Return-Path: Received: from mtain-mg10.r1000.mx.aol.com (mtain-mg10.r1000.mx.aol.com [172.29.96.210]) by air-mb08.mail.aol.com (v128.1) with ESMTP id MAILINMB084-a8064bb3df622c0; Wed, 31 Mar 2010 19:48:50 -0400 Received: from post.thorcom.com (post.thorcom.com [193.82.116.20]) by mtain-mg10.r1000.mx.aol.com (Internet Inbound) with ESMTP id 3DDB43800009E; Wed, 31 Mar 2010 19:48:48 -0400 (EDT) Received: from majordom by post.thorcom.com with local (Exim 4.14) id 1Nx7dT-0003Wz-2C for rs_out_1@blacksheep.org; Thu, 01 Apr 2010 00:47:47 +0100 Received: from [193.82.116.32] (helo=relay1.thorcom.net) by post.thorcom.com with esmtp (Exim 4.14) id 1Nx7dS-0003Wq-Ep for rsgb_lf_group@blacksheep.org; Thu, 01 Apr 2010 00:47:46 +0100 Received: from mx3.acantho.net ([213.174.182.196]) by relay1.thorcom.net with esmtp (Exim 4.63) (envelope-from ) id 1Nx7dQ-0001Zu-32 for rsgb_lf_group@blacksheep.org; Thu, 01 Apr 2010 00:47:46 +0100 Received: (from root@localhost) by mx3.acantho.net (8.13.4/8.13.4/Debian-3sarge1) id o2VNlbss018473 for ; Thu, 1 Apr 2010 01:47:37 +0200 Received: from PCNino ([213.209.195.148]) by mx3.acantho.net (8.13.4/8.13.4/Debian-3sarge1) with SMTP id o2VNlRQM018385 for ; Thu, 1 Apr 2010 01:47:28 +0200 X-Icontrol: Sent by Inrete Icontrol Message-ID: <643308F692D14E8180C87E7F4ECAF69F@PCNino> From: "Antonio Tagliavini" To: References: <4B9FD008.2070607@abelian.org> <4BAAA535.4050401@toya.net.pl> <4BAB1E85.1060304@abelian.org> <4BABA614.4030303@abelian.org> <4BABF362.8000703@toya.net.pl> <4BAC6F82.5020300@abelian.org> <4BB3D9FE.2010803@toya.net.pl> In-Reply-To: <4BB3D9FE.2010803@toya.net.pl> Date: Thu, 1 Apr 2010 01:47:20 +0200 MIME-Version: 1.0 X-Priority: 3 X-MSMail-Priority: Normal X-Mailer: Microsoft Windows Mail 6.0.6002.18005 X-MimeOLE: Produced By Microsoft MimeOLE V6.0.6002.18005 X-Spam-Score: 0.0 (/) X-Spam-Report: autolearn=disabled,HTML_MESSAGE=0.001 Subject: Re: LF: Ionospheric VLF propagation Content-Type: multipart/alternative; boundary="----=_NextPart_000_0030_01CAD13D.449AB400" X-Spam-Checker-Version: SpamAssassin 2.63 (2004-01-11) on post.thorcom.com X-Spam-Level: X-Spam-Status: No, hits=0.6 required=5.0 tests=HTML_20_30,HTML_MESSAGE, MISSING_OUTLOOK_NAME autolearn=no version=2.63 X-SA-Exim-Scanned: Yes Sender: owner-rsgb_lf_group@blacksheep.org Precedence: bulk Reply-To: rsgb_lf_group@blacksheep.org X-Listname: rsgb_lf_group X-SA-Exim-Rcpt-To: rs_out_1@blacksheep.org X-SA-Exim-Scanned: No; SAEximRunCond expanded to false x-aol-global-disposition: G x-aol-sid: 3039ac1d60d24bb3df60152d X-AOL-IP: 193.82.116.20 ------=_NextPart_000_0030_01CAD13D.449AB400 Content-Type: text/plain; charset="UTF-8" Content-Transfer-Encoding: quoted-printable Dear ultra-lowfers,=20 why not Mathematica? It is a very powerful tool containing all specia= l functions you need (e.g..: Legendre). No recipes, no subroutines, no= Fortran... Best regards Antonio ----- Original Message -----=20 From: "Piotr M=C5=82ynarski" To: Sent: Thursday, April 01, 2010 1:25 AM Subject: Re: LF: Ionospheric VLF propagation > Paul Nicholson wrote: >=20 >> >> 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 >=20 > Yes, you are right - it is some kind of challenge to calculate Lege= ndre=20 > functions with a complez > degree - well, at least because you rather do not do it on , say,=20 > everyday basis :) > Indeed, it is well known that you can compute Legendre functions= =20 > using 2F1 function of a complex argument > and further, usingasymptotic expansion but one must be careful with= =20 > some values of