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    Re: accuracy of glass artificial horizon figure
    From: Gary LaPook
    Date: 2008 Aug 22, 01:42 -0700

    George wrote:
    I wonder whether Gary has that right, or if he is a factor of 2 out?
    
    Yes, if the mirror angle is half a minute out, then the angle between
    the
    incident and reflected light becomes a whole minute out. But then, to
    arrive
    at a measured altitude, you have to divide that resulting angle by
    two. So I
    suggest that, if there were no other sources of error, the accuracy in
    measuring altitude will be no better than the accuracy achieved in
    levelling
    the mirror, and there is no such factor-of-two to apply.
    
    
    
    Gary replies:
     I drew a digram and I agree with George, the doubling of the angle is
    cancelled out by the division by 2 at the end so the error in the
    final altitude is equal to the amount that the miror was out of level.
    (that's why I use mercury.)
    
    
    George also wrote:
    
    Besides the factor of two reduction in instrument errors caused by
    the doubling of the measured angle, and the firm footing on land
    compared
    with a vessel, all the problems inherent in the natural horizon
    disappear,
    particularly the unpredictable refractive component of the dip. As
    long as
    the observed body, preferably a star, isn't too low down (but it can't
    be
    above 60�, of course), then I would expect altitudes to be measurable,
    with
    care, to around 0.3 arc-minutes, or so, as long as the glass plate can
    be
    levelled with corresponding accuracy. And that becomes the difficult
    bit.
    
    
    to which Gary adds:
    
    I have been working on this for the last couple of weeks. I wanted to
    test the accuracy of my marine sextants and I agree that you can get
    better measurements with the mercury artificial horizon for the same
    reasons that you mentioned. I am also planing to use the data to
    explore further the use of "slope" in improving the accuracy of a
    series of shots. I have been taking series of shots of Jupiter in my
    artificial horizon (since it is favorably placed) and I want to take
    several more series then I will write up what I found.
    
    gl
    
    On Aug 21, 1:51 pm, "George Huxtable" 
    wrote:
    > Gary LaPook wrote-
    > |
    > | Well, the ultimate limit is the 1/8th wavelength of light "Raleigh
    > | limit" since anything more perfect is not detectable due to the wave
    > | character of light. This is the standard for telescope mirrors. But,
    > | since you will not be trying see the moons of Saturn when doing celnav,
    > | the artificial horizon doesn't need to be that perfect. Since the angle
    > | of incidence equals the angle or reflection any error in the shape of
    > | the mirror is doubled in the reflected ray. So, the answer to your
    > | question is that it must be accurate to 1/2 the accuracy limit you are
    > | trying to achieve. If you only want sight accurate to one minute of arc
    > | then the mirror must be accurate to 1/2 of a minute. If working for one
    > | tenth of a minute accuracy then the mirror must be accurate to one
    > | twentieth of a minute.
    > |
    > | gl
    > || pls wrote:
    >
    > | > Does anyone know how accurate (i.e., level) the surface figure of a
    > | > sheet of black glass must be to serve as an artificial horizon?  In
    > | > particular I am trying to determine the point beyond which additional
    > | > accuracy is irrelevant in terms of the result, given the other
    > | > variables in a sighting with a hand-held sextant.
    > ======================
    >
    > I wonder whether Gary has that right, or if he is a factor of 2 out?
    >
    > Yes, if the mirror angle is half a minute out, then the angle between the
    > incident and reflected light becomes a whole minute out. But then, to arrive
    > at a measured altitude, you have to divide that resulting angle by two. So I
    > suggest that, if there were no other sources of error, the accuracy in
    > measuring altitude will be no better than the accuracy achieved in levelling
    > the mirror, and there is no such factor-of-two to apply.
    >
    > Maybe "pls" is concentrating on the wrong question. "Surface figure" refers
    > to flatness, in a plane, not level-ness. The difficult bit is not getting
    > the surface figure of the glass right; any decent glass flat will be good
    > enough. It's getting a sufficiently rigid mounting, that can be finely
    > adjusted, and tried with sufficiently sensitive levels, so that it can be
    > got level, and will stay level, throughout a measurement. It calls for a
    > sensitive spirit-level that's sufficiently light in weight so that its
    > weight shifting on the glass causes negligible deflection. It requires firm
    > ground so that no observable shift occurs as the observer moves his weight
    > around.
    >
    > If these requirements can be met (and they can be bypassed, in the right
    > conditions, by using a mercury reflecting surface) then altitudes can be
    > measured with much greater accuracy than is possible at sea using a natural
    > horizon. Besides the factor of two reduction in instrument errors caused by
    > the doubling of the measured angle, and the firm footing on land compared
    > with a vessel, all the problems inherent in the natural horizon disappear,
    > particularly the unpredictable refractive component of the dip. As long as
    > the observed body, preferably a star, isn't too low down (but it can't be
    > above 60�, of course), then I would expect altitudes to be measurable, with
    > care, to around 0.3 arc-minutes, or so, as long as the glass plate can be
    > levelled with corresponding accuracy. And that becomes the difficult bit.
    >
    > George.
    >
    > contact George Huxtable at geo...@huxtable.u-net.com
    > or at +44 1865 820222 (from UK, 01865 820222)
    > or at 1 Sandy Lane, Southmoor, Abingdon, Oxon OX13 5HX, UK.
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