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I agre with your diagram, but won't work with sat. You left one important factor out. Polarity. The other sats on either side will have opposite polarity and hence interfere with the main one.

Comptech said:

The other sats on either side will have opposite polarity and hence interfere with the main one.

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When you mean that the mirrored signal from the same satellite from the other side of the dish has a shifted phase, I can understand what you mean. Otherwise I don't; can you explain further?

I would guess that out of phase or more 'diffused' signal for "off-axis" satellite aiming would be greater for shorter focal length, than for longer focal length (assuming equal dish diameter).
That is because for a flatter dish (longer focal length), the parabolic curve is still rather like the spherical curve, so causing less 'off-axis parabolic aberration'.
That would be a counter-effect to what polgyver described above, I think.

But I have no idea how great these effects would be.

Greetz,
A33

a33 said:

When you mean that the mirrored signal from the same satellite from the other side of the dish has a shifted phase, I can understand what you mean. Otherwise I don't; can you explain further?

I would guess that out of phase or more 'diffused' signal for "off-axis" satellite aiming would be greater for shorter focal length, than for longer focal length (assuming equal dish diameter).
That is because for a flatter dish (longer focal length), the parabolic curve is still rather like the spherical curve, so causing less 'off-axis parabolic aberration'.
That would be a counter-effect to what polgyver described above, I think.

But I have no idea how great these effects would be.

Greetz,
A33

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All of this rant and not a single mention of scalar theory. There are a gazillion Indian college papers posted on the 'net describing 'their' opinions of the function of them.
Going with the etched-in-stone instructions of how to locate them on a dish with f, fD...bla bla bla crap.
Well I went that route. on a 12 footer with button hook feed. C-Band with a side-car Ku LNBF (no scalar on that one).
At first my signal sucked. In and out, left and right with the C-Band LNBF for what seemed hours over the course of days.

Then I said screw it and started moving the scalar in and out in small increments. And then the LNBF.
The sweet spot for the scalar was significantly closer towards the dish center (in optical terms) than all of the science extrapolated.
I came to terms that my calculated distance made the scalar "over illuminate" the dish.
Yet further away from the sweet spot signal peaking on the LNBF was lower. Days I tell you.
And then Squeeze Box came on the radio. Hah.
It makes me wonder if guys with triangular dish edge support rods to mount the scalar in a fixed position, determined from hard calculations, don't realize that moving the scalar in or out slightly can give several more dB of signal.
I understand optics well. I understand Newtonian telescopes better. And I just happen to love photography and have the fixer stains to prove it. Yup. Homie still does film.
From the above. A parabola is a parabola. Period. Anything less (or more) and you're having to load up the shuttle and head out to Hubble.
I happen to have a "shallow focus" dish. The calculations for f and fD didn't mean squat. It got me in the ballpark.
December 2, 2021. And that's my rant

arlo said:

The sweet spot for the scalar was significantly closer towards the dish center (in optical terms) than all of the science extrapolated.
I came to terms that my calculated distance made the scalar "over illuminate" the dish.

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I would say the parabolic form does not lie. So I'd be (scientifically) interested whether you based your calculated distance on just ONE measurement of the parabolic shape, that is depth at the center of the dish, as many people do; or whether you based it on multiple measurements of the parabolic shape at various points, so (also) on depth measurements further away from the center?

It is quite possible that the central area of the dish has another focal length than the outer area; so that just using the central depth measure is not the best procedure to use.
Just a hypothesis, though. That's my rant.

How to test such a hypothesis? Two procedures to calculate focal length from multiple depth measurements at prime focus dishes are here: Calculating focal length of a PrimeFocus dish that has a hole in the middle
When the resulting focal length outcomes have more error than normal measuring error, the cause would likely be parabolic shape error. I guess not something to be happy with....

