[TorpX]

I'm sure it will work within the constraints I mentioned. It was taught in the US Navy, and Dick O'Kane describes it in his book, CLEAR THE BRIDGE.

As far as being "longest way to intercept", that could be, but consider, intercepting at max. speed, intercepting at min. speed, and intercepting at X speed, are different options.

Let's say that after putting him on your starboard beam (90 deg. relative), you and him are now on similar courses.

This isn't really the case. The NAC is 90 deg. off the bearing, the target's course could be almost anything, nor do we need to know what it is.

This diagram shows what the NAC is:

The target track(s) is red, the sub is blue, the bearing line is green.

The bearing line is moving in the direction of the green arrow, so we set the course indicated by the blue line. Let's say the target track is the red line A. The NAC allows an intercept with a minimum speed. Another course with a shorter path may allow an intercept, but would require a greater speed.

If the target is on course B, we are farther off the target track, and must move faster to intercept. If the target is on course C, it is the opposite. We are closer to the track, and can intercept with less speed. In every case, the NAC gives us the best chance for an interception (that is with the least speed).

Note, that it is possible that we start on a NAC, at our best speed, and still loose bearing. This means an interception is not possible.

By monitoring the bearing of the target as time progresses, we will know if we can intercept or not. Gaining bearing means we would reach the point, where our tracks cross, ahead of the target. Loosing bearing means we would reach that point behind the target.

If you knew the target's course and speed, it would make sense to calculate a specific intercept course, but lacking such data, a NAC gives you the best chance to prevent the target getting by.