The Earl of Crawford's tracking arm

By Mel Bartels

An equatorially mounted telescope has it easy. The telescope can track the stars with a simple slow constant rotation about the polar axis. This is called "equatorial tracking". An altazimuth mount rooted firmly on the ground is simpler and surer but cannot easily track - after all there's no polar axis. Instead tracking is a complicated affair of ever varying drive rates in both altitude and azimuth.

The Earl of Crawford devised a clever way so that an altazimuth telescope can simulate equatorially tracking. A cord is attached from a point on the polar axis to the end of the telescope's tube. The telescope tube is weighted in the rear to keep the cord tight. As the telescope swings across the sky constrained by the cord, it describes an equatorial tracking arc.

Here we see an altazimuthly mounted telescope with the Earl of Crawford's tracking cord attached. The telescope is pointing at the celestial meridian (aimed southward, if in the northern hemisphere, aimed northward if in the southern hemisphere). The bottom of the tracking cord is attached to a point along the polar axis. Because the polar axis makes an angle of 45 degrees with respect to the horizon, the scope must be situated at a latitude of 45 degrees on Earth.

Now let's swing the telescope across the sky, keeping the cord tight. The telescope will simulate an equatorial tracking arc across the sky.

Ideally, the cord is attached to a point on the telescope's optical axis since it is this optical axis that ought to track equatorially. Attaching to the side of the tube causes tracking errors. That's because the optical axis is not coincident to the axis defined by the arm's attachment point to the telescope tube and the intersection of the three axes: the polar axis, the azimuth axis and the altitude axis.

The arc that the Crawford arm swings through is not the same arc that the telescope's optical axis swings through. The 'Crawford' arc can be calculated by lowering the telescope's altitude reading by the angle the attachment point to the telescope's tube makes with the intersection of the three axes.

The following graphic shows the telescope equatorially tracking perfectly for two hours. The arc shows the slow movement of the telescope's optical axis across the sky. Check out how the optical axis is perfectly aligned with the end of the tracking arc.

Now let's check out where the telescope is pointed after two hours of simulated equatorial tracking motion by the Earl of Crawford arm. You can see an error in the tracking motion. In this case it is a substantial six degrees. That means that an object will drift out of the field of view in 10-20 minutes.

You can see this for yourself by performing this simple experiment. Attach a small telescope to the side of a Dobsonian telescope at some crazy angle, so that it is not pointed in the same direction as the Dobsonian. Point the Dobsonian on a bright star and note the field in the small auxiliary telescope. Wait a dozen minutes and re-aim the Dobsonian. Inspect the field of view through the eyepiece of the auxiliary telescope; you'll see that the field has drifted. That's the Crawford arm tracking error.

In the case of a telescope pointed at the celestial meridian, the change in altitude is minimal. If the Crawford's arm tracking speed is adjusted, the tracking error can be significantly reduced. In the image above, the Crawford arm can be moved further along, reducing the error to about a degree.

The Crawford arm was used on Lord Rosse's 72 inch Leviathan, perhaps taking advantage of the minimal altitude change.

This is why a Crawford arm for an equatorial table will only work when the arm is tied to the telescope's optical axis.

What to do? The essential problem is field rotation: the tube does not rotate to match the sky's twisting motion. If the tube cannot rotate, then perhaps the arm can.

If the arm is attached to a slippery rotating ring and pulled tight, then perfect tracking is restored.

Another answer is to elevate the tube such that a line parallel to the rod's attachment point to the telescope tube goes through the center of rotation of both the azimuth and altitude axes. The tube's off-center location will cause it to pull against the rod as it is swung upward.

Yet another answer is to attach the arm to the optical axis that emerges from the back of the telescope tube. By adding a Declination clamp, we venture into the territory of the Morse Transformer, a wonderful analog equatorial to altazimuth calculator invented in the 1930's.

As I showed with the Morse Transformer, another possibility is to clone the telescope's altazimuth axes, moving them to the side of the telescope. Then a Crawford arm can be attached directly to the cloned optical axis that intersects the cloned polar axis. You can see that the tracking mechanism moves with the rocker box but the polar axis that intersects altitude axis and the cloned azimuth axis stays aligned with the sky.

Google Sketchups: the Earl of Crawford arm study; the Morse Equatorial Transformer

References

Three Crawford armed telescopes
Amateur Astronomer's Handbook by Sidgwick: a description
Old and New Astronomy by Proctor: note that this scope's tracking is perfect because the tube is offset
Maurice Gavin's Crawford modification
Crawford's 15" refractor