Traditional vs Modified Elevation/Declination Angles

Huevos said:

Dovercat, I've made a diagram of a traditionally set up polar mount (situated in London) so you (and anyone else) can easily see what we are talking about.

Click to expand...

(snigger)

Channel Hopper said:

(snigger)

Click to expand...

Opps, did I over complicate it a bit?

Seemed straight forward to me




(Well, relatively so)










Yours sincerely

A. Einstein

I quote an email received from Eric Johnston of Satsig.net for its interest value.
The set up angles for a polar mount are a compromise approximation.Therte is no perfect formula that give the correct angles.
The satellites are in a circle above the equator.The polar mount makes the beam point around a cone.The apex of the cone points in some direction(polar motor axis main angle) and the spread of the cone is related to the other angle.If the dish were far above the north pole the beam would make perfect pointing all round.On the equator the polar mount is simply up from east via above the west.Only on the equator,or far above the north pole,is a polar mount mathematically perfecttly correct for all satellites.ELSEWHERE THE CONE CAN NEVER MATCH INTO THE CIRCLE EXACTLY.Errors of about .1 deg are typical.
For a particular site you can set the main angle to the latitude and it works reasonably well.You might get better results with my angles which are slightly different.Note that a polar mount wont work with a very big dish or high frequencies as the errors are more than the antenna beamwith. (end of quote)
I have avoided the declination dish setting due to the bad scale
markings and using the elavation angle of the apex sat(at true north/south,imaginary or not) measured from the top of the lnbf to the bottom lip of the satellite dish coupled with site elevation angle from the Satsig web site (slightly higher than ones official latitude) with much success.Of course final fine tuning is still necessary.

I had a 3 meter Winegard with a Ajak H-H mount tracking perfectly on all sats, but 2 days later i lost sats at the edges due to movement in the ground, but it's possible with 3 meter and a bit of patience and a good spectrum meter, it was bolted on a 500kg concrete block.

Huevos said:

How is this corrected? Simple, tilt the motor axis forward towards the south by 0.63º (0.63º less motor elevation) and set the declination between the dish and motor to 6.74º.

Now lets look at how that works:
Southern satellite, 6.74º + 0.63º = 7.37º. Perfect alignment.
Northern satellite, 6.74º - 0.63º = 6.11º. Also perfect alignment.

Ok, so with the "modified" setup we have perfect tracking right across the arc, but is there any problem with this system? Well yes there is, the maths is a lot more complicated than "90º - latitude"...

Click to expand...

This is an old thread, but the only place where I found this way of calculating the modified motor settings, with a clear explanation.
I think this is a brilliant way: taking the mean of the southern and northern satellite declination! Not really difficult to calculate, though you have to take care to modify declination AND motor elevation.


I would think these angles lead to perfect alignment to the arc.
So why would it possibly be not perfect, as suggested by this post:

wium said:

I quote an email received from Eric Johnston of Satsig.net for its interest value.
The set up angles for a polar mount are a compromise approximation.Therte is no perfect formula that give the correct angles.

Click to expand...

Am I wrong to think that @Huevos way would be exactly right for the whole arc?

Greetz,
A33

Have you taken into account the non spherical shape of this planet ?

There is one tool, perhaps it is not finished yet, but even now it can help to visualize the tuning of the motorized antenna. Just download, unzip and run the program. Let me know if you can not start it. Dropbox - SAT_Tools_20.zip

Channel Hopper said:

Have you taken into account the non spherical shape of this planet ?

Click to expand...

The non-spherical shape you can take into account, if you want, with your declination-calculation. I don't know if the drawing of Huevos did it, but when you use a 'normal' formula for declination as I did, it's not that difficult.

I myself usually use the mean earth radius for calculations, as a way to take the anomalies of the sphere shape into account. Better than using 6378 km for the radius at the equator I think.

RimaNTSS said:

There is one tool, perhaps it is not finished yet, but even now it can help to visualize the tuning of the motorized antenna. Just download, unzip and run the program. Let me know if you can not start it. Dropbox - SAT_Tools_20.zip

Click to expand...

Well, it starts under Wine; but I found no exit buttons, so I had to reset my computer to close the programm.
Viewing the orbit tracking part of the tool: It's solely for a setup with motor axis parallel to earth polar axis?
I didn't see a tool to set polar axis tilt, aka modified motor elevation and modified dish declination? That is what Huevos' and my post were about.

greetz,
A33

a33 said:

The non-spherical shape you can take into account, if you want, with your declination-calculation. I don't know if the drawing of Huevos did it, but when you use a 'normal' formula for declination as I did, it's not that difficult.

