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From: "captbrian" <captbrian@ukonline.co.uk>
To: rsgb_lf_group@blacksheep.org
Date: Thu, 24 Jul 2003 15:40:34 +0100
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Subject: LF: Re: FS formula
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Quick ! , - Is it still there ?   ;-))

Bryan - G3GVB
-----Original Message-----
From: Dick Rollema <d.w.rollema@freeler.nl>
To: LF-Group <rsgb_lf_group@blacksheep.org>
Date: 24 July 2003 14:54
Subject: LF: FS formula


To All from PA0SE

William Oorschot, PA0WFO, has sent me a copy of a three part article by
Karl H. Hille, DL1VU, in the German 2002 magazine FUNK: "Die Bergantenne am
Herzogstand - Vor 75 Jahren eine technische Grosstat" (The mountain antenna
at the Herzogstand - For 75 years a technical amazing feat).  This concerns
the following.

The large VLF stations at Nauen and Eilvese in Germany that were on the air
around 1920 were built by Telefunken. The German firm Carl Lorenz AG would
like to supply VLF stations as well but were unable to do so. They could
supply arc-transmitters of sufficient power but not the enormous antenna
masts they had to offer with the transmitters in order to compete with
Telefunken. Steel masts were unacceptably expensive around 1920 due to the
unbelievable strong inflation that started at the same time Lorenz began
planning the station. So they looked for an alternative. There was an
example. For the VLF link between the Netherlands and the Netherlands East
Indies (now Indonesia) a large arc-transmitter hand been constructed at
Malabar on the island Java. The antenna hung over a valley between two
mountains, obviating the use of high masts.
Lorenz decided to do the same. They strung an antenna between two mountain
tops in the South of Germany, the mountains were the Herzogstand at 1735m
and the Stein at 940m. The horizontal distance between the mountain tops
was 2700m.  About one third from the low end of the sloping wire an
insulator was inserted and a vertical wire connected the part to the
Herzogstand to the transmitter in the valley. So an L-antenna resulted, fed
against an extensive earth system, using multiple electrodes in marsh land
around the station.. The efficiency of this configuration was found to be
higher than for a T-antenna, in which the whole sloping wire between the
mountain tops was used.
Using a 500W valve transmitter strength measurements were performed over
the whole of Germany and the efficiency of the antenna system was found to
be comparable to the one of Nauen, that consisted of two 250m masts, seven
210m masts, two 180m masts and four200m masts.
In 1926 the station was ready but it did not become operational as by that
time it  had been found that on short waves a few kilowatt and a small
antenna could provide long distance communication equal to or even better
than on VLF.
The reason I mention all this that the article contains an interesting
formula for field strength at the surface of the earth around  a vertical
antenna. The formula comes from a 1926 publication by  M. Bäumler.
(also as attachment).
Field Strength.jpg
E = field strength in V/m
I = current in the current maximum of the antenna.
hw = effective height in m.
lambda = wave length in m.
d = distance in m.
j = operator for 90 degrees phase shift.

The first part gives the far field; the second part the electric component
of the near field. The far field diminishes with 1/d, the near field with
1/d squared. At 2 wavelength distance the near field is 8% of the far
field, at 4 wavelength 4% and at 16 wavelength 1% of the far field.
It is clear that the formula is only correct over perfect earth. But at the
distances where field strength measurements are usually performed, and
certainly at VLF, the influence of the real earth on the field strength is
negligible.
The term effective height is now mostly used in connection with antennas
for reception.

Now an example:
A vertical antenna of 20m at 136kHz has an effective height of 10m and a
radiation resistance of 0.028 ohm.
To radiate 1kW the current must be 189A. The wavelength is 2205m. Entering
these figures into the formula we find the far field at 1km distance to be
0.323V/m, which compares well with the 300mV/m that is given by the CCIR
curves for ground wave propagation.

73, Dick, PA0SE
JN22GD