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and adjust/settle your speed to keep him on that 90/270 degree. After some time your speed does not need changing, so measure your own average motion (and time taken) during the adjusting speed period and presto!, his speed.
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That was actually the preferred method used in real life by the german U-Boat commanders. All data to estimate speed and course as well as zig-zagging pattern was obtained during the overhaul maneuver. The captain would order the U-Boat to change course until following a paralell course to the enemy. He estimated it by watching the tops of masts above the horizon and using the amount of mast visible to judge if the enemy got closer or farther, as well as using separation between masts to judge course changes. Once satisfied with the value collected, an intercept course was plotted and then the U-Boat went ahead full there.
If the U-Boat did not have time or position to do that maneuver, then the fixed wire method of speed measuring was used as quickest and most effective. It is of special good value when doing a dog-leg approach on surface, because you will be always pointing yoru bow at the target.
While at first the overhauling maneuver seems long and boring, it is without doubt the most recomendable method to really know what the target is doing.