RE: Dimensions of my flat spiral coil

["Tesla list" <tesla-at-pupman-dot-com>]

Original poster: "David Thomson by way of Terry Fritz <twftesla-at-qwest-dot-net>" <dave-at-volantis-dot-org>

Hi Peter,

>  the problem may be that the formula uH = R^2*N^2/(8*R+11*W) was found
empirically (inductance of lots of coils where measured and a formula that
computed those inductances from the coils' dimensions was guessed at until
one was found to agree "reasonably" close to measurement).

The first time I wound a large flat spiral secondary I just about went mad
trying to figure out what was wrong with my LCR meter.  I would measure my
solenoid coils and they measured close to calculation.  Then I would measure
my flat spiral and it was off by a wide margin.   After a while I just gave
up.

Then I started searching the Internet for a better flat spiral secondary
formula.  I realized that all flat spirals to date were merely flat spiral
primaries.  I'm sure the formula works reasonably well for a few turns.  But
as you point out, the formula was probably not tried on large spiral
secondaries.

My only claim about the formula is that it doesn't give the same result as
my LCR meter.

>Also, to predict resonant frequency another formula is needed for
self-capacitance, which as far as I know no one has ever tried to either
guess empirically or derive from EM principles for flat spiral coils.

I simply used the LCR meter to measure capacitance across the leads.  It
seems to work fine and give a reasonable value.  For example, my 13" single
wound coil measures 120pF self-capacitance and 35mH on my LCR meter.  The
quarterwave frequency is approximately 635KHz (I use the full quarterwave as
a matter of choice since I usually don't load the terminal) but the resonant
frequency of the coil is 77KHz.  I checked the resonant frequency with my
oscilloscope and signal generator and the resonant frequency range was from
50KHz to 100KHz.  So the LCR measurements of capacitance and inductance
appears to be about right.

But the kicker is that if I tried to run the primary at 77KHz or anywhere in
the resonant frequency range, the spark gap just wouldn't fire.  After I
couldn't get the coil to fire I started trying all different capacities
against the 10uH primary and it turned out that .026uF works the best.  That
puts the primary resonating at about 312KHz.  That's four times the resonant
frequency of the secondary.  Or in other words, the primary resonates at one
quarter the wavelength of the secondary.  Perhaps that is what Tesla meant
to say?

I'll be satisfied when other's have their flat spiral coils working and I
can see their proportions.

I just had an epiphany.  Tesla's large flat spiral secondary coil is 8 feet
in diameter and space wound with about 1/2" between turns.  Perhaps space
winding is essential to operating a flat spiral coil?  I guess I have yet
another project ahead of me.

Dave