I myself usually use the mean earth radius for calculations, as a way to take the anomalies of the sphere shape into account. Better than using 6378 km for the radius at the equator I think.

Click to expand...

That might be where you are going wrong, but I don't have the specific mathematic skill to confirm it.

The Clarke arc parameters are determined by the periodic rotation and the gravitational pull of the total mass of the planet in one direction. Since earth is not spherical the arc dimensions are determined by the average radius at a position somewhere north or south of the equator.
This means the actual arc is closer to the surface of the earth owing to the bulging and any polarmount installed elsewhere other than the equator, or the poles (not that they would see the geostationary satellites) needs revised adjustment of the elevation/declination settings to track correctly from horizon to horizon.

This mis-tracking is only likely to affect the largest of steerable dishes and a small motor at the feed or on the elevation will correct the focal error at the extremes without resorting to a bespoke earthshape design of dish mount.

As far as I know, it is impossible to perfectly adjust polar-mount (or motorized system) to the arc. There are always compromises present.

Please excuse me, as a total novice by comparison with all the previous posters, for posting this question which was prompted in my mind by the problem of making very fine adjustments to DiSqeC motor/dish combos where the elevation & declination markings on those units are pretty "approximate" and that the sizes and weights of the dishes makes that sort of adjustment pretty difficult:
Has anyone worked out ways of modifying the dish mount and/or the mount/dish connections to allow much finer adjustments of the two critical angles without "extreme" engineering (like RimaNTSS appears to be able to do "every day ) ?
(I think I may have, after a lot of thought, but I haven't yet had the opportunity to try my ideas out - and probably won't until the weather gets a lot better/warmer , when I aim to try them out when I remount the motor and TD88 on another steel pole - not going to try these on the TD110 until I think they will work).

Try the absinthe

Channel Hopper said:

The Clarke arc parameters are determined by the periodic rotation and the gravitational pull of the total mass of the planet in one direction. Since earth is not spherical the arc dimensions are determined by the average radius at a position somewhere north or south of the equator.
This means the actual arc is closer to the surface of the earth owing to the bulging and any polarmount installed elsewhere other than the equator, or the poles (not that they would see the geostationary satellites) needs revised adjustment of the elevation/declination settings to track correctly from horizon to horizon.

Click to expand...

I guess what you might be meaning here is that with a motor axis parallel to the earth's polar axis, but not at the poles themselves, there is a mismatch of the 'aiming circle' of the motor with the clarke belt circle.
This, however, has NOTHING to do with a non-spherical earth.
And this problem is in fact, as can be read throughout this topic and also in my post, 'solved' by using MODIFIED motor elevation and modified declination angle.

RimaNTSS said:

As far as I know, it is impossible to perfectly adjust polar-mount (or motorized system) to the arc. There are always compromises present.

Click to expand...

I read this topic again carefully: USALS Notebook , and in the posts of @pendragon it also sais that it never is fully perfect, and it might still leave errors of some hundredth of degrees.

However I find the @Huevos method easy to calculate in a spreadsheet calculator, and accept that that also is not without a little tracking error.

Thanks for responding!
Greetz,
A33

a33 said:

I guess what you might be meaning here is that with a motor axis parallel to the earth's polar axis, but not at the poles themselves, there is a mismatch of the 'aiming circle' of the motor with the clarke belt circle.
This, however, has NOTHING to do with a non-spherical earth.
And this problem is in fact, as can be read throughout this topic and also in my post, 'solved' by using MODIFIED motor elevation and modified declination angle.

Click to expand...

A non spherical earth will have an effect on the height of the Clarke belt but from memory it is in the region of no more than tens of metres difference from the true position of the satellites.

Channel Hopper said:

A non spherical earth will have an effect on the height of the Clarke belt but from memory it is in the region of no more than tens of metres difference from the true position of the satellites.

Click to expand...

So, the effect would not be noticable for an amateur like me, and for almost all the forum members here I guess.

