A Worm Turns

6 07 2009

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 1/30th 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.Drums 1The 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.

taper attachment

 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.

Conical worm

The last picture shows the before and after results.

New and old worms

Finally, graphs showing the before and after calibration results:Drums 2It 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!

The Case of the Broken Screw

24 05 2009

Many years ago, when I was a student, an emminent, but possibly not-very-gifted surgeon said to me, once he had stopped sweating, “Any fool can get into trouble. It’s getting out of it that counts.” A fellow enthusiast, wishing to do a complete overhaul on his vintage Hezzanith sextant, broke a vital screw when it was only part of the way out. He couldn’t get the rest of it out, nor could he screw it back in, and in this condition, the micrometer of the sextant was useless. He sent me the index arm with attached micrometer mechanism to me from England, together with an A10-A bubble sextant frame with a seized index prism shaft, but that’s another story.

Heath and Co.’s sextants with their Hezzanith Endless Rapid Reader Automatic Clamp differ in several ways from most other micrometer sextants: the rack is cut on the back of the limb rather than on the edge; the worm is swung out of the plane of the limb when the release catch is operated, rather than in the plane of the limb; and the worm shaft runs between two  screws, the 60 degree coned ends of which rest in the same centre holes on which the shaft rested when originally being turned. The screws have to be locked and a locknut is a simple way of doing this, though care has to be taken to check that the setting of the screw is not disturbed by tightening the nut. The chassis on which the worm shaft bearings are mounted, which I have chosen to call the swing arm since noone else seems to have given it a name at all, is also mounted between centres.

Mounting a shaft between centres is a very good way of maintaining concentricity, the centres can be adjusted so that for practical purposes there is no unwanted play (looseness) in the bearings, and they are very cheap to produce. The centres cannot sustain a heavy load at high speed for any length of time, as any turner will bear witness, but in a sextant, parts are always lightly loaded and slow moving. Running centres are hardened. The following picture shows the layout I have just explained in a rear view of the index arm expansion.


The hardening was the undoing of my friend’s sextant, since hardened parts have a tendency to crack, especially if they have sharp internal corners, as do screw threads. There are various ways of dealing with broken screws. If the other end is accessible and can be gripped in some way, it may be possible to back it out, but in this case, only the 60 degree point was projecting. If a hole can be drilled in the broken end, an easyout may be used. This is a tapered hardened tool with a coarse left hand thread that jams in the hole as it is screwed in, left-handed, and with luck then unscrews the offending broken screw; but in this case the screw was only 5/32 inch (3.96 mm) in diameter and anyway, it was hardened. For this reason too, it was not possible to try option 3, which is drill out at tapping size, leaving only the thread to remove with a tap. In desperation, one can trephine out the whole screw. A trephine is sort of tubular drill with cutting teeth on the business end. There are other methods not usually found in the home workshope, like spark erosion.

As I have no small carbide drills, I elected to try to soften the screw prior to drilling it out,  by heating it with a small blow lamp. As I did so, I noticed a bead of solder appearing, more or less at the same time that the local paint disappeared and it dawned on me that the screw was running in a brass bush that had been soldered into the bronze swing arm frame. If I could remove the bush, I could replace it with a new one and choose any size of thread that was close to the original for the cone-ended screw.

I had no idea about the exact form of the bush until I had removed it, so thought it best to remove it undamaged. The bush resisted my initial blandishments so I made up a gripping tool that would spare my blistered finger tips. This sort of tool, seen below, is very good for gripping delicate objects that have to be unscrewed without damaging them, like telescope lenses and threaded parts. It can be made of fine-grained hard wood or soft metal and, as can be seen, for a tool that would be used only once, I wasted no time on precision and finish apart from getting the size of the hole correct.

Bush repair

Back to the blowlamp and within minutes the bush was free. It then took only about twenty minutes to make a new one, identical to the old, except that the central hole was tapped 5/32 x 40 tpi instead of the original 48 tpi. It was the work of moments to solder it into the frame. A few more minutes saw the production of the cone-ended screw. The original had been hardened all through, the source of all the trouble. I hardened only the end and left the rest soft.

