Formula for sat dish offset
 

At 01:01:23 Fri, 14 Oct 2011, Java Jive wrote:
On Thu, 13 Oct 2011 15:27:45 +0100, John Legon
wrote:

It's a pity you don't still have that dish, but looking at your photos,
I think the curvature is consistent with my view that the axis of the
parabola is located on the lower rim. The LNB arm ought therefore to
have been bent slightly upwards to give optimum results.

So the pictures aren't good enough to test your formula when I do it,
but are when you do it?

The photos aren't good enough to test my formula by calculation, since
the depth of the dish can't be estimated with sufficient accuracy.
I have, however, plotted the curve using your measurements, with the
focus placed where I think it should be, and the result matches up
nicely with the curvature of the dish as seen in the photos.

I think the four formulae are complementary rather than competing.
The boresight method probably shows what the manufacturer intended the
offset to be, my formula shows what the offset actually is

No, it doesn't show what it actually is, because that's determined by
the actual position of the LNB. Your formula shows what the offset
would be if the LNB were the dish accurately constructed with the LNB
where it should be.

Any given dish has only one specific offset angle, which is given by my
formula regardless of the LNB. That in my view is what the offset angle
of the dish actually is! What the tilt of the dish will be when aligned
to a satellite is another matter...


, and your
two formulae show what offset could be assuming that the LNB arm was
accurately constructed :)

No, the 'universal' one shows what it actually is, as determined by
the actual position of the LNB.

I don't think so (see below).

The bottom-at-origin-assumption one
will only agree with the 'universal' one if the bottom of the dish is
actually at the origin.

Agreed. And since the origin is located at the bottom in the general
case, a discrepancy between the two methods will indicate that the LNB
is in the wrong place...

Certainly, your 'universal' formula can give a useful result, but unless
the LNB is at the focus of the dish,

No, as above, because my formula uses the actual rather than the
theoretically optimum position of the LNB, it measures the offset as
it actually is.

I don't think so.


there can be no single solution for the offset angle.
It will depend on the part of the dish that the beam
is reflected off from.

I suspect that in practice effectively parallel rays from the sat will
as near as dammit focus to a point even when arriving slightly above
or below the dish axis.

But unless the parallel rays from the satellite meet the dish at the
geometrically correct offset angle, as given by my formula, then there
can be no point of focus, and neither your formulae nor mine will show
what the effective working tilt of the dish might be.

The path lengths for rays reflected off different parts of the dish will
be different, the signals from top and bottom will become out of phase,
and only trial and error will give a result that can at best be only
sub-optimal.

Taking your old dish and measurements as an example, with the origin at
the bottom and the LNB as the source of the beam, I estimate that rays
reflected off the top and bottom of the dish will not be parallel but
will diverge by about three degrees. What, then, is the offset angle?

Your formulae for the offset are only valid when the LNB is located at
the focus of the parabola.


A more generalised method might be to measure the depth of the curvature
at several points, and use an interpolation formula to construct the
equation of the curve, which may or may not be strictly parabolic...

Yes, that would be the most accurate method, but it probably get us
into the messy iterative procedures that I was trying to avoid.

Agreed.

--
John Legon

Formula for sat dish offset
 

On Fri, 14 Oct 2011 07:58:57 +0100, John Legon
wrote:

The photos aren't good enough to test my formula by calculation, since
the depth of the dish can't be estimated with sufficient accuracy.
I have, however, plotted the curve using your measurements, with the
focus placed where I think it should be, and the result matches up
nicely with the curvature of the dish as seen in the photos.

You can't possibly justify that!

There is no view of the actual profile taken from the side from
half-way up its height. The only side view is distorted by being
taken from a vantage point well above the middle of it. In fact,
although the dish is tilted away from the camera, it looks to me as
though the vantage point was as high as or higher than even the top of
the dish.

From that photo, I'd have far more confidence in my depth measurement
than any attempt to obtain a profile of the dish.

Any given dish has only one specific offset angle, which is given by my
formula regardless of the LNB. That in my view is what the offset angle
of the dish actually is! What the tilt of the dish will be when aligned
to a satellite is another matter...

Well, again, it depends on how you define the offset. As we're
interested in knowing it in order to align the dish initially well
enough to get a signal to use for fine adjustment, the only definition
that makes sense to me is the difference in elevation between the dish
we're trying to align and an axi-symmetric equivalent which would
point directly at the sat.

Agreed. And since the origin is located at the bottom in the general
case, a discrepancy between the two methods will indicate that the LNB
is in the wrong place...

You can not justify such a sweeping claim.

Between the dishes we've measured and the ones in the literature we've
examined, we seem to have as many examples of the origin apparently
not being coincident with the bottom of the dish as being so, more if
we include your own before you 'corrected' it. You may argue that
it's actually the LNB that's in the wrong position, but that is your
assumption, which others are free to accept or not. I am prepared to
accept that it may sometimes be true, and possibly was in the case of
your own dish. It may also have been true of my old dish - I bought
it second-hand, so it may be that some idiot youth thought it would be
cool to have a swing on the LNB arm when it was under earlier
ownership. However, it may also be that it was built deliberately
that way, and that the LNB is actually at the correct focus. Without
access to the dish, either theory could be correct, and neither
accepts the other's interpretations of the photographs of it.

But even if it's true for both those dishes, that is too small a
sample to make such a sweeping claim as you make above.

Consider, why offset a dish? There are a number of advantages to
doing so, but probably the principal one is so that the LNB does not
shade, and therefore effectively waste, part of the reflecting
surface. But if you put both the bottom of the dish and the LNB on
the axis of the parabola, then the top of the LNB will be shading the
bottom of the dish. Why do half a job, why not make the bottom of the
dish a little higher so that NONE of the LNB shades the dish?

So I can see very good reasons why the bottom of the dish might not
always be at the origin of the parabola, and consequently that your
sweeping claim above is fundamentally unsound.

But unless the parallel rays from the satellite meet the dish at the
geometrically correct offset angle, as given by my formula, then there
can be no point of focus, and neither your formulae nor mine will show
what the effective working tilt of the dish might be.

The path lengths for rays reflected off different parts of the dish will
be different, the signals from top and bottom will become out of phase,
and only trial and error will give a result that can at best be only
sub-optimal.

Taking your old dish and measurements as an example, with the origin at
the bottom and the LNB as the source of the beam, I estimate that rays
reflected off the top and bottom of the dish will not be parallel but
will diverge by about three degrees. What, then, is the offset angle?

At that point between the two extremes that gives the best signal,
which - at a guess, I haven't checked - will probably be about
half-way between.

Your formulae for the offset are only valid when the LNB is located at
the focus of the parabola.

No, given the position of the LNB, whether it's where it ideally
should be or not, my formula should give something sufficiently close
to the optimum alignment of the dish to obtain an initial signal.

By contrast, yours, by taking no account of the actual position of the
LNB, and by making an unsound assumption which might not always be
true, is quite liable to be out, perhaps even badly enough out to be
unable to tune the sat.
--
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Formula for sat dish offset
 

At 20:46:41 Fri, 14 Oct 2011, Java Jive wrote:
On Fri, 14 Oct 2011 07:58:57 +0100, John Legon
wrote:

The photos aren't good enough to test my formula by calculation, since
the depth of the dish can't be estimated with sufficient accuracy.
I have, however, plotted the curve using your measurements, with the
focus placed where I think it should be, and the result matches up
nicely with the curvature of the dish as seen in the photos.

You can't possibly justify that!

It wasn't my intention to attempt to prove anything by it! Ironically,
the reconstruction of the focal point fell on the centre of the LNB
holder in the photo, thus showing that perspective distortion has indeed
skewed the result.

[...]

Any given dish has only one specific offset angle, which is given by my
formula regardless of the LNB. That in my view is what the offset angle
of the dish actually is! What the tilt of the dish will be when aligned
to a satellite is another matter...

Well, again, it depends on how you define the offset. As we're
interested in knowing it in order to align the dish initially well
enough to get a signal to use for fine adjustment, the only definition
that makes sense to me is the difference in elevation between the dish
we're trying to align and an axi-symmetric equivalent which would
point directly at the sat.

It's useful, though, to make a distinction between the offset which is a
fixed parameter of the dish itself, and the effective or working offset
which your formula provides.


Agreed. And since the origin is located at the bottom in the general
case, a discrepancy between the two methods will indicate that the LNB
is in the wrong place...

You can not justify such a sweeping claim.

Between the dishes we've measured and the ones in the literature we've
examined, we seem to have as many examples of the origin apparently
not being coincident with the bottom of the dish as being so, more if
we include your own before you 'corrected' it.

I don't know what these examples of dishes with the origin apparently
not on the bottom of the dish might be. In the pdf cited earlier in
this thread, the designer of the RCA offset dishes was quoted as saying
that the origin was on the lower rim. In the General Dynamics offset
dish geometry webpage, the vertex or origin of the parabola is shown to
be on the lower rim, and this applies to a wide range of dishes of
different sizes.

