White Board

I have posted my proposal of the Electric propulsion by the Tesla coil on my web page http://www.msu.edu/~liuxiaod. I am preparing to do it. Comments and suggestions welcome. Thanks.
regards, Xiaodong Liu.

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Windows & browser compatible math fonts from MIT: http://web.mit.edu/is/topics/webpublishing/mathml/index.html

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Date : Wed, 21 Jul 2004 17:49:37 -0600
Subject : http://www.emachineshop.com/. A friend just referred me to this on-line machine shop. You download a 5 meg CAD program, design whatever part you wish fabricated and then submit it for a quote. If you accept their price you can place an order for the thing to be created. RSG rotors, hubs and so on come to mind. Daniel.

Date : Thu, 15 Jul 2004 16:32:22 -0600. Subject : Re: machining copper

Original poster: Jim L.
I just received an interesting and useful piece of machining lore. When machining copper (which is difficult to machine): Sharp tools, Fast speeds, Condensed milk as a lubricant <<< this was the new thing. Apparently it's the "miracle lube" for copper cutting. Think about it... a colloidal dispersion of a high temperature oil (butter fat) in a water base. Stinks, goes sour, etc., but apparently it's the "miracle lube" for copper cutting. This came from a guy in our propulsion dept. who has to machine all sorts of exotic things (Inconel, Hastelloy, Kovar, you name it).

Involving yourself in the discharge

06-12-04 I finally rendered a clip from the Moody Bible Institute “Facts of Faith” film that was made back in the 1950’s. This is one of the most impressive demonstrations that I have ever seen done with a Tesla coil. The Clip can be found at http://webpages.charter.net/tcbofw/ http://webpages.charter.net/tcbofw/ I wouldn’t recommend that anyone try this at home…enjoy! Stephen M.
Wow! Cool! I think that it is Dr. Speake who passed this stunt on to Dean Ortner. A wonderful bit of history there! Of course, nobody go trying this stuff at home. Speake and Ortner have done this thousands of times and there are a ton of really important details that keep one from dying. They have also been injured on occasion but not seriously. But, it is always fun to watch someone "else" doing it ;-)). Cheers, Terry
Bill Wysock and Lowell Beazley did this many, many times. I think the max input power was 5, maybe 8 kVA, 90 to 120kHZ, I'll get the exact specs from Bill and will correct those approximate numbers. John C.

Q. Does anyone know what the average capacitance of the human body it? I'm getting 200pf from different web pages on the net.

A. For the FAA average weight human male, 170 lbs, its 165 pF.  Roughly .97 pF/lb with a human.  Slightly different value for aliens.

You can also do an interesting experiment with a TC, to calculate or measure the capacitance exactly.

Feed your coil with a signal generator, 2 turns around the very lowest part of the sec, and observe the res freq with an o-scope.  Record this freq.  Next, stand your victim (I mean partner) on a plastic or glass insulated stand elevated at least 48 inches from the floor, have them touch the sec toroid, and record this freq.

Subtract the two frequencies.  Knowing the inductance of your sec coil, substituting this value into the freq equation you can solve for C --- the value of capacitance of your test object/subject.

This is also a great way to measure the cap of balls, spheres, toroids, etc of unknown capacitance. Dr. Resonance.

Stripping Litz wire for soldering

Try methylene chloride, it takes a while depending on coating thickness but it eventually dissolves the enamel to leave bare, bright shiny copper.
6-13-04. I gave paint stripper another try, this time allowing the wire to be submerged for about a day and a half. In my previous attempt, I waited only about 5 minutes. This time after the long soak, the enamel washed right off the wire under a high pressure water rinse, and solder took to the wire like a duck to water. The paint stripper did contain methylene chloride among other nasty things. Thanks for the tip! Gary L.
6-20-04. Tesla List. I received your Litz sample in the mail today and easily soldered one end using the "copper tubing solder pot" and propane torch method that I believe I've described on the list before. No paint thinner, no aspirin, no strain, just a bit of rosin core solder. Thanks for sending the sample. As I suspected, you just weren't getting the solder hot enough to melt the enamel. Regards, Ed Wingate RATCB

