Convoy Interception Methods

[Rockin Robbins]

And I'll second the motion on evaluating, pulling out, leaving the escorts searching one side of the convoy while you do an end around to the other side. Actually, with a heavily guarded TMO convoy, that is sometimes the only way that works.

After awhile your spider senses just say, "This isn't working out just right. Time to scram." It's best to listen carefully to that small voice. It can pay off bigtime on the other side of the convoy!

[Frederf]

Anyone here decent at trig? I'm actually trying to make that manual lead table value but I keep coming up sour mathematically. The setup is pretty simple, three dots on a page, submarine position, target position, and intercept location. I know that all you need to find out your lead angle is the ratio of target/submarine speeds and the AoB angle.

An example would be something like "Target is half my speed, AoB is 120 degrees... lead angle solution is 22 degrees." You point 22 degrees from directly at the target in the direction it's moving and you run into it some time later with a big clang of metal.

[Rockin Robbins]

You end up with a sheaf of multi-column pages (it's been done). As a matter of fact, it was the reason for my developing the Dick O'Kane targeting technique. The complexity of picking the correct page, then the correct line and column opens up hundreds of possibilities for error and what seems at first to have been a good idea devolves into a litany of frustrating misses.

You're better off using the graphic solution of vector analysis, which can be done in seconds with much fewer opportunities for human error. Minimization of human error and mitigation of their inevitable effects is the hallmark of good attack practice.

War is fought by imperfect people who must be victorious anyway.

[Frederf]

I went through the math again and my page of equations was replaced by a simple few lines of better equations. It's simply:

EDIT
L = ArcSin ( C/S Sin A )

Where L is the lead angle, C is the speed of the target, S is the speed of the submarine, and A is AoB (0-180°). A very complete table would be huge but for reasonable speeds it could be small. A graph with several curves would be more compact, readable, and usable for common scenarios. I figure it's pretty useful as it works for both intercept and torpedo problems. It's nice to have a backup solution in case a juicy target starts slipping out of view and the TDC solution is discovered to be bad.

It's of note that such a graph or table might be slightly easier and faster to figure out the speed based on the angle instead of the usual reverse. Mostly I did it just to see if I could do the math still.

[Pisces]

Originally Posted by Frederf

I went through the math again and my page of equations was replaced by a simple few lines of better equations. It's simply:

L = ArcSin ( C/S Tan A )

Sorry, that is not entirely correct. Calculating "tan 90" for an AOB of 90 degrees is not possible because the result would be an infinately high number, yet arcsin can only handle numbers between -1 and 1. It's supposed to be "Sin A", not "Tan A". Because it is completely based on the "Law of sines" in a triangle of any shape:

edge_opposite_to_angle1/sin(angle1) =
edge_opposite_to_angle2/sin(angle2) =
edge_opposite_to_angle3/sin(angle3)

So the above formula would be:

L= Arcsin( C / S * Sin(A) ) [or: multiply C with Sin(A) , then divide result by S, then take Arcsin of next result ]

Also, for leading a torpedo C would be the speed of the target, but S would be the speed of the torpedo. S would only be the speed of the uboat incase you wanted to intercept the target yourself.

[Frederf]

You know I had it with 2 sines the first time when I actually worked it out but Subsim.com went down right when I tried to press the reply button. The second time (a day later) I typed it from memory and got it wrong.

Certainly C and S don't have to be the contact and the submarine. They can be anything where "C" is the speed of the "interceptee" and "S" is the speed of the "interceptor." Torpedo shooting is assumed to not be a factor since this thread is all about intercepting which is done at ranges far exceeding torpedo range.

Eventually I did end up using the law of sines to solve it rather quickly. You should see the 8 pages of very pretty and probably correct trigonometry that was leading me into madness.

[Rockin Robbins]

Yes, the underlying trig is actually fun when you're doing something destructive with it!

Similar trig functions were the genesis the the Dick O'Kane and John P Cromwell attacks. You should see all Nisgeis' and my e-mails back and forth in the development of that one! It all started out with a deceptively simple (evil) drawing he sent me one day, asking if there could be a rule of thumb attack similar to Dick O'Kane for that situation.

Here came the proverbial five pages of trigonometry! And at the end of that, a short list of rules for that precise angle setup, so that the user of the method didn't need my five pages of trig!

It's funny that when I was in school I was intimidated by math and now it almost qualifies as a hobby. How far the "mighty" have fallen!