Eric Dollard

[garrettm4]

Another Slice of Pi Anyone?

With all the mathematical slices of Pi being passed around... I thought I would add a few more to the party.

I've just remembered Arthur D. Delagrange's chapter in Jim Williams' (R.I.P) 1998 book The Art & Science of Analog Circuit Design. I found Delagrange's section of the book to be humorous and full of interesting and useful information. It just so happens that he has some mathematical fun to add to the Pi debate.





*Note to the unsuspecting; If you haven't already realized, these "proofs" are for fun, and NOT intended to provide any meaningful information other than a laugh or two. If you explain something the "right" way... you can confuse almost everyone into believing anything!

Garrett M

[rickinva]

.
.
.

Pi is causing me problems and I have an apology to make as some of my data is incorrect BUT only with respect to pi.
Have some questions waiting for an answer but not received as yet.

Actually went to the Lab and took out 2 stainless steel lids that were solid and rolled them along a tape measure many times.
Average pi returned was 3.16 for both lids, C = 524 & 411mm.
Also did it with a dressmaker's cotton tape measure with the same result.

My youthful experiment was only that I had done the same as the above and nothing at all to do with 3.24.
When you are working at about half a meter, it is easy to see any discrepancy.

.
.
.
Smokey

Smokey:

As long as you try to determine Pi by doing physical measurements, you will always have erroneous answers.

Any attempt to determine Pi by doing physical measurements (measuring the radius length and then rolling the circumference along a straight line and measuring that length) will "always" result in errors in trying to obtain the exact ratio. The reason being your inability to get the "exact" lengths involved. Errors in either or both measurements result in wrong values for Pi.

If what you are doing was that easy, the Ancients would have had the correct value long ago. The best the ancient Egyptians could come up with was 22/7, which was close (approximately 3.1429) verses ( a closer value of 3.1415 known today).

If we used exact measurement values:

R = 2"
then C approx 12.5664
Pi = 12.5664/2/2 = 3.1416 approximately

But if R is a little off

Let C= 12.5664

If R = 1.99 (off only .01" less than exact value)
Pi would be 12.5664/2/1.99 = 3.1574

If R = 1.98 (off only .02")
Pi would be 2.5664/2/1.98 = 3.1733

Now let your measurement of C be off a little

Let C = 12.5664 + .01 = 12.5764
Ir R = 2
Pi = 3.1441

Let C = 12.5664 - .01 = 12.5564
If R = 2 +.01 = 2.01
Pi = 3.1235

Let C = 12.5664 + .03 = 12.5964
If R = 2 - .02 = 1.98
Pi = 3.1809

Thus very, very small mismeasurements in either or both (the radius length and/or where the circumference point actually hits the straight line or the measurement of that length) will cause plenty of error in your results.

THAT is why it is calculated by mathematical means and NOT physical means. Only Calculus can give you a somewhat accurate approximate value. And that takes solving for the value of an infinite series to some determined degree of accuracy. Remember, we can NEVER KNOW the EXACT value for Pi, its decimal value never stops or repeats. and THAT fact about it IS KNOWN to be TRUE.

I say approximate, because, Pi has no "end" to its decimal value, nor does it repeat a set of digits to infinity at some point, thus it can never accurately be written as a fraction of whole Integers or as a decimal . We just can NOT measure matter accurately enough to ever get an exact value for Pi.

3.14159265358978323 is more than accurate enough for any physical use you will ever have.

Rick

[rickinva]

Occassional needs to adjust the value of Pi used

The problem, when the value of Pi is adjusted in a calculation, does NOT lie in the value of Pi, but rather in the inaccurate formula that is being used that includes Pi.

Mathematical equations, when used to model our observed reality, are not always accurate. Thus the need, from time to time, to use "fudge" factors to bring predicted outcomes closer to the true physical results.

So, rather then try to "redefine" Pi, consider refining your formulas, or determine the needed "fudge factor(s) that might be necessary to bring those formulas closer to observed reality.

Case in point:

My father was a self taught "electronics technician", working in an electronics manufacturing plant in the quality Control Section.

Often design engineers would bring their schematics to my father to have him figure out how to make the designed circuit really work.

In other words, equations can only take you so far, when components are not "accurate".

Rick

[t-rex]

Dr. Green, 3101 and 4594

1) The standing wave patterns you have shown show exactly what is in progress along the coil (resonator) distance variable. It is a transmission line problem but for longitudinal rather than transverse propagation.

