Hello Alex,

Interesting formula.
Assuming that the antenna capcity (C) is linear proportional to the antenna
length (Lant) this means that Lant*Xc is a constant.
Measurements have shown that the capacitance of an LF antenna is +/- 5pF/m
(single wire antenna), so that would make Lant*Xc = 2.34e+5.
At 136kHz eps0*w = 7.56e-6, so : a = 7.56e-6/S

This would simplify the formula  R = (Lant/Lcp)*a*Xc  to

R = 1.77/(S*Lcp)  (at 136kHz)

This makes sense as both increasing radial system as increasing ground
conductivity will reduce R.

I believe the limitations of the formula probably are :
1.The ratio Lant/Lcp should not be too big or small. Increasing Lcp far
beyond Lant won't be a great help. On the other hand, even with Lcp = 0 (no
cointerpoise wire) the loss resistance will not be endless.
2. S (ground conductivity) should not be too large or too small. If S is
too large (eg. salt water) the counterpoise won't be of much use. On the
other side even for s = 0 (worst soil you can think of) R won't be endless
as the counterpoise will still work.

thanks for deriving the formula,

73   Rik  ON7YD

At 16:17 14/05/02 +0000, you wrote:

Hi LF Group

On Sat, 23 Mar 2002, john sexton wrote:
If you do find a model that works, please let us know.

On the base of my own "generalased mirror reflection theory" I just have
derive the formula for ground loss resistance:


R = (lant/lcp)*a*Xc

where:

lant - wire length of antenna,
lcp  - wire length of ground system (conterpoint),
a = (eps0*w)/s,
eps0 - dielectric constant (8.85e-12 F/m),
w = 6.28*f - circular frequency,
s - ground conductivity.
Xc = 1/(w*C) - antenna reactance,
C - antenna capasitance.

For 136 kHz and s=1 mSm/m a is about 0.01


The formula is very aproximative but yelds reasonable value of R.

Now I work on more advanced formula wich should be more accurate.

Any coments please!

73 de RA9MB/Alex
http://www.qsl.net/ra9mb