That's all very nice. Let's see if it's useful for anything.

A while back, Cecil posted a model of a base loaded vertical antenna. It
has an inductor which is vertically oriented. The bottom of the inductor
is 1 foot from the ground and the inductor is 1 foot long and six inches
in diameter. Inductance is 38.5 uH and it's self resonant at 13.48 MHz.
(Moving it very far from ground changes the resonant frequency to 13.52
MHz.)

What's it's velocity factor, and how did you calculate it?

Roy Lewallen, W7EL


Richard Harrison wrote:
Reg, G4FGQ wrote:
"I`m even more certain you will find an equation for inductance of an
isolated wire of length L: and diameter D somewhere in the bibles."

Equation 14 on page 48 of Terman`s 1943 edition of "Radio Engineers`
Handbook is:

Lo = 0.00508 l (2.303 log 4l/d - 1+mu/4) microhenrys

Lo is the (approximate) low-frequency inductance and the dimensions are
in inches.

Terman also gives the (approximate) low-frequency inductance formula of
a single-layer solenoid on page 55 of the same book.

One can find the resonant frequency of the coil when using a known
capacitance to resonate the coil at a low frequency. Maybe a dip meter
could be used. Capacitive and inductive reactances are equal at
resonance. Self and stray capacitances are included with the known value
of capacitance used to resonate the coil at the low frequency. The
resonant frequency is lower than the known capacitance by itself would
produce.

The resonance formula used with the actual inductance of the coil will
give the capacitance of the resonant circuit

The difference between the calculated capacitance and the known
capacitor value is equal to the stray and self-capacitance total, so it
is good to minimise stray capacitance when seeking the self-capacitance
value of the coil.

An ARRL Single-Layer Coil Winding Calculator is a slide rule which makes
things easy.

Best regards, Richard Harrison, KB5WZI

Roy Lewallen wrote:

What's it's velocity factor, and how did you calculate it?

I can't believe I did that! It must be from spending too much time
reading Internet postings. Of course I meant:

What's its velocity factor, and how did you calculate it?
^^^
I knew better than that by the time I'd finished grade school. Hope it
isn't all downhill from here.

Roy Lewallen, W7EL

Roy, W7EL wrote:
"What is the velocity factor, and how did you calculate it?"

Given:
length = 12 inches
diamwter = 6 in.
L = 38.6 microhenry

I used formula (37) from Terman`s Handbook to calculate 25 turns in the
coil. 471 inches of wire are needed in the coil.

The velocity of the EM wave traveling around the turns of the coil is
almost equal to the velocity in a straight wire. But, the time required
to travel 471 inches is 40 times the time required to travel 12 inches.
The velocity factor is the reciprocal of 40 or 0.025.

Best regards, Richard Harrison, KB5WZI

Richard Harrison wrote:

Roy, W7EL wrote:
"What is the velocity factor, and how did you calculate it?"

Given:
length = 12 inches
diamwter = 6 in.
L = 38.6 microhenry

I used formula (37) from Terman`s Handbook to calculate 25 turns in the
coil. 471 inches of wire are needed in the coil.

The velocity of the EM wave traveling around the turns of the coil is
almost equal to the velocity in a straight wire. But, the time required
to travel 471 inches is 40 times the time required to travel 12 inches.
The velocity factor is the reciprocal of 40 or 0.025.

13.48 MHz is not exactly the self-resonant frequency of the
coil. At 13.48 MHz, the one foot bottom section is 0.0137
wavelengths long, i.e. 4.9 degrees. So the coil occupies
~85.1 degrees at self-resonance. The coil length is coincidentally
also one foot so the velocity factor is 4.9/85.1 = 0.058.

I don't have the Terman Handbook. Does he take adjacent coil
coupling into account in that formula? If not, that's the
difference in the two results.

In either case, the velocity factor is not anywhere near 1.0
as the lumped circuit model would have us believe.