This reduces to a basic Ohm's Law calculation,

Let Z = characteristic impedance, and

Let I = input current into line, and

Let E = output voltage at end of line.

When the line exhibits a Pi over two displacement between input and end of the line it is then;

Output E is the product of the input current, I, multiplied by the characteristic impedance, Z,

Basic Ohm's Law, E equals I times Z. This law also applies to analog nets, or ladder lines, both transverse and longitudinal networks.

2) It is further known that the product of the input current and the input EMF is equal to the product of the output potential and the displacement current at the output of the line. Also the magnification factor, n, applies to the ratio of the output potential to the input EMF but this is in a round about way. At the end of the type written part of my "Theory of Wireless Power", coil section, is the Steinmetz equations for the Pi over two (quarter wave) network, or line. See first chapters of "Transients in Space" a part of "Theory and Calculation of Transient Electric Waves".

In general, the output impedance of the network must be greater than the characteristic impedance, Z, of this network. This gives a rise in output potential, E. Likewise, the input impedance of the network must be less than the characteristic impedance, Z, of this network. This gives a rise in input current, I. Both these conditions must be met in order to maintain a Pi over two distribution on the coil or generalized network.

This relationship of input impedance and output impedance is best expressed in an alternate manner. Rather than use the dimensional relation of impedance in Ohms, the dimensional relation of admittance in Siemens is the proper expression of the output. Hence the relations input impedance, and output admittance. Zero input impedance gives rise to large resonant currents, reflecting the electric wave back into the network. Likewise zero output admittance gives rise to large resonant potentials, also reflecting the electric wave back into the network, back now in the reverse direction towards the zero impedance input. Large Kilovolt-amperes can be generated in this manner. This is the arch-principle of the "Resonant Transformer".

It is a property of a self resonant solenoid that in its resonant Pi over two mode, this coil also serves as a phase converter. In free oscillation the resonant coil exhibits only one active pole, the neutral. No return conductor is connected to this network, only the neutral terminal. This mono-pole is the current end of the resonant coil.. It is this essential element of Pi over two resonance that makes Telluric transmission possible. Electro-magnetic boundary conditions no longer have any meaning in this mode of electric wave transmission. Such transmission cannot be developed by the use of transverse E.M. structures, nor analog networks. It is a singular property of the resonant coil. Hence the transmission system envisioned by Nikola Tesla (Wardenclyffe).

3) The ability of a network to operate in the Pi over two mode is the result of an impedance and an admittance mis-match. If the input impedance matches the characteristic impedance of the network, and likewise, the output admittance matches the characteristic admittance of the network, then no energy is stored in the network as now the energy is transferred into, and then out of, the network structure. Such is called a transmission network. It is no longer a resonant network.

It is the asymmetry of the input and output mis-matches that gives rise to the Pi over two distribution. One side is high, the other side is low, with respect to the natural impedance of the network. Conversely, one side is low, the other side is high, with respect to the natural (Characteristic) admittance of the network. The low-impedance side, Z, is always current side, the low admittance side, Y, is always the potential side. Reversing ends with this relation reverses the Pi over two distribution along the network (coil). These two factors, the input impedance, Z, and the output admittance, Y allow for algebraic expression of the transfer constants of the network. The product ZY represents the square of the propagation constant. This relates to the frequency or wavelength. The ratio Z to Y represents the square of the characteristic impedance of the network. These relations allow for the calculation of network behavior.

4) Let us take the information given and apply it to the transitional point interconnecting the output side of the secondary coiled resonator and the input side of the extra coil resonator. There exists a definite current and voltage at this transition point. This transition point is a node of reflection to refraction. The expression of the ratio of the reflection to the refraction is related to the expression of magnification factor. It is a requirement that the input impedance of the extra coil must be less than the characteristic impedance. Also, it must be less than the output impedance at the high end of the extra coil. Hereby the Pi over two distribution can exist along the coil space (length) variable. In order to maximize reflection, this to create large magnification, the impedance connected to the input side must be very much less than both the characteristic impedance and the output impedance.

It can hereby be seen that the output impedance of the secondary coil is also the input impedance seen by the extra coil. This is the consequence of the nodal transition point which can exhibit only one ratio of voltage to current, that is, only a single impedance. Hence it is important that the output impedance of the secondary coil should be as low as possible, so as to bring the input impedance of the extra coil to a magnitude very much less than the natural impedance of this extra coil.

