I have two ships that see each other on the horizon and realize (because of location) they're friendly and turn toward each other. How long would it take to meet?
My problem is that using math and logic my equations don't match what I've read in books and seen in movies. A frigate, for example, has a mast about 125 feet tall. From the crow's nest, the horizon would be about 14 miles away. And a frigate can travel about 10-14 knots (which is about 12 mph). So...an object on the horizon could be reached in an hour or so using this math. Theoretically if two ships were heading toward each other (taking into account that they would travel at an angle to the wind) they could spot each other on the horizon and meet fairly quickly.
BUT. This is not the way it works. Ever. I'm reading a first-hand account of 17th century travel on a Spanish ship; they spot six sails on the horizon at sunset...and the sails are still on the horizon in the morning. They are STILL on the horizon again at mid-day. They think the boats are fishermen, and aren't particularly trying to avoid them; the Spanish ships are anchored offshore to get fresh water. By evening they realize the ships are too big to be fishermen and THEN they try to outrun them.
So...what am I missing? The journal is from the POV of a priest, so he's actually probably on deck and doesn't have a telescope, and without the height of the crow's nest he can likely only see about seven miles out. How can it possibly take the ships twelve plus hours to travel less than ten miles?
I know there's not always perfect conditions for sailing, but my math seems to be on one end of the extreme (and really off from how it's portrayed in fiction); what I'm reading seems so slow, though!
Do I really need to slow down the travel pace of my ships, or what?
SEARCHED: I have read A LOT of sites on British and Spanish navies and merchants in the 17th and 18th centuries, the age of sail, pirates, privateering, and have read a few books on the subject. Also a few sites that get into comparing modern and historic sailing, and so on.