Wire Insulation Thickness

From:  Hollmike-at-aol-dot-com [SMTP:Hollmike-at-aol-dot-com]
Sent:  Thursday, May 28, 1998 4:23 PM
To:  tesla-at-pupman-dot-com
Subject:  Re: Wire Insulation Thickness

Jim, all,
   I am not too familiar with the Medhurst formula for a coil's self
capacitance.  I have seen the equation and K values on Ed Sonderman's design
spreadsheet, but do not know how those values were obtained.  I have never
attempted to compare the results of that formula with measurements, so I
cannot say anything in regards to it.  
   What I can do is quote from a book titled Electrical Engineer's Handbook,
Communication Electronics,  published by Wiley & Sons in 1945 and edited by
Pender and McIlwain.
    First I will present a formula from this book for short (coil length
approximately equal to the coil diameter) single layer coil:

    Co = pi * D /  (3.6 cosh^-1(s/d))
where s = pitch of winding,  d = bare wire diam., and D = coil diam.  All
dimensions in centimeters.
      This is an empirically derived equation that according to the book
checks out "very well".  It does not state the max H/D ratio that it works
well for, but should give a general idea of the effect of space winding on a
coil's self capacitance.
    It goes on to say: "From the results given, it is evident that the
important parameters in the coil capacitance are the diameter of the winding
and the ratio of the pitch of the winding to the diameter of the bare wire.
The capacitance is practically independent of the number of turns."
      I had much trouble trying to figure out how to calculate an inverse
hyperbolic cosine on my calculator, so I dredged out my old calculus book and
found that :

   cosh^-1 (x) =  ln(x + SQRT(x^2  - 1))  where x > 1 
I would like to hear any thoughts on this as it seems to be an area of some
discrepancy for coil design.  
Mike Hollingsworth