# The distance to the horizon

When searching for Napoleon’s fleet in the Mediterranean, Admiral Lord Nelson positioned his own ships in a line, spaced as widely as possible while still allowing them to see one another. As it turns out, there is a fairly basic formula for calculating the distance to the horizon from any particular vantage point. This assumes the planet you are on to be perfectly spherical, but it should provide a decent approximation for slightly-squashed spheres such as the Earth. Obviously, the formula will be thrown off if you are on anything other than perfectly level ground. As such, it is better applied at sea than on land.

Where d = the distance to the horizon
h = the observer’s height above the ground
r= the radius of the planet

d = âˆš ( h^2 + 2rh )

Nelson’s flagship, the HMS Victory was 62.5m from waterline to the top of the mainmast. As such, someone sitting up there would have been able to see a bit more than 28km.

This formula is useful if you are on a planet with a known diameter and want to know how far away something on the horizon is (the diameter of the Earth is about 6365km). It could also be useful if you are on a planet with an unknown diameter that you want to know. Just drive a stake into the ground and walk away from it until it begins to vanish – then, apply the formula above to solve for the radius. Of course, you will need either sharp eyes or some kind of telescope if the planet you are on has any substantial size.

Incidentally, while they were still operating, the Concordes flew at 17,000m of altitude, allowing people looking out the windows to get a clear view of the curvature of the Earth.

## Author: Milan

In the spring of 2005, I graduated from the University of British Columbia with a degree in International Relations and a general focus in the area of environmental politics. In the fall of 2005, I began reading for an M.Phil in IR at Wadham College, Oxford. Outside school, I am very interested in photography, writing, and the outdoors. I am writing this blog to keep in touch with friends and family around the world, provide a more personal view of graduate student life in Oxford, and pass on some lessons I've learned here.

## One thought on “The distance to the horizon”

1. . says:

Legendary British warship ‘found’

A US-based salvage firm is believed to have found remains from the wreck of a legendary British warship which sank in the English Channel in 1744.

Odyssey Marine Exploration is expected to announce on Monday that it has found HMS Victory, the forerunner of Nelson’s famous flagship of the same name.