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Re: Conical primary formula questions.



Original poster: "Barton B. Anderson by way of Terry Fritz <twftesla-at-uswest-dot-net>" <tesla123-at-pacbell-dot-net>

Hi Pete, 

Good post! I too (many times) have found the conical equations odd in the
respect of increasing L as it varies up then down depending on degree input,
but I never asked the question or studied the problem. I use the conical
equations in my personal and JavaTC programs due the ability to enter angles
including 0 for flat and 90 for helical (and everything in between). However,
you are correct that there is error with the conical equation. 

I just ran a check. My primary input was as follows. 
12 turn, 0.375 wire dia., 0.158 spacing, 16.75 ID. 

At 0 degree, I calc 118.13uH. As an angle is entered, L increases to a max at
27 degrees at 123.94uH. It then begins to decrease down to 61.43uH at 90 deg.
It actually matches the 0 degree angle when 42.88 degrees is used. 

I then used Acmi to check. I used the highest inductance of 27 degrees calc'd
at 123.94uH with the conical equation. Acmi result was 116.7uH which is far
more reasonable than the conical equation. So, Acmi agrees with you, and
although I haven't been able to verify conical inductances yet with Acmi, I
have a good feeling that the current filiment solving method Paul has put
together is fairly accurate. 

It should be noted that using an angle of 0 for the flat primary results in a
pretty accurate inductance with the conical equation. 

I'm not sure how to fix this. You presented a method but I haven't checked that
yet. I will soon. If it fairs well, I'll replace the equations in my personal
and JavaTC programs. 

Thanks again for posting this. 

Bart 

Tesla list wrote: 
>
> Original poster: "Pete Komen by way of Terry Fritz <twftesla-at-uswest-dot-net>"
> <pkomen-at-zianet-dot-com> 
>
> After much fiddling with numbers on an Excel spreadsheet, I think that the 
> formula for the inverse conical coil is off or more precisely the 
> measurement of H and W and R are not what they should be.  If measured on 
> the cone shape they yield a higher value for the cone than for a flat or 
> helical coil of the same number of turns.  The reduction in radius for the 
> conical coil indicates to me that the inductance should fall, not increase. 
>
> >From the archives: 
>
> <http://www.pupman-dot-com/listarchives/1998/December/msg00023.html>http://www
> .pupman-dot-com/listarchives/1998/December/msg00023.html 
> Case 3: Inverse Conical Primary: 
>
>                                     / \ 
>     --  o                          /    o 
>      |   o                        /    o 
>      |    o   N turns            /    o 
>            o                 Z  /    o 
>      h      o                  /    o   / 
>              o                /    o   / 
>      |        o              /    o   /  Angle = X 
>      |         o              \  o   / 
>     --          o               o    ------------ 
>                         | 
>         |   w   |   R   | 
>                         | 
>             |<--  W  -->| 
>                         ^ 
>                  Center | Line 
>
>           Z = Coil Width (hypotenuse length) 
>           X = Angle of Cone 
>           h = Z*sin(X)  Effective vertical Height 
>           w = Z*cos(X)  Effective horizontal Width 
>           W = R + w/2   Average horizontal Radius 
>
>      L1 = W^2*N^2/(9*W+10*h)  (Vertical Inductance Component) 
>
>      L2 = W^2*N^2/(8*W+11*w)  (Horizontal Inductance Component) 
>
>       L = SQRT[(L1*Sin(X))^2 + (L2*cos(X))^2] 
>
> Call this one the Widely Accepted Method (WAM). 
>
> I feel a bit presumptuous and I could well be wrong, but I have a modified 
> method which gives what I believe are better results. 
>
> For example: 
>
> Assume 15 turns of 1/4 inch tubing spaced 3/8 inch apart.  W (spiral) equals 
> H (helical) equals Z above equals 9 inches (I've even wondered about that, 
> it doesn't really take into account the spiral...).  Assume that the radius 
> of the inner wind is 5.5 inches. 
>
> Helical:  R = 5.5 inches, H = 9 inches 
> Spiral:   R = 10 inches, W = 9 inches 
> I would use those values to calculate the inductance for the spiral and the 
> helix; then plug those inductances into the conical formula and vary only 
> the angle. 
>
> For the widely accepted method (WAM), the following would be used: 
> Angle of elevation of cone is X. 
> Helical:  R = 5.5 + 9 * cosine(X) / 2,  H = 9 * sine(X) 
> Spiral:  R = 5.5 + 9 * cosine(X) / 2,    W = 9 * cosine(X) 
>
> These are used to calculate the inductance for the helical and spiral 
> components for each angle considered.  Then those inductances are plugged 
> into the WAM equation. 
>
>                         in microhenries 
> Angle radians           My Method   Inductance WAM 
> 0     0                 125.70      125.70 
> 15    0.261799167       122.07      130.94 
> 30    0.523598333       111.56      131.58 
> 45    0.7853975          95.34      120.62 
> 60    1.047196667        75.73       99.76 
> 75    1.308995833        57.27       73.43 
> 90    1.570795           48.79       48.79 
>
> The key thing is the increase (over the larger R flat spiral) at 15 and 30 
> degrees (there is a maximum around 24.6 degrees).  I can imagine an ellipse 
> if this was graphed but not this bulge for low angled conical coils. 
>
> I also observe in these formulas that the inductance is (sort of) 
> proportional to the average radius.  So it doesn't make sense to me, that a 
> little angle from horizontal would increase the inductance. 
>
> My questions are these: 
>
> Where does the formula for conical primaries originate?  Has this been 
> checked against actual measurements?  (I would build and measure but I am 
> already spending enough building a coil.  Now is not the time to spend money 
> on test equipment).  Is there some reason that the inductance using WAM 
> increases for the conical primary beyond the flat spiral value while the 
> average radius is decreasing? 
>
> Pete Komen 
>
> Special thanks to Matt Behrend for his kind responses when I emailed him 
> with this question.