What is the curvature of the earth per mile?

Question

if you were to measure how much the earth has curved in a mile, what would it be?

Answer 1

I keep getting a slope of 0.0155 %, doing things a slightly different way.  About 9.8 inches per mile.  Trust his (that other guy's) answer, I have a paper covered with angles and sins and tans and stuff and had to do it about 5 times before I got what I think is the right answer.  Mine is based on the idea that the earth descends at an angle of 0.008957 degrees per km (at the equator).

thanks for the little brain teaser though, made me think about things I haven't for a while.

Answer 2

The earth curves at approximately 8 inches per mile. This can obviously vary according to the terrain of the earth but the natural ground level curves at this gradient.

Answer 3

Measuring a mile along the equator:

1 mile = 1.609344 km

Radius (r) of earth along the equator = 6,378.137 km  [source 1]

The angle in radians (a) between two points a distance (s) along the circumference of circle of radius (r) is:

a = s/r

We have measured one mile around, so

r = 6378137 metres

s = 1609.344 metres

a = 0.000252321356479612434

The distance along the radius that we have moved by moving around the earth is:

r - (r * cos(a))

cos(a) = 0.99999996816681556656998075613651

r * cos(a) = 6378136.7969635885373159573500023 metres

r - r cos(a) = 0.2030364 metres

So, for every mile around the circumference of the earth, the curvature drops by 20.3 cm, which is 7.994 inches.

Answer 4

8 inches for the first mile; 2 feet 8 inches for the second mile.