theta and modulus of "nu " > ( i use notation from Lowenfels paper ) The paper has a Matlab co= de =20 > which i am not even going to 'digest' > I do fortran programming and i prefer to do it 'from the scratch'= =20 > except that , of course, i have subroutines for > Legendre polynomials with integer degree and order which (as it= has=20 > appeared) were needed - I have found Jones and Burke paper > [Journal of Physics: A : Mathematical and General; Vol.23,=20 > 3159-3168(1990) ] where you can find a compact formulae > obtained by integration etc... those summations /formulae are real= ly=20 > compact and have very elegant (mathematically) form > so one deals with rather straightforward programming. Paul, i have= a=20 > pdf copy of that article and if you wish i can send it to you > directly as attachment (540kb) >=20 > On other issues related to Stefan VLF experiment... to make a lon= g=20 > story a short one... i was reading Lowenfels paper > and particulary did not like the numerical fits of attenuation const= ants=20 > alpha and of phase velocity ( chapter 5.3) > those fits involve polynomials up to 12th order! it is not good from= =20 > numerical point of view to use such a high degree etc.. > anyway, i was looking for papers where i could find those values = based=20 > 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=20 > and not going into ELF regions. > as a 'side product' of my search i have found an excellent review pa= per=20 > "ELF and VLF radio waves" by Barr, Jones > and Rodger. published in " Journal of Atmospheric and Solar-Terrest= rial=20 > 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 =20 > was used at f =3D25.3khz , > later it was also used at 104 Hz (ELF) with radiated pwr of 40mW= =20 > 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 wi= th=20 > his experiments > In 1993 , the loop wire was placed through a tunnel 1.2 km long = and =20 > going up along the mountain > through which the tunnel was made the apex was 600 m above the tun= nel=20 > 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.=20 > tunnel :) > now , comes really interesting experiment.. there was an unsuccessf= ul=20 > attempt to deploy a long wire ( a very very long wire) > from the Space Shuttle to generate electric power from its motion in= the=20 > earth's magnetic field and to radiate ELF signal. after > 19.7 km !!! wire in space it has been fractured but the pwr generat= ed=20 > was greater than expected, however no signal has been radiated. > it was 1996 mission. >=20 > = =20 > 73, piotr , sq7mpj > qth; Lodz /jo91rs/ >=20 >=20 >=20 > ------=_NextPart_000_0030_01CAD13D.449AB400 Content-Type: text/html; charset="UTF-8" Content-Transfer-Encoding: quoted-printable
Dear ultra-lowfers,
why not Mathematica? = It is=20 a very powerful tool containing all special functions you need (e= .g..:=20 Legendre). No recipes, no subroutines, no Fortran...
Best regards
Antonio
 
----- Original Message ----- <= /DIV>
From: "Piotr M=C5=82ynarski" <sq7mpj@toya.net.pl>
To: <rsgb_lf_grou= p@blacksheep.org>
Sent: Thursday, April 01, 2010 1:25= AM
Subject: Re: LF: Ionospheric VLF=20 propagation

> Paul Nicholson wrote:
>
>&g= t;
>> Piotr=20 wrote:
>> > I will also try to program these=20 formulae
>>
>> It's a challenge - those Legendre fun= ctions=20 with complex
>> parameters...  there's an expression inv= olving=20 hypergeometric
>> functions and some code for that in 'Numeri= cal=20 Recipes in C',
>> either that or (very!) carefully transcribe= /port the=20 code in
>> the paper's appendix.