This requirement is met by secondary coils of small inductance and large self capacity. These are coils of large diameter but small coil height. Flat spirals of few close turns suggest themselves as low impedance secondary structures.

5) It is a consequence of resonant coils that the output impedance is high, that is, many times greater than the natural impedance of the coil, such as the secondary. This further complicates providing the desired input impedance to the extra coil. Thus a secondary coil of very low natural impedance is required. This explains the extreme diameter ratios seen between secondary and extra coils used at Colorado Springs. See my analysis of the Colorado Springs setup.

In view of this secondary coil requirement, it is best that it be replaced by an equivalent network consisting of lumped coils and condensers. This is often in a configuration known as a "Pi network", one series arm with a pair of pillar, or shunt, arms on the input and output. This give the figure of the letter Pi. A phase leading network uses a series condenser, a phase lagging network uses a series inductor. The shunt arms are thus inductors or condensers respectively. Lead networks are LMD, and lag networks are TEM.

Lag networks are preferred since the armatures of the condensers can be put at ground potential. Also the lag network inhibits harmonic and transient frequencies. Formulae for the impedance transforming characteristics are found in the A.R.R.L. "Radio Amateur Handbook". Their use is shown in converting from low line impedance to high tube impedance, or the other way around. The material is listed in easy to use tables with diagram. The Pi network structure is by far the most effective means for exciting the extra coil into the resonant magnification of potential.

The use of the secondary coil is principle for basic Telluric transmission. The use of the extra coil is principly for magnification of potential. The Telluric work favors the secondary coil, whereas the vacuum tube (Crookes) work favors the extra coil. These are basic engineering considerations. It should be noted that the magnification of potential is very important in Telluric reception where a detector element is required, such as the grid of a vacuum tube. For the most part the interaction of the secondary and extra coils is a needless complication in experimental work along basic lines. This is to say, the Pi network is the best means by which to study extra coil behavior.

[garrettm4]

Pi(con)fusion

An Excursion into the World of Philosophy & Religion; Oh Sweet Persuasion

--Perfection & Idealism Vs. Actuality & Attainability--

In Smokey's defense, and in as realistic a way of thinking, mathematics relates to IMAGINARY PERFECTION, the universe around us does NOT embody this wishful IDEALISM, it embodies ACTUALITY engendered by ATTAINABILITY. That is, perfection can only be approximated. Just as we all strive to live like Jesus[1] - the only "perfect" man to live on Earth (or so I'm frequently told), we all fail to act exactly like him. We, despite our best efforts, reflect an imperfect image of a perfect idea.

So too does nature try to emulate, as best it can with the constraints placed upon it[2], a similar state of perfection. Pi, whatever its exact value in the arbitrary number system used[3], is a ratio who's value is imaginary, in the sense that it can not be produced to perfection outside of theory. We can only attain an approximation. Much like the seemingly innocent numbers zero & infinity. Can we really have "nothing"[4]? Is "empty" space really empty[5]? How can you have an endless amount of something? Can that really exist? Leaving these existential questions behind[6], and returning to Pi, we can safely say that the debated numeric value for Pi is purely situation dependent. As theoretical idealism is not attainable in actuality. Each situation, given its own unique conditions, would engender a specific condition of imperfection.

It's probable that NASA uses a different value for Pi[7] considering Outer Space isn't perfect, no planet is a perfect sphere, no orbit is a perfect circle - everything is spheroidal and elliptical. It would seem fit that a specific value for Pi that fits the actual situation seems in order. The famed "fudge-factor" makes its debut.

A less philosophical topic to the Pi debate is that of the method of measurement. Not in the physical sense, but in the analytical approach to using mathematical machinery to derive an answer. As evidenced by the various values suggested, there is more than one way to derive an answer. The two "proofs" given by myself earlier, show that there are no constraints on how you can attack the problem. While some approaches may be frowned upon it doesn't necessarily make them invalid. That said, any rigorous examination of this measurement problem is met, surprisingly, with similar results. Evidenced by all the different, but very close, values given for Pi throughout human history. People in places that had absolutely no communication with one another achieved very similar results. This forms the backbone of the corroborative and statistically relevant value for Pi. As humanity progressed its mathematical machinery, so too have we used it to examine this age old problem. This evolutionary process has lead to finding the decimal value of Pi to an enormously useless level of precision. Mathematicians have currently taken this holy crusade so far, its almost an effort in enlarging their own egos. Realistically, the further expansion of our decimal precision for Pi, is merely an effort futility. As 6 digits is about all that is ever used.

Concluding this discussion, does Pi relate to 3.1459..., 3.1464... or 3.24? Probably. It depends on how you got the answer and if you used a fudge-factor along the way. Certain situational context (NASA) may demand a different value for Pi than the Ivory Tower mathematical idealism provides. In the end, people will want to polarize the situation and demand that one value is more correct over another, much like religion and philosophy. Most people will go with the orthodox value while others will join a cult and believe in a different value. That said, the engineer will build using what works for him and using as few of decimal digits needed to get there[8].

*To cool down after all of that, please enjoy watching a short clip from the British 1980s TV show Hitchhiker's Guide to the Galaxy, a question about the universe, life and everything. (The best part starts @ 3:20 in the video, my favorite part (starts @ 4:02 in video) when the philosophers come in are talking about loosing their jobs.)

[1] If you're Cristian, that is.
[2] From gravity to magnetic and electrostatic forces to nuclear forces the natural world is pushed pulled, compress and contorted by many factors. The natural imbalance of these and many other forces, in the macro world, leads to inevitable imperfection in physical objects.
[3] Base-10 is not the only number system.
[4] The Einsteiners & Relativists would have you believe so.
[5] The Maxwellians would give a resounding NO. Modern QED physicists would also say no.
[6] These questions are best handled on the basis of "faith" as further scrutiny will yield no clear answer.
[7] This based purely on hearsay and the postulate that the universe is an imperfect structure having defects.
[8] Engineering is the heartland of approximations, where tolerances dictate the level of precision produced.

*Note, this was a satirical and slightly sarcastic write up of my thoughts on the recent discussion regarding Pi. In no way is this intended to offend anyone, merely to convey a different perspective with some hidden humor. No claims are made as to what the right answer is, just a philosophical overview of the situation. For argumentative replies please send as a PM.

Garrett M

[rickinva]

An Excursion into the World of Philosophy & Religion; Oh Sweet Persuasion

--Perfection & Idealism Vs. Actuality & Attainability--

In Smokey's defense, and in as realistic a way of thinking, mathematics relates to IMAGINARY PERFECTION, the universe around us does NOT embody this wishful IDEALISM, it embodies ACTUALITY engendered by ATTAINABILITY. That is, perfection can only be approximated. Just as we all strive to live like Jesus[1] - the only "perfect" man to live on Earth (or so I'm frequently told), we all fail to act exactly like him. We, despite our best efforts, reflect an imperfect image of a perfect idea.

So to does nature try to emulate, as best it can with the constraints placed upon it, a similar state of perfection. Pi, whatever its exact value in the arbitrary number system used[2], is a ratio who's value is imaginary, in the sense that it can not be produced to perfection outside of theory. We can only attain an approximation. Much like the seemingly innocent numbers zero & infinity. Can we really have "nothing"[3]? Is "empty" space really empty[4]? How can you have an endless amount of something? Can that really exist? Leaving these existential questions behind[5], and returning to Pi, we can safely say that the debated numeric value for Pi is purely situation dependent. As theoretical idealism is not attainable in actuality. Each situation, given its own unique conditions, would engender a specific condition of imperfection.

I have no doubt that NASA uses a different value for Pi because Outer Space isn't perfect, NO planet is a perfect sphere, NO orbit is a perfect circle - everything is spheroidal and elliptical. It would seem fit that a specific value for Pi that fits the actual situation seems in order. The famed "fudge-factor" makes its debut.

A less philosophical topic to the Pi debate is that of the method of measurement. Not in the physical sense, but in the analytical approach to using mathematical machinery to derive an answer. As evidenced by the various values suggested, there is more than one way to derive an answer. The two "proofs" given by myself earlier, show that there are no constraints on how you can attack the problem. While some approaches may be frowned upon it doesn't necessarily make them invalid. That said, any rigorous examination of this measurement problem is met, surprisingly, with similar results. Evidenced by all the different, but very close, values given for Pi throughout human history. People in places that had absolutely no communication with one another achieved very similar results. This forms the backbone of the corroborative and statistically relevant value for Pi. As humanity progressed its mathematical machinery, so too have we used it to examine this age old problem. This evolutionary process has lead to finding the decimal value of Pi to an enormously useless level of precision. Mathematicians have currently taken this holy crusade so far Its almost an effort in enlarging their own egos. Realistically, the further expansion of our decimal precision for Pi, is merely an effort futility. As 6 digits is about all that is ever used.

Concluding this discussion, does Pi relate to 3.1459..., 3.1464... or 3.24? Probably. It depends on how you got the answer and if you used a fudge-factor along the way. Certain situational context (NASA) may demand a different value for Pi than the Ivory Tower mathematical idealism provides.


[1] If your Cristian, that is.
[2] Base-10 is not the only number system.
[3] The Einsteiners & Relativists would have you believe so.
[4] The Maxwellians would give a resounding NO. Modern QED physicists would also say no.
[5] These questions are best handled on the bases of "faith" as further scrutiny will yield no clear answer.

Garrett M

The fact remains that "a cat is a cat", "red is red" and "one is one" by any other name. Some things in Life are socially "defined".

What number base (assuming you are using a positive rational number for the modulus) makes absolutely NO difference as to whether Pi is rational or irrational. In ALL positive rational number bases it is IRRATIONAL.

Pi is NOT something that can be fudged. It is a "defined" number. A DEFINED mathematical number. That is why it has a SPECIAL symbol that represents it and ONLY it in mathematics. (Just like "e").

Now the formulas you use are YOUR choice. The more accurate they are the closer your predictions will come to your observed results.

If you want to use Pi in your equations, THAT is YOUR choice. BUT, if you use it, then use it as it IS. I suggest that, if doing so, gives you results that do not match "reality" as you seemingly observe them, then the problem is NOT the value of PI, but your formula.

Your desire to use some hybrid number for "Pi" would be like wanting to use some other type curve (than one where its circumference was NOT equidistant from its center point) and call your curve a circle. A Circle is a circle and Pi is Pi. They have absolutely nothing inherently to do with reality. They a mathematical constructs.

If Pi doesn't work usefully in your formulas, then don't use it. But if you do use it, then don't try to set yourself apart by redefining it.

If NASA can't use it in their calculations, then maybe, just maybe, NASA should stop trying to calculate orbits, etc. based on "Relativity" and go back to a older model of space, taking into consideration the Ether. The problem doesn't lie in the value of Pi, it lies in their models of reality.

NASA and individuals do NOT define "mathematical" constants, mathematicians do. Using mathematical constants in formulas is a "choice" of the person doing the modeling. But, don't blame the "defined constant" if it doesn't yield a useful model equation/solution.

Whether or not you like the idea, there is ONE and ONLY ONE "defined" number called Pi, It IS the value that satisfies the equations that define it, as their result.

If Pi doesn't work for you, fine, then don't use it.

Use your own "Phooey" constant (lets give it the symbol "Fy" to represent it), if that seems to work better, but don't call your "fudge factor" (Fy) "Pi", unless it equals "Pi" in decimal value.

Ivory Towers have absolutely nothing to do with this issue. Mathematics is a construct; A language; A logical system A "defined" "science" in its own right. Other people are free to make use of it, if doing so proves useful to them, but those people are NOT FREE to redefine its terms, definitions or constants.

Any relationship between mathematics and the world around, in many cases, is purely accidental.

The world does not determine mathematics and mathematics does not define the world. Mathematics is to the "world around", what the Law is to "Justice".

Many, many aspects of mathematics have absolutely no reflection in the real world, whatsoever, as we perceive the world.

After all, who has ever really "seen" the "world around". I haven't, I've only "seen" what my "mind" presents to me as what it "thinks" the "outside" world must look, feel, smell, taste or sound like.

God only knows what it is really like, but I'm sure my mind is wrong.

Solids aren't solid, and there is no such thing as "color" or "sound" outside the mind, and no guarantees that what you experience as color or sound is exactly the same as what I do, even if we do call what we experience by the same "defined" names.

If our eyes and mind could "see" ALL frequencies of electromagnetic radiation, we would be totally blinded by the extreme bright white light all around us. Nature did us a favor by limiting what we can see (though personally, I do wish I could also see IR and UV radiation, like some creatures can).

Pi is still and always approximately 3.14159265358979323 in base 10.

