Re: Visual Slant Range for 30,000 foot aircraft



On 2005-08-02, Kevin Dunlevy <kevindunlevy@xxxxxxxxxxx> wrote:
>
> I figured 30,000 feet is about six miles. That would be the base of a right
> triangle, but I don't know the length of the side perpendicular to the base,
> so I can't figure the hypotenuse.

You are a point on the surface of the earth. The highest point you can
see is on a line tangent to the surface of the earth at the point where
you're standing. The leg perpendicular to that tangent is, of course,
the radius of the Earth (about 4000 miles). The most distant airplane
is a point along the tangent line that is also 6 miles away from the
surface of the earth. So the hypotenuse is r+6 (4006 miles). The
distance between you and the plane is the remaining side of a right
triangle:

sqrt(4006^2 - 4000^2) ~= 220 miles.

of course your actual height above the terrain between you and the plane
comes into play.

--
Ben Jackson
<ben@xxxxxxx>
http://www.ben.com/
.



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