It all has to do with height of eye. The numbers I posted were representative of the distance to spot an object at sea level. You can spot masts / smoke well beyond that.
If you were, for example, looking from a Type VII to a ship with a 120' mast, a good lookout could spot the mast at 12.8 nm. You probably wouldn't see the hull until about 7 nm or so.
That is why in historical accounts, the smoke was always the first indicator of a contact: it had the highest "height of eye"
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