We currently use only a CW track model to correct the pointing of JCMT for the irregularities of the antenna track, although the profile varies dynamically with the direction of motion of the antenna. Occasional measures are made with the antenna moving CCW, and the CW-CCW difference has remained stable over the years -- being essentially zero in the model terms known as F2 & F3 (roll & pitch), but reaching 3" in F1, yaw. This is big enough to warrant removal from the pointing error budget and means that, for the moment, sources in the red areas of the sky in the diagram below are subject to additional pointing errors due to the use of an inappropriate track model.

Ideally the TCS (telescope control system) would be able to toggle between CW and CCW models as the sense of antenna rotation changes. The issue discussed in this document applies in the less ideal case where the TCS is toggled between CW and CCW models based on the declination of the source being tracked or on its current azimuth.

If JCMT was on the equator, a hybrid track model could be created from separate CW and CCW models by switching between one and the other at azimuths 90 and 270 - i.e. using the CCW model between azimuths 0 & 90, CW between 90 & 270, and CCW between 270 and 450. This would be a toggle by declination. At our slightly northern latitude, of ~20degrees, sources that transit in the south -- even those that rise somewhat north of east -- always traverse the sky CW. However, some northern sources spend some time traversing the sky CW before becoming azimuthally stationary and then transitting CCW. A toggle based only on source declination would generate pointing errors for the area of sky (in the 1^st quadrant) shown in green in the diagram above.

Another alternative would be to toggle at some specified azimuth. But consider the illustration below, involving a hybrid model with the switch at azimuth 40 (and 320 in the west), and a star with declination = 50. Its motion may be divided into 4 sections :

• A : it rises at azimuth 35 (approx) and moves CW. This is within the CCW regime of the hybrid model - bad = red !
• B : after azimuth 40 it continues CW to azimuth 43 - good = green !
• C : at azimuth 43 it reaches azimuthal stationarity at point S, and, whilst still in the CW regime, moves CCW again - bad !
• D : it crosses back over azimuth 40 heading CCW in the CCW regime - good !

For all declinations north of our observatory, the sky then divides into 'red' and 'green' areas as shown below (in this case for a switch azimuth of 45 degrees) :

If we are limited to one track model in the current form of a lookup table organized solely in azimuth, the switch could be chosen either to

• minimize the area of the sky in which the wrong sense of model is used, or to
• minimize the time spent by objects in that space,

The following sequence of red-green diagrams shows the variation of the red and green areas as the switch takes values of 30, 40, 50, 60, 70 and 80 degrees :

The problem can be made more practical by limiting the calculations to elevations above, say, 20 or 30 degrees and below 85 degrees. Computations then show that the time spent in the red areas is a minimum, 12.1% and 7.4%, when the switch is set at 66 or 71 degrees, respectively.

This still gives equal weight to points at low and high elevations. If the weight at each point is made proportional to the noise levels applicable at those elevations, eg,

then the following results apply :

The above assumes an equal distribution of targets in declination. The diagram below shows the distribution of the elevations of the sources to be observed during semesters 98a and 98b :

and while there is a general decline in source numbers towards higher declinations, the occurrence this year of a cluster of targets at declination 52 highlights the danger in permanently adopting a switch that would adversely affect one declination in favour of another.

Conclusions

• Computation shows that a switch between CW and CCW track models at an azimuth of about 74 degrees can minimize the amount of time (weighted by the astronomical usefulness of that time) spent in regions of (az,el) space where the source motion and the sense of a hybrid track model are in disagreement. This is in contrast to the current situation where all counter-clockwise antenna motions are in such disagreement.

• This still leaves an unaesthetic sliver of 'red' (see the diagrams above) high in the ENE (and WNW on the other side). This sliver may seem important enough to warrant its green-ing, by setting the switch value to 90 degrees and tolerating a larger red area further down at the same azimuth. The (weighted) amount of 'red' sky would then be 9.7% rather than the optimal 7.0%.