Traditional vs Modified Elevation/Declination Angles

Hyperopia

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Modified Inclination (Elevation)/Declination

After studying the subject here, and on other websites, I want to share this solution which works well for me.

At the Equator:
Inclination is 90°, and declination is zero, therefore no corrections are required.

At the North and South poles:
In theory, inclination is zero, and declination is approximately 8.6° for all angles of longitude, therefore no corrections are required.

At other latitudes:
Due to the offset of the antenna from the Earth N/S polar axis, the line of sight to the geostationary orbit is shortest at the due South/North satellite (depending on the hemisphere) and longest at the East/West extreme satellites. If simple inclination/declination angles are used, the antenna line of sight should correctly intercept the geostationary orbit at the due South/North satellite but will demonstrate an increasing error towards the East/West extreme satellites.

Inclination/Declination corrections:
(Ignoring variations in the shape of the globe) …
To mitigate the errors at 'other latitudes', a correction factor is applied to inclination and declination. This brings the antenna line of sight closer to the geostationary orbit at all visible angles of longitude regardless of the variation in distance.

I am no mathematical ninja, and after trying (and failing) to visualise the implications of the longer formulae on the website below, I settled on a simplified expression which I translated as:
Δ = 0.69 sin 2θ
and for Microsoft Excel as:
(0.69*SIN(RADIANS(2*(L))))
where L = the address of the cell containing the local latitude in degrees.

I used this formula and my limited math to build a spreadsheet which uses accepted physical constants plus the local latitude to automatically calculate the variables needed for a polar mount installation which will track the geostationary orbit well.

I'm sure that further refinements are theoretically possible, but mostly impractical due to the mechanical limitations of affordable polar mounts.

The original source of the information is:
www.chishma.ru/antenna/modifis-polyrnaya-anten-podveska.html
Note: It is a Russian website, but the authors acknowledge that the original solution was proposed by an English guy back in the 1970’s.

My spreadsheet looks like this:

Correction factor calculation.gif
 

Manikm909

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i always miss the point when it comes to dish angle.
once you have the motor correct for your arc, dont you just peak signal for a TP on 1w (or your nearest south sat)
i have never had any clue about my dish angles, but they track the arc perfectly.
 

Hyperopia

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I agree with your point of view regarding the peaking at your closest to due South satellite. I think that most folks (myself included) use that method to ‘calibrate’ at the centre of their arc.

I had been a motorised sat user for quite a while before I read about modified inclination and declination, and initially, I couldn’t see the point. My inclination was set at 90° minus local latitude, and I just watched the signal strength and quality as I adjusted declination on Thor until it peaked – Job done! … Or almost done, it seems. Sure – I was tracking the arc quite well and accepting the drop-off near the extremes as attenuation of the signal from passing through a bit more atmosphere and maybe the occasional bit of foliage or ground clutter on the way to my dish. (Life is full of little disappointments).

I use a program called Fusion 360 for designing components to be made on my 3d printer. I played around with the geometric design features, creating the Earth and Clarke belt to scale, then used various cones, disks, and arcs on different planes until I could visualise how errors in tracking were present at the extremes of arc, and how modified inclination/declination could be used to mitigate this.

I included a screenshot of the spreadsheet in my original post so folks could see that I wasn’t using ‘smoke and mirrors’ to reach a solution. If anyone is interested, I can supply the formulas behind all the variables. Those who are just looking to set up a new polar mount from scratch would be interested in fewer items of data.

Simply use the formula and the local latitude to calculate the correction factor, then subtract this from ‘simple inclination’ and finally peak the signal at the due South satellite using the declination adjustment as normal. Happy tracking from there!
 

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The original source of the information is:
www.chishma.ru/antenna/modifis-polyrnaya-anten-podveska.html
Note: It is a Russian website, but the authors acknowledge that the original solution was proposed by an English guy back in the 1970’s.

Ah! I remember that I found that website in the past, and wondered who this "S.J. Burkhill" (google translate) was! Could not find anything about him, on the internet.

I now realize (done much more satellite reading in the meantime), that this must have been Stephen/Steve Birkill. :)


Apart from that: It doesn't matter much which method you use, to calculate the modified motor angles, it seems; as long as you use modified motor angles instead of the traditional ones.
I've never calculated with the 0.69 sin(2*LAT) equation, till now, to see how close that calculation is to e.g. the 0-90 or 0-180 fit approach. Might do that sometime....

Greetz,
A33
 

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Nice explanation. Here is the difference in arc tracking, represented as a graph.

The first graph is for standard (non modified) usals angles. It shows tracking errors of about 0.3 degrees
at the extremes (I am at 4.1East)
nonmod.pngWith the modified usals angles, you get this:
modified.png
Notice how the errors are much (300 times) smaller.
 

a33

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The first graph is for standard (non modified) usals angles. It shows tracking errors of about 0.3 degrees
at the extremes (I am at 4.1East)

What do you mean by azimuth error?
As the motor elevation angle and dish declination offset angle basically concern the inclination/declination of the dish aiming, I don't understand how you bring the azimuth in...

