Horizon calculator
Assumptions
This is basically just a restate of the execlleent Washington U reference below.
The Earth is a sphere of radius 6,378.1370 km, this is the equatorial radius of the elliptical earth.
The slant range \(s\) to the horizon \[ s = \sqrt{(R+h)^2 - R^2} \] rewritten \[ s = \sqrt{2Rh + h^2} \]
\(\ell\) is the distance along the ground. We assume that \(h \ll R\) so \(s \approx \ell\) and \[ s \approx \ell = \sqrt{2Rh + h^2} \approx \sqrt{2Rh} \] often restated as \[ s = k \sqrt{h} \] and found on-line with \(k=1.22459\) with \(h\) in feet and \(s\) in miles.