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Overtones and Velocity Factors Discussion

Date: Sun, 21 May 2006 15:25:03 -0600

From: Tesla list <tesla@pupman.com>

To: tesla@pupman.com

Subject: Overtones and velocity factors

Original poster: Paul Nicholson <paul@abelian.demon.co.uk>

Gerry wrote (in another thread):

> about tfss270501 and md110701 spectral graphs. It appears
> the first overtone is close to a 3rd harmonic frequency
> (but not quite) and higher overtones seem to be noticably
> lower in frequency than the 5th and 7th harmonics. Is it
> true that the spectral graphs are not harmonic in nature??

True. For example here are the resonant frequencies of an unloaded coil (one of Terry's, h/d=2.92)

   Freq Mode Ratio
   148.4kHz 1/4 wave 1.0
   353.4kHz 3/4 wave 2.38
   513.8kHz 5/4 wave 3.46
   666.4kHz 7/4 wave 4.49
   819.8kHz 9/4 wave 5.52
   977.4kHz 11/4 wave 6.59
   1133.1kHz 13/4 wave 7.64

As you can see, the mode frequency ratios are less than the quarter wave count. When the coil is loaded with a typical topload things change a bit,

   Freq Mode Ratio
   97.9kHz 1/4 wave 1.0
   321.4kHz 3/4 wave 3.28
   490.2kHz 5/4 wave 5.0

The 1/4 wave is pulled down by a greater factor than the higher modes. There's a particular value of top C that will make the 3/4 wave exactly 3 times the fundamental - that may or may not be a good thing for a square wave drive signal. Just by luck, this example has just the right topload to make the 5/4 overtone match the 5th harmonic.

I'll just say a bit about propagation velocity with respect to wire length. For the above coil, unloaded, 817 metres of wire, we have

   Freq Mode Overall wire velocity factor
   148.4kHz 1/4 wave 1.62
   353.4kHz 3/4 wave 1.28
   513.8kHz 5/4 wave 1.12
   666.4kHz 7/4 wave 1.04
   819.8kHz 9/4 wave 0.99
   977.4kHz 11/4 wave 0.97
   1133.1kHz 13/4 wave 0.95

in which the velocity factor is given by 817/n * 4 * Fres/c, where n is the number of 1/4 waves in the resonance and c is the fundamental constant 300e6.

Here are the figures for a coil h/d = 4.66, with 2078 metres of wire.

   Freq Mode Overall wire velocity factor
   61.9kHz 1/4 wave 1.72
   157.9kHz 3/4 wave 1.46
   229.7kHz 5/4 wave 1.27
   294.4kHz 7/4 wave 1.17
   355.6kHz 9/4 wave 1.09

These are typical patterns, with the velocity tending towards something below c as the in-coil wavelength becomes shorter. If the velocity factor was the same for all frequencies, you would get harmonic overtones, but you can see that instead we have a lot of dispersion. This dispersion originates in the long range 'longitudinal' coupling, ie mutual L and C between remote regions of the coil.

Long range coupling becomes less effective at high frequencies. The distributed mutual reactances are the same of course, but because the coil is now carrying several or many quarter wave sections, the L & C coupling to a point on the coil from some remote turn is, on average, balanced by an equal but opposite coupling from another turn at a similar range somewhere else. The longitudinal coupling becomes dominated by reactance just with neighbouring turns, h/d has less of an influence on velocity, and the winding pitch becomes more of a significant factor, eventually being dominated by the direct turn-turn coupling. I've no idea what the limiting velocity factor is or how to calculate it, but I've seen research on the topic which involves using tridiagonal matrices to represent the periodic coupling between adjacent turns.

At even higher frequencies the voltage around a turn is no longer uniform and we start to get an E-field component acting across the diameter of the coil - a component which can rotate at the signal frequency. The result is circularly polarised EM waves travelling along the coil and being radiated with reasonable efficiency, beaming along the axis. In this realm the pitch and circumference become the main determining factors of the resonant modes of the structure.

Bart wrote (in another thread):
> I started building a Seibt Coil myself, but I have yet to
> finish it.

Those Seibt coils might be good ones to use for examining propagation of the various modes.

> I have everything except the high voltages.

High voltages - who needs 'em :) Measurements are more rewarding in the long run. Making sparks - Bah! Hope you can measure some resonant frequencies and the associated in-coil wavelengths to demonstrate the above.
--
Paul Nicholson

Date: Mon, 22 May 2006 08:07:47 -0600

From: Tesla list <tesla@pupman.com>

To: tesla@pupman.com

Subject: Re: Overtones and velocity factors

Original poster: "Gerry Reynolds" <gerryreynolds@earthlink.net>

Hi Paul,

This is making good sense to me. The boundary conditions allow a voltage max at the top and voltage min at the bottom. A 1/4, 3/4, etc are eigen solutions to these boundary conditions. The corresponding frequencies (proportional to 1/lamda) dont scale the same, as you say, because the velocity factors are different. What
causes the velocity factor to get less than one??? If the net poynting vector were to follow the wire path, would this result in a velocity factor of 1.0 or .95 (waves propagate at 0.95c in copper, lets say)??? Im just not sure what you are normalizing velocity factors to.

So when others in the group use the 3rd harmonic terminology are they speaking loosely about the 3/4 wave overtone or the 3rd harmonic in the primary waveform??

It does seem that a seibt coil operates in high overtone mode (many standing waves up and down the tall skinny coil).

Lastly, in terms of measurements, is the only data you are seeking the resonant modes of a coil??? or are you also after the spectral content of a racing spark??? Maybe if we capture the fields using Terry's antenna and digital scope to store a one shot capture, one can post process that waveform to get the spectral contents. Would this work or is a spectrum analyser needed???

Gerry R.

