WolfMan wrote:
"And would there be an advantage with a 1/2-wave over a 1/4-wave?"

Short answer: Yes.

A dipole is directive. It has nulls at its ends and concentrates
response perpendicular to the wire. Even a very short, almost vanishing
dipole has these directional characteristics to some extent.

The theoretical isotropic antenna is the only truly nondirectional,
gainless antenna. Directive gain is the power intensity that is radiated
in the perferred direction versus the power intensity averaged in all
directions (1955 Terman, page 871).

Directive gain of an elementary doublet (dipole) is 1.5 as compared with
an isotropic. The gain of a resonant 1/2-wave is only 1.64, which is
only some better than a very short elementary doublet.

Gain and directivity are only part of the antenna story. Radiation
resistance and loss resistance appear as series components of a load
resistance. The larger the radiation resistance is as compared with loss
resistance, the more efficient is the antenna.

Radiation resistance of a short dipole is almost proportional to the
square of its length. So, it rised rapidly as the antenna gets longer in
terms of wavelength for the too short antenna. More radiation resistance
is usually better because efficiency rises.

Kraus says in his 1950 edition on page 137 that a dipole of 0.1
wavelength has a radiation resistance of 7.9 ohms. If the dipole is only
0,01 wavelength, its radiation resistance is 0.08 ohms. This agrees with
the length squared formula.

On page 146, Kraus says that the radiation resistance of an ordinary
1/2-wave dipole in free space is 73 ohms. This will be more efficient
than an antenna about 1/2 the size in nearly all cases.

Best regards, Richard Harrison, KB5WZI