Bob, K6RTM wrote:
"Discones are covered in section 8.37 and log periodics are covered in
section 8.21."

In my 3rd edition of the RSGB VHF/UHF Manual, the discone is on page
7.28 and the log periodic is on page 7.35.

Bob also wrote:
"The take-off angle increases with the frequency."

In my experience, the vertical angle of maximum radiation, in general,
decreases with antenna height above the earth, when the height of the
antenna in is not over 5/8 wavelength.

Increasing the frequency used with an antenna of fixed height is
equivalent to increasing the height of an antenna using a fixed
frequency because it is a function of antenna height above the
reflecting surface in terms of wavelength. It is all a matter of scale.
At double the frequency, an antenna only needs half the physical height
to be the same elevation above ground to have the same elevation in
terms of wavelength. Soil conductivity and depth of penetration in the
earth are being ignored in the comparison for simplicity. It`s no big
deal.

A 1/2-wave horizontal dipole erected 1/4-wave over good earth has its
maximum radiation toward the zenith. The same antenna elevated to
1/2-wave above the earth has a take-off angle near 30 degrees above the
horizon.

When antenna height exceeds 5/8 wavelength, added lobes appear in the
vertical radiation pattern. The additional lobes appear in the vertical
radiation patterns of vertical antennas too when their heights exceed
5/8-wavelength. It is for this reason that AM broadcast stations usually
limit their towers to no more than 5/8-wavelength. Sky wave propagation
could produce substantial interference with the ground wave signal at
relatively short distances at night from the high-angle radiation.

In a sense Bob is correct in that some of the take-off angle increases
with frequency, in that it produces growth of additional lobes in the
take-off pattern.

Best regards, Richard Harrison, KB5WZI