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Date: Fri, 29 Jan 2010 00:06:12 +0100
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Subject: LF: Signal strengths, WSPR reports , propagation
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Dear Rik, James,LF group

it is going to be long.... sorry...

Some time ago Jim, G7NKS began a new topic on this reflector. it was 
about a link budget
for wspr at  given distance. Recently, Rik, ON7YD has made a nice thing 
i.e. comparing reception
levels of three stations using a 'small statistics' - that is exactly 
what wspr stands for.
investigations of propagation paths, limits etc...
Being 'triggered' by these two mails and , additionaly, by a phrase 
'mill' used by Rik
which translated into polish sounds very much like my surname ( 
Mlynarski) Mlyn=mill  :)
I started to think  about the estimate of an effective electric field 
'felt' by RX station.
Later, I will use Rik's collected data  as numerical example.  Due to 
the enormous
and variable  noise at my qth  my reception data is not appropriate and 
lacks some stations.
I like to do such 'guesstimates' almost from the scratch, so let me start
 from the 'basics' i.e.  classical electrodynamics which states that in 
a free space
 the power P radiated by an isotropic antenna in a distance R has its 
density:
 D=P/(4*pi*R*R). On the other hand, the mean magnitude of a Poynting 
vector (D) can be expressed
 by an electric field: D = E*E/(2*120*pi) ( 120pi = 377ohm=impedance of 
a free space)
Combining these two one gets that the amplitude of an electric field E 
equals:
E = sqrt(60*P)/R. if R is in [km] then E is expressed in miliVolts/metr, 
P is in Watts.
I assume that we are dealing with a short vertical monopole so following 
Rik's explanations
( veeery useful post to the reflector! ) its directivity gain is 3 but 
as the power in wspr reports
is given as ERP power so it must be multiplied by a factor of 1.64 in 
order to replace
power P (isotropic) in the last formula by ERP*1.64 , where "ERP" is the 
reported erp power. Also,
we can multiply  E  by  0.707 to get the effective signal strength E(eff):
E(eff) = 0.707*sqrt(60*ERP*1.64)/R
I focus ONLY on the ionospheric propagation and  1 hop.
At the night, the absorption of incoming wave (500kHz) to the ionosphere 
is really small so ,
 at first approximation, can be simply ommited and we are left now with 
relatively
 simple geometric considearations with further assumption that the 
distance between
station a (TX) and station b (RX) is not an earth arc but a straight 
line, segment.
{sure, it can be done more precisely taking into account mean earth 
radius etc...)
The wave is propagating from  TX antenna with an elevation(take-off) 
angle alfa, the
 reflection takes place in  E layer, say, 120 km above earth (H) and the 
distance
 between stations a and b is "d". At the RX place we are interested in 
the vertical
 component of incoming reflected wave being doubled by reflection from 
the earth
and assumed  antenna characteristic is described by a certain function 
A(theta)
{theta= usual notation of one of the angles in spherical coordinate system)
In the case of a short vertical monopole:  A(theta) = sine(theta) = 
cosine(alfa)
so we have:
E(eff) = E(eff)*2*cos(alfa)*cos(alfa)
R in formula for E(eff) becomes: sqrt(d*d + 4*H*H)
and cos(alfa) = d/sqrt(d*d + 4*H*H)

(in the course of programming it is convenient to multiply E(eff) by 
1000 thus getting
 the values in microVolts/m)

The above final formula gives real values of an effective signal 
strength. It is a 'product'
of  fundamental physics and simple geometric considerations. Obviously, 
there is an ample room for
improvements but as i am not a radio-comm specialist i just do not know  
how to make it -
 some reflection losses, absorption attenuation which both seem to be 
frequency
 and (probably) time dependent etc..
Anyway, here comes  'numerical'side..
I took Rik's qth as  RX station and the values of erp power as reported 
in wspr database ( or e-mails)
 by the TX stations:
G4JNT: 420 km and 200 miliWatts of ERP pwr
G3ZJO: 411 km     0.2 mW
G3XBM: 337 km     1 mW
H = 120 km ( the height of reflection point) (have found in literature 
it is 110-120 km on average)
calculated values of E(eff) are:
G4JNT: 9.777 microVolt/m       G3ZJO: 0.311     G3XBM: 0.711
calculated relative differences of signal strengths: (first, 'left', 
stations are favored)
G4JNT-G3XBM: 22.77 dB
G4JNT-G3ZJO: 29.95 dB
G3XBM-G3ZJO:  7.18 dB
Now, the same differences made by Rik (night receptions, wspr readouts, 
averages etc..)
G4JNT-G3XBM:  15 dB
G4JNT-G3ZJO:  23 dB
G3XBM-G3ZJO:   8 dB
In the case of Roger,"Water Pistol", G3XBM and Eddie, "Dripping Tap", G3ZJO
theory and experiment are fairly consistent
if Andy, "Big Gun", G4JNT had run only 40 mW ERP then his E(eff) would 
be 4.372 microVolt/m
so then the calculated diferences:
G4JNT-G3XBM: 15.78 dB
G4JNT-G3ZJO: 22.96 dB
(pretty nice matching..)
Final conclusion: "Big Gun" shrinks !     :)

                                                         Yours, Piotr, 
sq7mpj
qth: Lodz /jo91rs/