The Distance to the Horizon calculator computes the straight line distance to the horizon from a specified height (h) using the.
INSTRUCTION: Choose units and enter the following:
Distance to Horizon: The calculator returns the distance to the horizon in meters. However, this can be automatically converted to other distanced units via the pull-down menu.
`d = sqrt(h*(2*Re + h))`
The graphic shows a right triangle, which is formed when looking to the horizon at any elevation (h). The sides of the right triangle are:
Using the Pythagorean theorem, we know:
d2 + Re2 = (h + Re)2
Now we can use simple algebra to isolate the distance to the horizon (d).
`d = sqrt(h*(h+2*Re))`
Unfortunately the Earth is not a perfect sphere. It has mountains and valley, but it also had a bulge around the Equator. This bulge makes Earth more of anthat is the shape one gets when rotating an ellipse about an axis. In the Earth's case, the ellipse is rotated around the polar axis (see diagram).
For this reason, this distance to the horizon equation is only an approximation. Better models would take into account the changes in terrain and Earth's oblateness.