However I made my spreadsheet in such a way, that a deviation from 42164 km (radius Clarke Belt, but I left the numbers behind the decimal comma) can be easily entered.
That will also be practical, when the mass of the earth would accidentally alter, and the clarkebelt would get a different radius (better be prepared ;)).

greetz,
A33

a33 said:

So, the effect would not be noticable for an amateur like me, and for almost all the forum members here I guess.

However I made my spreadsheet in such a way, that a deviation from 42164 km (radius Clarke Belt, but I left the numbers behind the decimal comma) can be easily entered.
That will also be practical, when the mass of the earth would accidentally alter, and the clarkebelt would get a different radius (better be prepared ;)).

greetz,
A33

Click to expand...

If the earth 'accidentally' alters its mass, there would - almost certainly - be a change in angular velocity and the satellites would no longer be geostationary.

Channel Hopper said:

If the earth 'accidentally' alters its mass, there would - almost certainly - be a change in angular velocity and the satellites would no longer be geostationary.

Click to expand...

And slight changes in sat orbits might a "minor" issue after that;) (well, someone had to say it)

RimaNTSS said:

As far as I know, it is impossible to perfectly adjust polar-mount (or motorized system) to the arc. There are always compromises present.

Click to expand...

I've thought a bit more about this perfect or imperfect tracking of the arc.
For any point on earth (between 0 and 81 degrees latitude), the arc has the shape of an ellips (when you're looking at it with axis parallel to the earth axis).
However, if you set the axis of your motor rotation in the right angle to the plane of the clarke belt, the rotation 'circle' can be made to follow that ellips again.
So mathemathically I think the Huevos method is sound and 'perfect'.
I don't think anymore that compromises are needed, in the calculation of modified motor settings.

If compromises are needed, I think that would be because in practice the Clarke Belt may not be a perfect circle around the center of the earth, due to gravity anomalies and so; or because an improper way of calculating is used.


I came to these conclusions based on another example of an ellips being perfectly tracked as a circle: an offset dish.
If you take the line Focal point to G-spot as 'rotation axis', the elliptical rim of the dish is seen as a perfect circle by an LNB feedhorn.
I was puzzled for a while that the program Parabola calculator 2.0 uses different feed illumination angles for the horizontal and vertical, as if there would be a kind of anomaly there. There isn't; there only is one illumination angle (and corresponding f/D-ratio-equivalent).
The trick is that you have to use the width of the dish where the Focal-Point-to-G-spot line crosses the face of the dish for the horizontal width of the dish, and calculate the LNB-illumination angle from there. Though this might feel contra-intuitive, the 'real' (maximum) width of the dish is not really relevant for that.
(So Parabola2 not only calculates wrong focal point for a normal offset dish, alas, it also gives misleading info about illumination angle. )


So also on the Clarke Belt arc, the widest point of the small axis of the 'ellips' (somewhere about +90 and -90 degrees from where you are) is not really important for the calculation. The north/south ends of the ellips at 0 and 180 degrees (as the hight of a dish, in the calculation of illumination angle of offset dish) are more important as starting points for the angle calculations.

It has been really interesting, to discover this all!

Greetz,
A33

I have to correct myself on the previous post, I discovered. So I add again to this old topic.

Though in general a rotation circle can be made to follow an ellips (as is the case with the offset dish example, that I gave), in the specific case of the Clarke Belt and a single-axis motor setup on the earth's surface it cannot, I discovered.

Recently I did the mathematical checking if the 'modified angles' perfectly track the arc, and the answer is alas NO. So I was wrong, in my earlier assumption.

I had expected a perfect match, due to what I understood about cones, circles and ellipses. However I tested if the modified angles, when perfectly aligned to the due south and the opposite satellite (at 180 degrees), hit exactly the arc at plus or minus 90 rotating degrees from south, using the forward axis tilt of the modified angles (so that the 90 degrees rotation sees a greater part of the satellite arc, than the 90 degrees rotation with an axis parallel to the earth axis).
My calculations indicate: At 90 degree rotation, the modified angle looks a little bit UNDER the clarke belt; with a maximum (at latitude about 35 degrees) of a little under 0.04 degrees.


I'm not sure what modified angles are the best compromise to use, now. I've used the '0-180 degrees fit' till now, some use the '0-90 degrees fit' I believe, but also the '0-horizon fit' could be good, or even a fit from 0 to only halfway or two-thirds towards horizon might be better (with 0 = clarke belt zenith).

It is all about just some hundredths of degrees, but maybe I'll check and calculate someday…

greetz,
A33