Ever stood on the coastline, gazing out over the horizon, and wondered what’s on the other side? Pondered where you’d end up if you could fly straight ahead until you hit land?
Turns out the answer might be surprising. And even if you pulled out an atlas — or, more realistically, your smartphone — you might have trouble figuring it out. Lines of latitude won’t help, and drawing a path on most maps will lead you astray.
Cartographer Andy Woodruff, who recently embarked on a project called Beyond the Sea to illustrate this puzzle, says there are two simple reasons why it’s harder than it seems to figure out which coast lies directly on the other side of the horizon.
First, coastlines are “wacky,” he writes on his blog. And second, well, the Earth is round.
The crookedness of the world’s coastlines means moving a few miles up or down the coast will leave you facing a different direction (assuming your gaze is straight out, perpendicular to the coast around you).
And because the Earth is round, a true straight line has nothing to with holding, say, a northwest or southeast bearing — that will actually send you on a “rhumb line,” which traces a spiral around the globe. Traveling along a single line of latitude also will send you out of your way, unless you happen to be exactly on the equator.
Instead, Woodruff explains, you need to find a “great circle” — the shortest path between two points on a globe. It’s the true “straight line” between two points on a sphere, even though it looks like a curve on most maps.
So he used a two different projections to find the answers: a Mercator projection, which preserves local angles, to find the angles of coastlines around the world, then an azimuthal equidistant projection, which preserves directions from the center point, to find the true straight line from that bearing.
You can view all the resulting maps here.
Woodruff notes his math might might occasionally be imperfect — “even we cartographers sometimes have a shaky grasp of map projections and spherical geometry,” he says.
But his maps show how counterintuitive the answer might be to a seemingly simple question: “What’s over the horizon?”
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