This was intended as an extension of the work in p/001/10, in which I showed that it is possible to reconstruct LY and RY results by suitable manipulation of radial-arm inclinometry. I had intended simply to apply the same analysis to more up to date datasets. However, during this work I discovered an error in the previous paper which has some implications for that paper as well as for p/001/14.

Data and tools

I used the radial-arm inclinometry from 16 may 1998, and a standard inclinometry set from 15 May 1998. I made extensive use of Excel and in particular the "solver" which I used to numerically optimise fits between observed and generated data.

Error in previous paper

The May 98 radial arm inclinometry was more clearly labeled than that for July 1997 and in looking through it I discovered that my assumption in the previous paper that the July data referred to a wheel 3 run was wrong. In fact the July 1997 data is wheel 2 inclinometry and the data channel I used was not the flexure of the arm, but its rotation. Now in principal the rotation of the arm that leads to wheel 2 will be related to the movements of wheel 1 and 3, but the fact that I was able to make as much progress as I did is remarkable. I think that this explains one puzzle from the previous paper. It was noted that an optimised fit between the radial-arm data for each wheel and, for example, the left-hand A-frame found that not only wheels 3 and 4, but also some component from the other two wheels, was involved. This is because the data I was using was in fact a convolved data set involving movements of both wheels 1 and 3, and not "pure" wheel 3 movements (the alert reader will recall that I had suspicion that something of this sort was going on but was unable to pin it down). Figure 5 shows the track profile used in this paper and the profile used in the previous paper, together with the Lieca survey results (see also p/001/13). I manually fitted the inclinometry data to the Leica data to arrive at a conversion factor of 0.015 mm/arcsec (the line marked "fitted" on the figure). This is important because it allows us to go from inclinometry (in arcsec) to actual track profile (in microns).

Generation of LY and RY from radial results

I used exactly the same methods as before (see p/001/10) taking account of the fact that this was a wheel 2 dataset and using only the four-variable model. The fits are slightly better than for the previous data sets, and the cross-coupling that was evident before has gone. The fitted parameters are as given in the table below, and are shown in figures 1, 2 and 3. I also refitted the data from the previous paper making allowance for the new interpretation; the previous results and the revised results for the four-parameter model are given in the table.
 

Diametrically-opposed track features.

 We now have a new, even more believable, idea of the true shape of the track. Since the track shape was a key element of the paper 001/14 (written before this one) I ran the new data through the same process as was used in that paper. In that paper it is shown that the form of the spikes in difference datasets for either A-frame is in direct proportion to the extent to which the front wheel of that A-frame and the rear wheel of the opposite A-frame both encounter track features at the same time. The new results are shown in figure 4. The same peaks are present as had featured in paper 001/14, but there are now deeper features as well. Recent work on studying dataset differences has (I think) shown features of that kind in a few cases but this should be checked.

Conclusions

A mistake in the work reported in paper p/001/10 lead me to use the member rotation data from a wheel 2 radial-arm inclinometry run in mistake for the true tilt data from a wheel 3 run. This is what lead to the apparent cross-coupling between results from the left-hand and right-hand sides. Now that this error has been fixed for a later dataset, the results are slightly better in terms of fit and the cross-coupling is no longer present in such a great degree. Furthermore, the conclusion which had been reached in p/001/14 also remains valid - the variation between datasets in particular places on the track in is direct proportion to the extent to which the relevant wheel pair both see large track features simultaneously at that azimuth. Indeed - subject to verification - the result may be even truer now than before. Note also that the two plots - for 1+3 and for 2+4 - are simply azimuth-shifted versions of each other. This is inevitable from the way they are generated.

The cross-coupling effects are worth re-iterating. What now seems to be the case is that the profiles from any single inclinometry run can be explained largely in terms of the wheel/track interactions for the relevant A-frame. The left-hand A frame sees track features encountered by wheels 3 and 4, the right hand sees 1 and 2. But when looking at differences between datasets, they seem to be governed by diametrically opposed pairs of wheels - wheels 2 and 4 for the left, wheels 1 and 3 for the right.

 
Figures follow: