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Turn rate of a CIWS varies from 50 to 115 degrees per second.

The F-22 can sustain over 30 degrees per second. The exact value, and the instantaneous value, are both classified.

That isn't way off. Limits are in place to prevent pilot blackout, but since we're discussing an AI pilot here, the limits could be removed.

But how many rounds are usually expended per missile intercept?

How many rounds does an aircraft carry?

Can CIWS intercept a Mach 3 missile while on an aircraft flying above Mach 1 (a relative speed of Mach 4+)?

Is it a good tactic to point your aircraft nose at an incoming missile?

Why hasn't this been done already?