curcumference of a circle = pi x (radius)^2 area of a sphere = 4pi x (radius)^2 This is elementary geometry. Only the profoundly ignorant do not know or use this.
it is spelled circumference
Earth curvature must figure into the problem at large distances.
yes, yet it is not. and we have multiple examples in which it is clearly violated (see the bottom of mountains from over 100 miles away)
that is entirely my point. you assume it is used, you are wrong.
Jump on a typo made with a tired mind. I'm shaking in my boots.
You are not really talking about curvature, but of the perceived horizon. In cases where it is possible to see as you claim (also seeing Chicago across Lake Michigan), what is in effect is the "fata morgana," a kind of atmospheric refraction that allows light to curve close to the curvature of the Earth. This is particularly the case with microwaves, which leads to calculating the radar horizon range as though the radius of the Earth were 4/3 of its physical value. (This effect goes away as the radar path becomes higher in the atmosphere.)
It is well understood that when the Sun is visibly touching the horizon, it is geometrically already under the horizon. This is due to refraction effects. But the sun still sinks lower and is progressively eclipsed by the horizon from the bottom to its top.
So microwave towers prove nothing for you. They are needed to "see" over the ground clutter and to have a communication path to the next nearest tower. They don't prove anything (you don't even hint at what they are supposed to prove).
it is spelled circumference
yes, yet it is not. and we have multiple examples in which it is clearly violated (see the bottom of mountains from over 100 miles away)
that is entirely my point. you assume it is used, you are wrong.
none. they prove my point
Jump on a typo made with a tired mind. I'm shaking in my boots.
You are not really talking about curvature, but of the perceived horizon. In cases where it is possible to see as you claim (also seeing Chicago across Lake Michigan), what is in effect is the "fata morgana," a kind of atmospheric refraction that allows light to curve close to the curvature of the Earth. This is particularly the case with microwaves, which leads to calculating the radar horizon range as though the radius of the Earth were 4/3 of its physical value. (This effect goes away as the radar path becomes higher in the atmosphere.)
It is well understood that when the Sun is visibly touching the horizon, it is geometrically already under the horizon. This is due to refraction effects. But the sun still sinks lower and is progressively eclipsed by the horizon from the bottom to its top.
So microwave towers prove nothing for you. They are needed to "see" over the ground clutter and to have a communication path to the next nearest tower. They don't prove anything (you don't even hint at what they are supposed to prove).