Re: LF: Ionospheric VLF propagation

["Antonio Tagliavini" <antonio.tagliavini@acantho.it>]

Dear ultra-lowfers,

why not Mathematica?  It is a very powerful tool containing all special functions you need (e.g..: Legendre). No recipes, no subroutines, no Fortran...

Best regards

Antonio

 

----- Original Message -----

From: "Piotr Młynarski" <sq7mpj@toya.net.pl>

To: <rsgb_lf_group@blacksheep.org>

Sent: Thursday, April 01, 2010 1:25 AM

Subject: Re: LF: Ionospheric VLF propagation

> Paul Nicholson wrote:
> 
>>
>> Piotr 
wrote:
>> > I will also try to program these 
formulae
>>
>> It's a challenge - those Legendre functions 
with complex
>> parameters...  there's an _expression_ involving 
hypergeometric
>> functions and some code for that in 'Numerical 
Recipes in C',
>> either that or (very!) carefully transcribe/port the 
code in
>> the paper's appendix.
>>
> Dear Paul, LF 
group
> 
> Yes, you are right - it is some kind of challenge 
to  calculate Legendre 
> functions with a complez
> degree - 
well, at least because you rather do not do it on , say, 
> everyday basis 
:)
> Indeed,  it  is well known that you can  compute 
Legendre functions 
> using  2F1 function of a complex 
argument
> and further, usingasymptotic expansion but  one must be 
careful with  
> some values of theta and  modulus of  "nu 
"
> ( i use  notation from Lowenfels paper )   The paper 
has a Matlab code  
> which i  am not even going to 
'digest'
> I do fortran  programming and i prefer  to do 
it  'from the scratch'  
> except that  , of course, i 
have  subroutines for
> Legendre polynomials  with  integer 
degree and order  which  (as it has 
> appeared) were  
needed  - I have found  Jones and Burke paper
> [Journal of 
Physics: A : Mathematical and General; Vol.23, 
> 3159-3168(1990) ] where 
you can find a compact formulae
> obtained by integration  etc... 
those  summations /formulae are really 
> compact and have very 
elegant (mathematically)  form
> so  one deals with rather 
straightforward programming. Paul, i have a 
> pdf  copy of that 
article and if you wish i can send it to you
> directly as attachment 
(540kb)
> 
> On other issues  related to Stefan  VLF 
experiment...  to make a long 
> story a short one... i was reading 
Lowenfels paper
> and particulary did not like the numerical fits of 
attenuation constants 
> alpha and of phase velocity ( chapter 
5.3)
> those fits involve polynomials up to 12th order! it is not good 
from 
> numerical point of view to use such a high degree etc..
> 
anyway, i was looking for papers where  i could find those values  
based 
> on some experimental data ( i did find it  for Stefan 
freq
> 8.97 kHz ) with MUCH simpler  fits.as i was interested only in 
one freq 
> and not going into ELF  regions.
> as a 'side 
product' of my search i have found an excellent review paper 
> "ELF and 
VLF radio waves" by  Barr, Jones
> and Rodger.  published in " 
Journal of Atmospheric and Solar-Terrestrial 
> Physics" Vol. 62, 
1689-1718(2000)
> some  info upon VLF antennae... for Stefan , for 
his consideration..
> in 1989 a balloon ( not kite ;)  )  lofted 
antenna 3.8 kilometers  long  
> was used at f =25.3khz 
,
> later it was also used at 104  Hz (ELF)  with radiated 
pwr of 40mW 
> which in terms of efficiency , was
> 
corresponding  to 1.6 Watt radiated vs 1 MW input TX pwr
> now 
something which should make Stefan  being even more satisfied with 
> 
his experiments
> In 1993 , the loop wire was placed  through a 
tunnel  1.2 km long  and  
> going up along the 
mountain
> through which the tunnel was made  the apex  was 
600 m above the tunnel 
> center. this system was radiating  75 mW 
for every kilowatt of
> input pwr at 10 khz ;  signal was detected at 
200 km from TX place  i.e. 
> tunnel :)
> now , comes really 
interesting  experiment.. there was an unsuccessful 
> attempt to 
deploy  a long wire ( a very very long wire)
> from the Space Shuttle 
to generate electric power from its motion in the 
> earth's magnetic 
field and to  radiate ELF signal. after
> 19.7 km !!! wire in space 
it has been fractured but  the pwr generated 
> was greater than 
expected, however no signal has been radiated.
>  it was 1996 
mission.
> 
>                                                                                 
> 73, piotr , sq7mpj
> qth; Lodz /jo91rs/
> 
> 
> 
>