Does anyone have a formula for what percentage of current is
induced in coils farther and farther away from the primary
coil? I haven't found such a formula in my references but it's
got to exist.
--
73, Cecil http://www.qsl.net/w5dxp

Cecil, W5DXP wrote:
"I don`t have the Terman Handbook."

Formula (37) on page 55 of the 1943 "Radio Engineers` Handbook is:

Lo = (r sq) (n sq) / 9(r) + 10(l)
Lo = approximate low-frequency inductance of a single-layer solenoid in
microhenries where r is the radius and l is the length of the coil in
inches.

Terman attributes the formula to H.A. Wheeler, "Simple Inductance
Formulas for Radio Coils", Proc. I.R.E., Vol 16, P1398, October 1928.

Best regards, Richard Harrison, KB5WZI

Richard Harrison wrote:
Roy, W7EL wrote:
"What is the velocity factor, and how did you calculate it?"

Given:
length = 12 inches
diamwter = 6 in.
L = 38.6 microhenry

I used formula (37) from Terman`s Handbook to calculate 25 turns in the
coil. 471 inches of wire are needed in the coil.

The velocity of the EM wave traveling around the turns of the coil is
almost equal to the velocity in a straight wire. But, the time required
to travel 471 inches is 40 times the time required to travel 12 inches.
The velocity factor is the reciprocal of 40 or 0.025.

Not quite what I was expecting, but let's see if I understand what it
means. This means that if we put a current into one end of the inductor,
it'll take about 40 ns for current to reach the other end, right? So we
should expect a phase delay in the current of 180 degrees at 6.15 MHz,
or about 30 degrees at 1 MHz, from one end to the other?

Roy Lewallen, W7EL

"Roy Lewallen" wrote:
Richard Harrison wrote:
The velocity of the EM wave traveling around the turns of the coil is
almost equal to the velocity in a straight wire. But, the time required
to travel 471 inches is 40 times the time required to travel 12 inches.
The velocity factor is the reciprocal of 40 or 0.025.

Not quite what I was expecting, but let's see if I understand what it
means. This means that if we put a current into one end of the inductor,
it'll take about 40 ns for current to reach the other end, right? So we
should expect a phase delay in the current of 180 degrees at 6.15 MHz,
or about 30 degrees at 1 MHz, from one end to the other?

Dr. Corum's VF equation predicts a VF of approximately double
Richard's with corresponding delays of 1/2 of your calculated
values.
--
73, Cecil, W5DXP

Cecil, W5DXP wrote:
"Dr. Corum`s VF equation predicts a VF of approximately double
Richard`s----."

I wonder why? Dr. Terman wrote that the wave follows the turns in a
coil. My recollection of common solid-dielectric coax VF is about 2/3
that of free-space due to the fense plastic.

Twice the velocity factor in a coil requires a wave traveling faster
than light or taking a short-cut around the turns.

I often learn from my mistakes. Where did I err?

Best regards, Richard Harrison, KB5WZI

"Richard Harrison" wrote:
Twice the velocity factor in a coil requires a wave traveling faster
than light or taking a short-cut around the turns.

I often learn from my mistakes. Where did I err?

The current does take a short-cut due to adjacent coil coupling.
But please note the velocity factor only approximately doubles
from the "round and round the coil" calculation. Even though a
VF of 0.04 is ~double the "round and round the coil" approximation,
it is still 96% away from the VF=1.0 originally asserted by W8JI
which assumes that all the coils couple 100% to all the other coils.
--
73, Cecil, W5DXP

Cecil, W5DXP wrote:
"The current does take a short-cut due to adjacent coil coupling."

R.W.P. King wrote on page 81 of Transmission Lines, Antennas, and Wave
Guides:
"The electromagnetic field in the near zone is characterized by an
inverse-square law for amplitude and by quasi-instantaneous action."

I still don`t know what to make of King`s assertion regards
instantaneous action.

Best regards, Richard Harrison, KB5WZI