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In the past I made a translucent box, a small opening on top in which a small brass outlet tube (from ballpen filling). Box partly filled with 96%-spirit. Also inside, a multi-gap spark bridge. Also in box, submerged, a wire wound resistor to heat the spirit. Prior to operation of the Wien bridge, the spirit was heated to the point that no air escaped from the exhaust but spirit fume, and than ignite it (sniff first!..). During operation of the bridge, heating was not needed. Operation of spark bridge was much better, because the copper disks hardly oxidized any more. The exhaust fume was ignited because I did not want free spirit fumes around and also the length of the flame is a good indicator of the internally generated heat. However, this set-up was used with two paralleled ignition coils as HV source and must be adapted to higher powers. I made this about 45 years ago. In the snipped correspondence, no mention was made of the amounts of carbon soot that were generated in the spark chamber. The chamber had to be cleaned from time to time and if it was opened before it had cooled down enough, the man who opened the little door got his face full with soot from the small explosion. It was a trick played upon newcomers...! Regards, Willem B.

Electrum: Greg did complete Electrum and installed it in New Zealand. There are plenty of pics of Electrum on Greg's site at: http://www.lod.org/electrum/electrumpics.html and http://www.lod.org/electrum/nzinstall.html

Initial primary to secondary diameters for the design stage: The best coils I ever built all had helical primaries. It is important to make the diameter at least 2x that of the secondary and perhaps larger while getting the turn-turn spacing as small as possible. Malcolm.

ULF Receiver For The Study Of Schumann Resonance http://www.iihr.uiowa.edu/projects/schumann/Index.html

Nitrogen/Air blast nozzles?

De-Lavel nozzle

Back To Index Back To Tesla Tips

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Bertan makes multi-kVDC power supplies that have very accurate current readout (fractions of a micro amp stuff). http://www.bertan.com/ You might want to look around their site or call an engineer there. The newer stuff is really nice. I have three of their supplies and they work great. They know a lot, so ask them for sure. There newer stuff is supposed to have far less output C which is nice when that 500kV shorts out

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The Inca program can model anything with axial symmetry, as a stack of toroids, for example. For a secondary coil, you still have to split it into a series of cylinders and specify different voltages for them. Not many sections are needed for a good sim. The Inca program is at: http://www.coe.ufrj.br/~acmq/programs. Antonio Carlos M. de Queiroz.

LTR Calcs

Q. 5-1-4 TL. What exactly is the LTR value of a cap? I understand for a static gap system it is pi/2 * the resonant cap size, but why. Also why should we use it?
Q. 4/30/2004, How do you compute the LTR cap value for a given transformer with a static gap? SRSG? I see that the Geek Group website has a table for a given range of NST sizes but what I'm after is the formula(s) to determine the recommended LTR cap value for a given transformer. I know how to determine the resonate cap value for a given neon but how do I arrive at LTR? I realize that the very nature of this thread suggests that the optimum LTR value might be up in the air. Daniel.
A. Terry F. Hi Daniel, Let me see if I can remember ;-)). Originally, LTR values were computed with long hard MicroSim simulations:
http://hot-streamer.com/TeslaCoils/Misc/NSTStudy/NSTStudy.htm
The equations for MMC also were known:
http://hot-streamer.com/TeslaCoils/MMCInfo/MMCPower4.html
These were combined into the program here:
http://hot-streamer.com/TeslaCoils/programs/Mmccalc2.zip
A modern Excel version is here:
http://hot-streamer.com/temp/MMCcalc2.xls
These two programs were used by Mark Broker to make the GeekGroup chart that everyone goes by now. Eventually the equations were justified:
http://www.pupman.com/listarchives/2002/April/msg00038.html
Cheers, Terry.

Resistors across each cap in an mmc, and why

1. 6-8-4. Has everyone forgotten the inexpensive VR37 resistors previously offered by Phillips and now distributed by Vishay (BC Components)? These are advertised as "High Ohmic - High Voltage Resistors", and the 1/2 Watt series is rated for 3500 VDC, 2500 VRMS. These resistors consist of a metal oxide film deposited on a ceramic core, covered by a hard baked lacquer finish. Although they cost more than the dirt-cheap garden-variety carbon film or carbon-composition resistors, the last time I bought the VR37's they were only 12 or 15 cents each. Given the cost and effort required to assemble a clean looking and conservatively-rated MMC, why use anything less?

