Francesco L., IK8VWA wrote:
"Once I saw an HF antenna called "the palm phased array",---. It was
based on two vertical dipoles strung onto two palm trees."

Sounds like a Franklin antenna, also known as a colinear array. Vertical
radiation pattern from a radiator that grows beyond 180-degrees starts
producing an undesired high-angle lobe in addition to the signal
radiated at low angles to the earth`s surface. The undesired radiation
is produced when current in the radiator reverses direction at the
180-degree mark. If we introduce a phase inverting device at the
180-degree mark on the radiator we increase radiation perpendicular to
the longer radiator without growing a high-angle lobe.

Many VHF colinear antennas use 1/4-wave stubs as phase inverters between
1/2-wave radiating sections. A resonant L-C circuit can be used in place
of a 1/4-wave short-circuit stub. A transformer can also be used to
reverse the phase as can various line feeds.

In the "International" edition or 3rd edition of Kraus` "Antennas" on
page 824 in Fig. 23-21(b) is shown a dipole made of (4) 1/2-wave
sections. It uses (2) self-resonant coils. Each coil separates a pair of
1/2-wave radiators so that all four radiators have current flowing in
the same direction through them at the same time.

Everyone needs access to the newest 3rd edition of "Antennas".

Best regards, Richard Harrison, KB5WZI