>Original poster: Paul Nicholson <paul@abelian.demon.co.uk>
>
>Gerry wrote (in another thread):
>
> > about tfss270501 and md110701 spectral graphs. It appears
> > the first overtone is close to a 3rd harmonic frequency
> > (but not quite) and higher overtones seem to be noticably
> > lower in frequency than the 5th and 7th harmonics. Is it
> > true that the spectral graphs are not harmonic in nature??
>
>True. For example here are the resonant frequencies of an
>unloaded coil (one of Terry's, h/d=2.92)
>
> Freq Mode Ratio
> 148.4kHz 1/4 wave 1.0
> 353.4kHz 3/4 wave 2.38
> 513.8kHz 5/4 wave 3.46
> 666.4kHz 7/4 wave 4.49
> 819.8kHz 9/4 wave 5.52
> 977.4kHz 11/4 wave 6.59
> 1133.1kHz 13/4 wave 7.64
>
>As you can see, the mode frequency ratios are less than the
>quarter wave count. When the coil is loaded with a typical
>topload things change a bit,
>
> Freq Mode Ratio
> 97.9kHz 1/4 wave 1.0
> 321.4kHz 3/4 wave 3.28
> 490.2kHz 5/4 wave 5.0
>
>The 1/4 wave is pulled down by a greater factor than the higher
>modes. There's a particular value of top C that will make the
>3/4 wave exactly 3 times the fundamental - that may or may not
>be a good thing for a square wave drive signal. Just by luck,
>this example has just the right topload to make the 5/4 overtone
>match the 5th harmonic.
>
>I'll just say a bit about propagation velocity with respect
>to wire length. For the above coil, unloaded, 817 metres
>of wire, we have
>
> Freq Mode Overall wire velocity factor
> 148.4kHz 1/4 wave 1.62
> 353.4kHz 3/4 wave 1.28
> 513.8kHz 5/4 wave 1.12
> 666.4kHz 7/4 wave 1.04
> 819.8kHz 9/4 wave 0.99
> 977.4kHz 11/4 wave 0.97
> 1133.1kHz 13/4 wave 0.95
>
>in which the velocity factor is given by 817/n * 4 * Fres/c,
>where n is the number of 1/4 waves in the resonance and c
>is the fundamental constant 300e6.
>
>Here are the figures for a coil h/d = 4.66, with 2078 metres
>of wire.
>
> Freq Mode Overall wire velocity factor
> 61.9kHz 1/4 wave 1.72
> 157.9kHz 3/4 wave 1.46
> 229.7kHz 5/4 wave 1.27
> 294.4kHz 7/4 wave 1.17
> 355.6kHz 9/4 wave 1.09
>
>These are typical patterns, with the velocity tending towards
>something below c as the in-coil wavelength becomes shorter.
>If the velocity factor was the same for all frequencies, you
>would get harmonic overtones, but you can see that instead we
>have a lot of dispersion. This dispersion originates in the
>long range 'longitudinal' coupling, ie mutual L and C between
>remote regions of the coil.
>
>Long range coupling becomes less effective at high frequencies. The
>distributed mutual reactances are the same of course, but because
>the coil is now carrying several or many quarter wave sections,
>the L & C coupling to a point on the coil from some remote turn is,
>on average, balanced by an equal but opposite coupling from another
>turn at a similar range somewhere else. The longitudinal coupling
>becomes dominated by reactance just with neighbouring turns, h/d
>has less of an influence on velocity, and the winding pitch becomes
>more of a significant factor, eventually being dominated by the
>direct turn-turn coupling. I've no idea what the limiting velocity
>factor is or how to calculate it, but I've seen research on the
>topic which involves using tridiagonal matrices to represent the
>periodic coupling between adjacent turns.
>
>At even higher frequencies the voltage around a turn is no
>longer uniform and we start to get an E-field component acting
>across the diameter of the coil - a component which can rotate at
>the signal frequency. The result is circularly polarised EM
>waves travelling along the coil and being radiated with reasonable
>efficiency, beaming along the axis. In this realm the pitch and
>circumference become the main determining factors of the resonant
>modes of the structure.
>
>Bart wrote (in another thread):
> > I started building a Seibt Coil myself, but I have yet to
> > finish it.
>
>Those Seibt coils might be good ones to use for examining
>propagation of the various modes.
>
> > I have everything except the high voltages.
>
>High voltages - who needs 'em :) Measurements are more rewarding
>in the long run. Making sparks - Bah! Hope you can measure
>some resonant frequencies and the associated in-coil wavelengths
>to demonstrate the above.
>--
>Paul Nicholson
>--

Date: Mon, 22 May 2006 10:59:28 -0600

From: Tesla list <tesla@pupman.com>

To: tesla@pupman.com

Subject: Re: Overtones and velocity factors

Original poster: dest <dest@alexandria.cc>

Hallo theorists (no any pun - i swear ^___^) : )

> Original poster: Paul Nicholson <paul@abelian.demon.co.uk>

> Gerry wrote (in another thread):

> > about tfss270501 and md110701 spectral graphs.
> > Is it true that the spectral graphs are not harmonic in nature??

> True. For example here are the resonant frequencies of an
> unloaded coil (one of Terry's, h/d=2.92)

and Marco Denicolai`s first coil (h:d = 4.58) for comparison (on the right):

http://www.pupman.com/listarchives/1998/June/msg00181.html

   |
   Freq Mode Ratio | Freq Mode Ratio
a. 148.4kHz 1/4 wave 1.0 | 324 KHz 1/4 1.00
b. 353.4kHz 3/4 wave 2.38 | 813 KHz 3/4 2.51
c. 513.8kHz 5/4 wave 3.46 | 1475 KHz 5/4 4.55
d. 666.4kHz 7/4 wave 4.49 | 1766 KHz 7/4 5.45
e. 819.8kHz 9/4 wave 5.52 | 2053 KHz 9/4 6.34
f. 977.4kHz 11/4 wave 6.59 |
10. 1133.1kHz 13/4 wave 7.64 |
   |

note that data in rows "a-b" is similar, but starting from the row "c" it looks like one sample is missing here, and all next data is shifted back. i wonder what`s caused this - different h:d or it`s just msms error?

> I'll just say a bit about propagation velocity with respect
> to wire length.

