Aunwin, we are talking about two different things.

If I want to communicate (optimally) with another station it is important
that I know the direction and elevation angle at which to point my antenna
such that the radio beam preferentially returns to Earth in the vicinity of
the other station.

Direction is found from a map of the Earth's surface plus a magnetic
compass.

The ONLY way to find the elevation angle is to CALCULATE it from the ground
path distance between the two stations, the height of the reflecting layer,
and the number of hops along the path.

It's purely a matter of Spherical Geometry. It has nothing to do with where
your antenna happens to be pointing. Or even whether or not you have an
antenna.

All good radio engineers do it that way. Caculating formulae can be found in
practical radio engineering books. Eznec won't tell you.

Use simple program TWOHOPS to do common calculations. Results are as
accurate as the inevitably uncertain input data.
---
.................................................. ..........
Regards from Reg, G4FGQ
For Free Radio Design Software go to
http://www.btinternet.com/~g4fgq.regp
.................................................. ..........

Reg, G4FGQ wrote:
"It`s purely a matter of Spherical Geometry"

Edmund A. Laport agrees with Reg in his book "Radio Antenna
Engineering". On page 227 Ed writes:
"If, for example, the computed vertical beam angle for a one-hop circuit
uses 6 degrees at an azimuth of 332 degrees and the horizon in this
direction consisted of a mountain range with a height of 8 degrees, the
performance of the circuit would be greatly compromised by the
obstruction of the mountains. In such a case it might be better to work
this circuit with two hops. Then a vertical beam angle of 20 degrees can
be used instead, with adequate horizon clearance for the wave path. Or
if the circuit required 6 degrees for a two-hop circuit 5400 kilometers
long, with the same obstruction cited, one could change to a three-hop
circuit which for the same layer height would permit the use of a beam
at 14 degrees."

Best regards, Richard Harrison, KB5WZI

"Richard Harrison" wrote in message
...
Reg, G4FGQ wrote:
"It`s purely a matter of Spherical Geometry"

Edmund A. Laport agrees with Reg in his book "Radio Antenna
Engineering". On page 227 Ed writes:
"If, for example, the computed vertical beam angle for a one-hop circuit
uses 6 degrees at an azimuth of 332 degrees and the horizon in this
direction consisted of a mountain range with a height of 8 degrees, the
performance of the circuit would be greatly compromised by the
obstruction of the mountains. In such a case it might be better to work
this circuit with two hops. Then a vertical beam angle of 20 degrees can
be used instead, with adequate horizon clearance for the wave path. Or
if the circuit required 6 degrees for a two-hop circuit 5400 kilometers
long, with the same obstruction cited, one could change to a three-hop
circuit which for the same layer height would permit the use of a beam
at 14 degrees."

Best regards, Richard Harrison, KB5WZI



OR ....... you take advantage of diffraction abilities of physical parts
such as
mountain edges or other physical parts that can deflect the rays AFTER it
leaves
the FEED POINT which does NOT exclude an antenna array of which the feed
point
is part. The point of confusion emanates from.calculating hop distance on
the
basis of a :"standard:". TOA The "magic" of a stacked antenna exposes
the difference
:that occurs with a different TOA.
I suppose you could use Reg's program so that when the ideal conditions do
occur
maybe after several hours of waiting , when one can say that the upper
layers are now
exactly such or such a height and the assumption used in formulating the
program
are now correct. The fact is that ham radio is about formulating an array
that will
provide the hop distance required by the operator since that is something
he can change.
I am quite sure that LaPorte does NOT say that no amount of shaking an
antenna can
change the hop distance which is what TOA is all about and the subject of
this thread.
Maybe we need another thread to clarify the question that Reg and yourself
are
apparently addressing.

Art

Reg, G4FGQ wrote:
"It`s purely a matter of Spherical Geometry."
The ARRL agrees with Reg. The 19th edition of the ARRL Antenna Book on
page 23-24 gives path distance versus vertical wave angle for a one-hop
transmission using the F2 layer in Fig 23. Of course these are only
based on a variable reflecting layer height.

For 500 miles, 40 to 70 degrees.

For 1000 miles, 20 to 35 degrees.

For 1500 miles, 10 to 22 degrees.

For 2000 miles, 4 to 15 degrees.

For 2500 miles, less than 8 degrees.

Neither elevation nor azimuth angles are exact as the wave is subject to
detours but it helps to have an idea of the usual best angles.

Best regards, Richard Harrison, KB5WZI