Musings on Medhurst

From:  Thomas McGahee [SMTP:tom_mcgahee-at-sigmais-dot-com]
Sent:  Thursday, June 04, 1998 2:45 PM
To:  tesla-at-pupman-dot-com
Subject:  Musings on Medhurst

Malcolm, Terry, and other interested coilers,

The recent discussions about the possibility of the
Cself of a secondary being dominated by the capacitance
between the coil and ground led me to the following

Assume that the same piece of wire of the same length
is used to build four Tesla coil secondaries...

A) A single wire stretched out straight would have 
zero "inter-turn" capacitance and maximum capacitance
due to exposed surface area. Inductance would be minimal.

B) A skinny coil would have a large inter-turn capacitance
and its exposed surface area capacitance would be
about half that of example (A), since the inside of the
coil would be shielded. Inductance would be medium.

C) A large diameter coil would have a larger inductance,
about the same inter-turn capacitance, (but with a larger
inductance per-turn than in (B)), and slightly larger exposed 
surface area capacitance, since shielding is not perfect. 

D) The final extreme. A single-turn secondary. Almost Zero
inter-turn capacitance. ALMOST maximum capacitance due to
exposed surface area capacitance. Fair sized inductance.

(A) and (D) would be pre-dominantly 1/4 wave devices.
According to the direction of the recent discussions on this
List, it would seem that (B) and (C) would not.

One method used to determine Cself is table-lookup, attributed to Medhurst:
        C  = K x D      (D 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

What is the correlation between H/D and K? Could it be related to
the fact that as H/D grows smaller the ratio of exposed area
capacitance and inter-turn area capacitance changes?

Things to think about...
Why does Medhurst's method only work if the base of the coil
is effectively connected to ground?
Coilers have often noted that certain H/D ratios work best for Tesla
coil secondaries of a given diameter. WHAT is maximized at these
particular ratios? Why is there not one single "best" H/D ratio
that would work for ALL coil sizes?
What is capacitively different about an operating Tesla secondary
and one that is just hanging around waiting for the juice to be turned
on? What is different about huge high power Tesla coils and smaller,
more efficient but lower power Tesla coils?

All of the above are bits and pieces of the same puzzle. 

Hope this helps.
Fr. Tom McGahee