2013 Chicagoland Bike Map is distorted

While waiting for the snow to melt, I've been looking at my new Chicagoland Bike Map from the Active Transportation Alliance.

What was the ATA thinking? They have published a map that is badly distorted, not drawn to scale. The purported scale is 1" on the map equals 1.5 miles on the ground. That scale holds true for the North-South dimension, but not for the East-West dimension.

Take any known mile and a half distance in a north-south direction, say Addison to Lawrence. That measures 1" on the map. Now pick a known mile and a half distance in an east-west direction. Say Kedzie to Damen. That measures almost 1-5/8" on the map.

And it's like that everywhere. Take a known mile square. Say from Lincoln-Belmont-Ashland to Lincoln-Fullerton-Halsted. Belmont to Fullerton is a mile, Ashland to Halsted is a mile. On any other map, Lincoln Ave. between these two points is a 45 degree angle. Not on this map. The Belmont-Ashland-Fullerton-Halsted square is a rectangle with a ratio of 8:5 instead of 1:1.

What bizarre kind of map projection is this? Did the ATA cartographers have to yield to the ATA graphic designers, who decided to junk the aspect ratio to fit the planned size of the map?

This should not have happened.

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Permalink Reply by Mike Schwab on March 11, 2014 at 1:31pm

I found this is called a cylindrical projection.

Mike Schwab said:

COS(41 degrees) is .75. So if it was set for 1 degree N/S = 1 degree E/W you would get E/W stretched by that percent.

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Permalink Reply by Lisa Curcio on March 11, 2014 at 1:48pm

MIke, I forgot trigonometry about three seconds after I passed the final exam, but this reminds me of my limited knowledge gained from learning to read nautical charts in which one degree of latitude is equal to one nautical mile but the length of one degree of longitude starts out close to one nautical mile at the equator but gets shorter the closer one gets to the poles because of the shape of the earth. Steve, did you check the east-west scale not only in the middle of the map but at the north end and the south end of the map? If this phenomenon has anything to do with the disproportionate scales the scale on the east-west axis would not be constant but would change from south to north.

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Permalink Reply by Skip Montanaro 0mi on March 11, 2014 at 1:56pm

Lisa Curcio 4.1 mi said:

... this reminds me of my limited knowledge gained from learning to read nautical charts in which one degree of latitude is equal to one nautical mile but the length of one degree of longitude starts out close to one nautical mile at the equator but gets shorter the closer one gets to the poles ...

I'm going to suggest this is not quite right. :-) If one degree of latitude (or longitude) was equal to one nautical mile, no matter where you measured it, wouldn't that imply that the circumference of the Earth was on the order of 360 nautical miles? Maybe you meant one second or (possibly) one minute of latitude (or longitude)?

Google tells me that Earth's circumference is 24901, which equates to about 69.1 miles per degree, and further tells me that 69.1 miles are about 60.1 nautical miles, so I think you were looking for 1 minute == 1 nautical mile.

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Permalink Reply by Lisa Curcio on March 11, 2014 at 2:01pm

Oops! You are right! One degree of latitude is equal to 60 nautical miles! And it does not give us the circumference since latitude is measured from equator to pole. The earth is not actually round, as we know. The distance from equator to north pole is then 5,400 miles.

Skip Montanaro 12mi said:

I'm going to suggest this is not quite right. :-) If one degree of latitude (or longitude) was equal to one nautical mile, no matter where you measured it, wouldn't that imply that the circumference of the Earth was on the order of 360 nautical miles? Maybe you meant one second or (possibly) one minute of latitude (or longitude)?

Google tells me that Earth's circumference is 24901, which equates to about 69.1 miles per degree, and further tells me that 69.1 miles are about 60.1 nautical miles, so I think you were looking for 1 minute == 1 nautical mile.