Rick

[dR-Green]

Thanks Garrett and Eric. It's late to get into a proper response now but I currently have a new secondary in the making. It was intended to be 20% height to diameter ratio with 17 turns, but it's not built yet so on the basis of this new information it will be 15% like the Colorado Springs coil. This new secondary frame also has a design improvement which should allow for better connection to the extra coil and ground. This will be used to gather some data before building a "full scale" coil for AM radio reception. I suppose for that a basic scaled down Colorado Springs unit should do, without any modifications? (Thanks for the scaling method by the way).

Tesla mentioned in an article, possibly The Problem Of Increasing Human Energy, that his Colorado coil was the "most powerful" design, but for Wardenclyffe he was planning on using the "best" design that he knew of. So I wonder in what way they are different in operation to such a degree for him to say that, and what "best" means?

On a side note I also have two flat spiral coils with 13 metres of secondary wire, which is equal to the secondary coil wire length I've been testing here. I was planning on combining one with the extra coil at some point to see what it did, and one was going to be used as a test receiver with the TMT. Basic Telluric work seems relatively straight forward compared to this extra coil business, so once a frequency is decided upon then it shouldn't take too long to do a little better than Meyl's boat demo I think, as a first step through giving the mystics entertaining things, bypassing their unsuspecting defences and planting the seed of truth.

One thing that came to mind on the secondary/concatenated coils frequency tests is that the condenser ring at the top of the secondary has always been connected throughout all tests which would have reduced its frequency somewhat, so I'll remove it and see what the new frequency is.

On the subject of earthquakes, this was repeated on the propaganda box earlier and fortunately it's also on youtube

Why Can't We Predict Earthquakes ? (BBC Documentary) - YouTube

The part at 40 minutes 45 seconds in particular is interesting and the guy that follows. By applying pressure to a rock, the rock starts to produce an electrical current. He believes before an earthquake the rocks could be producing thousands of amps.

SCIENCE HIGHLIGHT
Planetary Geodynamics Laboratory, Code 698
January 2005
Stress on Rocks Generates Electric Currents
Freund Leads Effort Connected to Possible Earthquake Precursor Signals
Earthquakes are the result of stresses that build up in the crust of the Earth, most often associated with plate motion. Stresses on rock may produce other observable phenomena in advance of the actual rupture (earthquake). One of these observables may be caused by weak currents generated in the rock by increased pressure associated with the build up of stress. This has been the focus of research by Friedemann Freund and co-workers. They have approached this problem from both a theoretical and experimental basis, and recently conducted a series of benchmark experiments which show that stresses on igneous rocks (like granite) convert mechanical energy into electric current. This results from the activation of charge carriers (including positive "defect electrons" formed within the stressed rock). The figure below shows the experimental apparatus recently used. If a circuit is available, the flow is out of the stressed rock into its surroundings, and lasts for hours even after the stresses are no longer increased.



Experimental apparatus for measuring the currents generated by stressing rocks. The experiments were carried out using the facilities at the Department of Civil Engineering, University of Maryland, College Park, and the Department of Civil Engineering, San Jose State University.

Planetary Geodynamics Laboratoy Science Highlight

[Raui]

Rick,

Socially defined things are not reality, they are just a predominant train of thought or an agreed view so to keep convention. What if the convention was based on spherical geometry as above where Garrett posted the page from The Art & Science of Analog Circuit Design. Pi would then be 2 and so is reality isn't it, it is socially defined?

Mathematics is only a tool to try to describe reaity and is not reality itself. So ideally I should calculate using pi to infinite decimal places? But then that would not match reality because circular objects in reality aren't perfect circles. Give me a situation where pi is used to somewhere more than 10 decimal places in reality, not maths which is just a tool, but reality.

I am not doubting that using the idea of a perfect circle is not useful BUT it is not reality.

[t-rex]

Dr Green 3101 and 4594 continues

1) The experimental work of Dr Green highlights some of what has been given here on resonant coils. It is unfortunate that only Dr Green gives us data for study, others just "hide away" their work or yield "multiply".

The standing wave patterns of Dr Green's setup for frequency 3101 clearly shows the Tandem mode, this where the Pi over two rise extends from one coil into the other coil, rendering them one Pi over two resonator.

The standing wave patterns for the 4594 frequency show that the transitional node impedance is much too high. It can be seen here that the Pi over two distribution on the extra coil is reversed. This shows that the secondary output impedance is much too high, even higher than the burden at the other end of the extra coil. This will be a relentless complication.

