I am interested in understanding the math, concepts, and theory behind
the motorized devices used to track/aim the 18-30 inch satellites
dishes at geosyncronous satellites located in the Clarke Belt.  The
primary objective is to accurately track the proper arc.

An example of this type of device can be found at:
http://www.microyal.com/home9.html.

An illustration can be found at: http://www.microyal.com/h2h-install.html.

Of paticular interest is the reason for the 30 degree angle that is
formed between the true axis of output shaft rotation and the dish
mounting shaft.  Simply stated:  Why is the motor shaft bent at a 30
degree angle?

Please note that a single motor is used to properly set both the
azimuth and elevation of the dish.

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Clarification of Question by jtl-ga on 13 Jan 2005 17:01 PST

Hi Denco-ga

When I first encountered this problem, I also thought the the 30
degree shaft offset angle was related to optimizing the tracking arc. 
However, after Googling for awhile (Search on: hh motor fta) and
looking at the different motors, I found that different
manufacturers/models use different angles and sell their products
world wide.   Also, there is no specification as to where the dish is
mounted on the bent/angled part of the shaft with respect to the end
of the shaft.  Therefore, I suspect there is another reason for the
angle.

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Request for Question Clarification by denco-ga on 13 Jan 2005 18:56 PST

Howdy jtl-ga,

It could be for physical clearance issues, but even after looking at a few
more motors, I still think it is an attempt to optimize tracking.  As there
are cost and engineering issues with placing a bend in the shaft, I could
see why the angles would vary.

Some companies might be shooting for 35 degrees, etc. so as to "mainstream"
the track, hence the angle variances. Also, as people in the U.S. are probably
the main players in the FTA (Free To Air) market, that could explain the lack
of "other country" variances.

The amount of variance in arc by moving the dish from closer to further out
the shaft would be negligible.  As some of the motors out there have straight
shafts, possibly out of cost cutting, some manufacturers might not think it
is all that critical to do any angle at all.  This could be because they don't
think the average user has a clear enough view to use the entire arc anyway.

The fact that any reasonable angle would indeed provide a better track, and
as I can't find any other reasonable explanation for the extra effort as well
as cost for the angle, I still think this (tracking) is the logical answer.

I could be wrong though.  It might be for torque issues of moving a straight
shaft with a weight on the end versus rotating an angled shaft with a weight
on the end.  It might be that one could use a less powerful motor if an angled
shaft is used.  I don't think that is the case because of the relatively light
load of the small dishes.

Looking Forward, denco-ga - Google Answers Researcher

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Clarification of Question by jtl-ga on 13 Jan 2005 20:01 PST

Denco-ga:

A polar mount where the axis of rotation is aligned parallel to the
earth's axis of rotation is an integral part of the design and
alignment of the dish positioners.

All of the motors are installed and aligned to true south/north and
the elevation is initially set to the site's latitude.  A declination
angle is applied to the dish which tilts it down a few degrees to
focus on the Clarke belt.  This setup does not produce a perfect
track, therefore the axis of rotation is adjusted slightly from the
latitude value and the declination of the dish readjusted to
compensate for the change in the axis of rotation tilt.  This slight
change is called a modified polar mount and produces an arc that is
much closer to tracking the Clarke Belt from horizon to horizon.

Many of the sat. dishes that are used with these motors are designed
to be mounted on a fixed plumb mast.  The declination adjustment of
many of the dishes is some what limited.  I am beginning to think that
the bend is to restore the mounting shaft to a more vertical angle
from the latitude angle of a straight shaft so the dish mount will
have enough range to focus on the high point of the arc which would be
at true south.

Howdy jtl-ga,

I will post this as a comment as I have not found a web page that explicitly
states the reason.  By placing the shaft at an angle the dish will go through
a skewed or angled arc, presumably to better track the horizon, and thus the
satellites lined up in orbit above that horizon.  If it weren't at an angle
it would point at a straight lined type of arc in the the sky.  The 30 degree
angle comes from that being almost the lowest angle of declination in the U.S.
As you probably know from experience, you then adjust the satellite dish to
point at an angle that deviates from the 30 degree start point.

Yes, the furthest southern points of the U.S., such as in Texas and Florida,
have less than 30 degrees declination, but since more than 99% of the U.S.
population are north of 30 degrees, this has become the default point to work
from when pointing satellite dishes.

Now, the skewed arc introduced by the 30 degree bend in the shaft will not
allow the dish to track the horizon arc perfectly, especially anywhere that
is not on the 30 degree declination, but it is better than not trying to
track it all.

If this answers your question, please tell me and I will repost it as such.

Looking Forward, denco-ga - Google Answers Researcher

When I did my C-band dish many years ago (in the USA), there were 2
angles to contend with. The main axis must be parallel with the
Earth's rotational axis and is exactly your latitude. The other offset
"lowers the view" to the Clarke Belt. Without it, you would trace an
arc above the CB equivalent to your direct height above the equatorial
plane.

JTL--

Your last Clarification of Question makes a lot of sense.  Setting the
angle of elevation equal to the latitude makes the dish rotate about
an axis parallel to the earth's axis.  The declination angle (0-4
degrees, depending on your latitude) aims the dish at the clarke belt
when it's pointing straight south.  But unless you're at the north
pole, in which case you can't see the clarke belt anyway, the dish
will deviate from the clarke belt when it is rotated.  Here is an
analogy: imagine standing on a basketball court directly under the
basket.  If you turn in place (rotate about a vertical axis), that is
analogous to a dish with elevation set equal to latitude (that is, one
that rotates about an axis parallel to the earth's axis).  Now tilt
your head down a few degrees so that you're looking at the 3-point
line, drawn on the floor 20 feet away or so.  As you turn in place,
without changing the angle your head is tilted, your eyes follow the
3-point line, because it is a circular arc with its center right under
the basket.  This would be the situation for a satellite dish at the
north pole (except that, again, the clarke belt would be below the
horizon).  Now take a step or two out into the key (toward the basket
at the other end of the court).  Since you are no longer at the center
of the circle defined by the three point line (some places on the
3-point line [like the top of the key--middle of the court] are closer
than others [near the baseline]), if you once again aim your eyes at
the 3-point line, as you turn in place, your eyes will not stay
pointed at the line.   This is analogous to a dish which is not at the
north pole.  You can improve the way your eyes track the line if
instead of rotating about a vertical axis, you rotate about a slightly
tilted axis.  Lean your body forward (toward the basket at the far end
of the court).  As you rotate about this tilted axis, your eyes follow
the 3-point line much more closely.  When you're looking straight
south (toward the far basket) the tilt makes you look downward at a
steeper angle than you would otherwise, so you're looking at a point
on the floor closer to yourself.  As you rotate, the downward angle of
your eyes decreases, making you look at points on the floor farther
from yourself.  That is why it helps to angle the axis of rotation of
the dish slightly away from the north pole (use an elevation slightly
larger than your latitude).  Of course you have to reduce the
declination (the downward tilt of your head in the analog) to
compensate.

As for why the shaft is bent, I don't know.  As far as tracking goes,
it makes exactly no difference.  Bending the shaft just changes the
declination angle, which is adjustable anyway.  My best guess is that
bending the shaft moves the center of mass of the dish closer to the
axis of rotation, so that gravity doesn't put a torque about the axis,
and the motor doesn't have to work as hard to turn the dish.

Interesting question.