I do not, by the way, undertake sextant repairs for gain, but people occasionally send me calls for help and post me bits of their sextants. I do my best to help them, especially if they have bought copies of my restoration manuals or my e-book, The Naked Nautical Sextant.

Worm with wrong thread angle?

5 05 2009

Just lately, I was  pleased with myself at having acquired and restored a rather corroded Heath and Co sextant. The last act was to have been to lubricate the rack, and a good way of distributing the oil to where is is needed is to wind the index arm the full length of the rack. On this occasion, as I did so, I noticed a slight periodic roughness each time the micrometer read around 55 minutes. Sometimes this happens when the worm shaft is slightly bent and the micrometer drum rubs against its index periodically, but in this instance, all was well in that area. I decided to have a very close look at the worm.

In Heath micrometer sextants, the worm shaft rotates between conical and adjustable centres that rest in conical holes in the ends of the shaft. This is a very good way to ensure concentricity of the worm, as the shaft rotates on the same centres that were used to produce it, and it is possible by careful adjustment to eliminate all backlash. To remove the worm shaft together with the micrometer drum, it is necessary to undo the locking nuts and back off both centres, when it is just possible to wiggle the shaft free. If necessary, the micrometer drum can then be removed from the shaft. The next pictures show the removal sequence.



I had already examined the worm using magnifying spectacles, but this time I used a stereo microscope. It was then possible to see fine burrs at one point on the crest of the threads and I became curious about how this had come about. I then noticed that the angle of the thread was unusually sharp and that the crests were not truncated as is usually the case.. It is perhaps just possible to see that the thread angle seems wrong in the next photograph. The lower, stainless steel worm is the original and the upper one is a bronze replacement.


In screws and nuts generally, it is important that the load is borne on the flanks of the threads and not on the crests. This is even more important in leading screws, and the worm and rack of a micrometer sextant is equivalent to a short screw rotating against a small part of the circumference of a very long nut. While the pitch of a thread is important, it is also important that the flank angles of the screw and nut are the same. The following sketch illustrates what happens when they are not.


In the upper half, the thread angles match and the threads are truncated to remove any possibility of their bearing on their crests. In the lower illustration, however, with mis-matched thread angles, the crest of the worm bears on the bottom of the rack and all wear and damage is likely to be concentrated on the crest of the worm.

At first, I thought that at some time in the past, the worm had been damaged. Someone had made a perfectly competent job of producing another one, except that he had made a wrong guess at the thread angle and had left the crest sharp, so that it bore on the bottom of the rack rather than on the flanks of the teeth. Without rather special measuring gear, it is not easy to measure the thread angle, but I made the assumption that in an English sextant made by a conservative maker around 1967, it was probably of Whitworth form, with an included angle of 55 degrees, but the rack angle seems to be about 60 degrees . I used some of my diminishing stock of drawn phosphor bronze bar to make a new shaft and worm with this angle, seen in the pictures above. The micrometer then moved the index arm with a pleasing smoothness and absence of periodic roughness. It will be interesting to re-calibrate the sextant and compare the results with those of the original certificate, which showed no more than 12 seconds of error.

A few days later, I was able to examine another Heath micrometer sextant and discovered that the thread angle of the worm was just as mine had been, unusually sharp. I conclude that Heath delibertely arranged for the crests of the worm to bear on the flanks of the rack teeth.

In the type of release catch used in this brand of sextant, some post-war Kelvin and Hughes sextants and the USSR SNO-T sextant, the worm is swung out of the plane of the rack to disengage it. The majority of sextants swing  the worm shaft and its bearings in the plane of the rack about a hinge on one end of the chassis (swing arm chassis) on which they are mounted. In the former type, it would be pointless to have a worm that was free of backlash unless the swing arm was also free of backlash. The final photograph shows Heath and Co.’s way of mounting it between centres to achieve this.


You can read much more about the fine detail of the nautical sextant in my book The Naked Nautical Sextant and its Intimate Anatomy

Postscript: Together with several other instruments, I calibrated the worm of this sextant on 5th July. You can see the results in the posting “A Worm Turns” (above).