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"Slinky" Primary / Sloped Archimedes Spiral Primary Equation


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From:  Bert Hickman [SMTP:bert.hickman-at-aquila-dot-com]
Sent:  Friday, August 14, 1998 12:06 AM
To:  Tesla List
Subject:  Re: "Slinky" Primary / Sloped Archimedes Spiral Primary Equation

Tesla List wrote:
> 
> ----------
> From:  Dave Sharpe [SMTP:sccr4us-at-erols-dot-com]
> Sent:  Wednesday, August 12, 1998 9:51 PM
> To:  Chip Atkinson
> Subject:  "Slinky" Primary / Sloped Archimedes Spiral Primary Equation
> 
> Chip, ALL
> 
> A while back, (before the detonation of my HD :^C ) I has saved a copy
> of a post for a sloped "pancake" primary inductance and tubing length
> based on coil ID, OD, spacing and included acute angle from horizontal
> plane.  I've tried searching in archives without success.  If someone
> could privide I would appreciate it greatly.  I'm contemplating building
> a small (450VA/ 15kV,30mA NST) system using a sloped primary where
> the HEIGHT (ie included length) is adjustable while running.  This
> would allow primary tuning, coincidental with coupling increase or
> decrease.  Any help appreciated
> 
> Regards,
> 
> DAVE SHARPE, TCBOR

Dave,

Hope this is what you're looking for. Included are Archimedes, helical,
and inverse conical primaries. The helical and Archimedes forms are from
Wheeler, and the inverse conical is a hybrid form that appropriately
weights the vertical and horizontal components of Helical and Archimedes
inductances. 

All dimensions are in inches, and L is in microHenries. While the
Inverse Conical calculation is a little "hairier" than the first two,
it's relatively easy to calculate for any desired angle, especially if
set up in a spreadsheet. 
------------------------------------------------------------------------
Case 1: Archimedes Spiral (Flat):

          Let R = Ave Radius  
              N = Number of Turns
              w = Width of Winding            


           |   R    |      N Turns 
      o o o o o o   |   o o o o o o 
      |    W    |   |


     L = (R^2)*(N^2)/(8*R+11*W)   (R^2 = R*R)


------------------------------------------------------------------------

Case 2: Helical Primary:

                |<- R ->|
            --  o       |       o
            |   o       |       o
                o       |       o 
            L   o       |       o  N Turns
                o       |       o 
            |   o       |       o
            --  o       |       o

      L = R^2*N^2/(9*R+10*L)  (Vertical Helix)

------------------------------------------------------------------------

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]  

------------------------------------------------------------------------
Safe coilin' to you, Dave! Hope to see you and Richard later this month!

-- Bert --