Re: quarter wave

["Tesla list" <tesla-at-pupman-dot-com>]

Original poster: "Gerry Reynolds" <gerryreynolds-at-earthlink-dot-net> 

Hi Paul,

Great explaination.  I was thinking that the energy was propagating at the
speed of light from the primary which I'm now thinking is wrong (sorta the
opposite from Jared's position).  What I'm getting from what you say is that
the EM fields (from primary as well as the fields from the secondary) travel
at speed of light but because of the distributed energy storage elements in
the secondary, the energy propagates slower than light traveling in a
straight line from bottom to top, but faster than if it took the wire path.
Also thanks for defining the velocity factor (wire length/apparent length
based on resonant frequency and resonant mode).

Next we need to explain the warp coil :-))

Gerry R

 > Original poster: "Paul Nicholson" <paul-at-abelian.demon.co.uk>
 >
 > Gerry wrote (on the 19th):
 >
 >  > Is the original difference of opinion that Jared is taking
 >  > a length of wire, calculating the resonance based on its
 >  > length (1/4 wave antenna theory), and then coiling it up
 >  > and thinking the resonance will be the same?
 >
 > Yes.   At least he could have used 0.95 as the velocity factor
 > for the original straight wire, but he seems fixed on 1.0, a priori.
 > He might be right, but the point is he doesn't seem to have measured
 > it.  This is a pity - and I'll try to show why in this post.
 >
 >  > is he also saying the original straight wire resonance will
 >  > remain and a new coiled resonance will be introduced
 >
 > Yes too.  He was observing slow cycling of the spark output at
 > some point during tuning and attributed this to beating between two
 > resonances, one of which was taken to be 'wire resonance' and the
 > other to be 'LC resonance' (each presumably with an independent pair
 > of storage mechanisms, the lack of which was stalling Jared's
 > further progress with that hypothesis).
 >
 >  > Seems like Jared believes the path of energy is conducted
 >  > thru the wire as oppose to thru the air being carried by
 >  > EM fields.
 >
 > Yes, a common enough belief. (After all, didn't 'Tesla Himself'
 > believe such things?)
 >
 >  > My cut on this (helical coil) is the entire coil is being
 >  > bathed by EM energy propagating thru the air at light speed
 >  > so it doesn't follow the wire path.
 >
 > Yes, there's no need to suggest the field is confined to propagating
 > along the wire (the charges are confined to the wire, but not
 > necessarily the energy flow or signal flow associated with them -
 > any more than they are in say a transformer. Energy and signals are
 > exchanged between the windings without a charge transfer.)
 >
 > One can certainly begin to picture the energy flow as spiraling
 > around the coil following the path of the current -  to a first
 > approximation.  Two main components of the field are a B field
 > parallel to the axis (due to the circular current motion) and a
 > radial E field.  Picture the cross product of these two as a
 > field of arrows which would join to make circles around the
 > solenoid.
 >
 > At the same time, we can cross product the radial E field with the
 > circular B field due to the net flow of charge up and down the coil.
 > The result is energy flow arrows pointing parallel to the axis.
 >
 > These up and down flow arrows added to the circling arrows give
 > an overall spiral with similar or perhaps the same pitch as the
 > turns of wire.
 >
 > To complete the picture, we must also look at the remaining field
 > components.  We have a vertical E-field, ie potential differences
 > along the coil, whose cross product with the circling B field
 > component points radially inwards and outwards from the coil,
 > representing the stored energy flowing to and fro into the
 > near field.
 >
 > Putting all this together, we might try to visualise the overall
 > effect as a spiralling energy flow, swelling outwards and collapsing
 > twice each RF cycle.  We know that for low frequencies at least,
 > the effective pitch of this spiral must be greater than the winding
 > pitch because signals from one end of the coil arrive at the other
 > end well before they would if confined to the same pitch as the
 > wire.  In terms of inductance and capacitance, we might say that
 > mutual coupling is allowing the signals to leapfrog the turns to
 > some extent (equivalently, those axial-pointing Poynting vectors).
 >
 > It is interesting to look at the velocity factor (with respect to
 > the wire) for a set of resonances.  With figures from one of
 > Marc Metlicka's coils (h/d=4.66, 2898 turns) with 2080 metres of
 > wire, we find
 >
 > Mode    Freq       Free space length    Velocity factor of wire
 > 1/4     61.9 kHz   4847m * 1/4 = 1212m    2080/1212 = 1.72 [+]
 > 3/4    157.9 kHz   1900m * 3/4 = 1425m    2080/1425 = 1.46
 > 5/4    229.7 kHz   1306m * 5/4 = 1633m    2080/1633 = 1.27
 > 7/4    294.4 kHz   1019m * 7/4 = 1783m    2080/1783 = 1.17
 > 9/4    355.6 kHz    844m * 9/4 = 1899m    2080/1899 = 1.10
 >
 > For shorter and shorter wavelengths in the coil, we find the wire
 > velocity factor coming down towards unity, as if the pitch of the
 > 'field spiral' was becoming more closely aligned with that of the
 > wire spiral.  Terry Fritz also provided some figures for a coil
