Just to second ridyard's last post: when you update the bearing and range in the tdc, the tdc just rotates the given AoB and speed to the new bearing and moves it in or out to the new range. So, you always need to adjust the AoB after updating the bearing, unless the actual bearing and predicted bearing from the tdc are the same.
Another thing I did to figure this stuff out was to just play around with the tdc and see how it works. For example, on the surface, dead in the water, just point the periscope dead ahead, and send the bearing and range to the tdc (no target, just point at empty sea). then enter in a random speed, like 5 knots, and an AoB like S90. Then start the PK and watch the target's predicted position move on the tdc and the attack map. Then change something and see what it does. For example, turn the periscope 90 degrees and send the bearing/range to tdc again, and you'll see that the target's course on the attack map will be changed 90 degrees from what it was before. WernerSobe's videos are good to watch too.
As far as calculating speed, I think SeaQueen's method, which is like the old speed button in SH3, is cool. I usually use the nav map - every 2 minutes or something, plot lines of bearing and put a mark at the range. then extend the line of bearing a bit and leave them there. that way if your ranges are off, you'll be able to see the fan of bearing lines and estimate a good course that goes between all the range marks and cuts the bearing lines in equal intervals. This is just like using speed strips in TMA, such as in DW. Works well if you've got time and in bad weather if you can't get good ranges.
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