The towed array is a linear stream of hydrophones. The resulting beam patterns are a 360 degree circle with an angular width oriented with the circle perpindicular and centered on the array line. The only angle that can be measured or calculated from these beams is the relative angle the contact's sound makes with the line of the array. If you imagine a contact 30 degrees off your starboard bow or 30 degrees off you port bow, it is in the same circular beam (30 degrees from the leading tip of the array line). Making a turn does not necessarily cause you to lose a given contact but bends the array which makes the bearings inaccurate since the beam pattern is now unknown. Later arrays have gyroscopic sensors which measure array curvature and permit tracking contacts with only modest degradation in bearing information during turns.
Determining which side of the array a contact is on is fairly simple: make a course change.
For example, if you have a contact 30 degrees off of your bow, it will appear at both 330 degrees and 30 degrees relative to your bow. If you make a 20 degree course change to the starboard and the contact is on the starboard side, the relative angle should decrease to 10 degrees and now appear at 350 degrees and 10 degrees relative. If on the other hand the contact is on the port side, the final bearing after the course change will be 50 degrees off of the bow (310 degrees and 50 degrees). Waiting for the array to stabilize takes too long, so the moment you see which direction the contact is moving (up or down the array) you will know which side it is on.
To make the rule of thumb as short as possible: the contact moves up the array after a turn toward it and down the array after a turn away from it. So if you turn to the starboard and the contact moves toward your bow, he is on the starboard side. Whereas if you turn to the starboard and the contact moves toward your stern, he is on the port side.
During my tenure as a submarine sonar tech, it was standard procedure to gain a contact with both towed array trackers to build up fire control data for both until the correct side could be established. Modern systems can use the natural wiggle caused by waterflow to automatically resolve the towed array's ambiguous bearing problem without making a course change.
One further complication is the bearing rate of the contact. If the contact's bearing is changing too fast, the relative motion may confuse which way the bearing changed during/after a course change. Of course anything moving that fast should either be close or loud and therefore be visible on the spherical array anyway.
It is scary how close 688(I) and Sub Command are to what I really did for a living. I hope you appreciate the effort that has been put into these games.
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