As regards my own dishes, my conclusion that the origin is located on
the lower rim is based upon measurements of the curvature at several
points across the dish, and an iterative curve-fitting procedure to find
the best fit to a parabolic curve.

Dishes of this standard circular type are made in vast numbers, and may
well be said to represent the "general case". I'm not saying that all
dishes are like this, simply that if your two formulae for the offset
don't give the same angle, then there's a good chance that it's because
the LNB is not accurately mounted.

In the case of your old dish, for which the curvature isn't known, the
'boresight' method will give a good indication of the intended offset
angle. The formula works, not simply because the LNB sees the dish as
being circular, but because the plane section through the paraboloid of
rotation describes an ellipse, and the projection of that ellipse onto a
plane at right angles to the axis gives a circle. Since the outer rim
of the dish represents a plane surface (unless the dish is warped or is
a Sky dish), the rim must be elliptical, and the boresight calculation
will give the intended offset.

However, your formulae based on the LNB position give offset values that
conflict with the ellipse calculation. It follows that the LNB on your
old dish could not have been where it should have been - regardless of
whether the origin is at the bottom of the dish or somewhere else.

You may argue that
it's actually the LNB that's in the wrong position, but that is your
assumption, which others are free to accept or not. I am prepared to
accept that it may sometimes be true, and possibly was in the case of
your own dish. It may also have been true of my old dish - I bought
it second-hand, so it may be that some idiot youth thought it would be
cool to have a swing on the LNB arm when it was under earlier
ownership. However, it may also be that it was built deliberately
that way, and that the LNB is actually at the correct focus. Without
access to the dish, either theory could be correct, and neither
accepts the other's interpretations of the photographs of it.

As I say, the boresight calculation shows that the LNB really was out of
alignment, for whatever reason.


But even if it's true for both those dishes, that is too small a
sample to make such a sweeping claim as you make above.

Consider, why offset a dish? There are a number of advantages to
doing so, but probably the principal one is so that the LNB does not
shade, and therefore effectively waste, part of the reflecting
surface. But if you put both the bottom of the dish and the LNB on
the axis of the parabola, then the top of the LNB will be shading the
bottom of the dish. Why do half a job, why not make the bottom of the
dish a little higher so that NONE of the LNB shades the dish?

Because the body of the LNB and the holder and supporting arm are below
the axis, just the top half of the feed horn intrudes, and in practice
this makes no difference at all...


So I can see very good reasons why the bottom of the dish might not
always be at the origin of the parabola, and consequently that your
sweeping claim above is fundamentally unsound.

I still haven't seen any real evidence to contradict my contention that
the great majority of circular offset dishes in general use for domestic
satellite TV are constructed as half a paraboloid. It doesn't matter to
me if this should turn out not to be the case - I just want to see the
evidence!


But unless the parallel rays from the satellite meet the dish at the
geometrically correct offset angle, as given by my formula, then there
can be no point of focus, and neither your formulae nor mine will show
what the effective working tilt of the dish might be.

The path lengths for rays reflected off different parts of the dish will
be different, the signals from top and bottom will become out of phase,
and only trial and error will give a result that can at best be only
sub-optimal.

Taking your old dish and measurements as an example, with the origin at
the bottom and the LNB as the source of the beam, I estimate that rays
reflected off the top and bottom of the dish will not be parallel but
will diverge by about three degrees. What, then, is the offset angle?

At that point between the two extremes that gives the best signal,
which - at a guess, I haven't checked - will probably be about
half-way between.

Your formulae for the offset are only valid when the LNB is located at
the focus of the parabola.

No, given the position of the LNB, whether it's where it ideally
should be or not, my formula should give something sufficiently close
to the optimum alignment of the dish to obtain an initial signal.

Well, that's probably true. Your "universal" formula should give a
result that works well enough in practice when the LNB isn't exactly
where it should be. But from the point of view of optimising the
performance of a dish, I would want to know whether the effective
working offset is the same as the offset of the dish itself, because
only then will the dish function as intended.


By contrast, yours, by taking no account of the actual position of the
LNB, and by making an unsound assumption which might not always be
true, is quite liable to be out, perhaps even badly enough out to be
unable to tune the sat.

But I never suggested that my formula should be used to calculate the
working offset of a dish when the LNB is in the wrong position! On the
contrary, the objective was to determine what the offset angle of the
dish itself really is as an entity, and from that result to work out
what the correct position for the LNB should be.

--
John Legon