Hi Piotr, Is it possible that Andy is radiating a much stronger ground-wave at 
that distance. I know the paths should be reciprocal, but if the weaker station 
ground wave was weaker, swamped in the noise??  Possibly the antennas for the 
others are radiating much more upward and the ground wave is being attenuated. 
The addition.subtraction of a ground wave at the same strength as the skywave 
could add or subtract 6dB (about the difference in the figures)....I know that 
the Lowfers in the States see a dead zone at their low power.....but that as 
with QRSS not a sophisticated system like WSPR. 

A slant range calculation formula is given on my web site. The apparent 
reflection height at 136kHz at night was lower of course 90-100km. At extreme 
range the apogee was calculated by raytracing at about 86km (from memory) At 
short range and high angles the signal will penerate further before being 
returned. The path calculated this was is in error because the refraction 
"shortens" the path over a "mirror reflection" model.
http://www.alan.melia.btinternet.co.uk/simple.htm.

http://www.alan.melia.btinternet.co.uk/fading.htm   Dont take too much notice 
of the text it is quite old now but the equations work and can be solved at 
fading nulls. You need two receivers at different distances to resolve the 
ambiguities.

An interesting point is that if you can calculate the ground-wave strength, you 
can estimate the skywave strength by the depth of the null(which asumes they 
are out of phase of course).

I used the thumbnail figure that a watt ERP at 1km generates 300uV/m, for my 
calculations. These kind of simple models can be very useful in trying to 
understand what is happening and calculating whether any particular path is 
possible...... and its good fun !!

Best Wishes
Alan G3NYK


--- On Thu, 28/1/10, Piotr Młynarski <[email protected]> wrote:

> From: Piotr Młynarski <[email protected]>
> Subject: LF: Signal strengths, WSPR reports , propagation
> To: [email protected]
> Date: Thursday, 28 January, 2010, 23:06
> 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/
> 
> 
>