> Here are the figures for a coil h/d = 4.66, with 2078 metres
> of wire.

and Marco`s coil again on the right (h:d = 4.58) approx with 425 m of wire:

   |
   Freq Mode Owvf | Freq Mode Owvf
a. 61.9kHz 1/4 wave 1.72 | 324 KHz 1/4 1.84
b. 157.9kHz 3/4 wave 1.46 | 813 KHz 3/4 1.54
c. 229.7kHz 5/4 wave 1.27 | 1475 KHz 5/4 1.67
d. 294.4kHz 7/4 wave 1.17 | 1766 KHz 7/4 1.43
e. 355.6kHz 9/4 wave 1.09 | 2053 KHz 9/4 1.29
   |

again some inconsistency here, but this time in the coil itself – what the @#$ row "c" is doing in there? : )
since this last coil has similar h:d ratio to Marco`s one, let`s calculate and compare all the numbers from the beginning:

   |
   Freq Mode Ratio | Freq Mode Ratio
a. 61.9kHz 1/4 wave 1.00 | 324 KHz 1/4 1.00
b. 157.9kHz 3/4 wave 2.55 | 813 KHz 3/4 2.51
c. 229.7kHz 5/4 wave 3.71 | 1475 KHz 5/4 4.55
d. 294.4kHz 7/4 wave 4.76 | 1766 KHz 7/4 5.45
e. 355.6kHz 9/4 wave 5.75 | 2053 KHz 9/4 6.34
   |

what if one sample is really absent here - something like that:

   |
   Freq Mode Ratio | Fr eq Mode Ratio
a. 61.9kHz 1/4 wave 1.00 | 324 KHz 1/4 1.00
b. 157.9kHz 3/4 wave 2.55 | 813 KHz 3/4 2.51
c. 229.7kHz 5/4 wave 3.71 | ? 5/4 ?
d. 294.4kHz 7/4 wave 4.76 | 1475 KHz 7/4 4.55
e. 355.6kHz 9/4 wave 5.75 | 1766 KHz 9/4 5.45
f. | 2053 KHz 11/4 6.34
   |

like it? : ) then finally:

   |
   Freq Mode Ratio Owvf | Freq Mode Ratio Owvf
a. 61.9kHz 1/4 1.00 1.72 | 324 KHz 1/4 1.00 1.84
b. 157.9kHz 3/4 2.55 1.46 | 813 KHz 3/4 2.51 1.54
c. 229.7kHz 5/4 3.71 1.27 | 1166 KHz 5/4 3.60 1.32
d. 294.4kHz 7/4 4.76 1.17 | 1475 KHz 7/4 4.55 1.19
e. 355.6kHz 9/4 5.75 1.09 | 1766 KHz 9/4 5.45 1.11
f. | 2053 KHz 11/4 6.34 1.06
   |

heck - you must be extremely careful when reading archives and must constantly do the reality check on all info - that`s really suxxx coz it takes a lot of time : E so i want to ask people here a somewhat offtopic question (this may help me to save some time):

very long time ago i have read a paper written by Marco Denicolai - "Tesla Coil Tuning (zipped Word document, 158 kB) A theoretical explanation of how optimal performance can be achieved (temptative)". you can find it here:

http://www.elisanet.fi/dncmrc/tuning.zip

there is a "Figure 5: Energy transfered and transfer time vs. coupling coefficient.", from which we can see, how much energy has left in the primary, when k is not one of the "magic" values, that permit full energy transfer. this plot is erroneous, if anybody have correct version - plz send it to me.
thnx.

Date: Mon, 22 May 2006 15:31:42 -0600

From: Tesla list <tesla@pupman.com>

To: tesla@pupman.com

Subject: Re: Overtones and velocity factors

Original poster: Vardan <vardan01@twfpowerelectronics.com>

Hi,

I have not been involved with this much since I have been "really busy" :o)))

I think D.C. and me are the only "low coupling" folks ;-)) If the primary system does not eat power like mad, low coupling losses in the primary circuit are less important and the coil naturally runs better. LTR systems tend to run at lower currents reducing losses and D.C.'s systems have big heavy primaries that have low loss too. The SISG will no doubt change all that an order of magnitude or two further...

Quench is also not too important if the streamers naturally use all the systems energy in the first cycle anyway... Coupling adjusts that...

Computer models tend to point to lower and lower coupling for best operation. However, the "energy rise time" of higher coupled systems is probably very important for long streamer formation. The Russians have specific numbers for this for there 400++ foot Marx generators!!!

I remember an out of tune coil once at a gathering... It had 1 foot long primary to secondary arcs!! We put a 3/16 sheet of G-10 fiberglass between them. The arcs "blew right through it"!! I though to myself at the time. "That is really screwed up and there is no explanation for it"!!! There still is not. But there are "many strange things" that go on down near the primary to secondary coupling area!!!

I always wrote it off to "transformer action" but Paul and Dmitry seem to have shot that idea out of the water...

>High voltages - who needs 'em :) Measurements are more rewarding
>in the long run. Making sparks - Bah! Hope you can measure
>some resonant frequencies and the associated in-coil wavelengths to demonstrate the above.

I too always wondered about people that did not watch sparks only on a "scope screen"... Your gonna go blind :O)))))

>A few. A tie-up between racing arcs and gap behaviour is a
>rich source of possibilities. We'd better go read Terry's old
>paper mentioned in
>
> > http://www.pupman.com/listarchives/1998/July/msg00019.html

The modern link is here:

http://hot-streamer.com/TeslaCoils/MyPapers/sgap/sgap.html

>Gerry wrote:
> > What measurements do you have in mind and what type and quality
> > equipment is needed for the measurement.
>
>Capture of a secondary base current waveform on a digital scope,
>transferred to a computer file for analysis. Only rough amplitude
>calibration needed. Wide bandwidth, though, say up to 30 times the
>TC operating frequency.

Gosh!! Who has equipment like that!!! :o)))

Would a single shot primary base current waveform capture of a spark with and without racing arcs help. The big old coil was good at that. I can fire at 5400V with the SISG (extremely repeatable).... I don't have enough section yet though for higher voltages. Maybe it would still race though since it had plenty or room for lowering. With all the new solid state stuff, "repeatability" is a giant new advantage we have ;-))

>One sample of the genuine phenomena is
>all that's needed, so no long damaging runs required. We would
>analyse the captured waveform to determine what signal components
>are present - chances are the offending signal(s) will be quite
>prominent. We would work out their voltage and current
>distributions and approximate gradients, and by modelling,
>determine which parts of the structure are involved in generating them.

I guess that is "yes"... My problem here is that the play rooms are about 1/4 their original size now... I might need to take a sawsall and start some serious "cleaning up"... :-))) The pool table is going out in 1/8th sections...

