Richard Harrison wrote:
. . .
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.

The dipole Kraus is analyzing (shown in his fig. 5-1 on p. 127) isn't
what we'd normally call an "ordinary dipole". As this figure and the
accompanying text show, Kraus' short dipole is heavily end loaded to
cause the current to be uniform along its length. This increases its
radiation resistance by exactly a factor of four over that of a short
unloaded dipole (a plain straight piece of wire fed in the center),
whose current drops uniformly from the center to a value of zero at the
ends.

The equation for a short unloaded dipole can be found in the same
edition of Kraus on p. 262 as eq. 10-63, R11 = 5 * (beta * L)^2. The
quantity in parentheses (beta * L) equals 2 * pi * the dipole length in
wavelengths, so for a 0.1 wavelength dipole, it gives the radiation
resistance as just a smidge under 2 ohms. (EZNEC gives just over 2 ohms
for example model Dipole1.ez with the frequency changed to 60 MHz to
make the antenna 0.1 wavelength long. Remember that the Kraus formula is
an approximation, and for an infinitesimally thin antenna.)

This makes Richard's observation about efficiency even more true.

Roy Lewallen, W7EL