Re: Inductance calculations

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

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>

Bart,

 > Tonight I wound a 5 turn helical at nearly 1 meter diameter. I read
 > inductance with the 27XT.

I was avoiding this... Thank you for the experiment.

 > 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

A tube?

 > 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.

(The numbers that I get with Fantc are a bit different. 49.39 in the
first case and 3.23 in the last.)
Really, in this condition the calculations agree well, and Nature
agrees with them all, what is very good. Note, however that
the coil where I noticed the difference was made with thinner wire, with
2 mm of thickness. Thin wire causes the Maxwell and Snow (Moshier)
formulas to give larger values. Ok that big coils with thin wire are
rare in Tesla coiling... With 2 mm wire, the difference appears again
when the number of turns is greater than 1:

height    turns    fantc    inca (e.f.)   moshier
-------    -----   -----    -----         -------
.092075    5       49.41    53.97           53.93
.051562    3       20.96    23.63           23.59
.010922    1        3.24     3.98            3.95

I have now implemented in the Inca program the same formula that Moshier
uses (Snow), for comparison. It doesn't agree exactly with Maxwell,
but gets always very close (0.1% of difference when the spiral
is considered), and is fast.

 > 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.

This will show a difference. Do you have some #18 wire around? with 1 mm
of wire diameter an even larger difference shall be noticeable.

Antonio Carlos M. de Queiroz