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 equatorial mount.

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 jack-screw.

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 degrees.


Conclusions:

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 angle.


Mel Bartels, January 2015