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    Re: Refraction
    From: Fred Hebard
    Date: 2005 Aug 4, 10:56 -0400

    Perhaps one of the real wizards, such as George H., will pop in here
    and give the formula.  It's very simple.  I'll look it up if nobody
    surfaces.  No integration is required for the calculation; I don't know
    about the derivation of the formula.
    How do you get into a negative altitude situation?
    On Aug 4, 2005, at 10:38 AM, Marcel E. Tschudin wrote:
    > Thank you Fred and Robert for all your support.
    > I found finally the "Table 6 - Refraction", previously Table 8... This
    > sould
    > help to derive some sort of table or function.
    > I do not quite agree with "black magic", it is actually very basic
    > physics
    > which can be calculated by integration over air layers. May be some
    > one out
    > there has even a programmed source code to do this. I actually came
    > across a
    > Basic program, but it can not handle negative altitudes, where certain
    > air
    > layers have to be passed twice. Furtheron, I am unfortunately not in a
    > position to adapt that Basic code to my needs.
    > So, as for the moment, I try to go on with this Table 6.
    > Marcel
    > ----- Original Message -----
    > From: "Fred Hebard" 
    > To: 
    > Sent: Thursday, August 04, 2005 3:56 PM
    > Subject: Re: Refraction
    >> Marcel,
    >> You can download copies of the Air Almanac from
    >> Fred
    >> On Aug 4, 2005, at 8:40 AM, Marcel E. Tschudin wrote:
    >>> Hello Robert
    >>> Thank you for your fast reply. Unfortunately I am not in possession
    >>> of
    >>> the Air Almanac; in addition I am for about an other year abroad in a
    >>> country where I am not able to order copies from a library. May I
    >>> therefore ask you, whether it would be possible for you to derive
    >>> from
    >>> the table you indicated one or the other benchmark value? As you
    >>> mentioned this would at least give a clue. Thanks a lot!
    >>> Like you I am still hoping that there is some one out there who
    >>> really
    >>> can provide a solution to this problem.
    >>> Marcel
    >>>> ----- Original Message -----
    >>>> From: Robert Eno
    >>>> Sent: Saturday, September 03, 2005 2:37 PM
    >>>> Subject: Re: Refraction
    >>>> Hello Marcel
    >>>> Refraction error makes the observed body appear to be higher than it
    >>>> actually is, ergo the same correction rules for postitive
    >>>> altitudes would apply to negative altitudes; only in this case the
    >>>> negative numbers would be added.  If, for example, your sextant
    >>>> altitude was minus 5 degrees, and the refraction correction was (I
    >>>> am
    >>>> just pulling a random number out of my head) minus 60 minutes
    >>>> (refraction correction is always subtracted from the sextant
    >>>> altitude), then your corrected altitude would be minus 6 degrees.
    >>>> Near as I can reckon, you would only experience negative altitudes
    >>>> from an aircraft flying at high altitudes or in the polar regions in
    >>>> winter.
    >>>> Have a look at Table # 6, HO 249, Sight Reduction Tables for Air
    >>>> Navigation and the correction tables at the back of the Air Almanac.
    >>>> These give you a bit of a clue as to what to expect. Other than
    >>>> these
    >>>> tables, I know of no other tables which provide refraction
    >>>> corrections for negative altitudes for observers at sea level.  If
    >>>> anyone out there is aware of such tables, do let me know. It is a
    >>>> question I have not pondered for some time now.
    >>>> Robert
    >>>>> ----- Original Message -----
    >>>>> From: Marcel E. Tschudin
    >>>>> Sent: Thursday, August 04, 2005 6:48 AM
    >>>>> Subject: Refraction
    >>>>> Hello
    >>>>> While searching with Google, I came across this mail list. May be
    >>>>> some one out here may be able to help me answering the following
    >>>>> question:
    >>>>> How do refraction values for negative elevations have to be
    >>>>> calculated, such as e.g. the horizon from a plane? (I am interested
    >>>>> in the range of 0? to approx. ?5?.)
    >>>>> Is Bennett?s approximation also valid for negative elevations? If
    >>>>> not, what other approximation formulae should be used, or, where
    >>>>> can
    >>>>> one find some benchmark values?
    >>>>> I am interested in formulae for both, refraction from apparent
    >>>>> position and from physical position.
    >>>>> Thank you for any input to my problem.
    >>>>> Marcel

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