Space winding

["Kennan C Herrick" <kcha1-at-juno-dot-com> (by way of Terry Fritz <twftesla-at-uswest-dot-net>)]

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 .25 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
0.25/0.25 of the old Q, or just the same.

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 1 (the same Q) = 0.5 times the close-wound voltage.  From this I
would conclude that tightly-wound is best, absent any problem due to
turn:turn sparking.

4.  >However<...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 may or may not overcome the reduction in initial
spark-voltage to 1/2, in producing a satisfactory spark.

So where do we stand on this?  Will it or won't it?  Who out there can
properly quantify all this?  Or correct me if I'm wrong?

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
________________________________________________________________