Tilted Equatorial Table by Mel Bartels
An equatorial table is a specially designed platform that allows any
telescope sitting on it to follow the stars, just like a traditional
The suggestion has been made over the years that tilting a table screws
will also work. Richard Berry suggested this soon after the Poncet
Platform was invented. There are two versions, the hexpod and the
We know that the hexpod works because the table can be made to rotate
as well as tip in two axis, equivalent to a three axis mounting. Any
three axis mount can simulate equatorial tracking motion with no field
rotation. Jeff Kingsley proposed a hexpod mount for a radio telescope. A hexpod 1.5 meter (60 inch) Ritchey-Chretien was built in 1999 for the Bochum - UNC observatory in Chile.
But what about a table that sits on three jack screws, not the six
extending arms of a hexpod? The Oregon Scope Werks group decided to
investigate this possibility. Here is my analysis and results.
Let's start by taking a platform and rotate it about a polar axis,
aimed upward at 45 degrees (equivalent to an equatorial mount placed at
a latitude of 45 degrees on Earth) simulating motion
required for tracking. Jerry Oltion and I did this with cardboard and
chopsticks (images by his wife, Kathy). (I recommend working through
the problem with a buddy - the visualizations are non-trivial). The
chopstick held in my hand (and hidden from the camera) on the right hand side
in the images represent the polar axis. The chopstick that points out
and away represents a telescope pointing south on the meridian. Jerry
on the left is working to tilt a tracking platform to match the
equatorial tracking table that I'm operating on the right.
The first image shows that the platforms are level with each other and
that the telescopes on both platforms point to the same position in the
sky. The second image shows one hour worth of tracking. Note that Jerry
has had to tip his platform a fair amount so that both telescopes are
pointed in the same direction. The final image shows the tilt table
after two hours of tracking. Jerry has had to tip the platform a good
deal to maintain the same telescope pointing angle.
Let'salso model this in Sketchup.
Here's an equatorial platform showing one hour tracking at latitude of
45 degrees. The scope is aimed to the south-east, about 25 degrees up
and 25 degrees over.
Next let's align the platforms at a common point for convenience's sake and add three tip-tilt points underneath.
Now let's align the two telescopes to point in the same direction using
only the three tilts afforded us. Oops, the lines representing pointing
to the pole no longer are coincident. That means that the tilt
movements must vary depending on telescope pointing
angle at the start of tracking.
A closeup shows that significant field rotation (25.8 degrees) has occurred during the one hour of tracking.
Let's see how much each tip point traversed for the one hour of
tracking. The three tips changed 14.7 degrees, -3 degrees and -11.8
1. A Tilted Equatorial Table can track.
2. The tilts required are significant.
3. Field rotation is significant.
4. Different amounts of tilt will be required depending on telescope pointing direction.
5. Therefore the tip rates will vary as the platform tracks across the sky.
Any platform that tips on an axis
different than the polar axis and that cannot rotate will encounter
field rotation, varying speeds of tilt and different amounts of needed tip
depending on telescope pointing direction.
Since the hexapod can rotate as well as tip, it can negate field
rotation. Since field rotation is constrained, the initial telescope
pointing direction no longer matters. The same changes in the hexpod
leg lengths can be used over and over again, just like an equatorial
table is reset to track again, regardless of initial telescope pointing
Mel Bartels, January 2015