NavList:
A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding
From: Bill Morris
Date: 2012 Apr 16, 03:27 -0700
Bill B wrote "...the errors along the arc are not a sine--or any
other wave. They come and go at their own pace."
The reasons for errors are complex. If the centre of rotation of the index arm is not at the centre of the rack, there will indeed be a sine error.
The teeth of the rack are cut on a hobbing machine. Simply put, a steel copy of the worm has longitudinal teeth cut in it and is rotated, so that when it is pressed against the proto-rack it tends to make it turn and excavates teeth at the same time. Since the worm , or hob, as it is called would then be dragging the proto-rack, the teeth spacing would not be accurate, so in practice, the hob and the rack are geared together, so that they rotate in the correct relationship to produce the correct tooth count and, if everything is perfect, perfectly even spacing of the teeth. In practice, the teeth are usually excavated to their full depth in one pass.
Everything seldom is perfect. The hob itself may not be perfectly centred on its shaft. The gears in the screw-cutting lathe or grinding machine used to make the thread form on the hob, that connect the lathe spindle with the cutting tool may be imperfectly centred or not have perfectly regular spacing,or there may be errors in the leadscrew bearings. In the hobbing machine, the gears that connect the hob to the rack may have similar imperfections. All these tend to be reflected in the finished rack, producing a very complex picture.
Add to this recipe various imperfections of the worm which are usually reflection of imperfections in the lathe that produced it and it is a minor wonder that makers of the SNO-T and C Plath sextants could regularly produce sextants that are indeed "free from error for practical purposes", which I take to mean errors of less than 12 arcseconds.
I personally would not be reassured to find that a modern sextant had errors in excess of 30 seconds, and 50 or 60 seconds is not acceptable, correction table or not. It reflects badly on the goodness of manufacture and implies worn out machinery, lack of expertise or lack of care. I suspect such sextants are now being produced simply so that the ship manager can say that they do indeed carry a sextant as the regulations demand.
Bill Morris
Pukenui
New Zealand
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