Message-ID: <4CCA5F64.60606@toya.net.pl>
Date: Fri, 29 Oct 2010 07:45:08 +0200
From: Piotr Mlynarski <sq7mpj@toya.net.pl>
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To: rsgb_lf_group@blacksheep.org
Subject: LF: vlf experiments-numerical considerations
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Dear LF Group, Dreamers


Recently, after 7th Stefan experiment on VLF band i came back to the 
numerical programme
i have written few months ago which gives us some insight about the 
e-field strength produced by
Stefan TX setup along with its kite antenna. Following Alan Melia 
suggestions concerning
 the ways of displaying results i have sent here few graphs illustrating 
the e-field strength vs distance
 for a given frequency.

The programme has been written basing  upon earth-ionosphere waveguide 
model proposed by
David F. Lowenfels:
http://dspace.mit.edu/bitstream/handle/1721.1/16973/53712465.pdf?sequence=1
(again, i am grateful to Paul Nicholson for this link)
The numerical simulation  covers wide range of frequencies starting from 
several Hertz up to 24 Khz
with an assumption that EM energy is transmitted from vertical electric 
field antennae
( so it does apply to Stefan kite antenna )
By the time the code was almost completed i've promised to put here, on 
the reflector, the source code so everybody
 could play her/himself with it for specific purposes. It is written in 
Fortran and can be downloaded from:
http://www.toya.net.pl/~mlynarski/mpj.zip
 ( i am sorry that instead of two weeks it took me few months
 to complete something which was almost completed - well, please, do not 
ask why ...  :) )
Basically, the programme solves normal mode equations for the TEM mode 
propagation in a spherical
waveguide ( eqns: 5.2 - 5.11 of Lowenfels paper). The numerical essence 
of the present source code
is connected with the calculation of the Legendre Function of a complex 
degree "nu" where the complex "nu"
accounts for the dispersive and dissipative properties of the 
earth-ionosphere waveguide. For that purpose
I have used an algorithm described in Jones and Burke paper published in 
J.Phys.A: Math.Gen, Vol.23, 3159(1990)
I did partial optimization of the fortran code , however, the used 
algorithm of zonal harmonic series expansion
is very efficient itself so the program should work  on modest PC 
machines and yet producing the final result
in a reasonable time ( seconds  of CPU time for , say, 1000 steps of 
frequency etc...)
After download and decompression the user will get 4 files:
propvlf.f
head.f
dane.dat
out.dat
The main fortran subroutine which calculates the propagation model  is 
in propvlf.f file.
The C(omment) lines at the begining of this subroutine describe its 
input/output formal parameters.
The second fortran file head.f is a simple example of so-called main 
program  showing how
 the  subroutine is called with user defined numerical inputs ( dane.dat 
file)
the out.dat file contains one line of numerical result which along with 
dane.dat file can be used
 as a reference when adopting/testing the program.
Of course, the user can easily modify the header program by defining 
loops over frequency, distance with incremental steps
allowing for different graphical displays, presentations etc...
The code is rather portable (generic names were used for intrinsic 
functions) so basically
 any fortran compiler on most platforms should do its work without 
problems - if otherwise, please
contact me either on or off the reflector.

Finally, please, feel absolutely free to change, adopt, modify, add , 
delete etc.. any part of this code.
I did it for our/dreamers/ purposes inspired by the wonderful (TX) work 
done by Stefan and others who do also a smart work
of RX'ing. Unfortunately, i could not take part in 8th Stefan 
experiment, though i am preparing my RX stuff for the 9th one :)

                                                                         
73, Piotr, sq7mpj
qth: Lodz /jo91rs/