On 7/25/2010 9:54 AM, Ronald Raygun wrote:
Terje Mathisen"terje.mathisen at tmsw.no" wrote:

brian whatcott wrote:
Not linear: for a ground level jammer,
The line of sight estimator for distance versus height above sea level
goes something like this:
distance n.m. = 1.2 sqrt (Height ft MSL)

That calculation follows directly from the Taylor series for Cosine:

1 - x^2/2! + x^4/4! - ...

It means that for very small angles, the height above the sea is

1 - (1 - x^2/2!) = x^2/2! = x^2/2 (when R == 1)

Hmm. Your working suggests that for R=1 the height is equal to 1-cos(x),
but that is not the case, it's actually equal to 1/cos(x)-1. By chance,
for very small angles, these two expressions are approximately equal.

Insert the radius of the Earth (in nautical miles, 3500 or so) and
multiply the result by the number of feet in a nautical mile (about
6000+) and the 1.2 factor should pop out.

Actually a factor of 1.0 would be a better approximation than 1.2,
since the factor which actually pops out, when I use R=6371km and
conversion factors 1852m/NM and 0.3048m/ft, is 1.064.

Even using alpha math engine, I get 1.07 with those other conversions
that Terje gave. hehe...

Brian W