In article <(E-Mail Removed) >,
Jeff Moon <(E-Mail Removed)> wrote:
:The maximum transmitting distance for any wireless transmissions above
:about 30MHz (which includes 802.11, Wi-Fi) is determined by:

= Sqrt(2*H)
:Where:

= maximum distances (in miles)
:H = The height above ground for your transmitting antenna (in feet)
Jeff, when I plow through the algebra, I get a result which is
about 5/6 times what your formula would calculate. But
it would depend on the assumptions, so let's cross-check: for the
formula you show to hold, is the assumption that the transmitter and
receiving are both at height H above the ground (relative to the local
'down')? Or does the formula assume that the transmitter is at ground
level and the receiver at that height? Also, which distance is that
formula measuring: the straight-line distance from the transmitter
to receiver, or the curvilinear distance around the Earth from the
transmitter to the base of the receiver pole?
The formula I get for the case where the transmitter is at ground
level is D = Sqrt(H^2 + 2RH) / 5280 where D is in miles, and H and
R are in feet, and R is the radius of the Earth. If one says that
R >> H then H^2 effectively vanishes compared to 2RH, allowing the
simplification D = Sqrt(2RH)/5280 . If one lets r be the radius of
the Earth in miles, then D = Sqrt(2rH * 5280) / 5280 and then
D = Sqrt(2H) * Sqrt(r/5280). r is about 3963 so the multiplier comes
out about 0.866, which is roughly 5/6.
D ~= 5/6 Sqrt(2*H)
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