Surface-to-Air
Arleigh Burke IIA vs. YJ-18A
Knowing number of attacks we can perform, let's now calculate chance of each of them shooting down a missile. For this we will use Surface-to-Air Attack flowchart.
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Probability of kill (Pk) for each missile type is different, but the difference between ESSM and SM2MR is very slight, so we will calculate Pk for ESSM first and then modify it for SM2MR.
First we put defending SAM's ATA (air-to-air) rating, taken from the weapons annex. This is rating that describes how well missile can intercept air targets - the higher the better.
ESSM's ATA is 4.0. We write it into Missile ATA Rtng box.
Next we add the Combat System Modifier. Better the platform's systems guiding missiles to their targets the better, obviously. This modifier uses different column, depending on target being aircraft or missile.
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For our situation we cross reference Missile Tgt ATA Mod column and 5/6A row (for 6th Gen Auto system), for a modifier of 1.5.
Going forward, we punch in target's Man Rtng (Maneuver Rating). It's pretty much the same thing as ATA rating, only describing how good airborne target can evade the attack.
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ASCMs don't really have Man Rtng values, it's more thing for the aircraft. Non-maneuvering targets, like ASCMs or straight flying aircraft, have Man Rtng value of 0.0 automatically. It is built into flowchart as shown below. Moving along the arrow we go through target evading - NO route to 0.0 Man Rtng.
Normally we would check Antiair Missile Countermeasures effects against the attacking SAM, but since ASCMs don't have jammers and decoys, we just put 0.0 into the next box. I followed arrow properly on the example just for formality.
Another modifier is what is called bearing rate. If target is coming at shooter directly, the apparent movement of it on the horizon will be minimal, no matter how fast it goes. The more the target is parallel to the shooter, the faster it will move along the horizon. The speed at which the target is moving "along the horizon" is what is called bearing rate. If target is going directly at you or away from you, hitting it is easier - you just go at it. Intercepting targets at higher bearing rates is tougher, as you need to perform more complex interception trajectories and lose more energy pursuing it.
Since Roosevelt is the target of the attack, the YJ-18As are coming directly at it and have bearing rate of more or less 0 degrees. So we write another modifier of 0 into the proper box.
The farther away target is the harder it is to hit, obviously. Because each range band is checked and resolved separately, this modifier need to be checked in each band and final hit chance for each band modified accordingly.
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But, because YJ-18A will first be intercepted in Medium 1 range band, and all range bands below it have modifier of 0, we can use this flowchart for every attack we perform, without creating other calculation variants because of range.
Smaller the target, harder it is to hit. Enough said, I think. YJ-18A size is Very Small (VSmall - taken from annex), yielding -1.0 modifier.
Faster the target, harder it is to hit. Rather self explanatory. For YJ-18A though, the modifier is complicated a little. As mentioned previously, YJ-18A has sprint vehicle, that detaches 10.8 nm from the target and accelerate the warhead to mach 3.0. This means that we will have two different modifiers, depending on the ASCM's portion of the movement. Which engagements are affected by it, we'll discuss later.
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Most of the trip YJ-18A is traveling at cruising speed of 528 kts. This gives Transonic modifier of 0.0. Final sprint is made at 1980 kts - Medium Supersonic - modifier of -2.0. All speeds are taken from weapon annex.
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Here I wrote sprint modifier above transonic modifier for example purposes, but normally I probably would just add it mentally at the end when I need it. Also, you probably won't have this situation often, as it is one of only two ASCMs that has this capability.
Last thing we check is if the target is sea-skimming. Our obviously is, as it is sea-skimming cruise missile. If you are not sure - every target that is moving in Very Low (VLow) altitude band is a sea-skimming target.
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Following YES arrow, we check if our system is sea-skimming capable. Targets traveling close to the sea waves can be hard to distinguish from them, and weapon system need to be designed to deal with this fact.
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Both ESSM's and SM2MR's attack envelopes start at VLow altitude band (checked in the weapons annex), which means they are fully capable of engaging sea-skimming targets, so modifier is 0.0.
Now that we have all the modifiers present, we can calculate final chance of a kill. Adding all of them, we get the final ATA value (Missile Index) of 4.5 for cruise portion and 2.5 for sprint part.
Looking at the Antiair Missile Attack table for 4.5 index, we get 75% chance of a kill with one missile salvo (One Msl), and 94% chance with two missile salvo (Two Msl). This are 55% and 80% for index of 2.5 (sprint part). If you happen to have target engaged by more then two missiles at the same time, you need to break down your attacks into one and two missile salvos.
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This are kill chances for ESSM, which has ATA rating of 4.0. SM2MR's ATA rating is 3.5, just 0.5 lower then ESSM's. Fortunately for us we don't need to create whole new flowchart for SM2MR, since all modifiers are exactly the same as for ESSM. So all we need to do, is to check kill chances one row higher then ESSM's. This gives us 70% and 91%, for one and two missile salvos respectively, for cruise speed, and 50% and 75% for sprint speed.
Getting back to our engagements. We can now calculate number of YJ-18A that can be taken down by Roosevelt, if we assume most deadly, Macross like salvos of missiles against infinite number of targets (all fractions are rounded to the nearest whole number).
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Now we need to address when to use "sprint" hit chances. Since YJ-18A launches sprint vehicle 10.8 nm away from the target and short range band has 15 nm, 2/3 of short and all point band engagements will be performed against sprint vehicle. So 2nd Short and Point band engagements use mach 3.0 speed as modifier.
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M (Medium): 12 ESSM attacks x 94% = 11 kills
S (Short) 1st: (4 ESSM attacks x 94% = 4 kills) + (8 SM2MR attacks x 91% = 7 kills) = 11 kills
S (Short) 2nd: 12 SM2MR attacks x 75% = 9 kills
P (Point): 9 SM2MR attacks x 75% = 7 kills
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Total number of presumed kills: 38
Of course during normal game you roll D100 for each attack, but this is good estimate, if your dice are not totally crooked. So if Chinese want to go through, they need to launch at least around 40 missiles. But that's not the end. Everything that gets through area defense, need to contend with point defense guns. We will calculate them next.