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So, a sail's been spotted, but how far away is the ship?
Can you see the whole ship or is it still hull down with just the sails showing?
What about that island the treasure map is pointing to?
Does it really matter? ;)
If it does, then I hope this spreadsheet will turn out helpful.
I've done it a bit hurriedly during boring parts of training, so it's a bit rough.
It does both simple and "complex" calculations for spotting land and ships. I've assumed Golarion has the same radius as Earth. I also assume the weather's fine and the lookout is eagle-eyed and sober.
An example: assuming a ship with a deck 10 feet above sea level and a lookout at the crosstrees 70 feet up. The ship is heading towards the White Cliffs of Dover (UK, not Golarion), they reach upwards of 350 feet above sea level.
That means that the lookout will be able to spot them at just over 33 miles. People on deck have an effective horizon of just under 4 miles. But since the cliffs are 350 feet tall, they'll be able to spot them when the ship gets to just under 27 miles.
They happen to be attempting to run the English Blockade. Unbeknownst to them, a British frigate is ahead. It's under full sail; it has somewhere to go, but won't mind turning to snatch up a blockade runner. Assuming the top of the frigate's sails are 120 feet above sea level, our blockade runner's lookout can spot the sails 23 miles out and it'll be hull up at 10 miles (the lookout's horizon).
If our lookout is hungover and is not paying attention, then the officer of the watch could spot the sails 17 miles out and it'd be hull up at under 4 miles.
Now the island. You might think you could spot it's location first from the vegetation or mountain peak (if it was a volcanic island). But no, you'd get a much earlier indication because of clouds that form above islands. An astute sailor could determine that there's something "thataway" due to a cloud bank on the horizon in an otherwise clear sky. So the ship might be able to spot it over 100 miles away.