Flat Topography and Curving Earth

Hello, I'm a middle school teacher and I had a bright student show to me the following: If the mean radius of the earth is 3959 miles (taken from space.com) and we assume the earth to be spherical, then we could use the Pythagorean thereom to show the difference between the hypotenuse from the radius over 10 miles to be 66.883 feet. We get after squaring the 3959 and adding 100 for 10 squared, and finding the square root, and finding the difference between the hypotenuse and the radius = 66.883'. The National Geodetic Survey shows only 7.874 inches of variation across the Bonneville Salt Flats. In other words the 10 mile stretch of the Bonneville Speed Track should dip down below the horizon from the start 66+' because of the curvature of the earth, but in fact, does not. I'd appreciate any help you can give me to explain to the student why the curvature of the earth does not seem to show itself on the salt flats. Thank you,
- Gerald Fluhrer (age 55)
Sandpoint, ID, Bonner

So far as I can tell from a standard topographic map () the flat part of the Salt Flats has a constant elevation to within about 6'. There are big areas that have constant elevation to within less than a foot, and those must be the ones you're describing. Those elevations already  take into account the curvature a spherical Earth would have. So if you were to do some sort of line-of-sight measurement, say with a laser, you'd see that the flats aren't flat in the usual plane geometry sense of the word. They do in fact "dip down".

Mike W.

(published on 07/09/2015)