What is distance of line of sight between 2 100' towers?

Answer 1

It's going to depend on the vertical gradient of refractivity in the atmosphere.

That directly affects the curvature of a beam of light or radio etc., so it directly

determines how far away the horizon is. Of course, maximum line of sight is

double the distance to the horizon.

Let's assume that the vertical gradient is zero, corresponding to a K-factor of 1,

meaning simply that the light doesn't curve at all, and follows a perfectly straight

path through the atmosphere between the tops of the towers. This is not too

common, but it's the way everybody always visualizes the situation ... as if light

doesn't bend ... and it makes the arithmetic easier.

We want d1d2/(1.5K) = 100-ftwhere d1 and d2 are the distances from each tower

to the horizon, or 1/2 of the total distance, and K = 1.

d2 = 150 and the total distance = 2d = 2 sqrt(150) = 24.5 miles (rounded)

(If you're following closely, you should be screaming in great irritation because of

the cavalier way in which we started with quantities in feet, and suddenly came up

with an answer in miles. You're entirely correct. The only reason that works is that

the number of feet in 1 mile happens to be so close to 1.5 times the number of miles

in the radius of the earth. That's the reason for the 1.5 in the denominator of the

deceptively simple formula highlighted above, and the reason why that formula is

only good for feet and miles, not for meters and Km.)