Single shot operation does very little damage in any case.... This would be on the big old secondary coil... It is still "just fine" ;-)))

>The cross check at that point would be detection of the
>offending resonances during low power sweeps and showing by probing
>and loading that the nodes and antinodes are in the predicted
>places. The tricky bit is getting a coil to display classic racing
>arcs on demand. Maybe John has pointed the way there.

Single shot operation makes racing arcs far more "safe". Would it matter if "miss tuning" was used to help at racing arcs along??

>Variation on the above: Just fire the primary under various gap
>operating conditions, without the secondary (is that possible
>or would that damage something?). See what frequencies are excited
>and at what levels. Knowing that, we can calculate how the
>secondary would cope with them.

Spark gaps are very unpredictable and have all kinds off odd quirks that might just add to the noise... Today, (literally - "TODAY" ;-))) we have new gaps that can remove those variations ;-))

Cheers, Terry
>--
>Paul Nicholson

Date: Mon, 22 May 2006 15:55:17 -0600

From: Tesla list <tesla@pupman.com>

To: tesla@pupman.com

Subject: Overtones and velocity factors

Original poster: Paul Nicholson <paul@abelian.demon.co.uk>

Gerry wrote:
> The boundary conditions allow a voltage max at the top and
> voltage min at the bottom.

Yes. And in between, alternating voltage maxima and minima at 1/4 wave intervals.

> The corresponding frequencies (proportional to 1/lamda) don’t
> scale the same, as you say, because the velocity factors are different.

Yes, both frequency and wavelength must be measured or calculated (for each mode the numbers will be different) in order to characterise the behaviour. To make matters even more interesting, the velocity (and therefore lambda) varies a little along the coil, depending on the particular distribution of reactance in any given setup. For example, added shunt C, such as that due to the proximity of a primary winding or a strike ring, causes a reduction of velocity in that region, shortening the wavelength a little, but these are small effects that only show up in precision measurements and models.

> What causes the velocity factor to get less than one???

My guess is the dominant factor is turn-to-turn capacitance, which is rather high in a closewound coil. As frequency goes up, the series inductance reduces to something more like the self-L of the wire as the mutual inductance contributions coming in from other turns begin to cancel out. The velocity values begin to depend more on wire diameter and the pitch and much less on h/d. The calculations for velocity and Z would be similar to those for a twin wire feeder but because of the close proximity of the wires, I would guess the velocity factor
might go as low as that of a coax cable. I've never pursued this in any detail because the frequencies where these factors become significant are very much higher than TC operating frequencies.

> when others in the group use the 3rd harmonic terminology are
> they speaking loosely about the 3/4 wave overtone or the 3rd
> harmonic in the primary waveform??

If they talk of '3rd harmonic' they should mean three times the fundamental drive frequency, not an overtone of the resonator, but - the terms are often used carelessly.

> Lastly, in terms of measurements, is the only data you are
> seeking the resonant modes of a coil??? or are you also after
> the spectral content of a racing spark???

The spectral content of a racing spark is what we're after (in the other thread). The 'racing' frequencies will correspond with one or a bunch of resonant modes of the system.

> Maybe if we capture the fields using Terry's antenna and
> digital scope to store a one shot capture, one can post
> process that waveform to get the spectral contents. Would
> this work...

Might do ok, but not so good. I asked for base current capture because the high frequency content is more easily seen in that waveform. In the top voltage, or in a distant E-field probe, the HF content will be rather harder to see and extract. The reason for that is the lower in-coil impedance of the higher overtones. Those signals propagate with a smaller V/I ratio than the lower modes, so appear in a smaller proportion in a
voltage or E-field probing. By measuring currents instead, the opposite applies - the HF stuff is easier to see.

The E-field probe is worse than a direct voltage probe because it is taking a kind of average of the E flux emanating from the resonator. Higher modes have several voltage maxima, each with opposite polarity of instantaneous voltage to the next, so tending to cancel one another out at a distant E-field probe.
This is the same 'averaging' effect that I mentioned in the previous post which causes reduction of long range mutual capacitance.

So, there are good fundamental reasons for choosing base current capture. In addition, it is also easy to calibrate and easy to screen.

Dest wrote:
> Marco Denicolai`s first coil (h:d = 4.58) for comparison
> http://www.pupman.com/listarchives/1998/June/msg00181.html

> Freq Mode Ratio | Freq Mode Ratio
> a. 148.4kHz 1/4 wave 1.0 | 324 KHz 1/4 1.00
> b. 353.4kHz 3/4 wave 2.38 | 813 KHz 3/4 2.51
> c. 513.8kHz 5/4 wave 3.46 | 1475 KHz 5/4 4.55
> d. 666.4kHz 7/4 wave 4.49 | 1766 KHz 7/4 5.45
> e. 819.8kHz 9/4 wave 5.52 | 2053 KHz 9/4 6.34

Yes, something suspicious about Marco's results there.

> Freq Mode Owvf | Freq Mode Owvf
> a. 61.9kHz 1/4 wave 1.72 | 324 KHz 1/4 1.84
> b. 157.9kHz 3/4 wave 1.46 | 813 KHz 3/4 1.54
> c. 229.7kHz 5/4 wave 1.27 | 1475 KHz 5/4 1.67
> d. 294.4kHz 7/4 wave 1.17 | 1766 KHz 7/4 1.43
> e. 355.6kHz 9/4 wave 1.09 | 2053 KHz 9/4 1.29

The owvf reveals it nicely, since it should change monotonically, but doesn't: surely a mode has been missed.

> Freq Mode Ratio Owvf | Freq Mode Ratio Owvf
> a. 61.9kHz 1/4 1.00 1.72 | 324 KHz 1/4 1.00 1.84
> b. 157.9kHz 3/4 2.55 1.46 | 813 KHz 3/4 2.51 1.54
> c. 229.7kHz 5/4 3.71 1.27 | 1166 KHz 5/4 3.60 1.32
> d. 294.4kHz 7/4 4.76 1.17 | 1475 KHz 7/4 4.55 1.19
> e. 355.6kHz 9/4 5.75 1.09 | 1766 KHz 9/4 5.45 1.11

> like it?

Yup. Nice job - that fits well. But something is still wrong, the owvf numbers above are too large for h/d=4.58; For that geometry, 1/4 wave should be 1.78; 3/4 should be 1.40; 5/4 should be 1.19; all give or take 5%. This error is because we don't know how many turns Marco used, so the wire length is unknown.

We can estimate it, though:- Let W = unknown wire length. Using the frequency measurements and the known dependence of velocity factor on h/d, we have:-

   W/1 * 4 * 324/300e3 = 1.78, so W = 412 metres;

   W/3 * 4 * 813/300e3 = 1.40, so W = 387 metres;

So he must have used 400m of wire, = 1165 turns, give or take
a few percent.

I put Marco's dimensions, with 1165 turns, and some guesses of the experimental arrangement, into our tssp model, to get

  Mode Measured Model Error
  1/4 324 kHz 328 kHz +1.2%
  3/4 813 kHz 809 kHz -0.5%
  5/4 n/a 1179 kHz
  7/4 1475 kHz 1502 kHz +1.8%
  9/4 1766 kHz 1854 kHz +5.0%
11/4 2053 kHz 2175 kHz +5.9%

The high +ve error of the model at the 1/4 wave suggests that some stray top C was present, say a few of cm of trailing wire: 1pF would be enough. That estimate of 1166 kHz for 5/4 mode looks like a pretty good one. The +ve error at the higher modes is quite common with this model - it doesn't allow for some E flux passing vertically through the coil former material.

> you must be extremely careful when reading archives and must
> constantly do the reality check on all info

Yes, and not just archives, but current posts, theories, results...

You can see from the question that Marco posed, and some of the other posts from that era, that nobody knew then how to work out the mode frequencies properly and the naive expectation was that they would be harmonic.
--
Paul Nicholson

Date: Mon, 22 May 2006 18:37:44 -0600

From: Tesla list <tesla@pupman.com>

To: tesla@pupman.com

Subject: Re: Overtones and velocity factors

Original poster: "Dr. Resonance" <resonance@jvlnet.com>

I think the sparks pri-sec area become displacement currents thru a dielectric. The plasma on one side if the conductor, the G-10 the insulator, and the plasma (spark) on the opposite side form the other conductor, ie, a capacitor. Caps have displacement currents thru the dielectrics.

BTW, nice job on the SISG principle. Another "Terry filter" in the making! When I finally get around to writing my book this winter you will be quite famous.

Dr. Resonance

>I have not been involved with this much since I have been "really busy" :o)))
>
>I think D.C. and me are the only "low coupling" folks ;-)) If the
>primary system does not eat power like mad, low coupling losses in
>the primary circuit are less important and the coil naturally runs
>better. LTR systems tend to run at lower currents reducing losses
>and D.C.'s systems have big heavy primaries that have low loss
>too. The SISG will no doubt change all that an order of
>magnitude or two further...
>
>Quench is also not too important if the streamers naturally use all
>the systems energy in the first cycle anyway... Coupling adjusts that...
>
>Computer models tend to point to lower and lower coupling for best
>operation. However, the "energy rise time" of higher coupled
>systems is probably very important for long streamer formation. The
>Russians have specific numbers for this for there 400++ foot Marx generators!!!
>
>I remember an out of tune coil once at a gathering... It had 1 foot
>long primary to secondary arcs!! We put a 3/16 sheet of G-10
>fiberglass between them. The arcs "blew right through it"!! I
>though to myself at the time. "That is really screwed up and there
>is no explanation for it"!!! There still is not. But there are
>"many strange things" that go on down near the primary to secondary coupling area!!!
>
>I always wrote it off to "transformer action" but Paul and Dmitry
>seem to have shot that idea out of the water...
>
>>High voltages - who needs 'em :) Measurements are more rewarding
>>in the long run. Making sparks - Bah! Hope you can measure
>>some resonant frequencies and the associated in-coil wavelengths
>>to demonstrate the above.
>
>I too always wondered about people that did not watch sparks only on
>a "scope screen"... Your gonna go blind :O)))))
>
>>A few. A tie-up between racing arcs and gap behaviour is a
>>rich source of possibilities. We'd better go read Terry's old
>>paper mentioned in
>>
>> > http://www.pupman.com/listarchives/1998/July/msg00019.html
>
>The modern link is here:
>
>http://hot-streamer.com/TeslaCoils/MyPapers/sgap/sgap.html
>
>>Gerry wrote:
>> > What measurements do you have in mind and what type and quality
>> > equipment is needed for the measurement.
>>
>>Capture of a secondary base current waveform on a digital scope,
>>transferred to a computer file for analysis. Only rough amplitude
>>calibration needed. Wide bandwidth, though, say up to 30 times the
>>TC operating frequency.
>
>Gosh!! Who has equipment like that!!! :o)))
>
>Would a single shot primary base current waveform capture of a spark
>with and without racing arcs help. The big old coil was good at
>that. I can fire at 5400V with the SISG (extremely
>repeatable).... I don't have enough section yet though for higher
>voltages. Maybe it would still race though since it had plenty or
>room for lowering. With all the new solid state stuff,
>"repeatability" is a giant new advantage we have ;-))
>
>>One sample of the genuine phenomena is
>>all that's needed, so no long damaging runs required. We would
>>analyse the captured waveform to determine what signal components
>>are present - chances are the offending signal(s) will be quite
>>prominent. We would work out their voltage and current
>>distributions and approximate gradients, and by modelling,
>>determine which parts of the structure are involved in generating them.
>
>I guess that is "yes"... My problem here is that the play rooms are
>about 1/4 their original size now... I might need to take a sawsall
>and start some serious "cleaning up"... :-))) The pool table is going out in 1/8th sections...
>
>Single shot operation does very little damage in any case.... This
>would be on the big old secondary coil... It is still "just fine" ;-)))
>
>>The cross check at that point would be detection of the
>>offending resonances during low power sweeps and showing by probing
>>and loading that the nodes and antinodes are in the predicted
>>places. The tricky bit is getting a coil to display classic racing
>>arcs on demand. Maybe John has pointed the way there.
>
>Single shot operation makes racing arcs far more "safe". Would it
>matter if "miss tuning" was used to help at racing arcs along??
>
>
>>Variation on the above: Just fire the primary under various gap
>>operating conditions, without the secondary (is that possible
>>or would that damage something?). See what frequencies are excited
>>and at what levels. Knowing that, we can calculate how the
>>secondary would cope with them.
>
>Spark gaps are very unpredictable and have all kinds off odd quirks
>that might just add to the noise... Today, (literally - "TODAY"
>;-))) we have new gaps that can remove those variations ;-))
>
>Cheers, Terry

Date: Tue, 23 May 2006 09:15:39 -0600

From: Tesla list <tesla@pupman.com>

To: tesla@pupman.com

Subject: Re: Overtones and velocity factors

Original poster: "Barton B. Anderson" <bartb@classictesla.com>

Hi Paul,

Tesla list wrote:

>Paul wrote:
>Those Seibt coils might be good ones to use for examining
>propagation of the various modes.
>
>High voltages - who needs 'em :) Measurements are more rewarding
>in the long run. Making sparks - Bah! Hope you can measure
>some resonant frequencies and the associated in-coil wavelengths
>to demonstrate the above.
>--
>Paul Nicholson
>--

I don't think the Seibt coil would be good at all for this test.
My Seibt (inches):
0.84185 = Radius 1
0.84185 = Radius 2
17.375 = Height 1
71.625 = Height 2
2410 = Turns
24 = Wire Awg

If I were to put a modest top load on it (removing the corona wires), a primary would also need to be built. For such a long h/d of 32, one would have need to build a helical primary to get the coupling in the range of what is normal if the primary is maintained at the bottom of the Seibt. And even with a helical primary, it's not a pretty picture:

2.5 = Radius 1
2.5 = Radius 2
17.375 = Height 1
27.345 = Height 2
15.03 = Turns
0.25 = Wire Diameter
0.01 = Primary Cap (uF)

The primary just makes k at 0.136 but note proximity of the coils and the 10" of perpendicular climb. I think there would be all sorts of pri to sec trouble.

The use of a Seibt may be getting off the path prematurely. What you want are base current captures from a normal coil producing racing sparks.

Take care, Bart

Date: Tue, 23 May 2006 09:16:04 -0600

From: Tesla list <tesla@pupman.com>

To: tesla@pupman.com

Subject: Re: Overtones and velocity factors

Original poster: "Gerry Reynolds" <gerryreynolds@earthlink.net>

Hi Terry,

>Original poster: Vardan <vardan01@twfpowerelectronics.com>
>
>>transferred to a computer file for analysis. Only rough amplitude
>>calibration needed. Wide bandwidth, though, say up to 30 times the
>>TC operating frequency.
>
>Gosh!! Who has equipment like that!!! :o)))

I have my small coil (3.75x18) that I dont care about any more. It also has a inverted conical primary so you can get larger coupling. We could use that for a test vehicle.

>My problem here is that the play rooms are about 1/4 their original
>size now... I might need to take a sawsall and start some serious
>"cleaning up"... :-))) The pool table is going out in 1/8th sections...

We can do the measure over here if you wish and dont want to go outside.

>Single shot operation makes racing arcs far more "safe". Would it
>matter if "miss tuning" was used to help at racing arcs along??

Im thinking there are many mechanisms to induce racing arcs, miss tuning is one of them. Maybe we ought to capture the waveform on several mechanisms - out of tune, top load too small, too much coupling, etc. Ive experienced the first two on the small coil so it is a good candidate.

>>Variation on the above: Just fire the primary under various gap
>>operating conditions, without the secondary (is that possible
>>or would that damage something?). See what frequencies are excited
>>and at what levels. Knowing that, we can calculate how the
>>secondary would cope with them.
>
>Spark gaps are very unpredictable and have all kinds off odd quirks
>that might just add to the noise... Today, (literally - "TODAY"
>;-))) we have new gaps that can remove those variations ;-))

We ought to do that as well to get the spectral content of the primary.

Gerry R.

Date: Tue, 23 May 2006 18:28:45 -0600

From: Tesla list <tesla@pupman.com>

To: tesla@pupman.com

Subject: Re: Overtones and velocity factors

Original poster: Paul Nicholson <paul@abelian.demon.co.uk>

Bart wrote:

> I don't think the Seibt coil would be good at all for
> this test.

Ah! No, I wasn't thinking of racing arcs on this coil - that's over on the other thread. No, I just wondered about some tests on velocity factors of high overtones and the chance to extend the validation of tssp models to some large h/d ratios.

A low power test - just a sig gen into the base, no topload. For each resonance, sweep with a voltage probe to locate the null positions - the voltage nodes - at each end of the voltage half-wave that straddles the center of the coil.

Oh, you'd have to remove those two corona wires, and be able to test up to about 6 MHz. If there's a possibility of a test, I'll post some predictions.
--
Paul Nicholson
--

Date: Wed, 24 May 2006 10:31:34 -0600

From: Tesla list <tesla@pupman.com>

To: tesla@pupman.com

Subject: Re: Overtones and velocity factors

Original poster: dest <dest@alexandria.cc>

Hallo Terry.

> Original poster: Vardan <vardan01@twfpowerelectronics.com>

> Quench is also not too important if the streamers naturally use all
> the systems energy in the first cycle anyway...

that`s impossible, only arc to ground can do that. or you are talking about breakpoint, which forces discharge as early as 100kv for example? imo this can`t change much.

> Computer models tend to point to lower and lower coupling for best
> operation.

which models exactly? any papers about them? : )

> However, the "energy rise time" of higher coupled systems
> is probably very important for long streamer formation. The Russians
> have specific numbers for this for there 400++ foot Marx generators!!!

coil with the same coupling but higher Fo would have higher "ert" automatically, does it meant that this coil would have longer sparks just from this? unlikely : )

> I too always wondered about people that did not watch sparks only on
> a "scope screen"... Your gonna go blind :O)))))

no way : p we just haven`t necessary equipment - there is 5 mhz single-beam single-channel, 15 mhz two-beam two-channel and 50 mhz single-beam two-channel scopes lying here, but none of them is storage
or digital -_-

> With all the new solid state stuff, "repeatability" is a giant new
> advantage we have ;-))

of coz you have - the "best man friend" like i`ve said : D

Date: Wed, 24 May 2006 11:46:36 -0600

From: Tesla list <tesla@pupman.com>

To: tesla@pupman.com

Subject: Re: Overtones and velocity factors

Original poster: Vardan <vardan01@twfpowerelectronics.com>

Hi dest,

At 08:35 AM 5/24/2006, you wrote:
>Hallo Terry.
>
> > Original poster: Vardan <vardan01@twfpowerelectronics.com>
>
> > Quench is also not too important if the streamers naturally use all
> > the systems energy in the first cycle anyway...
>
>that`s impossible, only arc to ground can do that. or you are talkin
>about breakpoint, which forces discharge as early as 100kv for
>example? imo this can`t change much.

