Summary

In this paper I look at time histories for "asymmetry" and height of "spikes", set against central bearing adjustments.

Datasets used

For the asymmetry I took the data "Lydata.dat" from /home/imc/pointing/progs/.

For spike data I used the "justin2.exe" program, modified to retain result files, in its "single azimuth" mode. This program goes through every valid dataset, subtracts a baseline dataset, and gives the differences. In single azimuth mode the result is a time history for a given azimuth. The baseline dataset was 990107. I took plots for azimuths at which I expected spikes to appear both on the basis of the theory expounded in p/001/21 and p/001/19, and on the basis of observation of the output of "justin2.exe" running in "movie" mode. Figure 1 is a plot showing the expected form of the spikes in LY and RY, and the azimuths at which I took histories. Figure 2 shows selected difference plots (selected for large LY and RY spikes), also with the selected azimuths. This method of deriving "spike heights" is not perfect in terms of the spike heights it produces. Each data set has had a mean removed which will vary according to how many spikes are present, and there are also underlying non-spike features visible in the difference plots which are not accounted for by this simple method.

General observations

Results for the spike heights, with the asymmetry superposed, are shown in figure 3. (reddish colours for spikes in LY, bluish for RY). The overall form of the asymmetry plot has been discussed elsewhere. It seems to be related to the central bearing adjustments as predicted by the theory, with variations which the theory says are caused by temperature effects when the rollers are too lightly loaded. Overall, the spike plots show the same general form which is encouraging - see below for correlations.

If the spikes behaved exactly as predicted by the theory, and if they were properly captured by the data reduction techniques, then they should have a constant relative size for each inclinometer. In other words, the result for spike "A" should always be the same distance above the result for spike "B". This is not the case (see figures), although the results tend to at least rank in the same sequence largest to smallest for each side. There would probably be more to be learned from the form of the plots in figure 3, but I suspect that in order for anything of value to be gained one would have to think up a better way of extracting accurate "spike" heights from the difference plots.

Asymmetry vs spikes

If all four wheels were in firm contact with the track at all times, then the left-hand A-frame should give the same results as the right-hand A frame 180 degrees away, and with the sign reversed. But if only the back wheels were in contact then there is no reason to expect any such similarity - because when the left-hand A frame gets to where the right-hand A frame was, its FRONT wheel is where the other's BACK wheel was.

Therefore any tendency for the front wheels to lift will lead to a so-called "asymmetry". The wheel lifting will also lead to spikes, and so we would expect the two to be correlated. I would not expect a linear correlation; the degree of asymmetry essentially measures the area of track features whereas the spikes measure only their heights.

To explore the correlation a little further, the results were sorted by the size of the asymmetry and correlations plotted in figures 4 and 5. The benefit of asymmetry as a measure of "goodness" of the data is that it does not introduce a baseline dataset with the attendant uncertainty as to its quality. On the basis of the results shown here, I would recommend that we continue to use asymmetry as a simple measure of how well the wheels are following the track.
 

Conclusion

I conclude, unsurprisingly, that the asymmetry measure is a good figure of merit for how "spikey" an individual dataset is. Further information may be gleaned by figuring out a better way to extract heights of actual spikes - but it is not clear if it would be worth the effort.

Figures follow