Re: Medhurst Formula

To: tesla-at-pupman-dot-com
Subject: Re: Medhurst Formula
From: MSR7-at-PO.CWRU.EDU
Date: Mon, 3 Jun 1996 07:26:36 -0400
Hello Coilers,
>-Ed Harris said
><snip>
>These formulas are, of course, only valid for coils which are
>base driven below the point of corona formation...
        This is an important point to remember.  One can use these formulas
to determine initial coil parameters, but expect the operating resonant
frequency to be lower due to extra capacitive effects caused by the corona
cloud.  For my little coils (3 foot sparks and less), I have to move out 1/2
to 1 turn on the primary coil as a result of this.  Plan accordingly.

>Mark R. posted the self capacitance formula due to Medhurst
>in a previous post. 
Here is a repeat of that old post:

        I use the formula attributed to Medhurst for self capacitance
estimation.  It gives values which are fairly close to what I measure
experimentally.  The formula does not take into account wire spacing, so it
may be in error somewhat for spacewound coils.  I suspect space winding does
not substantially alter the distributed capacitance, however.  I have seen
no formula for spacewound coils.

 Medhurst's formula:    C  = K x D

where:  C = capacitance in picofarads
        K = constant which depends on the ratio of the coil height to diameter
        x = means multiply K times D
        D = solenoidal coil diameter in centimeters
        H = coil height in centimeters

        H/D       K
        5.0     0.81
        4.5     0.77
        4.0     0.72
        3.5     0.67
        3.0     0.61
        2.5     0.56
        2.0     0.50
        1.5     0.47
        1.0     0.46


        Medhurst, R.G. "H.F. Resistance and self-capacitance of single-layer
solenoids", W.E. 24.281 (Feb 1947) p 35; and W.E. 24.282 (March 1947) p 80.
W.E. stands for Wireless Engineer, a British journal.
        Medhurst claimed 5% accuracy for his data, based on experimental
measurements.  He wrote the paper in response to earlier theoretical papers
by Palermo from 1937 and 1942.  Palermo predicted different distributed
capacitance values, based on a mathematical model.  He did minimal
experimental verification of his results.  Following Medhurst's papers,
Palermo's work has been pretty much discredited.
Regards,
Mark S. Rzeszotarski, Ph.D.