(I am playing around with a short story about the Age of Sail.)
Let’s say I am in the crow’s nest of a Napoleonic fighting ship and a similar ship is approaching. She has all he sails rigged, and is approaching at ninety degrees, and so is presenting maximum visibility. My lookout has eagle’s eyes and a good telescope.
Presuming exceptional viability, what is the maximum distance I can see her fighting tops at? This would be based on the curvature of the Earth and the height of the masts.
(I have no idea how tall these things were, that is why I am a superior writer, I am unencumbered by facts to get in the way of the story.)
Slight hijack, but would they speak of a “crow’s nest” in a fighting ship? I was under the impression that this was more of a sheltered lookout that you’d find in a whaler. You should probably check your terminology.
Anyway, according to http://mathcentral.uregina.ca/QQ/database/QQ.09.02/shirley3.html, a rule-of-thumb is c = 2/3 x**2, where c is the curvature of the earth in feet and x is the distance in miles. Assume your ships have masts of 100 feet each (ok, 94 feet with six foot sailors clinging to them), so a 200 foot curvature, then I get sqrt(300) or 17 miles.
100 feet is not a bad estimate. It would vary a lot, but the HMS Rose, which is intended as a reproduction of a 24 gun British frigate of the era has a 130 foot main mast:
They had what you might think of as “crow’s nests”, but would more properly be called a “fighting top” in ships of that era.
When you consider a similarly masted ship poking up above the horizon, the trigonometry will yield something like 30-40 miles. I somehow doubt that that would actually be achievable, however. Something tells me that the air is never going to be crystal clear enough to manage it, and the apparent size of the top of the approaching ship’s mast on the horizon is going to be damned small.
Addendum - the “fighting top” would typically be nowhere near the top of the mast. It would be located above the first sail, and below the topsail, topgallant, royal, etc. It was intended as a platform to post sharpshooters on during battles. I would suppose that a lookout would still be sent further aloft than that.
Another consideration is, what would be the average magnification of a 18th century spyglass? A quick Google search indicates probably 20-25x, so a ship 40 miles away would seem to be 2 miles away, which might still be too far away to tell what colors they were flying (except in the broadest sense–“blue with some red in it”).
If you’re writing something set in the Napoleonic era, you might want to pick up “A Sea of Words.” It was originally written as a guide for understanding the terminology and background on Patrick O’brians Aubrey/Maturin series (the age-of-sail literary benchmark ;)), but I think it would work well for a short story writer. It includes a couple of essays on how the British navy was organized, how medicine was practiced, and most pertinently it includes a fairly complete dictionary of nautical and period terms, some of which have essay-length explanations.
Might be worth picking up, especially since it’s <$12
Ideal conditions are unlikely, the air near the horizon is, by definition, near the sea and so is likely to be very humid, still these figures give me some ideas.
Argh!
Avast!
Yo Ho ho!
and of course, Shiver mi timbers!
A quick visit to the website of the HMS Victory reveals that her mainmast tops out at 205’, or 62.4m. First rate Ships of the Line were a smidgen taller than little unrated frigates.
I get 28.2km to horizon, or some 56k distance at which the tops’ls of an enemy Ship of the Line are visible, neglecting nitpicking details and assuming perfect visibility.
So, assuming you’re in a fast first-rate like Victory with the wind at your back and the other ship doesn’t move (otherwise the math gets too complicated for me), and you put every stitch of canvas up and get up to 9 knots, it would take you three hours and twenty minutes from seeing the first flash of sail on the horizon to get within the extreme range of the 32-pounders.
Then it’s just another mile and a quarter at a significantly lower speed (depending on how much of your rigging gets shot away – we’ll assume that whatever kept the enemy from running away didn’t affect their gunnery) to get to point-blank range and put a thousand pounds of iron into her stern.
