Lately on NavList there has been much written about accurate determination of index error, some of it relating to the instruments used and some relating to the observers’ physiology. Recently, Richard Pisko mentioned the subject of backlash, in the context of surveying instruments and I see there was quite extensive (though not always well-informed) discussion of this on the list in 2005. Not for the time being having any new sextants to pull apart, I have devoted a little time to considering aspects of accuracy of a few micrometer sextants of various ages. All are second hand but in good condition and have been completely overhauled.
I did a prelimary determination that each sextant could be reset to a given reading within the precision with which I can read the testing instrument, by taking a series of thirty readings, each time resetting the sextant to the initial reading, from the same direction, to avoid backlash. Give or take a second or two, all met this criterion.
Backlash or lost motion
Backlash due to lost axial motion in the micrometer mechanism was dealt with in three ways by different manufacturer.
C Plath seems to have got things correct from the beginning (in about 1909). Manufacturers, like W Ludolph, Tamaya and Astra who imitated his design principle did well to do so. In this design, a small leaf spring (labelled”pre-load spring” in Figure 1) bears on one end of the worm shaft to hold a shoulder on the shaft against some sort of thrust bearing, and axial clearance is automatically taken up.
Heath and Co, with their Patent Automatic Clamp arranged for the micrometer shaft to be held between two adjustable, hardened, conical centres (Figure 2). In principal, careful adjustment could remove for practical purposes all backlash while still allowing the shaft to rotate. It also allows for wear to be taken up if necessary. In theory, differential expansion of the shaft and the frame in which it is held might lead to end play developing.
The third group, which includes Freibergers, SNO-Ts and pre-WWII Husuns, attempted to eliminate backlash by careful construction at the manufacturing stage and made no provision for user or automatic adjustment for wear, though one would not expect much wear in slow moving surfaces.
In the Freiberger, the worm shaft runs in plain parallel bearings. A 1 mm-thick bronze washer, shown in Figures 3 and 4), separates two thrust surfaces at one end of the shaft and if wear develops the solution is to fit a thicker washer. “Thicker” means an increase as little as 2 or 3 thousandths of a millimetre. Six arc seconds was considered the maximum acceptable amount of backlash in its first cousin, the SNO-T.
Husun fitted two opposed conical surfaces on the shaft to matching surfaces in a split bearing. Careful fitting here could again remove backlash for practical purposes and if play did develop, then it could be taken up by closing up the bearing.
The micrometer mechanism is mounted on a frame to allow the worm to swing out of engagement with the rack. I have chosen to call it the “swing arm chassis” (Figure 1), since noone else seems to have given it a name . The swing arm chassis rotates around a bearing (Figure 1) that is attached to the expanded lower end of the index arm. Here, it is radial, rather than axial, play that can contribute to backlash.
In the original C Plath, this bearing was a tapered one, similar to the index arm bearing, with provision to reduce clearances by closing up the bearing, but by the second half of the twentieth century, most manufacturers that adopted Plath’s pattern settled for well-fitting plain parallel bearings without provision for adjustment. Provided that it was well made in the first place, this seems to have been satisfactory and little wear was to be expected.
Heath and later Kelvin and Hughes sextants mounted the swing arm chassis between adjustable centres (one of which is labelled “cone-pointed screw” in Figure 2).
Freibergers are altogether more complex. The bearings which carry the worm shaft rotate in a bearing machined in the casting carried on the end of the index arm. This bearing is eccentric, so that as it rotates against spring pressure in the indeex arm casting, the worm swings out of engagement with the rack. Axial backlash of this bearing can be taken up by tightening a nut which has a radial locking screw.
All micrometer sextants take up lost motion between the worm and the rack by spring loading the contact between the two in various ways, so that the only clearance between the two is occupied by the lubricating oil film. The spring is labelled “swing arm spring” in Figure 1 and a leaf spring lies between the swing arm and the index arm in Figure 2. Backlash here in a well made, undamaged sextant can arise if the oil is too thick, so that the thickness of the oil film varies with loading, or if it is too thin or absent, when “stick-slip” occurs to give irregular readings. Damage to the teeth of the rack or to the thread of the worm, while a cause of irregular movement and readings, should not in itself cause backlash, as contact is maintained by the spring loading. Rise or fall of the lower end of the index arm from the face of the limb with change in direction of rotation of the micrometer could in theory give rise to backlash, but in practice the keepers that hold the index arm close to the limb are usuallyadequate for their task.
Finally, incorrect adjustment or wear in the index arm bearing can cause backlash. Most bearings are tapered ones with provision to adjust the clearance by moving the conical bearing surfaces axially against each other by means of a slender screw. If too slack, there is lost movement and if too tight, stick-slip, sometimes called “stiction”.
