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    Re: An "alternative" sextant?
    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.
    
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