Lurker piping up here-
I've tried this once or twice, with not much luck, forgot to imput the bearings into the TDC.
I started off with a long-range visual contact, so I knew the basic position and course of the target, and the layout of the convoy. I picked out the light cruiser in the middle to track, because it was easier to isolate her screws from the others. Every three minutes, I would find the bearing from passive sonar and use it to draw a line from my sub's current position. After several measurements, I had several lines radiating out from my slowly moving sub.
Assuming that the target is moving at a constant speed and course, the target's course should intersect those radiating bearings at constant intervals, i.e. the distance from bearing 1 to bearing 2 is the same as the distance from bearing 2 to bearing 3. So I just eyeballed a line running across the bearings that seemed to match pretty well, and then used the compass to double-check and adjust the line.
Now that I had the course figured out, a new bearing reading would give me the distance and AOB, and measuring how far the target traveled over those 3-minute intervals would give me the speed.
After that, you just have to work as a sort of manual TDC, taking more bearings at finer time intervals to make sure all your numbers make sense, and that the target isn't doing anything unusual. Even then, a quick check with the periscope right before firing is necessary to get a precise fix.
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