To be honest, I mostly added the "armour" as an afterthought, because that's part of what battleships are known for. The main idea was a large gun platform with strong defenses. With enough laser AA, it could become extremely expensive to launch enough missiles to score a hit. And yes, it would probably have escorts; I'm not proposing a standalone do-everything weapon system here...
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On the other hand, we still build tanks. And supercarriers have deck armour (admittedly this probably has something to do with protection from flight-deck accidents) and torpedo defences. One strike won't bring down a warship that size unless it's a
really hard strike; even smaller ships without heavy armour have survived anti-ship missile strikes...
Then the inability to field practical armor against current weapons comes into play.
I'm not convinced of this. I was under the impression that it was mainly
nuclear weapons armour was deemed ineffective against. Certainly the 5" guns on a modern destroyer wouldn't scratch the paint on an Iowa-class BB; even a large missile wouldn't do it unless it were specially designed to penetrate heavy armour... Basically, armour means you have to dedicate expensive resources to penetrating it; it makes on-the-cheap asymmetric warfare solutions (see USS Cole) or even light conventional military weapons much less useful. No armoured platform is capable of withstanding its own firepower, yet we still make them...
Tank armour has gotten pretty sophisticated since WWII. Perhaps some of those techniques could be useful, at least against some types of missiles...? (Though HEAT-type shaped charges would seem to be much less useful against ships than against tanks.) And if you want to get fancy and expensive, our command of carbon allotropes is starting to get interesting...
Also, you're assuming the enemy has railguns and lasers too... which, considering the rate at which the Chinese seem to be stealing American stuff, may not be all that unreasonable...
A single enemy railgun mounted on a fast platform
Nitpick: If I recall correctly, supercarriers are actually the fastest ships in their battle groups, due to the availability of nuclear power. I don't know about maneuverability, but barring "a Polywell in every frigate" (to paraphrase the 1928 Hoover campaign), a ship large enough to pack reactors should be able to outrun (not necessarily outmaneuver) one that isn't. Especially if the smaller one is trying to charge a railgun at the same time...
A large vessel designed for durability, and without explosive magazines, should (I think) be fairly survivable against individual railgun rounds, even if they do penetrate the armour, simply due to its size. A smaller ship, with a much lower rate of fire and probably weapon caliber, should always lose such an engagement.
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I wonder if a megawatt-class laser could plausibly be used to target incoming railgun rounds... Completely vapourizing a 3.2 kg chunk of copper seems to take about 20 MJ, which means a very large FEL or an unavailably large dwell time (aluminium is about 15 MJ, tungsten 5, DU 2.5)... could a lower-energy pulse laser blow it apart and/or slow it down? Or is it still impractical for the foreseeable future (as I suspect) to reliably target an object that small and fast even with a laser?
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I love how Wiki lists the MXY-7 Ohka as an anti-ship missile...