Theoretically
Assuming:
The earth is perfectly round and flat, no high buildings, mountains, etc
Given:
r = radius of earth = 20925000 feet
l = seeing distance (in feet)
h = altitude (in feet)
1 nm = 6080 feet
We can calculate
r^2+l^2 = (r+h)^2
r^2+l^2 = r^2 + 2rh + h^2
l = sqrt(2rh + h^2)
l = sqrt(h*(2r+h) )
l = sqrt(2rh) -- drop h, because it is insignificant compared to 2r
l = sqrt(2*20925000*h)
l = 6500*sqrt(h)
l (converted to nm) = 6500*sqrt(h) / 6080 = 1.06*sqrt(h)
We find
Alt (ft) - Dist (nm)
01000 - 34
05000 - 75
10000 - 106
15000 - 130
20000 - 150
25000 - 168
30000 - 184
35000 - 198
40000 - 212
Does that sound/look right?
I drew a picture, but I don't have an area to upload.
Regards,
PieterPan