although most likely, it will be necessary for the attacker to strike at all the ships simultaneously, which means they don't get to help each other.

[CV32]

A lot of numbers are being tossed around, guys, but I'm going to suggest that you determine an example Chinese strike package(s) firstly. Otherwise, this thread is going to become pretty "frayed". [;)] Its already showing signs of that.

[VictorInThePacific]

an example Chinese strike package(s)

I think we're just about there.

Warhorse provided the following values. At this point I accept this data as is, with one possible exception (explanation below.) But these aren't just numbers. They represent the best weapons in the Chinese arsenal.

Fast PRC ASMs:

On the JH-7A, 2 * Kh-31A Krypton, range 27.5 nm, speed 1940 kts.
On the Su-30MK2, 4 * Kh-31P Krypton ARM, range 55 nm, speed 1940 kts, or 4 * Kh-31A.
On the H-6M, 4 * C803 (YJ-83), range 135 nm, speed 990 kts.

There are a number of other PRC aircraft with ASM loadouts, but the missiles are all subsonic.

So far, I haven't concerned myself with how these weapons will be delivered, and that will require some discussion. However, Warhorse has also provided the platforms.

The calculation I have done most recently (I called it "version 2") was based on the Russian high-speed long-range cruise missile. It looks like, when the Chinese got the Badger, they didn't get this missile.

Let's rule out the JH-7A. It is significantly inferior to the other 2.

Proposed strike package:

25 x Su-30MK2, each with 4 * Kh-31P Krypton ARM.
25 x H-6M, each with 4 * C803 (YJ-83).

Both of the proposed missiles are slightly or significantly better than what I have so far considered, so throwing in what the CV can do as well, I am suggesting that this strike package will strip the US fleet of anti-air weapons and leave it vulnerable to a follow-up attack with cheapo bombs.

Warhorse, do you have any data on warhead-less weapons (decoys) in the Chinese arsenal?

__________________________________________________________

Detailed calculation with the YJ-83.

People who don't like numbers can omit this section, but not the conclusion.

Take the point of first engagement to be 20 nm out. The radar horizon is about 25 nm from a ship, but we may need to allow some time for the ship radar to acquire the ASM.

Using the figure of 600 kn (constant), it takes 120 s to travel 20 nm. This is what I was using before, for a subsonic sea-skimmer, which gave the SAMs 4 shots, and almost 5.

The crucial question is whether the SAMs get the 4th shot against this faster ASM. It really comes down to a matter of seconds.

a) My numbers:

600 kn out to 16 nm, 880 kn until 11 nm, 1100 kn out to 4.5 nm, and then 1300 kn.

To go from 20 to 16 nm takes about 25 s.
To go from 16 to 11 nm takes about 20 s.
To go from 11 to 4.5 nm takes about 21 s.
To go from 4.5 to 16 nm takes about 12 s.

Total time = 78 s

The SAMs need 36 s to travel 20 nm. But they don't have to travel quite that far, because the ASMs are coming in. 30 s after the first engagement, the SAMs have travelled 16.7 nm, but the ASMs have travelled more than 4 nm. Therefore the next batch of SAMs is limited not by when the engagement occurs, but rather by the launcher cycle time. This is also true for the following batches. Therefore SAM batches 2, 3, and 4 are launched when there are 78, 48, and 18 s left on the clock. SAM batch 4 does get launched. To travel the 3 nm (minimum range limit) takes 5.5 s, at which point the ASMs are still 12.5 s out, which is more than 4.5 nm. So the 4th batch of SAMs not only gets launched, it will be active.

b) Using Warhorse's figure of 990 kn (constant), it takes 73 s to travel 20 nm.

30 s after the first engagement, the SAMs have travelled 16.7 nm, but the ASMs have travelled more than 8 nm. Therefore the next batch of SAMs is limited not by when the engagement occurs, but rather by the launcher cycle time. This is also true for the following batches. Therefore SAM batches 2, 3, and 4 are launched when there are 73, 43, and 13 s left on the clock. SAM batch 4 does get launched. To travel the 3 nm (minimum range limit) takes 5.5 s, at which point the ASMs are still 7.5 s out, which is only 2 nm. So the 4th batch of SAMs may not be active.

Conclusion:

There is a huge difference here. In the first case, 4 batches of SAMs get launched. In the second case, 3 batches of SAMs get launched. Which model is correct? And actually, a whole bunch of assumptions and modelling will need to be reconsidered.

[&:] [&:] [&:] [&:] [&:] [&:] [&:] [&:] [&:] [&:]

[CV32]

ORIGINAL: VictorInThePacific
People who don't like numbers can omit this section.

This whole analysis is pretty much about the numbers, isn't it? [&:] But, in any event, carry on. [8D]