The Vishay datasheet for the VR37 resistors can be seen at: http://www.vishay.com/docs/28733/vr37.pdf

Note that the peak pulse voltage rating (shown on page 3 of the spec) for a 10 meg resistor appears to be 10 KV! This implies a fair safety factor for flash-over or arcing.

Regardless of the resistor's actual flash-over voltage, I have seen more MMC's fail due to flashover to the adjacent capacitor than across a resistor. If you are mounting your MMC capacitors in parallel rows, I would leave no less than 1/2" to 3/4" gap between any resistor/capacitor pair and next resistor/capacitor in the string. Regards, Scott H.

2. 6-7-4. Terry Fritz did some testing a few years ago on the 10Meg, 1/2W, carbon comp resistors (the 10MH-ND from Digikey) and showed that they didn't break down for at least a few kV.  As I recall the resistor suffered from thermal issues long before voltage issues ;)  The results are buried in the pupman archives, but Terry may be able to post a link in shorter order than I....

Basically most people seem to use just a single 10Meg, 1/2W resistor without problems.  Some argue that's pushing one's luck and would recommend wiring several in series or using a single HV resistor.  The latter is significantly more expensive, though.

The value is not too important so long as the value isn't so small that it wastes significant energy nor too big so that you must wait several minutes before things are safe to touch (arguably about 20V).  It happens that 10Meg, 1/2W is a good compromise for 2kV.  I would not recommend using one resistor on a 3kV cap due to thermal problems. Mark B., Chief Engineer, The Geek Group.

3. 6-7-4. I use 3 bleed resistors per cap. Others use one standard one and get away with it. Others use none at all. I am not sure what the right approach is. I don't know anyone who is using the HV ones in view of the cost. Peter T.

I use four in series, or the smallest that I can find, arranged in a zigzag pattern across each capacitor (or array of capacitors in parallel). So far, no problem at all. I check the resistors periodically. Antonio C.Q.

4. 6-7-4. The main problem is no single relay can discharge a MMC capacitor string without bleed resistors installed. Any DC charge held within a series capacitor string can not be discharged without a DC path. Though AC is applied to the capacitors the last cycle of the AC leaves a + or - DC charge on the series string. Robert H.

5. Personally, I don't even want to bother with them. John C.

Skin Effect

At 08:19 AM 5/21/2004 -0600, you wrote:
>Original poster: mercurus2000
>I was just curious, I hear the skin effect in human beings still very deep at standard tesla coil frequencies, does anyone here have references or sources as to where the information is gathered about how deep currents penetrate into the human bodies at different frequencies? Thanks, Adam

The standard equation for skin depth

The skin depth is the depth of a layer that if, the current were uniformly distributed, would carry the same current density as the whole thing. In the real thing, the current density falls off as exp(-x), so the classic definition of skin depth is where the current is 1/e (exp(-1)) that at the surface. (integrate e^x, etc., and you see that it works out...).

The depth is inversely proportional to the square root of (conductivity*permeability*frequency)

In equations:

depth = c/sqrt(2*pi*sigma*mu*omega)
c= speed of light (3E8 m/sec)
sigma = conductivity
mu = permeability (4*pi*1E-7 for free space/non magnetic substances)
omega = (2*pi*frequency)

Some qualitative observations:

Higher conductivity: smaller skin depth
Ferrous materials: smaller skin depth (why steel is a good shield for magnetic fields)
Higher frequency: smaller skin depth. Jim L.

Capacitor Discharge Current

July 19, 2004. Original poster: Anthony. Hi guy I was wondering some body could tell how calculate discharge current of a capacitor?

Answer 1. July 19, 2004. It depends on the load you are discharging into. An inductor, like a TC primary circuit, tends to act as a resistance which in effect slows down the current as it flows in the inductor and builds up the magnetic field. The peak discharge current is limited by this effective resistance (and reactance).

(Hummm... An inductor produces a current that is proportional to the integral of the voltage. If a constant voltage is applied over an
inductor, the initial current is zero, and increases linearly with the time. So, it doesn't slow down the current as it builds up the
magnetic field, but increases it in proportion to the magnetic field. Antonio.)