Greetz,
A33
 

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A man after my own heart!

Suitably equipped with a Manchester Screwdriver, the world is your lobster :-rofl2

I micro-align the Azimuth of my Patio Mounted 1.1m by means of a judicious kick with the heel of my boot in the appropriate corner of the paving slab. Saves all that tricky spanner stuff. Elevation micro-alignment is by means of plywood wedges inserted under the relevant corners of the slab!

It's only a hobby, after all - and the results are excellent :)
I too have the "badr @26E"wedge,quite different from the "16E" wedge,much thinner
I even had a Hellas sat one,not in use anymore given the scarcity of its FTA offer
They all work fine.
Wedgeless is for 13&19E (monoblock) of course,and 7w works too,and so do the 1W and 4E for Ukraine
 

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What do you mean by azimuth error?
As the motor elevation angle and dish declination offset angle basically concern the inclination/declination of the dish aiming, I don't understand how you bring the azimuth in...

Greetz,
A33
That is a good question. I had to look up the code to find the answer. My code was written to simulate a badly aligned dish.
This enabled me to understand what is wrong with the setup.

So when your dish is badly aligned then you will find that sometimes you get a stronger signal by driving the dish
to a slightly wrong position.

The elevation error measures the vertical angle between the clark belt and the arc tracked by the dish.
The angle error then measures the angle between the dish axis and the line to the the sattelite, With a poorly aligned
dish, and after optimising usals position to get maximal signal, the satellite is not exactly above or below the position that that the dish points to, so this "angle error" is not measured in a vertical plane. The name on the legend is misleading. It should say "angle error" and not "azimuth error"
 

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I too have the "badr @26E"wedge,quite different from the "16E" wedge,much thinner
I even had a Hellas sat one,not in use anymore given the scarcity of its FTA offer
They all work fine.
Wedgeless is for 13&19E (monoblock) of course,and 7w works too,and so do the 1W and 4E for Ukraine
My last micro-alignment involved a crowbar and a shovel to throw some dirt underneath the ground stand. It got me
alsmost 0.5-1dB extra at the ends of the arc. It is actually relatively easy and the result is surprisingly stable.
 

a33

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That is a good question. I had to look up the code to find the answer. My code was written to simulate a badly aligned dish.
This enabled me to understand what is wrong with the setup.

So when your dish is badly aligned then you will find that sometimes you get a stronger signal by driving the dish
to a slightly wrong position.

The elevation error measures the vertical angle between the clark belt and the arc tracked by the dish.
The angle error then measures the angle between the dish axis and the line to the the sattelite, With a poorly aligned
dish, and after optimising usals position to get maximal signal, the satellite is not exactly above or below the position that that the dish points to, so this "angle error" is not measured in a vertical plane. The name on the legend is misleading. It should say "angle error" and not "azimuth error"


I'm trying to understand your 'angle error'.
You mean that the elevation angle error is the angle perpendicular to the clarke belt, right? And the angle error (which seems to be always a bit greater than the elevation angle error) is the angle error, relative to the satellite you were originally aimed at (so not vertical, but a bit diagonal)?


BTW for the USALS consequence of using modified motor angles, I proposed a method to still use the standard USALS calculation of the receiver here: USALS Notebook
Meaning simply: enter the MODIFIED latitude value as your latitude input value in your receiver.

But it seems that the actual rotation angle for this modified latitude input was not very different from the 'normal' calculated usals rotation angle, as I seem to have tested back then.

Greetz,
A33
 

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A33,
your interpretation of the angle error is correct. The angle error is what would determine the loss in signal after optimizing the signal by turning the dish. The other error is what you would get if just rotating to the official positions.

I am aware of your usals notebook thread. I read it several times a few years ago.
 

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My spreadsheet looks like this:

By the way (I just noticed):

"Declination (corrected) 7.99 degree" in the spreadsheet should of course be 6.63 degree.

Less motor axis inclination (= more motor axis declination) should be compensated with less dish offset declination.

Greetz,
A33
 

Hyperopia

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By the way (I just noticed):

"Declination (corrected) 7.99 degree" in the spreadsheet should of course be 6.63 degree.

Less motor axis inclination (= more motor axis declination) should be compensated with less dish offset declination.

Greetz,
A33
OOPS! - My bad :oops:
You are correct. Declination (corrected) should be 6.63 degrees in the example.
I had re-drawn the spreadsheet to share it on the forum, and I missed my blooper.
Thanks for the heads-up.
 

a33

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Errare humanum est; to err is human.:rolleyes:

I do it frequently, alas; sometimes even when (I thought) I checked (but obviously not good enough).....

As I am a big advocate for the modified angles, I don't want that they give confusion....

Greetz,
A33
 
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