London and Northwestern Railway Proves A Flat Earth

The London and Northwestern Railway forms a straight line180 miles long between London and Liverpool. The railroad’s highest point, midway at Birmingham station, is actually only 240 feet above sea-level.
With a global curve rate of 8 inches per mile squared (8”for the first mile of a track, and increasing at the square of the distance in miles- a NASA computation*), the180 mile stretch of rail should form an arc with the center point at Birmingham raising over a mile, a full 5,400 feet above London and Liverpool, which are both at sea level.
How could this be?
*Mile 1- 8 inches drop
  Mile 2- 8 inches x (2 x 2) = 32 inches drop
  Mile 3- 8 inches x (3 x 3) = 72 inches drop
  Mile 90 (Birmingham)- 8 inches x (90 x 90) = 64,800 inches = 5,400 feet
Another interesting question here is why googling how to compute this gives erroneous computation formulas on the first couple of pages of the search listing on google? Most of the links state that it’s 8 inches per mile which is obviously wrong since that’s just a sloping number and not a curvature. Obfuscation perhaps? If so why?

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