Why do planes from Boston to England cut through the Arctic Circle. True it's shorter, but why?

Question

I do not have a globe, but what else can I do to understand this? Does it have anything to do with great circles and such?

Answer 1

The problem, which I'll explain in detail below, is this:

Which is shorter -- a smaller piece of a larger circle, or a larger piece of a smaller circle?

The answer is, a smaller piece of a larger circle -- the "Great Circle" route.

Although I simpified the math a bit, the Great Circle route over Newfoundland and Scotland is about 150 miles shorter than the "parallel" route south of Nova Scotia and Ireland, assuming you're flying from Boston's Logan to London's Heathrow.

Boston appears to be at 42 degrees north latitude and 71 degrees west longitude, while London is at 51.5 N and 0 W.

To simplify the problem, but still keep it realistic, I calculated the distances, using the two routes, between 47 N, 72 W and 47 N, 0 W.

Having Boston and London at the same parallel made the problem much easier.

The Great Circle, centered at the center of the earth, passes through both Boston and London. Its radius is the radius of the earth (3960 miles), and its circumference is the circumference of the earth (24,880 miles).

The "central angle," located at the center of the earth, connecting Boston and London, is 47 degrees, so the Great Circle distance is (47/360) x 24880 = 3248 miles -- the smaller piece of a larger circle.

Turning to the smaller circle ... as the earth rotates, and you go further north, the circles of latitude get smaller and smaller. At the equator, the radius is 3960 miles, but at 47 degrees north, the radius is only 2700 miles. This is a considerably smaller circle, having a circumference of 16,970 miles (rather than 24,880).

The angle, in this smaller circle, connecting Boston and London is 72 degrees -- the difference in longitude between the two cities. So the distance on the "parallel" route is (72/360) x 16,970 = 3394 miles -- the larger piece of the smaller circle.

And by comparing the two distances -- 3248 versus 3394 miles -- we see that the Great Circle route is about 150 miles shorter.

Finally, to answer your question more directly, the reason one route is shorter than the other is that the smaller angle (47 degrees) on the larger circle more than compensates for the larger angle (72 degrees) on the smaller circle.

Answer 2

From Calgary, Canada.
When you look on a map, the North and South Pole areas are greatly distorted. The best way to view the travel line is to look on a globe. If you put a string on Boston and the other end on England and pull it tight, it will take you through the Arctic Circle. In aviation, this is called the "Great Circle Route" because on a map the straight line from the globe, becomes an arc - part of a circle.

Around the equator you will find that the travel line will be much straighter.

Out of curiosity, compare the size of Greenland on a globe, with the one on a regular map. It's not so big after all.

Answer 3

since you don't have a globe, just get a ball (the larger the better).
Now put two dots on the ball to represent the north and south poles. Now put two more dots in the northern hemisphere of the ball to represent London and Boston. Now you can stretch a string between the two cities and see that the line goes towards the north pole (i.e., through the Arctic Circle).

And, yes, you are right...it has everything to do with it being a great circle route.

Answer 4

Use a globe and a string to figure this out. The shortest distance between two points on the surface of a sphere is a Great Circle route. The center of a Great Circle goes through the center of the sphere.

Answer 5

The shortest and the longest distance between 2 points of a sphere is the great circle joining those 2 points. Boiston to Uk the great circle goes via artic.

Answer 6

Hi. Take a toy globe and stretch a string from Boston to England. That's why.

Answer 7

No, Stan. The Arctic circle does go Europe: Finland, Norway, Sweden, Iceland – crosses the island of Grímsey of which mainland territories lie approxiamtely fifty 5°N and seventy 5°N even as Arctic circle runs sixty six° 33? 39?N plus and part of Asia: alongside the nothern Russia. It crosses Alaska (u . s .), Northern Canada, Greenland (Denmark) in North u . s .. ***** Greenland, it really is compared to what we anticipate of, belongs to North u . s . not Europe.

Answer 8

Take a globe and a piece of string. Put one end on Boston and the other on England. Pull the string as tight as you can get it. Where does it go?

Answer 9

if planes were to travel along the equator it would take longer, because the earth is more broader at the equator. it would take a longer distance and time while at the north and south poles, the earth is even more narrower in terms of its circular diameter. hence, it is more shorter at the poles.

Answer 10

Ah the joys of non-euclidean geometry. If you had a globe rather than a flat map it would be obvious. Get one.