2) It is important that a radio frequency milli-ammeter be inserted in the secondary neutral to ground connection, this is the measure of Telluric activity. Potential and current probes always detune the coils, this is a major complication. This is why self contained devices such as small lamps are best, as they have no connection to external gear. A book called "UHF Radio Simplified", by Kiver is good information on measuring the non-meterable quantity and standing wave patterns.

For balanced, push pull setups like madhatter, no Telluric output exists, and the R.F. ammeter now connects between the two neutrals of the A and B secondaries. It is best that this junction NOT be connected to ground. For push pull the dielectric field around the coil pair resembles that of the magnetic field around a bar magnet, it is a CLOSED field. Hence the push pull system cannot transmit and thus is incapable of interference to other services. This pleases the radio authorities, such as the FCC.

73 DE N6KPH

Note read "Radio Engineers Handbook", by Terman page 210 to 214 of Pi networks

[madhatter]

For balanced, push pull setups like madhatter, no Telluric output exists, and the R.F. ammeter now connects between the two neutrals of the A and B secondaries. It is best that this junction NOT be connected to ground. For push pull the dielectric field around the coil pair resembles that of the magnetic field around a bar magnet, it is a CLOSED field. Hence the push pull system cannot transmit and thus is incapable of interference to other services. This pleases the radio authorities, such as the FCC.

73 DE N6KPH

T-Rex, thank you for the detail on that. I wasn't expecting any interference on from EM transmittance but was not 100% sure. I did get interference on the cell, but that's a capacitive device which is more likely to be effected, yes? granted the phone was in close proximity to the coils so hence it would have been in the dielectric field.

I will get more data to share as soon as the RF generator is fixed, sent it out for repairs. the last time it stopped working was when the push-pull coils were tuned. honestly I'm not familiar with the equipment enough to know what I did wrong. It's probably a good idea to separate the RF signal generator from the circuit, a 1:1 isolation coil perhaps?

I still wonder about the TEM signal, it's a counter-space field. a receptive means is possible, from what I've studied on USL/SL waves the signal can be picked up. I'll see about getting the NASA docs on it scanned and posted. the behavior of lighting and pulsars is fundamentally a TEM wave. it's also of benefit to overcome radio black out, for both benign and nefarious reasons.

need to locate Guillemins communication network books, anyone know of a scanned copy? I have is mathematics book on circuit analysis.

Eric, am I wrong in thinking that a two stage PFN where the extra coil is excited in the second stage with the kV output pulse is one half of a TEM transmitter?

[t-rex]

[t-rex]

Lightning Discharges

1) Lightning is a process of dielectric saturation, that is the flux density is beyond the capacity of the dielectric to hold. Where in magnetism flux lines are forced outward at the onset of saturation, it is the dielectric flux lines are drawn inward, towards each other. This leads to a concentration which gives rise to further saturation. A runaway process is possible, such as a lightning discharge.

The dielectric space in which the energy exists to power the discharge is near one cubic kilometer. It is like a condenser. The initial "charge" of this cube of space is derived from the condenser formed by the atmosphere between the ionosphere and the earth. This is the earth-ionosphere condenser. It is shown in the drawings of Nikola Tesla, theory to realization.

2) The thunder cloud utilizes movements of water in its formation of large quantities of dielectric induction. Water has a dielectric constant of 80. This in increase of capacitance 80 times. The velocity of light in the water is 9 times slower than free space, the square root of 80.

For a given quantity of charge the potential in the charge is inversely proportional to the capacitance of the charge. If a given charge exists in an 80 dielectric constant is suddenly existant in a unity dielectric constant, a large rise in potential will occur. These conditions exist in thunder clouds. Here is where the high voltage develops, this in a manner much like the Marx generator.

3) In the process of dielectric breakdown, various coronas or streamers appear in "fractal" geometric forms. This is the onset of saturation. The corona increases the capacitance and draws nearer to the opposite pole. If the potential is constant the saturation increases. Finally the saturation draws into a central core and a spark discharge occurs. This is total saturation.

The lightning discharge is this central core discharge, this discharging the one cubic kilometer condenser. The spark discharge disrupts the potential of this one cube condenser, it is a disruptive discharge. This gives rise to strong displacement currents in this cubic space, lines of force are moving transversely toward the core discharge. No magnetic avenue of escape exists in this radial implosion of transverse dielectric induction. The passage of this wave of flux will induce electric waves in transmission lines.

