Calculation for interception

[Avatar]

Hey fellas,
whats the equation for intercepting a convoy. Lets say you get a radio report of a convoy that's about 100km away, travelling at 7kts, course 030. You are travelling 000 at 18 kts and the convoy is bearing 315 from your position.
what calculation do you need to perform to intercept the convoy? Mostly I estimate it visually with good results, but sometimes I believe that the target got by.
Thanks for the formula, and I hope this isnt too much of a bonehead question
edit: I guess its a physics equation and here are the values you know:
1. target course: 030
2. target speed: 7kts
3. target distance: 100km
4. own course: 000
5. own speed : 18kts
6. target bearing: 315
also, I think you need to change the knots to meters per second, which I dont know how to do. any help appreciated!

[Gezur(Arbeit)]

http://www.subsim.com/radioroom/showthread.php?t=88961

This gives you a plan

http://www.subsim.com/radioroom/showthread.php?t=96026


Some other helpful stuff

[seafarer]

Or, use MoBo

http://www.subsim.com/radioroom/showthread.php?t=116572

[Avatar]

Thanks!
that's it!

[Puster Bill]

Might I also suggest using a whiz-wheel or slide rule, for that authentic juiced-in U-boat flavor.

[CapitanPiluso]

MoBo is by far the best answer to your question

[Pisces]

Intercepting is as 'simple' as the following formula:

lead_angle = arcsine( speed_target*sin(AOB) / speed_uboot )

lead_angle is the angle between the line target_to_uboot and your new course to follow.

AOB (Angle on the (target) Bow) is the angle between target's course and the line target_to_uboot. Because your course is due north, the angle between the target bearing (315) and his course (30) is 75deg, so the AOB is the left-over part to 180, which is 105deg.

So, first you multiply target speed by sin(AOB) (7*0.966=6.761; if this is above your max speed forget about intercepting him! you won't make it!), then divide by your speed (=6.761/18=0.376). If the result is over 1 you made a mistake somewhere (or you are too slow). If not, you have done it correctly sofar, and you do the arcsin function on it to get the lead_angle (arcsin 0.376= 22 deg). Now your new course is: 0(current course) + 315 (relative bearing) + 22deg (intercept angle)= 327 deg

Range:

Range has no influence on the course to take, only on the time it takes to get there. First draw the triangle on the map based on target course, the line to the target, and your new intercept course. Then measure from that the distance along the intercept course you follow. If you divide the intercept range (in km) by 1.852 km you get it in nautical miles. Then divide that nautical-mile distance by your speed and get the amount of hours it takes. No need to mess with meter per seconds. Those meter/second calculations are going to take longer than the 3h14min of your intercept.

Also, your max (flank) speed may not be a good idea if you want to safe fuel. Flank speed creates extra holes in you fueltank. Lower speeds may also get the job done while allowing you to stay on patrol longer. Try and see how much is really needed. If at the end of the intercept you cannot see the target listen on hydrophone because it can hear farther (34km) than you can see.

But I myself do like the (circular) slideruler method 1st and foremost, then map drawing 2nd, last but not least digital calculator. My 'least' is (gu)estimating.