Re: Inductance calculations

["Tesla list" <tesla-at-pupman-dot-com>]

Original poster: "Barton B. Anderson by way of Terry Fritz <teslalist-at-qwest-dot-net>" <classictesla-at-netzero-dot-com>

Antonio,

Tonight I wound a 5 turn helical at nearly 1 meter diameter. I read 
inductance with the 27XT.
For the measurement values, I already removed lead length inductance 
(dimensions in meters, L in uH). The 27XT cannot show enough digits beyond 
1mH, but ok to see how programs parallel.

Final dimensions:  r1,r2= .485775,  b=0, wd=.009525

height    turns    meas.    fantc    inca.g    moshier
-------    -----    -----    -----    ------    -------
.092075    5        49       49.33    49.3      49.15
.082042    4.5      42       41.37    -----     41.2
.071882    4        33       33.97    33.79     33.79
.061722    3.5      27       27.14    -----     26.96
.051562    3        20       20.92    20.83     20.73
.041402    2.5      15       15.36    -----     15.17
.031242    2        9        10.5     10.38     10.31
.021082    1.5      6        6.4      -----     6.23
.010922    1        2        3.32     3.02      2.99

As you can see, they all agree with measurement and follow as expected. I 
don't think the problem realized is with small number of turns (although 
the small turns will aggravate the problem). The problem I see occurs when 
the loop itself falls away from the horizontal and tends towards the 
vertical, as if it is stretched out. The further it is stretched, the more 
it resembles a straight conductor. Fantc, Acmi, and MandK move toward 
Wheeler as the coil is stretched which are is the geometry we've been 
discussing. Because of this coils large radius and distant proximity, the 
single turn should be very near to the straight wire inductance. When I 
tear down this 5 turn primary, I'll stretch it out to where the height = 
diameter and measure.

Take care,
Bart



Tesla list wrote:

>Original poster: "Antonio Carlos M. de Queiroz by way of Terry Fritz 
><teslalist-at-qwest-dot-net>" <acmq-at-compuland-dot-com.br>
>
>Tesla list wrote:
> >
> > Original poster: "Barton B. Anderson by way of Terry Fritz 
> <teslalist-at-qwest-dot-net>" <classictesla-at-netzero-dot-com>
> >
> > Hi Antonio,
> >
> > Ok, checking "Maxwell L" and "Elliptic fun" I get 45.96uH. I downloaded,
> > unzipped, and ran Steve Moshier's coil program. There certainly is
> > consistency between programs for the inductances identified. I ran each,
> > changing only heights to get a few rows of data ( r1r2=.5m, wd=.002m, t=5).
> >
> > ht      Fantc   Acmi    MandK  |  Inca     Moshier
> > 0.2m    39.35   39.32   39.44  |  45.96    46.38
> > 0.5m    25.87   25.84   25.93  |  35.29    35.74
> > 0.75m   20.45   20.43   20.50  |  31.11    31.60
> > 1.0m    16.96   16.93   16.99  |  28.48    29.04
>
>With the version now in my site the numbers will be a bit different,
>because I improved the precision of the elliptic functions:
>46.43, 35.75, 31.57, 28.94
>Even closer to Moshier, but our methods are very different.
>Numerical integration with 5000 segments/turn gives:
>46.41, 35.77, 31.64, 29.09
>So, the formula used in the coil program appears to take the spiral
>into account. Better than my rather dumb integrals that take forever
>to finish. I will try the formula in Moshier's program with my elliptic
>functions to see if they agree.
>
> > Maybe Paul can identify what is going on. Moshier's c-source is included
> > and appears well written and documented with referecences. I ran geometry 8
> > (Single-layer circular helical solenoid of round wire). coil.c points for
> > geo 8 points to "helsol" located in "formulae.c". There, Moshier references
> > Chester Snow '1952. I'm looking for papers on C. Snow but I'm not finding
> > much other than references. Somethings wrong on one side of the line or the
> > other if all are representing the same inductance inclusions.
>
>The problem appears when the number of turns is small.
>Testing a flat spiral, varying the external radius:
>Internal radius = 0.50, wire diameter = 0.002, meters.
>
>With 1 turn: Large difference.
>r2    Wheller   Inca (el. fun.) Inca (numerical) Fantc
>0.5   2.46 uH   4.11 uH         4.11 uH          4.11 uH
>0.75  1.98 uH   5.31 uH         5.30 uH          1.96 uH
>1     1.93 uH   6.55 uH         6.56 uH          1.89 uH
>1.25  1.98 uH   7.81 uH         7.88 uH          1.95 uH
>
>With 10 turns: Still significant difference.
>r2    Wheller  Inca (el. fun.) Fantc
>0.75  198 uH   210 uH          197 uH
>1     193 uH   212 uH          189 uH
>1.25  198 uH   226 uH          195 uH
>
>With 100 turns: Close.
>r2    Wheller  Inca (el. fun.) Fantc
>0.75  19.8 mH   19.6 uH        19.6 mH
>1     19.3 uH   19.0 uH        18.9 mH
>1.25  19.8 uH   19.6 uH        19.5 mH
>
>Some experimental measurements on coils with small number of turns
>would be useful. A problem is that the problematic coils mut be large
>to have easily measurable low-frequency inductances.
>
>Antonio Carlos M. de Queiroz
>
>
>
>