The worst case for your capacitor would be a direct short circuit. Then the current would be limited by the resistance of the shorting material and the internal inductance of the capacitor.

(Ok. Antonio C.)

A typical TC primary circuit, with secondary coil in place, is probably in the range of 5-20 Ohms impedance (inductive reactance plus resistance) which sets the max current value.  I recall Terry Fritz has taken some measurements of this information and might post them for you to review.

If you have access to a DSO you can freeze the discharge and actually see the waveform to measure the values more exactly.  Sometimes a local college or university will take enough interest in your project to help you make some measurements on your coil.  It never hurts to wander in and ask.  Try the physics research dept or the electrical engineering dept.

A nice DSO picture of your waveform will also tell you if you are getting full energy transfer in the first two or three "notches" for good efficiency.  If not it may be time to make some adjustments to the coeff. of coupling by raising the sec coil in small increments to find the "sweet spot". Dr. R.

Dr. R. Follow-up to Antonio's comments, inserted above. I think we are both saying the same thing in a slightly different way. With impulse generators, as an example, resistance and/or inductance is commonly added to "stretch" the waveform over time. A typical lightning impulse, ie, a 1.5-50 uSec waveform, can be slowed down to a 50-200 uS switching waveform. This is usually varied by adding resistance in series with the spark gaps but in some cases large inductors are added especially if undesirable "ringing" occurs. Dr. Resonance.

Answer 2. July 19, 2004. Original poster: tamp elektronik. Hey Anthony:
I= CdV/dt
to find the discharge current so you need to measure voltage and take the time derivative multiply by capacitance. Lutfi.

Answer 3. July 19, 2004. Original poster: Gerry R. Hi Anthony: If you discharge into your primary inductance and assume no losses, then the inductive energy will equal the capacitive energy:
1/2 LI^2 = 1/2 CV^2
Imax = Vmax / sqrt(L/C)

Answer 4. July 19, 2004. Original poster: Scot D. all depends on the internal resistance of the cap the amount of mF and the voltages involved. Normally most capacitors can deliver hundreds of amps of current in milliseconds... um make that uSecs...Some caps are designed to deliver megawatts of power in sub uSec times. even a 16VDC 3000 uF cap can weld itself ( its leads ) to the shorting device. The caps used for quarter shrinking and can crushing can be in the 100,000 amp range for a few uSeconds the more uF, the less the resistance = impressive current flow.

Date : Thu, 01 Jul 2004 16:16:20 -0600. Subject : Re: Capacitance of the human body

Original poster: "Peter Terren"
I imagine modelling of an irregular surface for E fields and capacitance is tricky but this group does it.
http://www3.interscience.wiley.com/cgi-bin/abstract/94518807/ABSTRACT . The result of 60 - 120 pF varies because of proximity to the ground plane. 120pf is with 10mm elevation i.e., shoes. Peter (Tesla Downunder), http://tesladownunder.iinet.net.au

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Measuring ac Voltage and current on your TC

Question: > I am in the process of trying to work out a way to measure AC voltage and current flowing into my coil, and have run into a few problems in the availability (and price) of AC meters. I have worked out a method to use the much cheaper DC versions that I can easily get. Can someone please offer some advice on if this setup will work, or if I have missed some vital point. (Wouldn't surprise me!). Tristin.

Date : Mon, 04 Oct 2004 19:06:38 -0600
Subject : Re: Ammeter Configurations

This is how we do it.  Since the coil is powered by an AC transformer, just use a 0-250 full scale AC voltmeter that the dial faceplate is re-calibrated in 0-16,363 Volts.  We usually round this off to 16,500 VAC full scale.

In normal operation the meter will read 14,400 Volts at 220 Volts input. This is the Erms potential and the cap will fire at 1.414 * Erms (actually this depends on your spark gap setting for exact value).

A cheap easy way to accomplish the task and no messy HV dividers necessary. Also, very accurate for TC work requirements.

