Math CentralQuandaries & Queries


Question from Nev, a parent:

formule: Distance Seen
S = 1.225 x square root of H
S = Distance seen in Miles
H = Height in Feet

What dose 1.225 Relate To ? Please

Nev Cooper

Hi Nev.

It looks like it is a ratio that incorporates the curvature of the earth together with the units of miles and feet as an approximation good for a useful range of distances and heights for estimating the distance of an object on the horizon whose height you know.

Clearly this won't work without limit, since it implies that the earth is sloped, but not curved. However it is probably useful for normal human visibility on a clear day.

If you were measuring in other units (kilometers and meters perhaps), you would have a different value. Just as you would on the moon - although with no atmosphere on the moon, you can see as far as you like along the horizon so the curvature of the moon would be more of a problem for you.

Stephen La Rocque.

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