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Message-ID: <3.0.1.16.20020514104945.21f7a680@pb623250.kuleuven.be>
Date: Tue, 14 May 2002 10:49:45
To: rsgb_lf_group@blacksheep.org
From: "Rik Strobbe" <rik.strobbe@fys.kuleuven.ac.be>
Subject: RE: LF: Ground loss
In-reply-to: <Pine.LNX.3.95.1020514160150.229A-100000@fitec.omskcity.com >
References: <Pine.LNX.3.95.1020323205929.257B-100000@fitec.omskcity.com>
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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
>
>
>
>