We also do this with NST's, just using a different value.  The math is a simple ratio proportion:

X = (250 V. * 14.4 kV) / 220 VAC        X = 16.353 kV full scale reading for a pole transformer

or X = (150 VAC * 12 kV) / 120 VAC    X = 15 kV full scale for a 12 kV NST

Dr. Resonance

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Calculating Capacitance of Stacked Toroids

Date : Thu, 09 Sep 2004 07:41:53 -0600. Subject : Re: Calculating capacitance of stacked toroids . . .

Question: Anyways, if you have two stacked toroids, what approximations can you use to get a ballpark number for capacitance of the toroid stack?

Answer: The result depends on the aspect ratio of the toroids, but doesn't vary much. The Inca program can easily calculate the capacitances (considering the toroids far from anything else, one directly above the other).

Some examples:
Two 3x1 toroids: multiply by 164/135 = 1.21
Two 4x1 toroids: multiply by 203/172 = 1.18
Two 5x1 toroids: multiply by 241/207 = 1.16
Two 6x1 toroids: multiply by 278/242 = 1.15

The effect is smaller with thinner toroids. The factor tends to 1 for very thin toroids. Better to make a larger toroid, if you want more capacitance, or if you use two toroids, place them at some distance.
Two 3x1 toroids with a total height of 3 units: multiply by 185/135=1.37
Two 6x1 toroids with a total height of 6 units: multiply by 357/242=1.48
Antonio Carlos M. de Queiroz

Answer 2: We measured this with a pair of 48 x 12 toroid. It worked out to 1.5 * cap of single toroid. It also worked out the same for a pair of 34.5 x 8 inch toroids.

We took this measurement with toroids elevated on a plastic tube to their approx height above the floor that would be equal to their operating position, ie, approx 10 ft. Outdoors, in the open. Dr. Resonance

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> I have a demo version of (OrCAD) PSpice; this program suite contains a lot of (sub) programs, none of >which seem to be able to do anything useful with a <file>.cir file (which is a text file). What particular program >do I need to run a simulation from a 'cir' file?

Try SwitcherCad III: http://www.linear.com/company/software.jsp
Small, easy to use, complete, free, and much, much, faster than the recent incarnations of Pspice.
Antonio Carlos M. de Queiroz.

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Can anyone tell me which polarity will form more corona and arc further at a given DC voltage? David R.

Hi David, In non-scientific terms, IIRC, the terminal that is "pushing extra electrons into the air" will form a local cloud of charge easier than the one that is trying to "suck electrons out of the air." That would make negative the right answer. Matt D.

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Date : Sat, 02 Oct 2004 12:40:42 -0600. Subject : Re: Flat-Copper-Strip Flat-Spiral-Primary Inductance Calc'sready

Original poster: "Kurt Schraner"

All, metal ribbon type spiral primary inductance calculation is now available, in form of a zipped Excel, at:

http://home.datacomm.ch/k.schraner/FlatRibbonCoil.zip  (~57kB)

The calculations have also been integrated into my TC-design tool:

http://home.datacomm.ch/k.schraner/TCplan.zip  (272kB; now vers.2.00)

The calculation is now in excellent agreement with my measured L values: about 1% average error above turn 2. (Inductance meter is of insufficient precision below ~3uH)
A graph is at:

http://home.tiscalinet.ch/m.schraner/Lstrip_NBS.gif

...as before, calculation by the Wheeler formula, gives about 17% high values, compared to the experiments:

http://home.tiscalinet.ch/m.schraner/Lstrip_Wheeler.gif

A method, easier to implement, than the one in Patent:

http://hot-streamer.com/TeslaCoils/OtherPapers/J-Reed/us5079482.pdf

...mentioned by Terry, was found in the famous NBS Circular 74 of 1918, Pages 250 to 262 + 285. It can be had at:

http://hot-streamer.com/TeslaCoils/OtherPapers/Circ74/
(download Part5_10.tif till Part5_16.tif and Part5_27.tif)

I've not yet checked (i.e. vs. Antonio's INCA), if the method also works for the design of the very low, single turn primary inductance of modern solid state TC's (OLTC,DRSSTC), but may be...?

