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    Re: Refraction near the Horizon ? Observation vs. Calculation
    From: Marcel Tschudin
    Date: 2013 Apr 7, 14:14 +0300

    Brad,
    
    1) Regarding your 4 dip equations and their plot: If all these
    equations would be related to the same earth radius and the
    conversions between feet and meter would not be rounded then all 4
    equations should actually have the same position in your figure.
    
    2) The values used in my example (Re=6400000 and k=0.164, then
    actually calculated wrongly with k=0.168) are NOT my "preferred"
    values. They were just used for the purpose of my explanations. Use in
    your calculations values which are at least as accurate "as
    reasonable" for what you are doing; however, you always can use values
    which are more accurate than necessary, but things may then turn out
    to become more complicated. The value k=0.164 was selected because
    this value, together with Re=6380000m, would provide the same results
    as the formula DIP[moa]=1.76*sqrt(HoE in m) or the corresponding one
    for HoE in feet. If you want your calculated dips to agree with this
    "1.76-formula" and using Re=6371000m then k would have to be k=0.165.
    (I do not know which values for k and Re were used when they
    simplified the formula and ended with the (rounded) factor 1.76, or
    its corresponding value for HoE in feet.)
    
    3) I do not have a copy of the N.A., so I do not know the content you
    are referring to. Could it be that you mix up astronomical refraction
    with terrestrial refraction, i.e. the refraction from light passing
    through all of the atmosphere until observer and light passing only
    between horizon and observer? A light passing all of the atmosphere
    and then grazing the apparent horizon (grazing the dip location)
    before touching your eyes is on all of its path much more refracted
    than the light from the apparent horizon which reaches your eyes, but
    for you looking at them they come from the same location, from the
    dip. It could eventually also be that the N.A. takes into account that
    for the dip the conversion between different T (and P) deviates from
    the relationship "generally" used for converting refraction (your
    formula for Q), but I doubt it. May be someone who knows what you are
    referring to in the N.A. may help you here.
    
    Marcel
    
    On Sun, Apr 7, 2013 at 3:30 AM, Brad Morris  wrote:
    > ________________________________
    >
    > Hi Marcel
    >
    > Thank you for your attention to this discussion. I was able to follow your
    > procedure and indeed, have created a graph of the dip when affected by
    > pressure and temperature.
    >
    > What temperature and pressure? Why the highest values recorded on earth, as
    > recognized in Wikipedia. The highest pressure was 32inHg=1083mb. The lowest
    > (non-tornado) pressure was 26inHg=880mb. The highest temp was in Death
    > Valley 56.7C=329.8K. The lowest temperature was in Antarctica -89.2C =
    > 183.9K. You may find a graph of this, along with the nominal P&T, up to 304
    > meters.
    >
    > I then went ahead and pulled out the values for 31.312 meters (103 feet,
    > corresponding to the bridge of Jeremy's merchant vessel).
    > Pressure Temperature Dip(P,T)
    > 1010mb 283.15k 9'49.9"
    > 880mb 283.15k 9'57.0"
    > 1083mb 283.15k 9'45.9"
    > 1010mb 183.9k 10'9.3"
    > 1010mb 329.8k 9'40.8"
    > You may wish to confirm these values.
    >
    > These values are remarkably different from the Nautical Almanac. Using the
    > A4 Altitude Correction Tables", we find that our temperature and pressures
    > are well beyond those charted, but we can just take the values shown to see
    > what the adjustment should be. I will use the "App Alt" to be 0deg0min.
    > The correction for 1010mb -30C is an additional -7.3 minutes.
    > The correction for 1010mb +35C is an additional +6.9 minutes
    > The correction for 970mb 10C is an additional +1.0 minutes
    > The correction for 1050mb 10C is an additional -1.1 minutes
    >
    > It is possible that I did not perform your procedure correctly. Its also
    > possible that the Nautical Almanac is wrong or that I used it improperly.
    > Failing that, you must try to understand why the variation for pressure and
    > temperature as given by the NA differs so wildly from your results.
    >
    > Regards
    > Brad
    >
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    >
    > Attached File:
    > DipExtremePressureTemperatur.pdf (no preview available)
    >
    > View and reply to this message: http://fer3.com/arc/m2.aspx?i=123404
    

       
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