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Original poster: "Barton B. Anderson" <bartb@xxxxxxxxxxxxxxxx>

Hi Gerry,

Yes, there is much to be pondered on Gary's work. With this particular paper, I was impressed with his methods of measurement. I was satisfied that he explained the difficulties and how he overcame them. I was also very impressed with his adding of C to the topload to drop the frequency and how he went about it.

I'm not satisfied that his conclusions are right or wrong on every aspect (some are obviously correct, others require further assessment and measurement).

For the post at hand, Gary has already done the hard work for us. All we need to do is verify with a number of coils to get a good realization of our secondary losses. I don't expect Medhurst to perform well with our coils. His data just does not represent the full spectrum. It is correct for the spectrum he measured, but it would be helpful to simply perform the same with our coil specification range. If I had the time and the money, I'd love nothing more than to do just that. Such is life.

BTW, I expect your coil based on Terman at 53.92 ohms, and interestingly, Antonio's form at 61.95 ohms. Quite a difference! Also, both are quite different from the standard text book 38.24 ohms. I wonder which is right? Q will tell the tale, but that assumes Q measurement is correct, and we all know, there are a lot of "what can go wrong will go wrong" when measuring Q.

I'll be interested in what you come up with. Do you have all the goodies? Low Z amp? etc... If you need one, just ask. I can send my own your way or Terry may be able to londer his, etc. I think it's definitely worthwhile. Also, I would set up a flat ground plane for measurement somewhere where external effects are not capable of much influence. When I make Q measurements, I always do these in the backyard so that there is nothing to affect the reading. I keep the probe at least 10 feet away from the coil at center toroid height. I'll usually throw down a flat metal plate equal to the toroid OD for the ground plane. My personal coils have been rather low Q (300's range). It will be interesting if you can measure in the predicted 600's range.

Take care,
Bart

Tesla list wrote:

Original poster: "Gerry  Reynolds" <gerryreynolds@xxxxxxxxxxxxx>


Hi Bart,

Yeh, Fraga, Predos, and Chen did work on proximitry effects that I haven't read yet. Thankyou for explaining "T", I must have missed that connection. T is sorta like an absolute temperature based on the material (probably where the material superconducts) and not absolute zero. He just quoted the equations and didn't derive them since this has been in the literature since like the beginning of time :o)) His contribution seems to be presenting all this great theory in the context of TC's (at least the first part of his paper). There is much to ponder on with this paper.

Gerry R.


Original poster: "Barton B. Anderson" <bartb@xxxxxxxxxxxxxxxx>

Hi Gerry,

Yes, Gary has written an excellent paper and did well to check out Termans work as well as Fraga, Predos, Chen, etc.. as to how they compare with low and high h/d coils at low and high frequency's. Actually, Fraga has a closed loop equation which includes both proximity and skin losses which would be ideal (page 6-19). It appears good for closewound coils with an h/d of >> 4. Because most coils are in that range (not all), I think it's worth a look.

Otherwise, yes, the table can be put to good use, or even better, Antonio's calculation is easily implemented:
Rac/Rdc = (wr/sd)2/(2wr/sd-1)
A 5% swing is good enough for the task.


BTW, T is temp (page 6-4, eq.7)

Gary makes some interesting observations throughout his work on these losses.
Here are a few which stood out to me:

"It appears that as coils get shorter and fatter, the interior current in the coil gets larger
and the effective resistance increases as compared with the predictions of Medhurst and Fraga." (page 6-28).


"This table (3) indicates that the proximity effect can easily double or triple the measured
input resistance over that predicted by Rac for a straight wire of the same length." (page 6-11).


Yes,  some prediction by other are as hi as 5X


"Figs. 3 and 4 also show another effect, a very interesting concept that is otherwise difficult
to explain. This concept is that there is little penalty in performance if one uses a smaller wire
in a coil. That is, the effect on spark length is not as strongly related to the wire resistance
as one would expect." (page 6-25).


Just some eye catching paragraphs.

Take care,
Bart

Tesla list wrote:

Original poster: "Gerry Reynolds" <mailto:gerryreynolds@xxxxxxxxxxxxx><gerryreynolds@xxxxxxxxxxxxx>

Hi Jim and Bart,

The work that Dr Gary Johnson did for AC resistance seems to solve the Rac/Rdc problem for round wires (no proximitry effects). The differential equation for the current density J(r) is:

d^2 J/dr^2  +dJ/rdr +T^2 J =0  (not sure what T is)

The solution is a Bessel function of the first kind zero order and the solution does involve an infinite series. The current density is complex and has real and imaginary parts that vary with radius from the wire center. He carves up the wire into cylindrical shells and computes the average current density, cross sectional area, and current for each shell (still a complex number). He then computes the power in each shell by multiplying the current by its complex conjugate to get the real portion of I^2 for each shell. From this, the power in each shell is known. He then sums up the shell powers to get total power and divides by Rdc*|I|^2. Now for the good part.
He has created a table of Rac/Rdc for various ratios of wire_radius(wr)/flat_plane_skin_depth(sd). The following table shows this for wr/sd up to 8.


wr/sd      Rac/Rdc
------------------
  1            1.020
  2            1.263
  3            1.763
  4            2.261
  5            2.743
  6            3.221
  7            3.693
  8            4.154

Bart, what I'm thinking is since you compute the sd and know the wr, you can just interpolate into the table and use the Rdc to compute the Rac.

Jim, how does Gary's table compare to the RDRE table???

Gerry R.