I'm not entirely happy with the intercept image, but since I made it at 5am I won't worry too much about it, but here's how I intercepted a convoy last night. This is with map contacts off, so no ghost to follow for me.
Here you see the first contact report, at 05:26 about a large convoy 614km away, moving towards me at 13kts. What you don't see is that at the time I started this plot it was already 05:45, so I should have taken that into account.
Next comes the big messy picture!
Step 1: I use the protractor to draw from my u-boat to the contact, then out along it's path of travel. When I did this, I made three mistakes. First was waiting so long to start it, second was not bringing the line out far enough and third was not getting the angle of travel perfect.
Step 2: I draw a line from the contact out along it's direction of travel according to it's speed. Since it's traveling at 13kts and was 600km+ away, I picked a multiplier of 20, meaning the line I drew was 260 (13 x 20) km long. If we were closer I might have picked a multiplier of .5 or 2 or something to plot a line 6.5 or 26km long, depending.
Step 3: I use the compass to draw a circle from the end point of the line I drew in step 2 which is equal to my speed (13.6) times the multiplier I used before, which would be a circle with a radius of 272 km.
Step 4: I find the point where the circle crosses the original bearing to the contact, the first protractor line I drew. I measure the angle from the end point of step 2 to the meeting point of bearing and circle then towards the contact. In this case you can kinda see it's 32 degrees.
Step 5: I now take that 32 degrees angle and measuring from the line towards the contact, to my u-boat, then towards the path of travel of the contact and draw out the 32 angle line till it crosses the travel line. This is where I made another mistake, since the original protractor I hadn't drawn out long enough, so I had to use a ruler to make it longer. That's the extra 170km line there.
Step 6: The point where the step 5 angle and the step 2 course lines meet is where I'll intercept. I'll place my waypoint at that point and head towards it at my current speed. It's Mark 1 in that image.
So now I'm chugging along towards the intercept point. I draw a 30km circle around the point to represent basically the hydrophone range around the spot where I should be able to hear the convoy.
What's this!? At 17:28 I get a hydrophone contact from my sonarman saying he hears something coming from the general direction of where the convoy should be. But as you can see I'm still some 80km or so away from the intercept point!
In order to cheat a little I draw out a 50 degree angle from the front of my boat to the left (360 - 310 contact bearing = 50 degrees port) and send my external camera to see what's there.
And there it is! The beautiful, battleship escorted giant convoy! Turns out it was only traveling at 9kts by the time I reached it (which is why I met it ahead and past it rather than right on) and also changed course a bit too I think. It's changes like that which can cause you to miss convoys a lot, especially at ranges of 600km+ like this one was.
So, took me 12 hours or so to intercept it, and I almost missed it, but I got close enough to be able to intercept and sink 4 ships from it!