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Fw: Fw: Space winding
So...It's now morning & I see still another error in my postings of
yesterday: In 2.1 the square root of 0.5 is, of course, 0.707 and not
0.25. Thus, in 2.2, Q will increase to 0.707/0.25 = 2.8 times what it
was. And from that, in 3.1, the new voltage is going to be 0.5 x 2.8 =
1.4 x the old. So space-wound is better! Plus, even better than that by
my reasoning re the frequency.
I'm correcting my comments below, accordingly. So ignore my 2 prior
postings & think on this one.
KCH
--------- Forwarded message ----------
From: Kennan C Herrick <kcha1-at-juno-dot-com>
To: tesla-at-pupman-dot-com
Date: Fri, 11 Aug 2000 22:47:26 -0700
Subject: Fw: Space winding
Message-ID: <20000811.224729.-204753.1.kcha1-at-juno-dot-com>
Hold it...stop the presses! In my comments in my earlier posting of
today (included herewith) I forgot about "f"! The resonant frequency is
going to increase because a) L decreases (see 2.1 below) and b) the
distributed capacitance decreases because of the turn-spacing. By how
much, I don't know at the moment (it's past my bedtime + the 50-year
problem). But it means that Q will increase--perhaps by a lot--and so,
the developed voltage will not decrease so much if at all. Who can
quantify this for us?
KCH
--------- Forwarded message ----------
From: Kennan C Herrick <kcha1-at-juno-dot-com>
To: tesla-at-pupman-dot-com
Date: Fri, 11 Aug 2000 12:08:27 -0700
Subject: Space winding
Message-ID: <20000811.120830.-160465.0.kcha1-at-juno-dot-com>
I'm a bit reluctant to continue commenting on this subject: Although I'm
an E.E. college-graduate, it was 50 years ago & many of the details have
long gone. However...
First, I repeat the tabulation & commentary given recently by Mark S.
Rzeszotarski:
"...data from Medhurst to give you an idea of the extent of the
[proximity] effect, based on a 4:1 length to diameter ratio for the coil:
w factor
1.0 3.54
0.9 3.05
0.8 2.60
0.7 2.27
0.6 2.01
0.5 1.70
0.4 1.54
0.3 1.32
0.2 1.15
0.1 1.04
where w is the ratio of the wire diameter to the wire spacing (1.0 =
closewound, 0.1 means spacewound with 1 turn followed by 9 open spaces),
and factor is the multiplication factor compared to the AC resistance of
the same length of wire if it were in a straight line. If there are
currents flowing in two conductors which are close together, the electron
flow is compressed to a small fraction of the wire diameter, increasing
the
effective resistance significantly compared to the DC resistance of the
wire. Skin effect, which is the tendency of alternating currents to flow
on
the outside surface of the conductor, is frequency dependent while
proximity effect is primarily geometry dependent. It varies a bit with
solenoidal length:diameter ratio, being higher for low L:D coils than for
long coils.
Proximity effects further constrain the current flow inside the wire to
primarily the inside surface of the wire next to coil form, where the
electromagnetic repulsion from currents flowing in adjacent wires is a
minimum. This reduces the secondary coil Q fairly significantly (from
300
to 100 or so, ballpark). However, in an operating coil, the Q is killed
by
the primary anyway, and I see little to be gained by space winding since
there is a significant inductance penalty, and the goal of high output
voltage depends directly on the square root of Ls/Lp. My experiments
suggest that as long as the wire is not TOO small in diameter, the
effects
can be ignored in a coil designed to break out with sparks."
Now...my comments:
1. Secondary Q = wL/R where w=2 x pi x resonant frequency, L =
inductance & R = effective resistance. Also, L is proportional to n^2,
the square of the quantity of turns, other coil-shape factors being
equal.
2. From the tabulation, R diminishes, due to diminished
proximity-effect, by 1/2 for a tabulation-"w" of 0.5; that is, for the
case where the space between turns = the wire diameter.
2.1 But for that case, n has diminished to 1/2 of the prior quantity and
so L diminishes to (1/2)^(1/2) or .707 and also, ohmic R diminishes by
1/2 since the total wire length is 1/2 of what it was.
2.2 Thus, it would seem, total effective R will have diminished to 1/2 x
1/2 = 1/4 of that for the close-wound case. And thus, the new Q becomes
0.707/0.25 of the old Q, or 2.83 times greater.
3. The ultimate voltage developed in the secondary prior to a spark is
going to be directly proportional to n and also to Q, given a big enough
top toroid. (I differ with Dr. Rzeszotarski's assertion that the Q is
"killed by the primary": During the time of voltage build-up prior to
the spark, the higher the Q the higher the voltage--given a large enough
top toroid. Once the spark commences, the secondary's Q does become
immaterial, because of the major loading by the spark. Then,
power-delivery from the primary becomes important, in maintaining and
lengthening the spark. So, one might more properly say that the Q is
"killed by the spark".)
3.1 Thus, the 50%-space-wound secondary voltage is going to be 0.5 (the
new n) x 2.83 (the new Q) = 1.41 times the close-wound voltage. From
this I would conclude that space-wound is best. Plus, as I realized in
my 1st correction, f will increase and so Q will increase more because of
that.
4. >Furthermore<...consider this: With secondary n diminished to 1/2,
perhaps 2x the current can be delivered into the secondary from the
primary >after< the spark starts. That doubled current will act to
fatten and extend the spark to a greater degree than where n was not
diminished. That effect will tend to produce an even more satisfactory
spark.
So where do we stand on this? Who out there can properly quantify all
this? Or correct me if I'm wrong? Perhaps someone will provide a
tabulation such as Dr. Rzeszotarski's that includes "w", "factor", Q, f,
and then the resultant V (the relative secondary voltage absent a spark).
I'm in the process of space-winding a 12" x 48" Sonotube-secondary.
Perhaps I'll finish that and then make another exactly the same except
close-wound, & compare the two (With my self-tuned solid-state primary I
will be able to do that as quickly as I can swap one for the other; all
else will remain exactly the same.).
Ken Herrick
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