Re: Quarter Wavelength Frequency

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

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

Hi Paul,

I think it has been hypothesised that as H/d go to infinity the velocity
factor goes to 1.0 and the end effects for shorter H/D coils bring the
velocity factor to greater than one.  I'm wondering if an oppocite
hypothesis might be true.   That is, an infinitely large H/d would have a
velocity factor of something around 2 and the end effects for shorter coils
would reduce the velocity factor.

Gerry R


 >  > The observations are that:-
 >  >
 >  > a) Ed's calculations tend to velocity factor 2.0 as h/d tends to
 >  > infinity.  We might have expected unity here on the basis that
 >  > the coil's becoming more stretched out like a straight wire.
 >  >
 >  > b) The actual figure that Ed's calcs tend to is an exact 2.0000...
 >  > which probably indicates a mathematical limiting value.
 >  >
 >  > In order to see where these observations stand, I ran through my
 >  > database of about a dozen accurately measured coils.  The following
 >  > table reports the measured frequencies and wire lengths, and the
 >  > velocity factor calculated from them:-
 >  >
 >  > System       Fres    c/fres/4  wire      h/d   vfactor
 >  > sk38b50    221.3kHz    338.9m  417.4m   1.15   1.23
 >  > pn1        150.7kHz    497.7m  659.9m   1.36   1.33
 >  > pn2         92.0kHz    815.2m 1321.0m   2.84   1.62
 >  > tfltr      148.4kHz    505.4m  818.7m   2.92   1.62
 >  > sk20b49    217.2kHz    345.3m  607.9m   3.26   1.76
 >  > mwa1-4hd0  224.0kHz    334.8m  582.5m   4.00   1.74
 >  > mm3         61.9kHz   1211.6m 2077.9m   4.65   1.71
 >  > sk12b49    405.1kHz    185.1m  340.4m   4.83   1.84
 >  > tfsm1      358.8kHz    209.0m  398.8m   6.15   1.91
 >  > mm4        237.0kHz    316.5m  572.0m   6.78   1.81
 >  > sk5b503    979.7kHz     76.6m  149.9m   8.04   1.96
 >  > sk16b50    152.3kHz    492.4m  999.5m   8.71   2.03
 >  > mm1        455.5kHz    164.7m  347.3m   8.92   2.11
 >  > mm2        276.9kHz    270.9m  577.1m   9.97   2.13
 >  >
 >  > (The above are all bare coils, ie no toploads or top probes or
 >  > anything to perturb the frequency.  c = 300e6).
 >  >
 >  > Bearing in mind that these are measured values, we do seem to have the
 >  > real coils tending to a high velocity factor as h/d increases.
 >  >
 >  > Is there anybody out there with a coil with h/d > 10 ???  If so,
 >  > we want your measurements!
 >  >
 >  > The interesting thing is that these coils all have a variety of
 >  > turns and pitches, yet they all land within a narrow range of
 >  > one another when h/d is plotted against velocity factor.
 >  >
 >  > This implies that we can get a good estimate for Fres by simply
 >  > taking the free space quarterwave frequency for the straight wire and
 >  > then multiplying by the corresponding velocity factor for the given
 >  > h/d.

 >  > Paul Nicholson