This is great. I enjoy playing this way as well. I have done all the math and created tracking spreadsheets in my iPad Numbers app to do similar things.
The first I have is a target tracking spreadsheet into which I feed observations on target and own sub position, and it tells me the target's course and speed. Only plotting own sub position is required.
The second spreadsheet I have calculates optimal (minimum time) intercept course for the target or any point I choose relative to the target, using only results calculated by the first spreadsheet and my chosen speed to intercept. It also tells me if an intercept is not possible at a given speed.
Using the two, you could actually intercept and sink a target in the least amount of time without ever plotting the target's position. I've never tried to intercept "blind" like that, but you could. Maybe I'll try it and record a video.
And with your equations you could also set up your firing solution.
I could try to figure out a way to share the spreadsheets, or even just the math. I could also put your equations into one of the tabs.
What would be extremely cool is to find a way to auto-plot the data entered into the first spreadsheet. I find the plotting to be tedious and it adds a fair bit of error into the solution.
Also: in a third spreadsheet I've attempted the math to solve for target's course using the "three bearing method", but with the advantage that you don't have to take the bearings at fixed time intervals which gives you the chance to be more precise and get a better solution. You do have to be stationary though, which I find is rarely practical. I'd like to do the "moving sub" version, and also add the fourth bearing to determine target position and speed as well, but I don't know the math for those yet.
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