The Nautical Sextant

Recently, there was a wide-ranging discussion on NavList about how accurately it was possible to measure star-star angular distances using a sextant. It took in the physiology of vision, the resolving ability of telescopes and, my contribution, the ability of the sextant to measure the angles with accuracy.

 An inspection certificate that gives the errors of the instrument every fifteen or twenty degrees is of limited use. When one looks at many of them, it is apparent that there is often no obvious pattern to the errors, making it unsafe to interpolate. In addition, they are always given to a whole number of degrees, so in effect they are assessing only dividing and eccentricity errors of the rack, and ignore the micrometer.

 This led me, out of curiosity,  to calibrate a number of micrometer sextants, ancient and modern, at intervals of five minutes over a whole rotation. The results tell us about the micrometer screw or worm, and dividing and eccentricity errors of the micrometer drum. The latter would have to be very gross to have a significant effect on the micrometer reading. For example, if the drum were mounted 0.04 mm eccentric, say by loose fitting on the shaft (and it would be a very noticeably slack fit), a reading would be 0.2 degrees in error on a drum of 40 mm diameter. As the drum is divided into 60 minutes, this would be 1/30^th of a division, a negligible amount. Thus, we may ascribe most of any error to errors in the worm.

 A progressive error in pitch of the worm is when the pitch of the thread is larger or smaller than it should be. It can generally be discounted, given the short length of worm in engagement with what is in effect a very long partial nut, the rack. An error will result if the axis of the worm is parallel, but not coaxial with its bearings and a much greater error if the axis of the worm is not parallel with the axis of its bearings.

 A more difficult error to assess by examination of the micrometer readings is periodic error of the worm thread, in which the pitch varies periodically along the length of the thread at regular intervals over a single rotation. This is generally due to errors in the leadscrew bearings of the lathe that produced it. Combine the various sources of error and it can be very difficult indeed to sort them out, still less to correct them. In general, the best cure for a defective micrometer worm is to replace it!

 With this in mind, I set about calibrating some sextant micrometers. This is a relatively simple matter using an autocollimator. This instrument shines the image of a cross wire onto the index mirror and measures by how much its reflection is deflected on its return to the instrument. A typical instrument gives a readout on a drum with least graduations of 0.2 seconds and has a range of 10 minutes, so three steps are necessary to calibrate a sextant through a whole rotation of the micrometer (recall that a change in 1 degree readout of a sextant represents a rotation of half that amount of the index mirror).

 The first sextant I tested was a 1982 Soviet SNO-T. These superbly constructed instruments seem to be undervalued, though they were quite possibly the best sextants ever produced. The graph of its micrometer error, shown in black below, is well within the 6 seconds allowable by its specification.The next was a forty year-old veteran by Heath Navigational. While not quite in the same class as the SNO-T, the results were nevertheless acceptable. A Tamaya from 1948 was just acceptable except at one point. More surprising was the graph of a much younger Tamaya, apparently in good condition, with errors of up to half a minute. The failure of the graphs to “close” back to zero or indeed for the graphs to be identical over two rotations should not be given too much significance and is accounted for by stick-slip or “stiction” in the bearings and at the worm-rack interface.

 The worst was a 1937 Husun, with large errors that varied wildly. This led me to examine the worm with a stereo microscope and it was apparent that at some time the worm had been dragged across the rack, leaving burrs on the crests of the thread. This in itself is not necessarily a major problem, as threads should engage on the flanks of the rack teeth, not on the tips, and burrs can be carefully filed off. After I had  done this, the errors were still present and on examining the worm with the microscope, I could see it moving slightly out of engagement with the rack at one point as it rotated, suggesting that the worm and its bearing were not in line. There was slight run-out of the drum as well, confirming the impression that at some time the the shaft had been bent and repaired, albeit imperfectly. The solution was to replace the worm and its shaft.

 After seventy years, spares are not of course to be had, so I had to make a new one. To ensure concentricity and correct alignment of the axes of the worm and its bearings, they ideally have to be turned between dead centres. These are 60 degree cones that fit into suitably shaped holes in each end of the work piece. While there are special lathes in which neither centre rotates and the workpiece is rotated about them, nearly the same results can be obtained by turning a centre cone on a piece of steel held in the chuck and driving the workpiece with a “dog” that engages with one of the chuck jaws. This ensures that the centre does not describe a little orbit that would be reflected on the workpiece, if the centre were not absolutely true. The other end is supported on a standard dead centre held in the tailstock of the lathe. The next  photograph shows the idea.

The parallel bits involve straightforward turning and fitting. The opposed 45 degree cones that form the thrust surfaces are easiest formed by using a 90 degree form tool, taking a little off one of the faces until the bearing fits exactly when assembled around it.

The conical screw thread, however, can only be cut using a taper-turning attachment. This is a bar at the back of the lathe set at the required angle and it guides a follower slide that is attached to the cross slide, so that the tool follows the angle of the bar to produce a tapered workpiece. Screw cutting is otherwise as normal except that the tool axis is at right angles to the surface of the cone rather than to the axis of rotation. The top slide is used to put on cut.

 The gears between the rotating headstock spindle and the screw that moves the tool along are selected to produce the correct pitch of thread. For example, if the gear ratio is one to one, a screw of the same pitch as this leadscrew will be produced. If the gearing is three to one, then the cut thread will be one third of the leadscrew’s pitch. The Husun worm is of 18 threads per inch, one provided for by the gearing of most lathes with an imperial lead screw.

As asides, some turners may not know the trick of wrapping a slender part with some lead wire, in this case, multicore solder, in order to reduce the tendency of slender parts to chatter. Another tip is to grind a flat  on the tail centre, prior to aligning the tail stock to turn parallel, so that it is always replaced in the same orientation used during alignment.

The last picture shows the before and after results.

Finally, graphs showing the before and after calibration results:It is not possible to say when variation arises from imperfections in the screw thread itself and when it arises from stick-slip, but I am sure all would agree that the results are much better than before. None of these results, except those for the SNO-T, which are excellent, should be seen as reflecting on a particular make of sextant. The SNO-T had been well used and showed it, as did the Husun. Apart from verdigris on the brass screw heads, the Heath looked near-new. The older Tamaya I suspect had not been used since its importation into the USA after WW II by a returning serviceman, while the younger one had, to judge by the battered state of its case, lived in uncertain times. 

Ideally, when buying a second hand sextant, you should examine it before buying. In the context of this post, first check that the rack and worm are clean and free from dried up oil and dirt. If there is a cover over the worm, ask the seller to remove it for you. Then rotate the micrometer drum slowly by hand over several rotations, while you feel for irregularities in drag. Examine the whole of the worm’s thread closely with a hand lens to look for nicks and flats (to get the best out of a hand lens, you should place your eye against the lens and bring the object into focus by moving the object, not the lens). Then look at the interface between the rack and the worm as you turn it. If you see the thickness of the oil film varying, or worse, see a gap developing and fading, as you rotate the worm through a full rotation, you may take it that the worm is bent on its shaft. Of course, you should check the rack too, as well as the other bits, but that’s for another story.

I don’t make or restore sextants for a living, but the Internet has made it easier to make friends in distant lands, while living in an isolated corner of an isolated country in the South Pacific, so I am sometimes able to help out by making or mending parts, though not for gain. I have no formal engineering qualifications, so think of me as an engineer of last resort before contacting me about  a lame sextant!