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Re: An "alternative" sextant?
From: George Huxtable
Date: 2008 Dec 20, 16:35 -0000
From: George Huxtable
Date: 2008 Dec 20, 16:35 -0000
Thanks to Scott Owen for taking an interest in my proposal for an "alternative" sextant design. He has made some perceptive comments, but I need to explain the layout more clearly. Then I would like to hear what he has to say next. Drawing is not my forte, as will be clear from the attached sketch, which is intended to show the mirror positions and light paths, nothing more. HM and IM are horizon and index mirrors. There's a view from the observer's left and another from above his head. With this layout, a standard sextant arc would allow measurement only to 60º. If the mechanism was redesigned to allow the platform of the index mirror to be rotated by 180º about the pivot axis, as shown by dotted lines, then viewing the horizon astern would be possible. I will copy my original message, with Scott's interpolations marked between parallel lines, and with my own responses shown between {{ brackets like this}} with the letters G and S to clarify what's from me and what's from Scott. G The following idea may be a bit daft, and if it is I hope Navlist members will identify the snags and point them out. ============================================================ S I'm not sure I can point out any snags but I have some questions and comments, so your patience is requested. ============================================================ G What follows is an alternative way to reassemble the basic components of a sextant in a new geometry, which will give it different characteristics from the standard instrument. It's difficult to illustrate the notion without making a perspective drawing (at which I am hopelessly bad), so instead I'll try to paint a word-picture. ================================================================ S With my feeble brain a flat side view would be very helpful and a perspective view wouldn't necessarily be needed. ================================================================ G {{I will try}} G Start by taking a normal sextant and rebuild it. I'm not asking you to demolish your favourite instrument; just imagine it in your head, which is all I've done, so far. The angling of the index mirror has to change. Instead of its plane being perpendicular to the frame, it's now placed at exactly 45º to the frame, in such a way that incoming light from the observed body is now reflected to travel along the pivot line of the arm. The horizon mirror is shifted and fixed to a bracket that places it so that the pivot line passes through its centre, with a few centimetres spacing between the two mirrors. The horizon mirror, too, is angled by exactly 45º to the plane of the frame (about a vertical axis). In that way light from the observed body, travelling along the pivot line, is reflected into the telescope, which is aligned to point to the horizon as normal, and relocated to centralise the horizon mirror in its view. The horizon mirror is half silvered, as normal, so the observer sees, in the telescope, a direct view of the horizon and superimposed, a view of the celestial object, reflected via both mirrors, just as with a sextant. ================================================================= S The "shifting" of the horizon mirror position and the resulting location of the telescope seems to be the tricky part, at least for me anyway. If I understand this correctly, and I don't think that I do, you want to relocate the horizon mirror to a position a few centimeters "down" and connected to the index arm then relocate shades and move the telescope "back". Is that right? or are you envisioning something like a dual frame with the index arm "inside"? ================================================================= G {{No, not a bit like that. Stick with a perfectly standard sextant frame. Look at the instrument face-on, with its frame vertical. Your eye is placed on the pivot axis, looking horizontally. The index mirror is fixed to the index arm, centred on its pivot axis, bur now twisted through 45º so that it reflects the incoming light towards your eye, along the horizontal line of that pivot axis. Undo the horizon mirror from its normal location and move it bodily up and right, a few centimetres , so that it intercepts your view (along the pivot axis) of the index mirror and it, too, is centred on the pivot axis. Of course, it has to be moved towards your eye a bit, away from the frame, so that the mirrors don't clash, and space is left to insert the index shades between the mirrors, and maybe a bit extra. It's now fixed to the frame there on a new bracket; re-angled so the horizon mirror is now in a vertical plane, but twisted about a vertical axis until its exactly 45º from the plane of the frame. Now light travelling along the pivot axis is reflected by the horizon mirror towards the right, still travelling horizontally. That's where you relocate the telescope, to collect that light, and also, as normal, to have a view of the horizon, alongside or through the horizon glass. So now, the telescope is in the same horizontal plane as the pivot axis: not below it, as before.. When the index is set to zero, so that light from the horizon is seen in both views, all light paths are in a horizontal plane, and light travelling via the index mirror undergoes two 90º bends. to end up pointing in its original direction. If the index arm, with its mirror, could be rotated clockwise through 90º (for which a redesigned arc and frame would be required), then light from a zenith star would be reflected into a horizontal direction. And so on.}} G The essential feature of the Hadley 2-mirror invention is then retained; that after two reflections the image of the observed body will shift about in the view exactly the same as the direct view does, so that motion of the instrument in a seaway will not cause any relative motion between the two views. ============================================ S No problem there you still have two mirrors. ============================================ G At the index-arm position when the two mirrors become exactly parallel, it should be at its zero mark, and the two images of any distant object should coincide, allowing checking of index zero-error as with the usual sextant. =========================================================== S I'm guessing the "zero mark" to be near the 3 or 4 o'clock position, is that right? or is it near the 6 o'clock position? =========================================================== G {{just as with a normal sextant, the direction of the index arm and the arc-zero, when measuring zero, can be placed, together, at any arbitrary direction. For convenience, it's conventional to put the zero starting-point of the scale somewhere near the observer's chin, but it might well be elsewhere.