I'm also not certain about the higher frequency influence on the calculated values. Anyway, tapping my primaries of little twin UBTT, at the predicted turn values, seems to make perfect sense:

http://home.tiscalinet.ch/m.schraner/TwinWithRotaryinAction.jpg
(Pic shot by Urs Lauterburg at Physics Institute of University Bern)

BTW: a 27 page report about the UBTT (Uni-Bern-Tesla-Twin) is ready for download at:

http://home.tiscalinet.ch/m.schraner/UBTT-Betrieb.pdf  (4.4 MB)

Sorry, the report is in GERMAN language, and a little big. And thanks to Richie Burnett, allowing me the use of his classic TC explanation method and pic's in the report. Best regards, Kurt.

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Lightning Detectors

Date : Mon, 26 Jul 2004 18:24:11 -0600. Subject : Lightning & TCs

Original poster: "J. B. Weazle McCreath"
Hello Coilers,

The recent thread on lightning and Tesla coils led me to do some web browsing for lightning detectors.  One site caught my attention when it was suggested that the radio-active component of a smoke detector could be used to build a lightning detector.

With my curiosity now activated, I wondered if an un-modified smoke detector could be made to detect an electric field.  I hooked up the mains powered detector that I had in my junk box and fired a charge at it using a Zero-Stat(R) static gun that I had left over from my record album days (now I'm dating myself).  Sure enough, the charge from the gun triggered the detector!

The next step was to solder a ten foot long wire to the metal cage that surrounds the radio-active sensor portion of the detector and route it out through a hole in the plastic case.  I then installed the unit in my shop, about twenty feet from my coil, and with the sensing wire running horizontally.  I fired up the coil, and to no
surprise the detector went off, indicating that the electric field had triggered it.

From a purely safety conscious standpoint I would recommend using a battery powered detector rather than a mains one so that there is no chance of 120 appearing on the added sense wire.  My next test will be to hook it up outside to a longer wire and wait for the next lightning storm to come my way. 73, Weazle, VE3EAR/VE3WZL

Details of my "Hyperbaric Gap" and Tesla coil are at: http://www.hurontel.on.ca/~weazle

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Circuit Textbooks

Date : Sun, 26 Sep 2004 10:21:41 -0600. Subject : Free series of textbooks on circuits

Hello all, This link might be helpful to any newbies. It has free downloadable books (6 volumes) on electrical circuits. http://www.ibiblio.org/obp/electricCircuits/. Bill Mck.

Date : Sat, 24 Jul 2004 12:02:26 -0600. Subject : Wire length, coil geometry, and velocity factor

Original poster: "Paul Nicholson"

Recently Ed Phillips noticed that wire length divided by the free space wavelength of the quarter wave resonance of an unloaded coil was a smooth function of the h/d ratio and largely independent of the turn count.

It is commonly understood (we hope) by coilers that the resonant frequency of a coil is not given by the quarter wave resonance of the straight wire from which the coil was wound.   The actual frequency usually exceeds the straight wire prediction by 50% or more in typical TC secondaries.

This implies that signals (EM waves) at TC frequencies traverse the coil faster than they would do if strictly confined to the helical path of the winding.  This is not unreasonable because each turn of the coil has some degree of interaction with all the other turns via their E and H fields (inductive and capacitive mutual coupling).

We can indicate numerically the extent to which signals 'leapfrog' the turns of the winding by expressing the apparent or effective speed of propagation along the wire as a ratio with the speed of light.   This is the velocity factor of the wire when wound [+].

For example, if a particular coil has a velocity factor of 1.72, this in effect means that:

*) The 1/4 wave frequency will be 72% higher than that predicted for its straight wire.

*) A signal entering the coil will appear at the other end as if it had travelled the wire at 1.72 times the speed of light.

*) If we imagine the EM signal to be spiralling along the coil, the pitch of this spiral would be 72% greater than that of the winding.

Ed's observation recognises that the velocity factor for a coil is a function largely of the overall geometry of the coil and does not depend very much on how many turns are put in.   This means that it is worth while defining a geometry factor with which to relate the velocity factor directly to the h/d ratio of the coil.

The graph

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

shows (green crosses) measured velocity factors for a bunch of coils of varying sizes and turns.   The blue line is a logarithmic function chosen for a reasonable fit.  The function used is

    Ph1(h/d) = ln(h/d) * 0.39 + 1.19

where ln() is the natural logarithm.  The trial function has been tested against a larger set of modelled coils, and the results are plotted in the red dots.

