You can sail from the west coast of Canada in a straight line around the world and arrive on the east coast of Canada.

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# Cooke Passage – Longest Straight Line Sail Around the World

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3 thoughts on “Cooke Passage – Longest Straight Line Sail Around the World”

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You can sail from the west coast of Canada in a straight line around the world and arrive on the east coast of Canada.

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We all agree there are no actual straight lines on Earth’s surface — so what do we mean when we speak of traveling along “a straight line”?

Draw a 1-meter circle on Earth’s surface. All agreed that’s not a straight line? Why not?

For one thing, the shortest route between two points on the 1-meter circle cuts across the circle — it doesn’t follow the circle. Whatever we mean by “a straight line” should mean it’s the shortest route (on Earth’s surface) between the line’s endpoints.

(One niggling exception: if the “straight line” wraps 190 degrees around the earth, the shortest route between its endpoints isn’t on the straight line.)

Probably we agree a 1-meter circle isn’t a straight line. How about a 10-meter circle? How about a 100-meter? When does a circle start being “a straight line”?

That is, when does the shortest surface path between two points on the circle follow the circle?

When it’s a great circle — the largest possible circle on the surface. Having the largest possible radius, it has to be the shortest surface route between two points on it. In other words, a “straight line” on Earth’s surface follows a great circle.

Pick two points on Cooke’s line, a few thousand kilometers apart. Calculate “the distance” between them, which means the distance via the shortest route. You can also calculate the distance following Cooke’s line — that’s more work, but still doable. It will be longer than the shortest route.

People who think the Cooke Passage is a straight line seem to think that if you follow the parallel of 10 degrees north latitude, you’re following a straight line. Aim your boat east, center the rudder, and the boat will stay at the same latitude, they think. So how about when you’re at 89.999 degrees north latitude? Point the boat east and center the rudder — will it follow a 2-km circle, counterclockwise? And if the boat starts out pointed west, it will do a 2-km clockwise circle, still with the centered rudder?

On investigation, it turns out the Cooke Passage has the same radius as the 4-point-something parallel of latitude. On further investigation, it turns out no great circle between British Columbia and Quebec misses land.

I looked up the numbers for the Cooke Passage. The radius of the arc is the same as the 4.933-degree parallel of latitude; if you rotate the 4.933-deg-north parallel 121.829 degrees southward, with its axis on longitude 93.702 degrees West, you’ve got the Cooke Passage.

Well, thanks for the input. I am sure any reader stumbling across this post will enjoy the insight!