}} G However, there's another "essential" feature of the normal sextant that will no longer apply. Normally, as the angle of the index mirror changes, the deflection of light changes by twice that angle. But that law is only true when all light paths are kept in the same plane. With this alternative instrument, the light paths are in very different planes (except at the zero-check position), such that the deflection of light becomes equal to, not double, the angling of the mirrors. (If anyone can offer disproof, please do so). ============================================================ S This seems correct to me but are the light paths in different planes because you "tilted" the mirrors 45deg or because you've moved the horizon mirror and tilted it 45deg too? Sorry if some of these questions seem rather stupid, but as this experiment intrigues me, the only way for me to fully understand is to ask some stupid questions. ============================================================ G {{Fair enough. It should all suddenly fall into place when the penny drops, because it's quite a simple picture}} G Horizon shades will be placed in the direct view line through the horizon glass, as usual. Index shades will go into the space between the two mirrors. What would be the consequences of the new geometry? Most obvious is the doubling of the angular motion of the arm, that's called for to achieve the same angular range. A standard sextant frame, only 60º wide, would only be able to measure up to 60º of arc, not 120º as with the standard sextant, so this would clearly be insufficient. The arc length would need to be doubled to subtend 120º, or even (for reasons we will see) 180º. That would lead to a large, clumsy instrument, except for the following... ============================================================ S With an arc of 180degs doesn't the index arm get in the way of the telescopic observation as the index arm approaches the horizontal position? ============================================================= G {{I don't see why. If the index arm starts to obscure the outer fringes of incoming light, the index mirror can be spaced away from it, a bit. What I've explained, so far (with the aim of simplifying the picture) is how you could adapt an existing sextant to cope with the different geometry, but that world work only for angles up to 60º. For angles greater than 60º, however, and especially if extending the range to180º, mechanical redesign becomes necessary, and with the arc-radius reduced to (say) 9cm, radical redesign become very possible, indeed rather easy. For example, there could be advantages in having the drum and worm in a fixed position on the frame, and the (semicircular) arc moving with (or replacing) the index arm, rather than vice versa as at present.}} G Because each measured degree now corresponds to a whole degree subtended on the engraved arc, and not half a degree as with the normal sextant, the degree markings, and the teeth of the rack, now become twice as far apart as they were. Or, to put it another way, the same precision as before can now be achieved by halving the radius of the arc. So a standard sextant with a 60º arc and 18cm. radius could be replaced by one of 180º arc and 9 cm radius, which would be no less compact. There would be a few advantages, if only minor ones. Because each mirror always reflects through 90º, there's no shrinkage in the view to a letter-box shape, as you get with a sextant at large angles. That implies you could use the instrument right up to 180º, wall-to-wall between horizons. to measure dip, as long as one proviso has been met. That is, that the sideways displacement between the two sight-lines is enough to allow incoming light from astern to miss the ear of even the most jug-eared navigator. That's why there has to be a certain minimum spacing between the two mirrors. ================================================================== S Won't this "sideways displacement" between the sight lines affect the split horizon mirror and effectively shrink the sight picture "side to side"? ================================================================== G {{No. Or at least, I don't see why it would.}} G Another minor advantage would be that there's no vertical offset between the two view-lines, only a horizontal one instead. So instead of calling for a distant horizon to zero-check on, to avoid parallax errors, that job could be done with something quite close-up. Also, it means the same instrument could be used for on-land close-up angular measurements for surveying purposes, which presently call for a theodolite because of the parallax error that offset causes.. I haven't yet discovered any major drawbacks to such a redesign, and hope that Navlist members will point out any there may be. For example, is its calibration unduly sensitive to the exactness of those 45º twists? Drawbacks there must be, I presume, if in all the years of sextant development, nobody has tried, or even proposed, such an alternative construction. Perhaps someone has, that I'm unaware of; dicovered the snags, and dropped the notion. ============================================================ S I've no more questions but that picture sure would come in handy about now. --Scott ============================================================ G {{I'll do my best to attach something that makes more sense}} G The era of the sextant has been and gone; now is not the moment to be proposing a redesign, and that's not what I am doing. I am just asking the question; could sextants have been made in quite a different way, and if not, why not? If no serious objections emerge to the principles of what's been suggested, I can proceed to the practical details of how such a very-different instrument might have been constructed, which I've been pondering on, a bit. George. contact George Huxtable, at george@hux.me.uk or at +44 1865 820222 (from UK, 01865 820222) or at 1 Sandy Lane, Southmoor, Abingdon, Oxon OX13 5HX, UK. --~--~---------~--~----~------------~-------~--~----~ Navigation List archive: www.fer3.com/arc To post, email NavList@fer3.com To , email NavList-@fer3.com -~----------~----~----~----~------~----~------~--~---