The red dots actually represent 2732 assorted coils ranging from as few as 50 turns up to 3000 turns.  Resonant frequencies of some of these coils go up into the Mhz range.  We still see a reasonably
good fit to Ph1(h/d) even when faced with such a wide range of hypothetical coils.

The residual (the difference between Ph1(h/d) and the measured or modelled velocity factor) is about +/-5%.  Closer inspection of the comparison database reveals that about half of this residual is due to variation of coil base height above the modelled ground plane.

The function Ph1() can be used to directly estimate the quarter wave Fres from the h/d ratio and the wire length:=

    Fres = (0.39 * ln(h/d) + 1.19) * 75e6/wire_length  (Hertz)

where wire_length is the total length of wire in metres.  It seems we should expect this prediction to be within about +/-5% of the actual frequency for most coils.   This is obviously a very much more direct approach to Fres than the conventional route via calculations of inductance and capacitance.

All of the above refers the the fundamental (1/4 wave) free resonance of the unloaded coil.  Velocity factors for other frequencies will be different.

The next two overtones, 3/4 wave and 5/4 wave also follow a compact smooth curve when their velocity factor is plotted against h/d ratio.  The independence from turns continues.  However, these overtones don't seem to follow quite the same sort of logarithmic function of h/d.  (A database of modelled coils is available in csv format if anyone wants to try for a fit).

It is clear that the function Ph1 (and the coils) tend towards some velocity factor greater than 2 for large h/d. No measurements are currently available for h/d > 10 so we can only speculate.

One common factor with all the coils modelled and measured in this comparison is that they are all fairly close wound. The smallest modelled spacing ratio is 0.55, and our models continue to refer to close wound behaviour as we let h/d tend to infinity.   For this reason we should not be surprised that the velocity tends to some number rather larger than, say, the 0.95 we would expect from a straight wire.

To reach this straight wire velocity factor, our models and calculations would have to allow the pitch to increase to infinity as well as the h/d ratio.  This they do not do.

We might anticipate that the compact distribution of velocity factors would be lost if we allowed the pitch to increase substantially.   Unfortunately our software models are not qualified for large pitch coils since they rely on some approximations which are only accurate when each turn is almost a circle.  Helical antenna modelling software might be tried instead, but those packages tend to bog down when dealing with large numbers of turns.   For that reason it might have to be a task for the experimenters to tell us what happens at pitch
angles larger than say 5 or 10 degrees.

[+]
The velocity factor of the wire when straight would be about 0.95, depending on thickness.  The velocity factor of the winding is given by

    4 * wire_length * Fres / c

where c is 300e6 metres/sec, wire_length in metres, Fres in Hz. Paul Nicholson.

Date : Thu, 24 Jun 2004 21:00:20 -0600. Subject : some of the reason why energy and power definitions are confusing

Original poster: "Alfred Erpel"

Howdy all,

A coulomb is (to me) an unsimplifiable property of the universe.  It is 6.41418*10^18 electrons.  You can't state this in a simpler form another way in terms of ¹distance, mass, time and energy.  It bugs the hell out of me that the coulomb in the SI system is defined as a DERIVED unit in terms of amperes. And amperes has the status of being a basic unit. Amperes is defined as coulombs/second.  Amperes were INVENTED by man yet have been conferred the status of a basic unit.  This I believe obfuscates and confuses many issues.  I have no idea why this was done.  It is my opinion that energy has nothing to do with time, however with this artificial definition, joules (energy) = watts * seconds.  With this system the energy unit has time in it and the power unit doesn't.

remember, amps = coulombs / seconds  below and:

joules = watts * seconds

joules = volts * amps * seconds

joules = volts * (coulombs / seconds) * seconds

joules = volts * coulombs

Hence, joules should (IMHO) always be spoken of as being equal to volt * coulombs. This is a more basic unit and without reference to time.  Power would be volt * coulombs / second.  This is way less confusing.

If anyone has a clue why the SI system made this exception to defining basic units, I sure would like to hear it.

¹ distance, mass, time, and energy is it baby, that and nothing else, comprises all that we know.

Regards, Al Erpel.

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