4) The central core is the seat of electrical conduction, this through the actions of the electrons and ions released by the disruptive discharge. Hence the actual lightning discharge, as seen in the lightning itself, is a long thin conductor. This a perfect birthplace for magnetism. Rings of magnetic induction expand outward from the core, much like waves. Hence the actual luminous discharge is the "converter" from dielectricity to magnetism. Where the dielectric goes in, the magnetic goes out. Like the dielectric motions, the magnetic can induce electric waves in transmission systems.

Lagging the outward expanding rings of magnetism and also expanding outward is the electric current. This current wave is derived from the electronic current of the lightning strike. The radial voltage gradient of this current wave can electrocute one standing upon it. This is what most often is the cause of death in a lightning mishap.

73 DE N6KPH

[David G Dawson]

Test loading Pics

This is a test to see if I can't upload pictures:



This is my CSI setup with a variable Condenser between Secondary and Extra.

Have been delayed in powering up due to heatwave conditions here which makes work tedious, not as young as I used to be.

Difficult to 'hide' my data as I have presented everything that was of interest but making an attempt to see if we can't give you what you require.

Smokey

[David G Dawson]

Picture Test

Are you now able to see those pics?

25 in there, only asked for the one but gave the lot.

Smokey

[madhatter]

Lightning Discharges

1) Lightning is a process of dielectric saturation, that is the flux density is beyond the capacity of the dielectric to hold. Where in magnetism flux lines are forced outward at the onset of saturation, it is the dielectric flux lines are drawn inward, towards each other. This leads to a concentration which gives rise to further saturation. A runaway process is possible, such as a lightning discharge.

The dielectric space in which the energy exists to power the discharge is near one cubic kilometer. It is like a condenser. The initial "charge" of this cube of space is derived from the condenser formed by the atmosphere between the ionosphere and the earth. This is the earth-ionosphere condenser. It is shown in the drawings of Nikola Tesla, theory to realization.

2) The thunder cloud utilizes movements of water in its formation of large quantities of dielectric induction. Water has a dielectric constant of 80. This in increase of capacitance 80 times. The velocity of light in the water is 9 times slower than free space, the square root of 80.

For a given quantity of charge the potential in the charge is inversely proportional to the capacitance of the charge. If a given charge exists in an 80 dielectric constant is suddenly existant in a unity dielectric constant, a large rise in potential will occur. These conditions exist in thunder clouds. Here is where the high voltage develops, this in a manner much like the Marx generator.

3) In the process of dielectric breakdown, various coronas or streamers appear in "fractal" geometric forms. This is the onset of saturation. The corona increases the capacitance and draws nearer to the opposite pole. If the potential is constant the saturation increases. Finally the saturation draws into a central core and a spark discharge occurs. This is total saturation.

The lightning discharge is this central core discharge, this discharging the one cubic kilometer condenser. The spark discharge disrupts the potential of this one cube condenser, it is a disruptive discharge. This gives rise to strong displacement currents in this cubic space, lines of force are moving transversely toward the core discharge. No magnetic avenue of escape exists in this radial implosion of transverse dielectric induction. The passage of this wave of flux will induce electric waves in transmission lines.

4) The central core is the seat of electrical conduction, this through the actions of the electrons and ions released by the disruptive discharge. Hence the actual lightning discharge, as seen in the lightning itself, is a long thin conductor. This a perfect birthplace for magnetism. Rings of magnetic induction expand outward from the core, much like waves. Hence the actual luminous discharge is the "converter" from dielectricity to magnetism. Where the dielectric goes in, the magnetic goes out. Like the dielectric motions, the magnetic can induce electric waves in transmission systems.

Lagging the outward expanding rings of magnetism and also expanding outward is the electric current. This current wave is derived from the electronic current of the lightning strike. The radial voltage gradient of this current wave can electrocute one standing upon it. This is what most often is the cause of death in a lightning mishap.

73 DE N6KPH

this is a fascinating phenomenon, I'm short on time right now. later this evening I can post more.
the research papers cover the intra cloud RF radiation and the lack of EM waves, the unknown reason for the delay, absence or advance of the RF radiation in a discharge. this is covered in plasma work as well and I have some papers correlating the two. this is transverse EM research from the late 50's thru 80's