My previous post has the "Historically correct", sort of, method. It's relative plotting.
The easy way to do it, in SHIII, since the chart display is a True Motion Display, is obviously true motion plotting.
Trace your course on the chart, as a reference (This is not strictly necessary, but it will make marking relative bearing easier)
At the beginning of the interval, mark your target's range and bearing on the chart. This is point M. At half the interval, mark the target again. At the end of the interval, mark the target. This is point T. You should also mark your position at the end of the interval, if you want to obtain CPA data.
Add ownship's course and speed (Vector MO) at point M. Remember that it's Motion of Ownship, so from M toward O. Linking O and T gives you the relative vector, the extension of which will give you CPA.
The rest is as explained above.
Should you want to intercept (IE, obtain a CPA of 0), trace a line from T to your position (The one you used as a reference for the CPA). Prolong this line to the other side of T. Place a range circle around point M, whose radius is equal to the lenght of MO. The point where this circle intersect the prolongation of your desired relative movement vector is point O prime. The vector linking M and O is MO prime. The angle North-M-O prime is your course to steer, essentially. Don't forget to add 180 degree if it's west.
Yeah, that's hugely simplified, especially the course-to-intercept part... But taking into account the imprecisions in the games, and the slow speed involved, it'll get you within visual range. Very close visual range.
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