Richard Fry wrote:
. . .
Using your statements above the line, one might think that it rather
pointless to use anything longer than a 1/4-wave vertical. But going
from a 1/4-wave to a 1/2-wave vertical in fact will add ~1.6dB of gain
at the peak of the pattern envelope, and a 5/8-wave vertical will add
almost 3dB. These are worthwhile improvements in system performance.
Broadcast engineering consultants have recognized this, and used it to
advantage for decades.
. . .

It's important to realize that the graphs you posted are for surface
wave field strengths. This is equivalent to far field strengths at zero
elevation angle over perfect ground.

Amateurs seldom communicate by surface wave, except for local contacts.
When the vertical is surrounded by real ground, attenuation of the sky
wave at lower angles occurs. One of the results of this is that the
antennas which concentrate energy more at lower angles end up losing a
greater fraction of the total radiated energy. This tends to decrease
the gain difference between a 5/8 and 1/4 wave vertical, for example,
over a typical sky wave path.

In the case of VHF/UHF mobile operations, which are essentially line of
sight, the finite size of most ground planes (e.g. a car top) can affect
the pattern considerably, again altering the gain difference between
various heights of verticals.

While there's an extensive body of well established and proven knowledge
in the broadcast industry, we have to be careful in applying it to
typical amteur communications. Often, the conditions are different (as
in this discussion, of surface vs sky wave propagation; or fixed vs
variable frequency operation), and the important criteria are different
(a few percent difference in coverage area is important to a broadcaster
because of its impact on advertising revenue, but a fraction of a dB is
seldom important to an amateur; a broadcast phased array can take a long
time to design and adjust, but amateurs want to switch or change
directions). So we can't just assume that an antenna or method that's
best for a broadcaster is best for us.

Roy Lewallen, W7EL