Re: Quarter Wavelength Frequency

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

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

Hi Ed,

Could you give a quick qualitative definition of velocity factor.  Im
thinking a factor of 2.0 does not mean 2x the speed of light.  Yet the
formula below suggest just that.  How does one get faster than "c".  Maybe
you don't have 1/4 wave or...  could the velocity factor be comparing the
uncoiled propagation time (with velocity of c) to the coiled propagation
time (expected to be smaller)??

Gerry R.

 > Original poster: Ed Phillips <evp-at-pacbell-dot-net>
 >
the data.
 >
 > "Let's tabulate the velocity factor (along the wire) as
 > calculated by
 >
 >     velocity = 4 * wire_length * Fres
 >              = 4 * wire_length * c/lambda
 >
 >     velocity_factor = v/c = 4 * wire_length/lambda.
 >
 > (the 4 because we're supposed to be measuring the 1/4 wave).
 >
 > Then your table becomes:-
 >
 >    L/D   length of wire/lambda     velocity_factor
 >    0.5   0.228                      0.912
 >    1.0   0.298                      1.192
 >    1.5   0.343                      1.372
 >    2.0   0.374                      1.496
 >    3.0   0.413                      1.652
 >    4.0   0.435                      1.740
 >    5.0   0.449                      1.796
 >    7.0   0.466                      1.864
 >    10    0.478                      1.912
 >    100   0.49998                    1.99992
 >    1000  0.50000                    2.00000
 >
 > I would expect the factor to be a greater than unity
 > for typical TC L/D ratios, which they are, but it should tend
 > down to unity, not up to 2."
 >
 > Hadn't thought about this at all so no useful comments.  When I have a
 > chance I'll go over stuff on helical antennas.  "REFERENCE DATA FOR
 > RADIO ENGINEERS" by FT&T has quite a bit on them but I've never paid
 > much attention.  I have always thought of an unloaded TC as being
 > equivalent to an extremely short helical antenna and tried to calculate
 > the radiation resistance once.  It turns out to be nil which probably
 > explains why our coils don't create more of a ruckus than they do.
 >
 > The program is a few lines of QuickBasic code and I'll send the text
 > listing later.  In order to call it forth I have to shut down this Mac
 > and restart it in a different mode, something I don't want to bother to
 > do right now.  Here is the listing for the inductance calculation:
 >
 > "Calculation of inductance by Lundin's approximation to Nagaoka's
 > constant.
 > [Letter to Proceedings of the IEEE, Volume 75, Number 9, September 1985
 > pp 1428 =1429]
 >
 > FOR A SOLENOID OF DIMENSIONS:
 > DIAMETER  (INCHES) = D
 > LENGTH  (INCHES) = LE
 > NUMBER OF TURNS = N
 >
 > CALCULATE
 > X=D/LE
 > X2=X^2
 >
 > A(X)=(1+.383901*X+.017108*X^2)/(1+.258952*X)
 > B(X)=(.093842*X+.002029*X^2-.000801*X^3)
 >
 > IF X = > 1
 > K = (.6366198#/X)*((LOG(4*X)-.5)*FNA(1/X2)+FNB(1/X2))
 > INDUCTANCE =.0250688*D*X*N^2*K    MICROHENRIES
 >
 > IF X < = 1
 > K=FNA(X2)-.42441318#*X
 > IND=.0250688*D*X*N^2*K    MICROHENRIES
 >
 >   I can't find the original letter, so the stuff above is a rewrite of
 > the expressions in the Basic program I wrote at the time; hope I didn't
 > make any mistakes.  "Just in case" here are the original Basic
 > statements:
 >
 > INPUT "DIAMETER, LENGTH, (INCHES) AND NUMBER OF TURNS"; D,L,N
 > DEF FNA(X)=(1+.383901*X+.017108*X^2)/(1+.258952*X)
 >
 > DEF FNB(X)=(.093842*X+.002029*X^2-.000801*X^3)
 > X=D/L
 > X2=X^2
 > IF X<1 THEN LT1
 > K=(.6366198#/X)*((LOG(4*X)-.5)*FNA(1/X2)+FNB(1/X2))
 >
 > LT1:
 > K=FNA(X2)-.42441318#*X
 > IND=.0250688*D*X*N^2*K    ' INDUCTANCE IN MICROHENRIES"
 >
 > Wow but this is long but may of interest to someone besides Paul or I'd
 > try to send it direct.  Criticisms and corrections and rebuttals
 > welcome.
 >
 > Ed
 >
 >