Your chart is remarkably similar to what I've got down in my notebook. I just sat down and tested everything. First I ran through your example numbers and got the same result as you (good!). I'm documenting everthing here in the hopes that another reader finds it useful... Starvingartist, you already -know- all this stuff but feel free to critique.
I realized I must be the only person who can't figure out how to switch SH4 from metric to imperial measurement... although I'm entirely used comfortable with metric (SI technically), despite being born in the United States.
Anyway, a quick lookup of meters/second to knots yields a conversion factor of 1.94384. That really helps in setting speed for your torps, using my math
Then I loaded up Ol' Faithful - the third sub school exercise, where you start with a not-quite perpendicular cruiser in the exact same place every time. I've trained with this scenario so much I know what the ranges, speed, and angles are, along with the proper torpedo settings. I use manual targeting but have map contacts on, so I can resort to the map for a quick range check / AoB check. This allows me to verify my solutions.
My previous method of calculating speed involved an observation period of 3 minutes 15 seconds, so I was very drawn to this method as it allows any two bearing/range checks to suffice - the further apart the better as it allows finer resolution. I immediately got range/bearing information, waited 1 minute 40 seconds (which works out to 100 seconds, making the math later a little easy... not neccessary but helpful) and took my second range/bearing information.
Relevent data (pretend it's in a sketched out table):
Range, Bearing, Time
1500 meters, 322 deg, 0 seconds
1200 meters, 337 deg, 100 seconds
Also sketched out is what I am going to call the triangle of torpedo love... see the above posts for starvingartists's images of the ABC triangle... I'm sure there's a technical name, so pardon me. Each side has the relevant data filled in, and the direction of travel is indicated just to make sure I don't forget. It helps to remember that the sub is at angle C, and if you view the triangle from that perspective (flip it upside down mentally or on paper), it becomes very clear which measurements are which.
I won't illustrate my math here, mostly because I can't represent exponents properly, but I ended up with the target's net distance travelled of 461 meters, at a net speed of 4.6 meters per second, or 8.964 knots, basically 9 knots... the speed I'd been using all along in this scenario. Yay! Angle on bow was calculating using the above formulas and resulted in 42 degrees, updated to 57 degrees at the time of second observation. This was exactly accurate according to the map (well, depending on where the line is drawn to your ship - it was perfect for my forward torpedo tubes.)
Torpedo solution was similar to every other solution I have used in that scenario... 3 torpedoes fired, 1 premature detonation, 2 hits, slightly aft of where I had been aiming. I did not enable the position keeper quickly enough, so the range solution was slightly too long, resulting in my torps hitting slightly aft - at least, that's what I believe happened. Overall, I was impressed with the accuracy. It took me a lot longer to calculate this by hand than is acceptable in a submarine environment, but the game has a pause key for a reason! I imagine I will get a lot faster with practice. Right now every step was written out so I could verify I didn't make any stupid math mistakes - a classic problem when I was in college
I'm going to start using this out on patrols now