Greetz,
A33

a33 said:

It is quite possible that the central area of the dish has another focal length than the outer area

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For sure, this is the case if the dish is a part of a sphere (like, Arecibo - this info I got from Paul Wade articles). Not sure if there were trials to combine more paraboloids of rotation into one shape, though...
If there is just one paraboloid, it has only one focal spot.
This thread got enriched by more info about other reception problems and possible solutions, but still needs the conclusions about values-parameters needed to calculate Angle of View of a dish, Theta.
From Wikipedia, we need to input coefficient "lambda" (wavelength in cm), multiplied by somewhat arbitrary factor of "70" and all - divided by the dish diameter "d". I did not like that the formula omitted "f", the only factor defining parabola. Maybe it is somewhat contained in this "70" ?
As an alternative, I tried to use another formula :
Theta = arc tg (0.76 lambda / f
The coefficient 0.76 I found somewhere on Internet, it helps determine active focal cloud diameter in front of LNBF.
Both equations give very similar results.
My 4' Ariza dish has horizontal dia = 120 cm, and "f" = 72 cm.
From Wiki formula, it has Theta (Ku) = 1.46*, and for C-band Theta=4.37*
Using arc tg and "f", it is - respectively - 1.5* and 4.5*
A few photos/scans follow :

polgyver said:

For sure, this is the case if the dish is a part of a sphere. (....)
If there is just one paraboloid, it has only one focal spot.

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But of course, I was mentioning this for a paraboloid dish that was intended as a paraboloid, but was manufactured badly.
In that case, just one depth measurement is not the way, to get a meaningful idea of where to put the feedhorn...

But, back on topic, as you wish...

Greetz,
A33

a33 said:

But of course, I was mentioning this for a paraboloid dish that was intended as a paraboloid, but was manufactured badly.
In that case, just one depth measurement is not the way, to get a meaningful idea of where to put the feedhorn...

But, back on topic, as you wish...

Greetz,
A33

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99.99% of new people in the sat hobby who come across a dish for the taking may have all of the hardware to reassemble it on site.
Or in the case of the cheap ones tek2000 sells (sold) that have spotty at most and poorly translated instructions.
So where do you run to? Google a quick "how to" to find out.
Agreed?
You run string. You take measurements. You put the thing together. You might head out to the hardware store for hardware and conduit. Smash the ends in a vice and drill holes and bend a few angles.
Stick in your feed and hook it up and go signal searching.
And like me, you find the best signal and strengths and bolt the lnbf down and head inside.
Agreed? I think you will.
Not much is said about heading to the health food store for a bottle of einsteinium-Q10 first.
The calcs are based on a true parabola.
You do state some interesting reading. Above a guy like me for the most part.
All I'm getting at is that a person should experiment and veer from all of the hard calculations, engineer for a little wiggle room, and not assume anything. Especially when it comes to scalar placement. If you use one. In the case of a prime feed antenna. That 'should' be a true parabola.

polgyver said:

I think that the only factor which determines the angle of a cone what the dish "sees" - is its focal length.

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This was my initial suggestion submitted in my original post. I asked for other Members' opinion, and they stated that the dish's selectivity depends on its diameter: the formula (equation) in Wikipedia for "angle of view" = theta, contains no focal length as a factor. I disagreed, but recently realized that I was only partially right:
The angle of view - indeed - depends ALSO on the dish's diameter, but - not exclusively: it depends on its focal length, too.
For explanation, the reverse process could be used : the LNB could be assumed as a source or radiation so the dish could truly ILLUMINATE the Clarke Belt, as if it were driven by B.U.C.
Using some idealization, first we can imagine that in the focal spot there is ideally small source of radiation, sort of geometrical, dimensionless point. If the paraboloid is also ideally correct, then the radiation reflected from dish would take shape of cylindrical beam, going to infinity, all rays - parallel.
In reality, there is no dimensionless spot - there is certain Focal Cloud, its size depending on used frequency of radiation.
I memorized from Internet article, that "conventional" diameter of focal cloud can be derived as a product of wavelength and certain factor or coefficient = 0.76. For 12 GHz, the wavelength = 25 mm, (1") thus FC diameter = 19 mm or 3/4".
If such a Focal Cloud radiates energy, then - due to its size - reflection from dish will be a cone, not a cylinder, as every point on dish's surface will reflect the energy according to laws of optics, and the radiation rays will spread out.
The farther the dish's reflecting spot from its Focal Cloud - the narrower the radiated cone.
Reversing the settings from radiation (illumination) to reception should also be true.
Thus John Legon was correct : wider parts of truncated dish increase its selectivity.
A sketch of drawing follows: