Ronald Raygun wrote:
Terje Mathisen"terje.mathisen at tmsw.no" wrote:
d^2 = (R+h)^2 - R^2 = 2Rh + h^2 = 2Rh(1 + h/R)

Actually 2Rh(1 + h/2R) but that's OK.

where for small angles (hR) the h/R term can be dropped and we get

I believe that h/2R term is significantly smaller than the normal
atmospheric effects, i.e. today I can see features on the other side of
the Oslo fjord that I know should be below the horizon. :-)

d = sqrt(2Rh). Under small angle conditions the straight-line eye
distance and curved foot-distance can be treated as equal.

With a height of 6 feet we get about 3.5 miles, right?

Wrong :-)

Oops!

Doing sqrt(3) ~= 1.7321 or so, from memory, and then multiplying by 2
instead of sqrt(2) ~= 1.4142 gave a pretty bad end result.

sqrt(6) should be close to 2.45, since 25^2 is 625 and 24^2 is 576.

Thanks for catching my error.

The ratio of 1.8 m to 6400 km is about 3.5e6, so the second-order term
requires 13 digits while most calculators are happy to show 8 or 10,
right?

Quite.



--
- Terje.Mathisen at tmsw.no
"almost all programming can be viewed as an exercise in caching"