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    Re: Bubble Horizon Altitude Corrections
    From: George Huxtable
    Date: 2004 Jul 5, 17:33 +0100

    There are a few matters to clear up in Frank Reed's reply to Bill's
    question about bubble sextants observation.
    
    Frank wrote-
    "By the way, since you're inland, be
    advised that you should use "sea level" barometric pressure. This differs a
    little from the pressure usually reported in weather reports (but not very much
    unless you're at Denver-like altitudes)."
    
    Frank nearly always gets things right, but on this point he is wrong.
    Refraction, in the path of a light ray from outer space, through the
    atmosphere, to the observer's eye, is proportional to (the local
    coefficient of refraction minus 1) at the location of the observer. That is
    proportional to the local density of the air, which is what the correction
    table for temperature and pressure is there to calculate. What's needed is
    a barometer that was set correctly in millibars at sea level somewhere:
    then, in a mountain location, its reading falls to the local value.
    
    Climb 1000 feet, and the barometer reading will drop to reflect the reduced
    amount of atmosphere above you. And the refraction, and its correction,
    will reduce correspondingly.
    
    Except for those at sea level, sea-level pressures and temperatures are
    irrelevant. Navigating on the Great Lakes, for example, it's the local
    pressure at the level of the lake, not at sea level, that applies.
    
    =========================
    
    On temperature / pressure corrections, Bill asked-
    
    "... Howell suggests
    ignoring temp/pressure corrections while the almanac says to include them."
    
    and Frank replied-
    
    >Sue was wrong on that point. You should include corrections for non-standard
    >temperature and pressure when correcting any sextant observation. Note though
    >that they are very small in most cases.
    
    I would agree with Howell's view here, not with Frank. Because those
    corrections are so very small, and because the inherent accuracy of a
    bubble=-sextant (even on a steady platform with a steady hand) is so much
    worse than that of a sextant using a sea-horizon or liquid
    artificial-horizon, then such temperature / pressure corrections will have
    little practical effect on the answer, except under extreme climatic
    conditions.
    
    Bill writes- "Howell suggests
    ignoring temp/pressure corrections while the almanac says to include them.
    Perhaps the artificial horizons double angle cancels that out while a direct
    shot with a bubble would not?"
    
    No, that's not the case at all. The corrections for refraction apply
    exactly the same to both types of instrument. It's just that the bubble
    instrument is inherently so much less precise that such a small correction
    for temperature / pressure isn't worth making anyway..
    
    ======================
    
    I find the temperature / pressure corrections at the beginning of the
    Nautical Almanac rather awkward to use, and cater only for the range of
    pressures occurring near sea-level, not up mountains. If you really find
    the need to make this correction, then instead of that table just multiply
    refraction R by P/1010, and by 283 / (273 + T), with local pressure P in
    millibars and local temperature T in degrees Celsius (= Centigrade).
    
    If writing a computer program to make these corrections, instead of a
    lookup refraction table, try-
    
    R = tan (90 - .999139*alt - 7.31 / (alt + 4.4)) where R is the refraction
    correction in arc-minutes (to subtract) and alt is in degrees and decimals.
    
    This is a slightly-modified version of George Bennett's formula, quoted in
    Meeus' "Astronomical Algorithms".
    
    ===============================
    
    For Sun altitudes, the Nautical Almanac does its best to make life easy for
    the user of an ordinary sextant by combining, in one correction,
    refraction, semidiameter, and parallax. But that works to the detriment of
    the bubble-sextant observer, who is aligning the Sun's centre, not a limb,
    with a bubble, so doesn't need or want any semidiameter correction.
    Averaging UL and LL corrections is a rather awkward artifice to get around
    this: in my opinion it is far simpler for the observer to just subtract the
    refraction using the "stars & planets" correction table, or the equation
    above, instead, which are for pure refraction only.  True, Sun parallax
    would then not be corrected, but that never exceeds 9 arc-seconds (to add),
    and at the low precision available from a bubble sextant, that amount can
    be cheerfully written off.
    
    For Moon altitudes, using a bubble-sextant is somewhat trickier. Because
    the Moon isn't round (except when full) it's awkward to fit it into the
    circle of the bubble. The Moon has a sharply-defined round limb over half
    its periphery, and a fuzzier shadowed limb over the rest. Somehow, you have
    to keep the round limb (imagining the missing part) concentric with the
    bubble, and ignore the rest. This is the same as putting the centre of the
    bubble at the same point as the mid-point of the line joining the two
    horns. Neither of these is easy to do with any precision.
    
    Now for the Moon's corrections. The Moon has an immense parallax of up to a
    degree, which can't possibly be neglected! You can obtain the Moon
    correction for a bubble-sextant altitude in the way the almanac suggests,
    using averaged UL and LL corrections from pages xxxiv and xxxv, but to my
    mind it's far simpler and more understandable to correct separately for
    refraction (by subtracting the value in the "stars & planets" table), and
    then to take the HP (Moon's horizontal parallax) in arc-minutes, at the
    nearest hour, from the almanac, multiply it by cos alt, and add it as the
    parallax correction. This ignores a latitude-dependent correction,
    "reduction in the Moon's horizontal parallax", which is always less than a
    fifth of an arc-minute, and negligible in the context of the lower accuracy
    of a bubble observation.
    
    So to summarise my recommendations, with a bubble observation-
    
    The dip and semidiameter corrections are zero.
    For all bodies, use the refraction table for stars & planets (and subtract
    it). Don't bother with temperature and pressure correction, except in
    extreme conditions.
    For the Moon, be careful how you centre its non-disc with the centre of the
    bubble.
    For the Moon only, correct for parallax by adding HP x cos alt. For
    anything else, ignore parallax.
    Remember that even the best observer in ideal conditions won't expect to
    approach the precision available with an ordinary sextant.
    
    But I should point out that I have made few bubble-sextant observations,
    and don't own such an instrument, so I am no expert on the matter.
    
    George.
    
    ================================================================
    contact George Huxtable by email at george@huxtable.u-net.com, by phone at
    01865 820222 (from outside UK, +44 1865 820222), or by mail at 1 Sandy
    Lane, Southmoor, Abingdon, Oxon OX13 5HX, UK.
    ================================================================
    
    
    

       
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