In item 2 you make an unsupported statement: "Give that the coil is 90
degrees at the self-resonant frequency,..."

Self resonance only means that the capacitive and inductive reactances,
both distributed, are equal. That does not validate a 90 degree
assumption. Without that validation, IMO, the subsequent discussion is
questionable.



Cecil Moore wrote:

Dave wrote:

I gave up on the 'missing degrees' and all variations topic about 1
month ago. Hit the KILL Button and read on!


For those who didn't give up, here is a summary of what I
was able to do with EZNEC. This exercise should be able
to be repeated in the real world.

1. Using the helix feature of EZNEC, I created a 100 turn
octagonal coil, 6 inches in diameter, 4 turns per inch.

2. I installed it as a base loading coil over a mininec
ground plane and removed turns until it was self-resonant
on 4 MHz. That left a total of 69 turns on a 1.435 foot
long coil. Give that the coil is 90 degrees at the self-
resonant frequency, I calculated a velocity factor of
0.023 for the coil.

3. The coil was then trimmed to half size, i.e. 34.5 turns.
Assuming it was then 45 degrees long, the Z0 was determined
to be approximately 2200 ohms by looking at the feedpoint
impedance reported by EZNEC. 45 degrees from 0-j0 on the
Smith Chart is at -j1.0.

4. A stinger was added to the above 45 degrees of coil to
bring the antenna back to resonance on 4 MHz. It took 7 ft.
of stinger, or 10.2 degrees. 10.2 degrees from 0-j*infinity
on the Smith Chart is at -j4.8.

5. The ratio of -j4.8/-j1.0 is the ratio of the Z0 of the
coil to the Z0 of the stinger. If the Z0 of the coil is
indeed 2200 ohms, the Z0 of the stinger is 458 ohms, just
about where it should be. The impedance discontinuity
provides the "missing" ~35 degrees of the antenna.

6. Using Dr. Corum's equation for velocity factor yields
0.02 for that coil, a value 13% lower than the one
predicted by EZNEC, well within the ballpark for
expectations.

My conclusions: The delay through a loading coil is in
the tens of degrees. The delay through the elements of
the antenna do not add up to 90 degrees. In the above
EZNEC example, the delay from feedpoint to the tip of
the antenna is only 55 degrees. The "missing"
degrees are provided by the impedance discontinuity
between the coil and the stinger. There is no real-
time delay associated with those "missing" degrees.