The 2 leg attack path planning problem
 

Inspired by this post (http://www.subsim.com/radioroom/show...04&postcount=9), I came up with a scenario for Wolfpack as a research problem/quiz yet to be solved using the in-game map or a paper Maneuvering Board. (I've read the USN Maneuvering Board manual quite a lot and thought this maybe an interesting and practical problem.)

Let's say we've run into a fleet moving at 8kts, 7km away from us, and a course of 120deg.

Assuming an enemy visual detection range of 4km, how can we plan a fastest 2 leg attack route in order to overtake the fleet at 15kts on the surface, and perform a submerged 5kts approach to a 90deg attack position within 2km from the enemy course. We also need to ensure that our 30kts torpedo actually have the time to hit a target.

Only in-game map, a paper Maneuvering Board, or any historical dial is allowed.

I'll try the method from 2001 USN maneuvering board manual chapter 6, example 31, "COURSE AND SPEED TO PASS ANOTHER SHIP AT A SPECIFIED DISTANCE".

If we don't take the submerged part into account, we basically just need to pass ahead of the fleet with a CPA of 4km. This matches the situation in the manual very much.

1) So let's plot ownship at the center of the Mobo, and M1 representing the ship 7km ahead of us.

2) Draw the fleet vector r (the red one) with course 120deg at 8kts.

3) From M1 draw a line tangent to the 4 km red circle at M2. This satisfies the requirement of passing with a CPA of 4km from ownship.

4) From r draw a line parallel to M1-M2, intersecting the 15-knot speed circle at the blue arrow.

5) The blue vector is the course we want to follow.

Proved with MoBo V1.3 using the advance function.

http://www.subsim.com/radioroom/pict...ictureid=10300

http://www.subsim.com/radioroom/pict...ictureid=10301

Tried on my last sortie and worked pretty well. I'm able to position myself well ahead of the convoy while keeping a minimum distance.

Plotted with in-game map using a scale of 1000m = 1kts. The target was moving on course 160deg at 6.5kts, with a true bearing of 269deg and a distance of 7200m. I wanted to keep a minimum distance of 5km while moving to a intercept position.
http://www.subsim.com/radioroom/pict...ictureid=10308