I am talking about very low coupling in the 0.03 to 0.1 range. The energy transfer gets so slow much never makes it back to the primary. But those are with older models. Newer models tend to point to the .1 to .15 range. The DRSSTC folks seem to get better results with very high coupling in the 0.2 to 0.25 range. They think
it is due to "ERT".

> > Computer models tend to point to lower and lower coupling for best
> > operation.
>
>which models exactly? any papers about them? : )

Models like the one used here:

http://hot-streamer.com/TeslaCoils/MyPapers/modact/modact.html

tend to optimize to very low coupling coefficients. However, ScanTesla likes higher ones. ScanTesla takes much more into account and optimized far better of course.

> > However, the "energy rise time" of higher coupled systems
> > is probably very important for long streamer formation. The Russians
> > have specific numbers for this for there 400++ foot Marx generators!!!
>
>coil with the same coupling but higher Fo would have higher "ert"
>automatically, does it meant that this coil would have longer sparks just from this? unlikely : )

You need a "just right" ERT and then a whole lot of energy then to feed the streamer. If you don't have the energy, or too fast of ERT, or to slow of ERT, then the streamers get shorter. I forget the number right off but it is in the spark book or archives.

> > I too always wondered about people that did not watch sparks only on
> > a "scope screen"... Your gonna go blind :O)))))
>
>no way : p we just haven`t necessary equipment - there is 5 mhz
>single-beam single-channel, 15 mhz two-beam two-channel and 50 mhz
>single-beam two-channel scopes lying here, but none of them is storage
>or digital -_-

:o)) You have fine equipment there. But I know "I" tend to really get caught up far more in "technical details" than "pretty sparks"...

> > With all the new solid state stuff, "repeatability" is a giant new
> > advantage we have ;-))
>
>of coz you have - the "best man friend" like i`ve said : D

I was doing repeatability experiments yesterday and the SISG is very impressive :-))) I was also trying to get some racing arcs for Paul's thing but I could not get any yet...

Cheers, Terry

Date: Wed, 24 May 2006 22:37:04 -0600

From: Tesla list <tesla@pupman.com>

To: tesla@pupman.com

Subject: Re: Overtones and velocity factors

Original poster: "Barton B. Anderson" <bartb@classictesla.com>

Hi Paul,

Ok, I see now. The gen can't sweep past 1.1MHz, and for some reason, I was thinking it went to 2Mhz. I set up the coil anyway outside, threw down a 4 foot ground plane, and hooked up the equipment. Found f1 at 598 kHz and decided I would increase f just to see if f2 was in range (nope, it's not). There's not much use in doing much here if only f1 is attainable. Guess I really do need to upgrade my equipment (a new scope and generator are at the top of the list).

Take care, Bart

Tesla list wrote:

>Original poster: Paul Nicholson <paul@abelian.demon.co.uk>
>
>Bart wrote:
>
> > I don't think the Seibt coil would be good at all for this test.
>
>Ah! No, I wasn't thinking of racing arcs on this coil - that's
>over on the other thread. No, I just wondered about some
>tests on velocity factors of high overtones and the chance to
>extend the validation of tssp models to some large h/d ratios.
>
>A low power test - just a sig gen into the base, no topload.
>For each resonance, sweep with a voltage probe to locate the
>null positions - the voltage nodes - at each end of the voltage
>half-wave that straddles the center of the coil.
>
>Oh, you'd have to remove those two corona wires, and be able
>to test up to about 6 MHz. If there's a possibility of a
>test, I'll post some predictions.
>--
>Paul Nicholson
>--

Date: Wed, 24 May 2006 23:27:30 -0600

From: Tesla list <tesla@pupman.com>

To: tesla@pupman.com

Subject: Re: Overtones and velocity factors

Original poster: Vardan <vardan01@twfpowerelectronics.com>

Hi dest,

>>which models exactly? any papers about them? : )
>
>Models like the one used here:
>
>http://hot-streamer.com/TeslaCoils/MyPapers/modact/modact.html
>
>tend to optimize to very low coupling coefficients. However,
>ScanTesla likes higher ones. ScanTesla takes much more into account
>and optimized far better of course.

ScanTesla is here:

http://hot-streamer.com/temp/ScanTesla740a.zip

It can run simulations over "millions" of coil parameters "very very fast"... I am running it now for the SISG coil thing... I updated the documents of this nasty program a little here. But the code has not changed in almost a year.

It is one of the most powerful programs out there... But one of the most difficult to "explain"... It basically does MicroSim style coil models at "very high speed" searching for the "best" parameters...

I think you came on the list after it... You should check it out since you might like it ;-))

I think most folks get way totally lost by it... But it is one of my "secret weapons" ;-)))

Cheers, Terry

Date: Thu, 25 May 2006 11:56:42 -0600

From: Tesla list <tesla@pupman.com>

To: tesla@pupman.com

Subject: Re: Overtones and velocity factors

Original poster: dest <dest@alexandria.cc>

Hallo Terry.

> Original poster: Vardan <vardan01@twfpowerelectronics.com>

>> > Quench is also not too important if the streamers naturally use all
>> > the systems energy in the first cycle anyway...
>>
>>that`s impossible, only arc to ground can do that.

> I am talking about very low coupling in the 0.03 to 0.1 range. The
> energy transfer gets so slow much never makes it back to the
> primary.

even 0.1 is looking terrible - 11 cycles, who uses this? 0.03 is just for crazyest crazy imo % ) i`m not considering ss gaps here : ) but even if i set k=0.1 and load secondary (after full transfer) with 500 kOhm, about 8kv (from initial 20kv) will show up in the primary. Of coz i don`t have a model of real sg, so maybe all of this is wrong.