 > (h/d=2.92, 1000 turns), this one with 819 metres of wire,
 >
 > Mode     Freq       Free space length    Velocity factor of wire
 > 1/4     148.4kHz     2022m * 1/4 = 506m      819/506 = 1.59 [+]
 > 3/4     353.4kHz      849m * 3/4 = 637m      819/637 = 1.29
 > 5/4     513.8kHz      584m * 5/4 = 730m      819/730 = 1.12
 > 7/4     666.4kHz      450m * 7/4 = 788m      819/788 = 1.04
 > 9/4     819.8kHz      366m * 9/4 = 824m      819/824 = 0.99
 > 11/4    977.4kHz      307m * 11/4 = 844m     819/844 = 0.97
 > 13/4   1133.1kHz      265m * 13/4 = 861m     819/861 = 0.95
 >
 > We see with this coil the along-wire velocity is pulled right
 > down to a value 0.95 which would be a typical factor for a
 > straight wire.  The coil is behaving at these higher frequencies as
 > if it were not wound at all.
 >
 > Now there are a few speculative matters worth listing:-
 >
 > a) As the in-coil wavelength becomes shorter, the total mutual
 > coupling affecting a given point on the coil becomes an average
 > over more and more wavelengths of the signal and therefore might
 > be expected to tend to zero. If so, the propagating wave is
 > not able to 'leapfrog' so much, and the velocity comes down to
 > that of the wire itself.
 >
 > b) It may turn out that for an infinite solenoid, the velocity
 > factor is unity (or some other constant near unity) for all
 > frequencies, perhaps for reason (a).
 >
 > c) If (b) is so, then we might legitimately interpret the trend
 > towards effectively higher velocity factors for low frequencies as
 > simply an end effect, ie brought on by the finite length of the
 > coil interrupting long-range cancellation of mutual coupling when
 > below some frequency.
 >
 > With these kind of considerations in mind, it would be interesting
 > to see what the velocity factors were for each mode of a toroidal
 > coil so that we are free of major end effects.  It may turn out that
 > as Jared was assuming, the velocities measured along the wire are
 > all close to unity for that type of coil.
 >
 > On the other hand, it may turn out that the toroidal coil mode
 > spectrum also exhibits the same trend from high velocity factor down
 > towards unity with increasing frequency that we always see with
 > solenoid coils.
 >
 > So there's an experiment to try.  The result would determine whether
 > we should view the departures from unity velocity factor as
 >
 > 1) something inherent in the helical winding - a consequence of
 > frequency dependence of the mutual coupling.
 >
 > and/or
 >
 > 2) something resulting from the finite lengths of our solenoids, so
 > that an infinite solenoid would show no dispersion (ie a constant
 > velocity <= 1.0 at all frequencies).
 >
 > In other words, when we like to say that L and C are altered in a
 > complicated way during winding such that their product LC does not
 > stay constant, we could then say whether this was actually due to
 > the winding itself, or due to the winding coming to an abrupt end,
 > or maybe some mixture of both.
 >
 > Another way to present the 'end-effects are the cause' view is to
 > picture the waves travelling at 'c' following the wire spiral, but
 > allowing that they don't have to complete a full traverse of the
 > coil.  The impedance changes as you approach the ends and so a
 > travelling wave would see a gradual rather than a sudden sharp
 > discontinuity, especially at low frequencies.  Thus some of the wave
 > energy would begin to reflect early and so the effective axial
 > length of the coil for that particular mode would be reduced below
 > the overall physical length of the coil.
 >
 > The 'mutual coupling averages to zero at HF' hypothesis would be an
 > effect dependent on the mean distance spanned by the mutual coupling
 > from any given turn.  We might picture the distribution of mutual
 > coupling (both L and C) as say a roughly triangular shaped function.
 > As soon as the along-axis wavelength gets down to this length or
 > shorter, we can imagine that any positive contribution from one turn
 > to another would likely be matched by a roughly equal negative
 > contribution from some other turn within the range of the mutual
 > coupling.  If this case applies, then we should still see a pattern
 > of dispersion in a coil without end effects.
 >
 > Well, some experiments there which would help us decide how to
 > view the coil's behaviour: Does an infinite or toroidal solenoid
 > show the same pattern of dispersion as we see documented above with
 > Marc and Terry's coils?
 >
 > (It's typical that we can predict by calculation all the above
 > measured overtone frequencies quite accurately, and we can get the
 > computer to plot the fields and so on for any given coil and
 > frequency.  But that doesn't necessarily help us to decide how to
 > interpret or visualise the general behaviour in terms of the
 > underlying physics.  Here is a clear case where experiment can help
 > us to decide which physical principles form the best foundation for
 > our mental visualisation of how the energy propagates along the
 > coil.)
 >
 > [+]  We can note that these figures for the quarter wave velocity
 > factor are in good agreement with the table provided recently by
 > Ed Phillips in another thread.  I'll write about those later.
 > --
 > Paul Nicholson
 > --
 >
 >