Richard Fry wrote:
But it doesn't mean that
a self-resonant, normal-mode helix has the radiation resistance and
radiation system efficiency of a linear, 1/4-wave monopole (other
things equal).

Here's a data point. Awhile back, using EZNEC to simulate
the delay through a 75m bugcatcher loading coil, I used
the coil pretty close to its self-resonant frequency of
~7 MHz. It had a 4 inch bottom section and a 4 inch
stinger so the antenna is about 14 inches long. The
resonant feedpoint impedance is 2 ohms (not including
ground losses) and the maximum gain is -14.8 dB.

Assuming a typical 1/4WL monopole has a maximum gain of
0 dB, the 1/4WL monopole is 30x the efficiency of this
short "helical" antenna on 6.85 MHz. So it seems that
the radiation resistance is ~1/30 that of a 1/4WL
monopole using mininec ground simulation.

Incidentally, a resonant helical monopole obviously
has a 90 degree delay from feedpoint to tip. The reason
that virtually zero phase shift occurs through the coil
is that one is sampling standing-wave current phase which
doesn't change (much) whether it is through a coil or
through a 1/4WL wire. Quoting my web page at:

http://www.w5dxp.com/current2.htm

"Standing wave current cannot be used to directly measure
either a valid amplitude change or a valid phase shift through
a loading coil. All of the reported conclusions based on
loading coil measurements using standing-wave current on
standing-wave antennas are conceptually flawed."
--
73, Cecil http://www.w5dxp.com