Medhurst's Proximity-Effect Table for Solenoids
Factor Phi is the multiplication factor compared to the AC resistance of the
same length of wire if it were in a straight line. (See also Dr.Mark Rzeszotarski's text below, after line 55)
      Medhurst d/s and H/d vs. Phi table from paper (transposed)  
solenoid  
height to Wire diameter / Wire center-center Spacing: d/s  
diameter d/s  
H/D 1 0,9 0,8 0,7 0,6 0,5 0,4 0,3 0,2 0,1 row
0 5,31 3,73 2,74 2,12 1,74 1,44 1,26 1,16 1,07 1,02 11 d/s column
0,2 5,45 3,84 2,83 2,2 1,77 1,48 1,29 1,19 1,08 1,02 12 0,1 11
0,4 5,65 3,99 2,97 2,28 1,83 1,54 1,33 1,21 1,08 1,03 13 0,2 10
0,6 5,8 4,11 3,1 2,38 1,89 1,6 1,38 1,22 1,1 1,03 14 0,3 9
0,8 5,8 4,17 3,2 2,44 1,92 1,64 1,42 1,23 1,1 1,03 15 0,4 8
1 5,55 4,1 3,17 2,47 1,94 1,67 1,45 1,24 1,1 1,03 16 0,5 7
2 4,1 3,36 2,74 2,32 1,98 1,74 1,5 1,28 1,13 1,04 17 0,6 6
4 3,54 3,05 2,6 2,27 2,01 1,78 1,54 1,32 1,15 1,04 18 0,7 5
6 3,31 2,92 2,6 2,29 2,03 1,8 1,56 1,34 1,16 1,04 19 0,8 4
8 3,2 2,9 2,62 2,34 2,08 1,81 1,57 1,34 1,16 1,04 20 0,9 3
10 3,23 2,93 2,65 2,37 2,1 1,83 1,58 1,35 1,17 1,04 21 1 2
20 3,231818 2,931818 2,651616 2,369394 2,101212 1,83101 1,580707 1,350505 1,170202 1,040101 22
1000 3,41 3,11 2,81 2,31 2,22 1,93 1,65 1,4 1,19 1,05 23
Secondary Proxy-Effect:  
2 dimensional linear interpolation
row col d/s H/D Phi
i j xi yj zij=f(xi,yj) df/dx df/dy
d/s = x = 0,92 18 2 1 4 3,54 4,4000 -0,0900
H/D = y = 5,00 18 3 0,9 4 3,05 Dx Dy
19 2 1 6 3,31 -0,08047 1,0025
19 3 0,9 6 2,92
f(x,y)  ~  f(xo,yo) + (df/dx)*Dx + (df/dy)*Dy =zij =Phi 3,095706
Primary Proxy-Effect: rough guess; every primary taken as a helical-coil (=solenoid)
2 dimensional linear interpolation
row col d/s H/D Phi
i j xi yj zij=f(xi,yj) df/dx df/dy
d/s = x = 0,40 12 7 0,5 0,2 1,48 2,0000 0,2500
H/D = y = 0,37 12 8 0,4 0,2 1,29 Dx Dy
13 7 0,5 0,4 1,54 -0,1 0,166606
13 8 0,4 0,4 1,33
f(x,y)  ~  f(xo,yo) + (df/dx)*Dx + (df/dy)*Dy =zij =Phi 1,321651
 
Proximity Effect
Subject:  Re: space winding
From:  "Tesla list" <tesla@pupman.com>
Date:  Thu, 10 Aug 2000 12:26:14 -0600
Original poster: "Mark S. Rzeszotarski, Ph.D." <mrzeszotarsk@MetroHealth.org> 
Hello All:
Malcolm Watts replied in part to Robin Copini's questions about proximity
effect, and I thought I'd add a few comments as well:
>>  I have a question as to this 'proximity effect'?
        I have studied proximity effects quite a bit both through
experimentation and using computer modelling.  Here is some data from
Medhurst to give you an idea of the extent of the effect, based on a 4:1
length to diameter ratio for the coil:
 w   factor
1 3,54 w  =  d / s
0,9 3,05
0,8 2,6
0,7 2,27
0,6 2,01
0,5 1,7
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 tendancy 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.
>>  As I understand it, the effect comes about due to the field generated
>> by the wire affecting the adjacent wire. Now, considering that the
>> high current carrying part of the coil is the lower, say third, of the
>> secondary, would there be any advantage in spacewinding the lowest
>> quarter, or third of the secondary and then going closewound for the
>> rest. I assume someone would have done this, is there any quantitative,
>> (qualitative - bigger/brighter sparks :-)  ), results to this method?
>It would be tricky to wind a graded winding but I believe it 
>has been done by Dr Rzsesotarski or Terry. It would tend to 
>change the voltage profile of a bare resonator to something 
>more linear.
        Terry has some data on that on his web site which I also
participated in along these lines.  While altering the turns spacing does
improve the voltage profile along the secondary, the electrostatic
properties of a toroid do much the same thing in a standard coil system.  I
do not see an avenue for significant gains here since you are losing
inductance when you space wind.  You can control the breakout at the top
using the electrostatic shaping caused by the toroid by adjusting the height
and diameter of the toroid.  The fundamental limit appears to be resistive
losses in the primary circuit and poor energy transfer from the power supply
(poor design or inadequate NST performance).
>  As for turn-to-turn arcing, I too had some problem with this but it was
> eliminated after carefully fine tuning the coil.
        The standing waves that develop along the secondary are quite
complex if the primary and secondary are overcoupled, due to frequency
splitting.  (An overcoupled coil has dual resonance peaks, one above and one
below the driving frequency.)  A similar effect is seen with
primary/secondary tuned to different frequencies.  It canot be easily
modelled but is simple to rectify by starting with very loose coupling until
you get the tuning right.  I have looked at this with a coil that has
back-to-back LED's place every two inches along its lengh.  The standing
wave patterns are quite distinct for various tuning circumstances.  Get your
tuning right first, using a secondary at least one secondary diameter above
the top turn of the primary, then bring it down to increase the coupling to
the 15-23% range.  Stop when you start to get spurious breakout under LOW
POWER operation so you don't damage the coils.
Regards,
Mark S. Rzeszotarski, Ph.D.
Mark S. Rzeszotarski, Ph.D., MetroHealth Medical Center,Radiology
Department, Cleveland OH 44109-1998