> Models like the one used here:
> http://hot-streamer.com/TeslaCoils/MyPapers/modact/modact.html
> tend to optimize to very low coupling coefficients.

thnx, i`ll look at this. and probably ask more then : )

> You need a "just right" ERT and then a whole lot of energy then to
> feed the streamer. If you don't have the energy, or too fast of ERT,
> or to slow of ERT, then the streamers get shorter.

correct me if i`m wrong, but aren`t the "russians" studied influence of VRT in case when breakdown starts before full marx erection? And they just don`t need/want to get all energy in the system before start
of breakdown? when you use breakpoint on toroid, you get the same situation, but who forces "me" to use it? why "i" can`t wait when most of the bang happily climbs on the top, and then suddently jump from there in violent capacitive discharge? : ) i`m kinda dreamer, you know : D

> I was doing repeatability experiments yesterday and the SISG is very
> impressive :-)))

yeah, now you can build a factory and start to stamp the coils with +-0.1" in output spark length tolerance. decorative coils in the kitchen, wc, your car, on your work, and even on your grandma lawn : )

> I was also trying to get some racing arcs for Paul's thing but I
> could not get any yet...

haven`t you measured Q primary with "gap" yet? % )

> ScanTesla
> I think you came on the list after it... You should check it out
> since you might like it ;-))

you`re right on both cases, so be prepared to some number of questions. next week probably : )

Date: Thu, 25 May 2006 15:11:54 -0600

From: Tesla list <tesla@pupman.com>

To: tesla@pupman.com

Subject: Re: Overtones and velocity factors

Original poster: Paul Nicholson <paul@abelian.demon.co.uk>

Bart wrote:
> threw down a 4 foot ground plane, and hooked up the equipment.
> Found f1 at 598 kHz and decided I would increase f just to see
> if f2 was in range (nope, it's not).

Thanks Bart - even that one measurement is well worthwhile.

Tssp returns 595.3 kHz for the 1/4 wave, so that's a good sign. Next higher mode is 1577 kHz. I ran the model up to 23 quarter waves (up at around 7574 kHz) but I don't think there's much accuracy above about the 11/4 wave.

> There's not much use in doing much here if only f1 is attainable.
> Guess I really do need to upgrade my equipment (a new scope and
> generator are at the top of the list).

Well, the gear you've got is more than adequate for coiling. Surely not worth investing in new kit just for one or two experiments. Anyway I should leave it for now - the coil will always be there for when an opportunity to measure arises - so long as you don't destroy it with that silly sparking :)

Dest wrote (in another thread):
> i know nothing about this [velocity h/d] dependence - i`m reading
> archives currently, not your web site

There's nothing on tssp site about this - yet. There's lots of stuff that still needs finishing, checking, writing up (the whole site could do with a revamp). Most of it has been talked about on here. The relevant part is that for low modes the overall wire velocity factor is a smooth function of h/d ratio,

  http://www.abelian.demon.co.uk/tmp/ph1.gif
  http://www.abelian.demon.co.uk/tmp/ph3.gif
  http://www.abelian.demon.co.uk/tmp/ph5.gif

and the functions fitted to the measured and modelled points are

  1/4 wave: Ph1(h/d) = ln(h/d) * 0.39 + 1.19
  3/4 wave: Ph3(h/d) = ln(h/d + 2.7) * 0.6 + 0.21
  5/4 wave: Ph5(h/d) = ln(h/d + 5) * 0.65 - 0.28

I've seen a reference to similar curves in radio handbooks (for the fundamental only), but I think ours may be a little more accurate.

The measurement point that Bart has just supplied extends the 1/4 wave curve out to h/d = 32: curve predicts owvf = 2.54; measured = 2.58; error = -1.6%.

This smooth relation between h/d and wire velocity was first pointed out to the list by one Ed Harris,

  http://www.pupman.com/listarchives/1996/january/msg00096.html

Recently it was rediscovered for us independently by Ed Phillips.
--
Paul Nicholson
Manchester, UK.

Date: Thu, 25 May 2006 16:43:46 -0600

From: Tesla list <tesla@pupman.com>

To: tesla@pupman.com

Subject: Re: Overtones and velocity factors
--

Original poster: Vardan <vardan01@twfpowerelectronics.com>

At 11:10 AM 5/25/2006, you wrote:
>Hallo Terry.
>...........
> > I was also trying to get some racing arcs for Paul's thing but I could not get any yet...
>
>haven`t you measured Q primary with "gap" yet? % )

Indirectly... But it was SO good I did not care anymore ;-))

It is easy to find:

Q = 1/R x SQRT(L/C) = 1/ 0.1 x SQRT(16.83E-6/150.5E-9) = 105.75

> > ScanTesla
> > I think you came on the list after it... You should check it out since you might like it ;-))
>
>you`re right on both cases, so be prepared to some number of questions. next week probably : )

:-)))

Here are some PDFs:

Another "attempt" at making instructions:

http://drsstc.com/~terrell/modeling/ScanTeslaInstructions-700.pdf

It basically generates data for other programs to analize.

BigCoil analysis:

http://drsstc.com/~terrell/modeling/BigCoilDRSSTC.pdf

Steve Ward's coil:

http://drsstc.com/~terrell/modeling/SteveWardCoil-ScanTesla700.pdf

http://drsstc.com/~terrell/modeling/StreamerTime.pdf

http://drsstc.com/~terrell/modeling/WardsCoil-18vs25.pdf

There is also a three coil system version:

http://drsstc.com/~terrell/modeling/ScanTesla-TRSSTC-740.ZIP

I have the input file for Tesla's Colorado Springs coil somewhere...

The program needs some bug fixes still too...

Cheers, Terry

Date: Fri, 26 May 2006 11:54:06 -0600

From: Tesla list <tesla@pupman.com>

To: tesla@pupman.com

Subject: Re: Overtones and velocity factors

Original poster: "Barton B. Anderson" <bartb@classictesla.com>

Tesla list wrote:
(Paul wrote)

>Well, the gear you've got is more than adequate for coiling. Surely
>not worth investing in new kit just for one or two experiments.

Surely not worth just these experiments, but there have been many such situations with similar limitations which add up to a need for new equipment.

>Anyway I should leave it for now - the coil will always be there
>for when an opportunity to measure arises - so long as you don't destroy it with that silly sparking :)

No worries.

Take care, Bart