Richard Fry wrote:
"Was the 0.05 lambda the pitch of the helix? If so, how many turns?"

I`ll quote Bill Orr for accuracy:
"Resonance can be established at a given frequency by the use of a
short, helically-wound element (Fig. 14). Treated bamboo poles (J L`s
choice), PVC plastic tubing, or fiberglass quad antenna spreaders can be
used as a form on which to wind the helix. Diameter for the helix must
be small in relation to length and a practical design makes use of a one
inch (25,4 mm) winding form. A helix length of about .05 wavelength or
more provides good results as a substitute for a full-size quarter
wavelength vertical antenna.

The amount of wire required for the winding depends upon helix length
and pitch (turns per inch). In general, a half-wavelength of no. 14
Formvar-coated wire is spirally wrapped on the form, with spacing
approximately equal to the wire diameter. This amount of wire
approximates a auarter-wave resonance"

There are helical antennas of two types. The "axial mode" invented by
John D. Kraus which radiates in the direction of the coil axis and the
"normal mode" helical antenna which radiates in directions perpendicular
to the coil axis, as does a short straight wire. Carried to extremes,
the pitch could go to zero,in which case the coil becomes a loop, or the
coil is stretched out to a straight wire. The helical antenna referred
to by Orr, is the normal-node helical antenna.

While the axial-mode helix is a broad-band antenna, the normal-mode
helix is a high-Q antenna and has restricted bandwidth. Orr has
something to say about the high-Q normal-mode helix:
"In order to prevent any high voltage discharge, a 12-ibch (30 cm)
diameter wire top hat is attached to the helix. Antenna resonance can be
adjusted by varying the size of the hat, or by adding a small extra
inductance at the base of the antenna."

There was also a question about directive gain which often brings a
surprised response. Terman is my source for directive gain. On page 871
of his 1955 edition of "Electronic and Radio Engineering" he gives the
directive gain, not in decibles, of 1.5 for the directive gain of the
elementary doublet. It is not isotropic. It is however infinitesimally
short. In the same Table 23-1, Terman gives the gain of the full
half-wave dipole as 1.64. There is precious little difference in
directivity or gain, which are two sides of the same coin, more or less.
Maybe Art can make a high-gain antenna of very short elements if he can
just get them to take a lot of current and not waste much to loss

Best regards, Richard Harrison, KB5WZI