This is perhaps a good place to warn inveterate fiddlers about overtightening the screw. The washer beneath the head of the screw usually has a square hole in it that fits on to a square on the shaft, or there is some other means of preventing the washer from rotating on the shaft. This ensures that as the shaft rotates, no rotational forces get transmitted to the screw head. The purpose of the screw is simply to move the shaft axially until there is a little drag indicating that clearance has been taken up. The screw may feel quite slack at this point. If you “firm it up” as one does with most screws, you may introduce stick-slip or, worse, twist its head off. Freiberger, SNO-T and some later C Plath sextants used well-fitting plain parallel index arm bearings that have no provision for adjustment.
To measure backlash I used an autocollimator to project a light beam on to the index mirror of the sextant and to measure the deviation of the reflected beam after changing the micrometer reading (next photo). The least graduation of the autocollimator is 0.2 arc seconds, and people who used this particular type frequently were in ideal circumstances able to achieve an accuracy approaching 0.3 arcseconds. I find I can get reproducible readings to within 2 or 3 seconds.
To measure backlash, I approached a zero micrometer reading alternately increasing or decreasing the reading to zero, and noted the differences between the two readings. I took the mean of ten pairs and calculated the standard deviation (SD). The latter is an estimate of the dispersion of the results around the mean. 1.96 SDs each side of the mean includes 95 percent of the data and a small SD implies that the results are tightly clustered about the mean (thirty readings might have been better, but there are limits to everyone’s patience…).
b) Worm errors
These are often neglected and much attention given to calibration charts that says there is no error over the whole range of the sextant at 15 degree intervals, or that the instrument is “free from error for practical use”, generally meaning that the maximum error at these points does not exceed 6 or 12 seconds. But of course, this tells us nothing of the points between, nor of the errors within each degree
I used the same autocollimator set-up to estimate errors of the micrometer worm, by using the autocollimator to measure the error for each 5 minute step around a full rotation of the micrometer drum. Most people will be surprised at the size of some of these errors. It may be that the second-hand sextants that I used had been damaged, but I chose ones from my collection that I had carefully examined for damage during the course of their restoration or overhaul.
Tamaya 1977 Mean 0.9” SD 1.1
SNO-M 1966 Mean 1” SD 0.8
Mk II (Ajax Engineering) Mean 1” SD 0.8
Freiberger trommelsextant Mean 6” SD 0.7
Ditto, after adjustment Mean 2” SD 2
Hughes and Son 1938 Mean 6″ SD 2.5
Heath Navigational 1977 Mean 1’ 15” SD 2.3
The first three sextants all have leaf springs that oppose axial movements of the worm shaft, following the principle established by C Plath’s original design. It is easy to see how effective the method is in removing backlash, and the usual admonishment to always make a measurement turning the drum in the same direction can probably be ignored for this type of instrument.
The Freiberger trommelsextant had backlash within its design parameters (assuming they were the same as for the SNO-T). However, I made up a washer a little thicker than 1 mm (1.01 mm) and then hand lapped it to reduce it in thickness until the shaft just turned with a trace of drag. By then it was 0.99 mm thick and non-engineers may be surprised to know that the shaft would not turn at all when it was only 0.02 mm (less than a thousandth of an inch) thicker. The reduction in backlash was obvious.
I could by no means reduce the backlash of the Heath sextant to less than 75”. The reason for it quite mystifies me and it may be something to do with the way the worm is skewed across the rack in this design of sextant. Making a new worm reduced the maximum worm error somewhat and certainly reduced the individual errors around the circumference. Truly, the heyday of British sextant making had long passed when this instrument was made.
b) Worm error
Many people, I am sure, will be surprised at the size of some of the errors at first glance at the graphs. Bear in mind that the worst are those that deviate most from a horizontal straight line as, over a full rotation, there are always exactly 360 degrees in a circle and the errors have to sum to zero (in practice there is nearly always a deficit of plus or minus a handful of seconds).
On this basis, the SNO-T, a 1938 Husun with a new worm, a 1938 Husun with the original worm, an Ajax Engineering US Navy MkII and a Freiberger all perform well, but before deciding that the Tamaya, Heath and SNO-M don’t cut the mustard, consider that they were second-hand instruments and that 10 seconds at the periphery of a radius of 150 mm represents a movement of about 4 thousandths of a millimetre. Invisible particles of dust and fibres and invisible nicks can thus easily lead to variations of this amount. Perhaps the moral of this story is to be careful not to drag the worm across the rack, to keep it well brushed and to oil it regularly.