It's really quite simple and fundamental. The "takeoff angle" (elevation
angle at which the pattern is maximum) depends on both the height and
the free-space vertical pattern of the antenna. Yagis end up having a
vertical pattern similar to a dipole in the forward direction because
the Yagi provides very little concentration in the elevation plane. Some
antennas do provide substantial concentration in the elevation plane,
however, such as a W8JK, or collinear as you mention. The elevation
patterns of vertically polarized antennas are further modified by the
different reflection coefficient encountered by vertically polarized waves.

Kraus has a good discussion of ground reflection coefficient in
_Antennas_. The vertical patterns reported by AO and similar programs
can be derived by hand from the free space pattern and reflections from
the ground using the reflection coefficients derived in Kraus.

Roy Lewallen, W7EL

Art Unwin KB9MZ wrote:
I had always thought that take off angle was
a function purely based on ht over ground
and nothing else.
When experimenting with my AO computor program
on colliear arangements I.E. without booms, I
am finding that the 'Take off' angle becomes lower
with increasing gain over a dipole.
The top edge of the leading lobe stays constant
with that of a single dipole but with the slight
lowering of the lobe angle as much as 1db of
increase in gain are obtainable at the LOWEST angle.
Does anyone know of a text book that discusses the
why's and wherefores of these lower angle gains
together with its 'known' limitations?
Is it possible that it is a parallelogram
resultant of increased vector value versus the
ground influence constant?

Regards
Art Unwin