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Once you pass head to wind you have no rights under rule 13, until you reach a close-hauled course. I'm not entirely sure what constitutes a closed hauled course. Must your sails be trimmed properly or is it simply the boat's course that matters?

sail under them and try calling them up, but then you would've overtaken from astern and have no rights.

What rule is that from? Rule 17 only prevents a leeward boat that acquire overlap from astern from sailing above her proper course, but a boat has no proper course before the race starts.