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Subject: Re: LF: Ionospheric VLF propagation
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Paul Nicholson wrote:

> Alexander RA9MB wrote:
> > Fore large distanses i expect behaviour E ~ 1/sqrt(d).
>
> This would be the most straightforward explanation
> for the high signal strength.
>
> The signal expands with 1/r^2 power density and 1/r field
> strength until it is constrained by the Earth-ionosphere
> cavity, at say r = 100km.   Thereafter, expansion is
> 1/r power density and 1/sqrt(r) field strength.
>
> For long distances, we can just assume 1/sqrt(r) field
> strength.
>
> We have then B = sqrt( 9.5e-21 * ERP/r) for a daytime
> D-layer at a height of 70km.
>
> For 1mW ERP over 850km, that gives 3.3fT which is a much
> better estimate than the 1/r^2.  With multi-path interference,
> it could vary between zero and twice that figure.
>
> For conservation of energy, it cannot be higher than
> that, so that gives an upper bound.
>
> Then there must be the exponential factor for attenuation...
> -- 
> Paul Nicholson
> -- 
>
>
Dear Paul, Alexander, Markus , Stefan  & other "Dreamers"...  :)

First of all, my congratulations   to all of you for  remarkable experiments
at  VLF.  I  read all  your posts with a great  interest and find it 
very, very useful
at least because it has opened some theoretical discussions upon 
different models of  radio waves
 propagation at  VLF frequencies.. In the light of the above 
discussions  i think, one can mention
the semiempirical Austin equation  describing  E field  dependence upon 
distance  based on the idea
 of a spatial waveguide: earth-ionosphere.
Based  on  Stefan, DK7FC  2nd TX  transmissions  and his reports about 
antenna current of 480mA and
100m length of his kite antenna the estimated  erp pwr at 8.97 kHz  is 
abt 1.5 miliWatt
and i took this value for the further calculations of E =E(r)  
function.  It is plotted in the attached  picture.
Here, i only recall that  at the 858.7 km distance ( Paul, Stefan)  my 
calculated effective field  strength is 0.274 microVolts/m
the Austin eqn  can be described here as  a product of  3 factors:  F1*F2*F3
F1  is simply a  piece of a fundamental electrodynamics  i.e.  E -field  
as a function of r in a free space
(i described it  in more detail in my post sent a few weeks ago , 
concerning ionospheric prop ,wspr, 600m band etc.. ) 
F2 is defined as sqrt(alfa/sin(alfa))  where alfa (in radians) is 
defined as r/R ; R is earth radius
F3 is defined as  exp(-0.0014*r/lambda**0.6)  where r and lambda are 
expressed in km
As Markus has pointed out  Paul recording was 0.93 microV/m  ( taken 
from E = cB, B=3.1 femtoTesla)
Markus estimate upon E as 1/r  dependence gives value 0.251 mcroV/m   so 
it is almost the same as mine  in this present calculations
while both ( 0.274, 0.251)  are much lower than equivalent E-field of 
calibrated B measurement.
my next step was to quickly ( and naively) calculate  pure ionospheric 
prop. this time i got  field strength of 0.595 microVolt/m
( i assumed that D layer height is/was  75 km)
i have a feeling  that Austin eqn is ok( as a crude approxim.) for 
longer, say, 5000 km distances
on shorter ones  the prop is much more complicated being a mixture of 
ionospheric , surface(ground) modes etc..

                                         yours, Piotr, sq7mpj
qth: Lodz /jo91rs/

p.s. at the city location i must forget about  looking for Stefan TX'ed  
K's etc...but , of course, i immediately did 
almost the same what  Rik did  i.e. i took 2 ferrite antennae and 
constructed  "TX" and  "RX"  stns  - got full success
at qrb =  0.005 km  at 8.97 khz  :)

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