Checking if your interception course is right

[palmic]

Originally Posted by kstanb

No worries, still any chance you can post a clean version of the board?

Also, if you have time, would you solve the following scenario in the maneuver board:
same idea as before, the contact is at 20 degrees heading, 20K meters away, course is 100 and the speed is 8
your maximum speed is 15 knots, your cruise speed is 12 knots

how would you intercept it, optimally, if you want to be at least 8km away until you reach your desired periscope position (this so that it won't spot you during your cruise?

thanks again!!

When you already see your target and you know their course, you dont need to calculating anything.
Just set the same course with higher speed and put him behind enough to have time to prepare and then set course to get closer and closer to his track.
When you think its close enough, turn the sub to have perpendicular course to its course to prepare sub to best firing position and tune distance from periscope depth as he is closing..
(for instance if their course is 100, you'll have to prepare sub to course 10 and wait until he will be before you)



Until you see your target
So here you have this triangle:
AoB (angle C) = 100 degrees (angle between his course and the bearing of 20)
his speed (side b) = 8
your speed (side c) = 12


What you want here is the angle between the bearing which you see the target and your desired course (angle B)
The law of sines for angle B here is that:
b/sin(B) = c/sin(C)
8/sin(B) = 12/sin(100)
8/sin(B) = 12/1
8/sin(B) = 12
sin(B) = 8/12
sin(B) = 0.7
B = 45 degrees

So your desired course to meet your target by the speed of 12 kts is the current absolute bearing + 45 => 20 + 45 = 65.

You can see here that since you have your target with AoB about 80-100 degrees, you can calculate the sine of angle between the bearing and desired course simply as his speed / your speed.
Its about 10 seconds to get your desired course..
You can round sines to whole numbers, theres no need to be very precise since your input data are also rough. Try it and youll see it works.