We can use the Pythagrean Theorem to determine the amount of c | Phil Godlewski 3.0

We can use the Pythagrean Theorem to determine the amount of curvature variation there should allegedly be

Essentially you can draw a right triangle consisting of the Earth's alleged radius (a), the distance being observed along the surface of water (b), and using the theorem to solve for (c). Then we subtract (a) from (c) to determine the amount of declination

The Pythagrean Theorem is a² + b² = c²

Let's say we're observing a 10 mile wide lake to determine its alleged convexity. It would look something like this:

a² + b² = c²
(3,963 x 3,963)+(10 x 10)=c²
(15,705,369)+(100)=c²
15,705,469=c²
(Find square root)
C = 3,963.0126

Now that we solved for the hypotenuse (c) we can subtract it from our radius (a) to find the amount of curvature variation:

(c)3,963.0126 - (a)3,963 = 0.0126 miles

To convert that decimal in miles to feet we simply multiply by 5,280 (that's how many feet there are per mile):

0.0126 x 5,280 = 66.528 ft of curvature over a 10 mile long body of water

Instead of going through alllllll that we can, instead, simply use the parabolic curve formula of: 8 inches per mile²:

8 inches per mile²
8 x (10 x 10) = curve
8 x 100 = curve
Curve = 800 inches
(To convert to feet, divide by 12):

800 ÷ 12 = 66.6 ft of curvature over a 10 mile long body of water