Hi,
Just to follow up... If we take the example Dest gave:
http://www.pupman.com/listarchives/2006/May/msg00381.html
and convert it to "inches stuff" with just minor length changes to
get round numbers we get:
Primary
Solenoid - 6 inches high, 12 turns, 11 inches in diameter of 3/8
inch copper tube.
Secondary - 28 inches long, 1500 turns, 7 inches diameter. 0.015 wire.
Firing voltage 20kV.
But he does not mention Cprimary... That value is needed to know
di/dt which is critical factor too...
So we add a 6 x 24 toroid top terminal with a centerline six inches
above the top of the secondary. We can now go to JAVATC to find Fo and such...
http://drsstc.com/~sisg/files/RaceArc-01.gif
91.67kHz and the primary is 39.462uH with a coupling of 0.306...
We will assume now that the primary is tuned 5% low as usual and
find Cprimary as 85nF. A coil this size with 0.3+ coupling and 17
joules per bang "should" be a racing arc disaster!!!
Totally ignoring any "resonant" effects and totally relying on "pure
transformer action", the voltage induced in the secondary is:
V2 = M x di(Lp)/dt
Since M varies drastically along the length of the coil, we have to
chop it up and calculate it in little chunks or sections... We'll
do every 0.1 inch since the computer is doing all the work ;-)) So
I pump it into MandK and get this:
http://drsstc.com/~sisg/files/RACEARC4.TXT
So we know the mutual inductance of each little section now...
To find di/dt we know Ip is in the first instant of firing:
I(t) = Vfire x SQRT(Cp / Lp) x SIN (t / SQRT(Cp x Lp))
If we take the derivative:
dI(t)/dt = Vfire x SQRT(Cp / Lp) x 1 / SQRT(Cp x Lp) x COS(t /
SQRT( Cp x LP))
If t ~~= 0 and with some simplification we get:
dI(t)/dt = Vfire / Lp == 20000 / 39.462uH == 507e6 A/S
Now we can get out the spreadsheet and make some numbers:
http://drsstc.com/~sisg/files/RaceArc6.csv
and we can make pretty graphs:
http://drsstc.com/~sisg/files/Voltage-length.gif
http://drsstc.com/~sisg/files/VoltageEveryInch.gif
So at 3 inches, the voltage stress along the primary is 35000 volts
/ inch in the first fraction of a microsecond after firing.... Dest
got 40kV/inch too!!! We can look at this chart:
http://hot-streamer.com/TeslaCoils/Misc/SGapVolt.jpg
To see that it will jump 1.26 inches!!! We have an arc for sure,
and super sure too since it is a surface creepage arc that will
actually arc at even far lower voltage...
Worse yet, once the arc is established, it will look much like a
short on the secondary and will very quickly absorb all the energy
in the bang. Thus explaining why they are "bright" arcs that do a
lot of damage...
On the good side, thick layers of insulation should protect against
such voltage breakdown!! Put that poly coating in real thick ;-))
Of course, once the resonance is established, such effects will
"ride" on top of the voltage on the secondary too... I imagine that
will explain the arcs occurring at places other than the base of the
secondary...
The voltage profiles Paul has at:
http://www.abelian.demon.co.uk/tssp/pn040502/
Will enter into this all too...
Of course, Gerry's paper provided the key to it all ;-)))
http://hot-streamer.com/temp/GerryReynolds/In_search_of_a_better_primary.pdf
I CC'ed dest too incase he has comments...
Cheers,
Terry
Hi,
Dest also looked into this:
http://www.pupman.com/listarchives/2006/May/msg00387.html
But I don't think he did it quite right... The links are dead so I
can't check now. ...........