Welcome to Subsim!
Five approaches come to mind, four of which I've done myself:
A. When you get a range and bearing (by periscope, radar, magic 8-ball, whatever), go to the map screen and pause the game. Plot the range and bearing from your boat (keep in mind, reported bearings are relative, so you'll need to convert to absolute) and make a mark on the map. Use the in-game stopwatch for timing, since it will pause when you pause. Eventually, you'll have a plot of the target that you can use to get your information.
When I've used this method, I've kept a log of Mark, Time, Bearing, Range, and a running calculation of his distance traveled, speed, course, and AoB as well as my own course and speed for reference. Bonus, no special tools needed.
(Pausing may feel like cheating, but a real skipper had a whole party for tracking a contact.)
2. Use a maneuvering board. Since all marks are relative to your boat at the center, you can keep a log of contact time, bearing, and range (in fact, the maneuvering board has spaces for these notes on it) and plot these on the board as you have time.
Downside: Special tools, such as parallel ruler and dividers/compass become
very useful, as well as learning how to use the board.
- Slide rule- There's a method (here) where using two bearing/range fixes and a known time interval between them, you can figure out speed and AoB using a slide rule with a sine scale.
Downside: Some effort is needed, but otherwise, none. Everyone owns a sliderule, right? (A Submarine Attack Course Finder is rather simple to construct, completely authentic, and a very useful tool for figuring certain problems. It also happens to be a slide rule with a sine scale. In fact, you should make one anyway, since it's so useful, and so damn awesome to hold in your hands the exact same tool that was in use during the war.)
IV. Estimate/Guess/Eyeball. This is probably the single most common method used during the war. Dick O'Kane was known for his ability to determine AoB to within a degree by looking at a target. (Not so good at estimating tonnage, but that's a different story.) Practice and experience as well as knowing what to look for are key to making this work.
Downside: Practice and experience as well as knowing what to look for are key to making this work.
> Draw your own plot. This one I haven't done. Get a large sheet of paper. Figure out a distance scale to use. Draw your location on the paper, and draw the target location each time you get a fix. You'll need to keep an eye on your own speed and course, so that you can update your location each time you update the plot.
Downsides: Swapping between the computer and a table to draw the plot. Finding large sheets of paper. Convincing a friend to act as the tracking party and stand there while you call out numbers for him to plot and report back to you.