What is the curvature of the earth per mile?
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.
