The easiest method I found was posted over in the 'hitting fast targets' thread.
Put your periscope just ahead of the ship crossing your FOV. As soon as the bow touches a vertical line, start the stopwatch. Stop it when the stern crosses the line. You already know how long the ship is in meters from your recognition manual, and you know have the time he took to cross that distance.
The EXACT speed is thus:
V (knots) = 1.9438444908 * Length (meters) / T (seconds)
...or you could replace the constant with 1.95, or 2x for a very quick estimate (and one you can likely do in your head. Double the ship's length, and divide by the time it took to cross bow-to-stern through your 'scopes line)
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