"Cecil Moore" bravely wrote to "All" (04 Mar 05 09:58:05)
--- on the heady topic of " How can I measure or observe my hf antenna's
take off angle?"

CM From: Cecil Moore
CM Xref: aeinews rec.radio.amateur.antenna:26384

CM wrote:
TOA is deemed to be the angle at which maximum gain occurs.
Seems like you are fishing for something, but you will not get
it from me.

CM The problem seems to be that the definition of TOA is
CM not standardized. Literally, TOA can be any angle but
CM has a special meaning when quoting EZNEC. Neither my
CM antenna books nor "The IEEE Dictionary" define TOA.
CM I did a search for "take off angle" and "TOA" on my
CM ARRL Antenna Book CD with zero results.

I hope this, from an old antenna book, is relevant in finding
something called "vertical lobing".

It has:
(for a 1/2 wave vertical dipole, I gather)

N = Height in ft. x Frequency in Mc
------------
984

where the number N is number of wavelengths. It locates the angle
above ground at which the 1st maximum lobe is transmitted.

then using this approximation gets the maximum signal at:
tan (theta) = H/D

and the zero signal:
sin (theta) = 1/2N

where H is the height above "flat" earth of the receiving antenna
and D is the path length (in the same units)

when H/D = 1/(4N) a 1st maximum lobe is attained at the receiving
antenna.

There's more for the actual height at the receiving location and other
lobes, nulls, etc...

A*s*i*m*o*v

.... And some fell upon stony ground and had no THC at all.