>>
> Dear Pau= l, LF=20 group
>
> Yes, you are right - it is some kind of challen= ge=20 to  calculate Legendre
> functions with a complez
>= degree -=20 well, at least because you rather do not do it on , say,
> ever= yday basis=20 :)
> Indeed,  it  is well known that you can  com= pute=20 Legendre functions
> using  2F1 function of a complex=20 argument
> and further, usingasymptotic expansion but  one= must be=20 careful with 
> some values of theta and  modulus of&= nbsp; "nu=20 "
> ( i use  notation from Lowenfels paper )   Th= e paper=20 has a Matlab code 
> which i  am not even going to=20 'digest'
> I do fortran  programming and i prefer  to= do=20 it  'from the scratch' 
> except that  , of cour= se, i=20 have  subroutines for
> Legendre polynomials  with&nbs= p; integer=20 degree and order  which  (as it has
> appeared) were&= nbsp;=20 needed  - I have found  Jones and Burke paper
> [Journ= al of=20 Physics: A : Mathematical and General; Vol.23,
> 3159-3168(1990= ) ] where=20 you can find a compact formulae
> obtained by integration = etc...=20 those  summations /formulae are really
> compact and have= very=20 elegant (mathematically)  form
> so  one deals with ra= ther=20 straightforward programming. Paul, i have a
> pdf  copy of= that=20 article and if you wish i can send it to you
> directly as attac= hment=20 (540kb)
>
> On other issues  related to Stefan = VLF=20 experiment...  to make a long
> story a short one... i was= reading=20 Lowenfels paper
> and particulary did not like the numerical fit= s of=20 attenuation constants
> alpha and of phase velocity ( chapter= =20 5.3)
> those fits involve polynomials up to 12th order! it is no= t good=20 from
> numerical point of view to use such a high degree etc..<= BR>>=20 anyway, i was looking for papers where  i could find those values=  =20 based
> on some experimental data ( i did find it  for Ste= fan=20 freq
> 8.97 kHz ) with MUCH simpler  fits.as i was interest= ed only in=20 one freq
> and not going into ELF  regions.
> as a= 'side=20 product' of my search i have found an excellent review paper
>= "ELF and=20 VLF radio waves" by  Barr, Jones
> and Rodger.  publis= hed in "=20 Journal of Atmospheric and Solar-Terrestrial
> Physics" Vol. 62= ,=20 1689-1718(2000)
> some  info upon VLF antennae... for Stefa= n , for=20 his consideration..
> in 1989 a balloon ( not kite ;)  )&nb= sp; lofted=20 antenna 3.8 kilometers  long 
> was used at f =3D25.3= khz=20 ,
> later it was also used at 104  Hz (ELF)  with= radiated=20 pwr of 40mW
> which in terms of efficiency , was
>=20 corresponding  to 1.6 Watt radiated vs 1 MW input TX pwr
>= now=20 something which should make Stefan  being even more satisfied wit= h
>=20 his experiments
> In 1993 , the loop wire was placed  throu= gh a=20 tunnel  1.2 km long  and 
> going up along the= =20 mountain
> through which the tunnel was made  the apex=   was=20 600 m above the tunnel
> center. this system was radiating = ; 75 mW=20 for every kilowatt of
> input pwr at 10 khz ;  signal was= detected at=20 200 km from TX place  i.e.
> tunnel :)
> now , comes= really=20 interesting  experiment.. there was an unsuccessful
> atte= mpt to=20 deploy  a long wire ( a very very long wire)
> from the Spa= ce Shuttle=20 to generate electric power from its motion in the
> earth's mag= netic=20 field and to  radiate ELF signal. after
> 19.7 km !!! wire= in space=20 it has been fractured but  the pwr generated
> was greater= than=20 expected, however no signal has been radiated.
>  it was 19= 96=20 mission.
>=20
>          &n= bsp;           =            &nbs= p;           &n= bsp;           =            &nbs= p;           = =20
> 73, piotr , sq7mpj
> qth; Lodz /jo91rs/
>
>= ;
>=20
> ------=_NextPart_000_0030_01CAD13D.449AB400--