Some one mentioned the Ageis missle boat...
I ask this question...how do missle cruisers defend against missle attack? Chaff, Phalanx canon, missle to missle... Which is more reliable?
"Defense in Depth" - not a choice of defending weapons. It also depends on the number and type of US ships. Typically the carrier is at the center of the battle group. If a hostile force is in the area, the carriers planes will be in "chain-saw" mode -I.e. each in turn (or pairs) flying out to near their range limit and after their dwell they return for fuel, perhaps a new pilot, and a new one arrives to take up the outter guard posts. They may be able to shoot down a cruise missle, especially subsonic ones. As soon as an attacking cruise missle breaks the any ship's radar horizon an SM will launch to fly out at it from the periferal ship (hopefully an Aegis ship) on the side the attack is coming from. In recent years, the big radar picture has been fully intergrated - not just one ship's radar data view. (This is called "cooperative engagement" - APL developed that too.)
Without this ablility a large attack could exhaust the load out of missles availible in that periferial ship. - With cooperative engagement system, some of the missles defending ships under attack may come even from a ships on the other side of the carrier and be "handed off" to ship best positioned to help them engage the target. Typically there will be 3 or 4 opportunities to knock down the incoming older (subsonic) cruise missles, such as Chinese silkworms* etc., but modern supersonic Sea-skimmers like the French Exocet are may not be detected until closer (radar horizon is closer for sea skimmer) and as going faster, may only get one engagement opportunity with the Standard Missiles. then shorter range, cheaper (and I think faster) missiles, like the Nato Sea Sparrow, will try to shoot the incoming "leaker" (leaked thru the outer defense) down. If that too fails then the CIWS (close in weapon system) takes over. The CIWS is basicall atomomous - its radar track its own out-going bullets and the incoming threat and "merges" them. I.e. thousands of bullets make a "flying wall of steel" for the cruise missle to try to fly thru. There are electronic jaming efforts, perhaps heat decoys, during this entire time as the incoming cruise missle needs its radar and or IR system to know where its target ship is. I do not think Chaff is ever used - the ships radar cross section is just too big to decoy with chaff, and its centrod is not high above the sea.
To evaluate the performance of thisw defense in depth one used Monte-Carlo analysis. I.e. the subsequent battle -every thing from which ship is guiding and which is engaging etc. changes completely with the results of the very first engagement (a kill or a leaker) Thus you fight the battle several hundred times in Monte-Carlo simulation and average the results to evaluate all your options for defense of the battle group. There are at least two subs under the carrier battle group to keep enemy subs away. Defense in depth would be impossible if cruse missles were to suddenlt pop up out of the sea a half mile from the ship. There are some slow cruise missle that do the reverse - I.e. if they can get close enough (not possible against a battle group but a sea skimmer might have slight chance against an isolated ship) they dive into the water and become a torpedo, and then no longer a radar object. Noise decoys and shallow depth charges are then used.
The USSR made a very good, VERY FAST, dangerous, enormous (size of some smaller submarines) "wake homing" torpedo. - Imho, IT WAS THE GREATEST THREAT TO THE CARRIER. I neither recall nor had real data, but think it could go faster than 60 mph under the water while closing on the stern wake of the carrier. Perhaps it could be fired from 25 miles behind the carrier, if it could get that close. The USSR made a few enormous subs that could launch one, (or two?) Fortunately, they made much more noise than US subs and could be taken out by a US sub, but if the launching sub was lying quiet on the bottom and got lucky - a Carrier crossed near by - it might have sunk a carrier. Other than that, there is no way to attack the carrier in its battle group at sea. (On a port call, that is another question - not related to cruise missiles.)
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*I believe Iran has quite a few of them, for more than 20 years, and in the narrow St. of Hormuz, they are something to worry about, especially if launched out of a cave in one of Iran's many off-shore islands. An oil tankeer would be a "sitting duck" for one and even a US warship is not entirely safe - MHO - it they got lucky.