I've been spending a bit more time than I can justify playing Silent Hunter III, a PC game that simulates WWII U-boat warfare. I'm enjoying a chance to relearn some of the trigonometry that I know, but forget I know. For example, "Ship sighted!" I'm headed due east, the target's on bearing 330 from me (ahead left), but I'm viewing them from an angle of 135 degrees on the starboard side (behind right, from their perspective). I need to get ahead of them, so what course do I command in order to run parallel to the ship while I overtake her? "Jawohl, Herr Kaleun! New course einz - null - fuenf!" Once I reach attack position, I need to be able to calculate an interception course of about 90 degrees for optimum firing position.
But you don't have to be lined up perfectly, although it's easier that way. You just have to make the torpedo travel on an angle that will intercept a moving target. What I never appreciated from watching Das Boot is that the submarine carried a sophisticated mechanical computer for aiming the computers. Remember how the commander always calls out the target's course, speed, and range? One of his crew is setting those numbers into the TDC - Torpedo Data Computer. But that's not quite enough information. We know what the target is doing now, but we haven't told the crewman whether the target is to the left, the right, dead ahead, or just where. Ah, we don't have to! The TDC knows because it has a connection to the periscope and knows which way it's turned (relative to the sub's bow). So once you've entered the target's range, course, and speed, the TDC will recalculate the firing solution as it detects the periscope's angle changing; the commander can now aim just by pointing the periscope at his target, regardless of which way his submarine is pointing. The TDC has been updating the setting of a gyroscope in the torpedo itself. Once the torpedo is launched, the gyroscope will keep the torpedo turning until it feels itself lined up with the angle the TDC wanted for it.
The fascinating part of this is that it was all done mechanically; this is years before ENIAC, let alone Commodore. For a sense of what it took to create a mechanical calculator like this, take a look at the American Mark 3 from the same era:
Pretty complicated, huh? All analog and, needless to say, highly classified. No doubt it was extremely expensive, too. This one could even track the target's movements (and compensate for the submarine's motion) in real time, which made it even more advanced than the German computer. And those poor guys in WWI had to do the same thing with a slide rule.
Speaking of which, there are some really hard core sub gamers out there who love doing things the hard way. They want to calculate the target's course manually, measure the angle to the mast to determine the range (have to know what ship you're looking at, so you know how tall the mast actually is), and use a stopwatch to determine the ship's speed. And they just love trying to recreate old targeting aids like this:
It's kind of like a WWII version of SCA - where else do you find guys eager to learn how a slide rule is used?