Yet, so many sources, to include your wiki article, say different. There's another application for this as well. Avoiding a mid air collision. If you're flying into a traffic pattern especially, were there's a high traffic density, you look out for other aircraft entering from a different point. If you spot one and realize it's not moving for or aft, constant relative bearing, then you know that if neither you nor he change course you will hit. The same works out for ships at sea. Constant Bearing Decreasing Range. Neither a small aircraft nor a small boat will have radar providing range info.
This works out in reverse as well. If you see another aircraft and then maneuver yours to hold the other guy at a constant relative bearing, you will collide. Both of you flying a straight line after the constant bearing has been set. With noone having range info. Neither the aviator nor a missile AI know or need to know a value for place or time of a future collision point. As long as one keeps the other on a constant relative bearing, their paths will intersect. For non-maneuvering objects, that means a straight line for both of them.
Conflict Detection
Using a line of constant bearing between converging traffic is one of the simplest tools available to a radar controller to detect potential collisions between aircraft.
The “Blossom Effect”
Motion is invaluable in drawing the eye’s attention. Yet two aircraft on a collision course will appear virtually motionless to each other, or maintain a constant relative bearing (CRB). When observed from the cockpit, the conflicting target will look like a small, stationary speck until it is at a distance from which it may be too close to react to, when it suddenly appears to grow much larger, a phenomenon called the “blossom effect.” If a pilot sees an aircraft that remains in the same spot in the windshield (unless it is directly ahead and moving in the same direction), there is a high probability the two aircraft will collide unless one changes course. Once a threat has been identified, it’s essential to keep the other aircraft in sight until the threat is resolved. That may require turning toward the target to maintain visual contact.
If you see an airplane, first determine whether it is moving in your field of vision. An airplane that has no relative motion is an airplane that you stand a chance of hitting. The old nautical saying that applies here is "a steady bearing off the bow": if it isn't moving right or left in your field of vision, your paths are going to converge. It may be approaching you, or you may be overtaking it -- and yes, you can overtake other aircraft, even if you're flying a common training aircraft like a Piper Cherokee or Cessna 172.
Further visualized in the two images below:
Img 1 shows objects A and B moving at the same speed. At the same point in time the angle from A to B is always constant at 12.5° while range changes.
Img 2 shows A moving at 1,5 times the speed of B. With the angle between the two remaining at 23.25° through a constantly decreasing range, they will meet at the same point in time and space.
They have no other chance actually. The triangles that form in every timeframe are similar to each other and will form the next one by simply scaling up or down.
If you don't believe these publications, go to a flight school and ask any instructor. If that's not enough take up flight lessons and try it out. It actually and really does work in real live.
I'm wondering if you have "homing" in mind when you make your statments perhaps? The wiki article erroneously describes PN as a guidance law used in some form or another by most homing air target missiles. Homing and PN are two distinct methods of navigation / guidance.
Homing has the missile aim for the targeted objects at all time and simply chase it. That is an older and rather ineffective way, since it'll indeed force the interceptor into a constant maneuver even when going after a non-maneuvering target.
The whole point of PN is to have the interceptor act smarter and aim in front of the target.
A threat going very fast from left to right isn't an issue, since lateral movement won't bring it closer to the ship. Eventually, when finally going to attack a ship within a group, the AShM will have to go towards that ship. That inevitably decreases the rate of lateral movement.
For objects 3m above the surface earth-curvature becomes an issue at just beyond 12km, so any CIWS should be fine.
The center intercept, displaying the non-efficient homing geometry is ment to display a miss indeed. However, I don't see the issue with the bottom (PN) one, that actually takes place at the same range and from the explanation takes maybe 6-7 seconds to complete. For the Sidewinder rocket motor I can find figures of between 2.2 and 5 seconds burn time. Meaning there's enough time for the missile to acelerate to max speed before the intercept.
Going from 0 to M2.5 in 5sec requires an average acceleration of 17,5g, meaning a linear acceleration will take place in 2150m. In realitly, with acceleration being slower at higher speeds it'll be longer. But not by that much.
maybe you know all what's inside ...)
