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Musein' and mathin'



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All,

What follows is a long and perhaps for some, tedious diatribe, but is speaks
to many points which I and others have labored over on this list in the last
year or so.

I was working on a supplement to an article which was published recently and
began to muse on the peak impulse powers found in Tesla systems.  Naturally
as an engineer, I have to try to organize a scheme that would be credible
and take place in steps before an answer might be forthcoming.

Let us pose the question;  what might the peak impulse power be in the Tesla
spark in a 1 kilowatt Tesla coil system?

Lets muse a bit and assume we use a 15,000 volt 60ma neon transformer.  Why?
Well because its nameplate states 960VA which is close to the 1000VA we look
for.  Secondly, the transformer designed and is regulated by magnetic shunts
to self-limit at the stated level. 

Now Let us muse further and assume that due to calculations, we arrive at an
optimum capacitor for the this transformer of .01ufd.  This calculation can
be done and is done regularly by many on this list and has had a lot of
adherents.  Many state that even a slightly larger cap might be used, but we
will err on the low side of caution to make the math guys happy.

Now let us muse some more and make a note and astute observation that most
normal coils in this power class are in the frequency range of 300 to 500
kilohertz resonant.  There are some lower and a few higher depending on
design. Let us assume the middle ground of 400 kilohertz.  For this
frequency and cap used in the tank  (.01ufd) the primary tune point would be
in the 16uh range.  Do the math guys!

Now we can stop musin' and assumin' and start mathin' for real.  The
transformer in use has a peak voltage on the order of 21,000 volts.  (1.414
X15,000) Let us again muse and assume that we have a synchronous gap and pop
the circuit 120 times per second at the exact peak of the wave.  It could
happen!

The next thing we might wish to coagulate is the probable surge impedance of
the primary tank system where the electrical rubber meets th' road.

As Zsurge = sqr root of (L/C)

We see that in a perfect circuit we might expect only 40 ohms of impedance.
OOOPS!  We gotta gap in series there!  From my own experience and many
calculations and measurements and a general concensus of opinion, a good
median gap resistance in this class system would be assumed to be about 10
ohms.  Thus, we have to assume about 50 ohms in the tank as a realistic
surge impedance.

Thus the peak current which we might expect in the tank is based on the peak
capacitor voltage and the surge impedance.  Such that... I peak = 21,000/50 or
420 amps   From this we compute peak impulse power = 420 X 21000 = 8.82
megawatts!!!!!


Now do we really believe that we get this out the top of the coil?  Do we
really even believe we really get this in the tank circuit?  If we do we are
six times a fool.  Let's examine our wrong turns.  Was the math wrong.  Math
is never wrong!  Right?  If the math is correct and based on solid physics
and electrical concepts, where did we do wrong?

Answer.

It started at the wall plug and went down hill from there.  The biggest part
was the museins'- go back and count 'em.  It continues with the assumptions.
(count them too.)  and finally the math and its application is flawed.  Each
equation taken by itself is rock solid and in an isolated ideal circuit
(like in the stinkin' college lab) always solves out fine.  But all these
interact in a dynamic way that we did reckon or assume on.  Pspice and its
ilk can help here but then there are those nasty museins' and assumptions.
This is were pspice and such programs can die on their mathematical vine.

What are some of the other problems?

Well do we really believe the transformer will ever reach 21,000 peak at max
charge over time? go figure!  Do we really think that we have a KW
transformer? I hope not.  Do we really think that the cap and transformer
interact the way we imagine?  Again, dreamland.  Finally, do we think that
an amateur tank circuit with normal leads are going to efficiently handle
400 RF amps.  There are lots of more gotchas, but I continue to digress.

Let us assume (again!) that all the unknowns conspire to chew up 50% of our
calculated stuff above.  Now we are down to a puney 4.4 megawatts. We are
still in the primary tank!  We have magnetic coupling and resonator Q losses
to consider.  Others on this list have held that resonant losses in such a
circuit are minimal refering to switching supply efficiencies.  I would
guess 10% loss here based on what the other guys believe.....  3.9megawatts
left in mag energy in the resonator.  The resonator losses are a lot more
difficult to figure on.  From here I'm really shootin' blind and will kill
another 15% before spark issues.  This leaves about 3 megawatts of real peak
energy in the spark.  Maybe, we hope, I think.  

Based on best calculation?

NO  Not by the rules! (every one knows the rules)

Based on Best assumption!
  
As no measurements were ever taken, and all values stuffed into the math
were best guesses. (indeed made by oneone who has been around Tesla coils a
while) The very finest we might say for the final 3 megawatt pronouncement
is that it is pure ASSUMPTION!  Some might still want to cling to the math
and say AHH, but an assumption made through the good offices of calculation.
Bullshit!

In engineering, the bottom line is always the COP.  (coefficient of performance)
This rules all the mathematical machinations, pantywaist and effete
arguments about process minutia, invalid and voids a lot of wind.  This cuts
through the bull and tells you just what you get for your money.  In the
above case you would need two critical power measurements. One just
difficult to make, the other near impossible.  1.We need to know the time
averaged power expended at the AC meter base.  Tough to do with a coil
system, but doable with a moderate amount of instrumentation. 2. we need the
total time averaged and summed power output of the sparks and RF energy of
the resonator.  This is the really tough one.  How do we measure it?  What
is a properly defined load of a free sparking system?  (the load is wildly
varying of course)  What is the quintesential component of the spark which
is measureable and at what point?  I opt for the best guess with or without
mathematics.  Who's going to challenge you?  Why anyone with a better
thought will, that's who.  Anyone with a better or later version of Pspice
will lunge at you will fresh output hot off the microchip.  But, will his
assumptions be any better of worse than yours.  Depends, but not likely.

The bottom line is experience from the doing and valid measurement.  Some of
the biggest math heads have not one of these at their command. 

Again... What is the peak power in the output of a 1KW coil? 

 ahhhhh two megawatts....
 No you are too low man.  I think it's about 3 megawatts....
 Wait you guys, my Pspice says 5.68499 megawatts.... 
ahhh.. I though we only put in a kilowatt ...... Wow! above unity!!!!!

There are all types and levels of experience.  There are all sorts of
persons to chew the data, but little to really build on.  The measurements
are complicated the interactions many and not fully understood well enough
to reduce to anything which a moderate computer model could predict to even
20%.  Even if the model was dead on, who would believe it other than its
champion.  Can he build the thing and make measurements to convince others?
I think not.

Still this is a fun thing lookin' for that pot o' gold.  After all, its just
at the end of that next model. (read rainbow)


Richard Hull, TCBOR

I still sorta think 3 megawatts peak is close.






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