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    Re: Refraction
    From: Fred Hebard
    Date: 2005 Aug 17, 09:18 -0400

    Thanks Wolfgang,
    I went to the website of the Royal Institute of Navigation, and it is a
    wonderful resource. 
    On Aug 17, 2005, at 7:18 AM, Wolfgang K?berer wrote:
    > Marcel,
    > The article by D.H.Sadler is in Vol. 5 (1952) of the (then) "Journal
    > of the
    > Royal Institute of Navigation". The Institute of Navigation recently
    > published the whole run of their journal up to 2003 (Vol. 56) on
    > CD-ROM and
    > DVD which I have. I could send you the article off list, if you like.
    > W. K?berer
    > -----Urspr?ngliche Nachricht-----
    > Von: Navigation Mailing List
    > Auftrag von Fred Hebard
    > Gesendet: Dienstag, 16. August 2005 23:01
    > Betreff: Re: Refraction
    > Marcel,
    > You seem to be making progress.  The name of the Royal Institute of
    > Navigation, UK,'s journal is the "Journal of Navigation."  The American
    > institute's journal is named the "Journal of the Institute of
    > Navigation" or "Navigation."  The email from the USNO, included below,
    > used the wrong name.
    > I was able to check the table of contents of the American journal (the
    > wrong one) and E.H. Sadler's paper is not in it, although there are
    > some papers by him on unification of the British and American NAs and
    > Air Almanacs that might assist accurate dating of related discussion
    > here.  I was not able to find a table of contents on line for the
    > correct journal, the "Journal of Navigation."  You might be able to get
    > a full citation from HMNAO or even a reprint.  Or perhaps one of our
    > members with access to a scholarly library (Frank?) might be able to
    > send you a copy.  I will send you one if you can get the citation,
    > which I need for remote access to a scholarly library.
    > You can google the Journal of Navigation, but the site is most
    > unhelpful.
    > Fred
    > On Aug 16, 2005, at 10:33 AM, Marcel E. Tschudin wrote:
    >> I just received the follwing information from USNO, refering to the
    >> table 6
    >> quote
    >> Pub 249 is indeed a publication of NGA, not USNO.  It is regrettable
    >> that they are unable to support their own product.  I will answer this
    >> question as best as I can, but be aware that I am working from an old
    >> (epoch 1995.0) copy of Pub 249.  It does appear that the refraction
    >> table in Pub 249 was derived from the more detailed refraction table
    >> published annually in the Air Almanac.  The Air Almanac table first
    >> appeared in the AA for 1953. The scientific underpinnings of the Air
    >> Almanac table were published in a paper, "The Refraction Table in the
    >> Air Almanac," by D.H. Sadler, former Superintendent of H.M. Nautical
    >> Almanac Office (UK).  The paper likely appeared during the first half
    >> of
    >> the 1950s in the (British) journal, Navigation (may have been called
    >> the
    >> Journal of the Institute of Navigation).  That's the best I can do
    >> regarding the reference.  Perhaps a good library can help with the
    >> literature search.
    >> Astronomical Applications Dept.
    >> US Naval Observatory
    >> unquote
    >> Does anyone of you know more about the mentioned paper from D.H.
    >> Sadler or
    >> the journal where it was published?
    >> Marcel
    >> ----- Original Message -----
    >> From: "Gary J. LaPook" 
    >> To: 
    >> Sent: Tuesday, August 16, 2005 9:05 AM
    >> Subject: Re: Refraction
    >>> Any idea how the refraction tables in the Air Almanac and HO 249 were
    >>> computed? They show values for altitudes down to 3?53' below the
    >>> horizon, from a height of eye of 55,000 feet at which point the
    >>> refraction is 60'. The refraction is also listed as 60' for -2?53'
    >>> when
    >>> observed from 30,000 feet. It should be noted that for altitudes
    >>> below
    >>> about 1? the refraction correction is only listed by 5' intervals.
    >>> Gary LaPook
    >>> george huxtable wrote:
    >>>> This is the second attempt to send this message to nav-l.
    >>>> Previously,
    >>>> on 14
    >>>> August, I had a bounce message. Don't know why.
    >>>> ==============================================
    >>>> Marcel Tschudin wrote- further about refraction.
    >>>> Unfortunately, there is no TRUE value for refraction at low angles
    >>>> of
    >>>> altitude, close above the horizon. Pulkova observatory near St
    >>>> Petersburg
    >>>> has been running a programme of measurements over many years, that
    >>>> as far
    >>>> as I'm aware still continues. Every now and then, a revised
    >>>> publication
    >>>> emerges with improved and updated results. Because refraction  at
    >>>> low
    >>>> angles varies with the local weather (and not just the air density
    >>>> at the
    >>>> observer), quoted values are average results, over a long time. On
    >>>> any
    >>>> day
    >>>> the actual refraction can differ, as distortions in the apparent
    >>>> disc
    >>>> of a
    >>>> low Sun clearly indicate.. Correcting for local temperature and
    >>>> pressure
    >>>> will do something to iron out those variations, but significant
    >>>> differences
    >>>> will remain.
    >>>> Bennet has provided a  formula which is an empirical attempt to fit
    >>>> that
    >>>> averaged data. At large angles of altitude, it becomes proportion to
    >>>> the
    >>>> tan of the zenith angle, as Snell's law requires. Near the horizon,
    >>>> where
    >>>> refraction rises sharply, the divergence from Snell's law shows up
    >>>> in
    >>>> correction terms which turn out to be remarkably simple. However,  I
    >>>> doubt
    >>>> whether those terms have any backing in terms of the physics of the
    >>>> refraction process; more likely, they are just empirical attempts to
    >>>> get as
    >>>> good a fit as possible, compatible with a simple calculation. It was
    >>>> devised in the days before everyone had a computer / calculator.
    >>>> So it's no surprise that tabulated refraction values agree well with
    >>>> Bennett. His formula was devised to replicate those values. In some
    >>>> publications, such as the Nautical Almanac, it appears that
    >>>> Bennett's
    >>>> formula itself is used as the basis for the refraction tables
    >>>> (though the
    >>>> constants have recently been tinkered-with a bit to improve the fit
    >>>> to
    >>>> recent Pulkova data) so it's not surprising that it shows good
    >>>> agreement.
    >>>> The almanac wisely states that-"the actual values of the dip and of
    >>>> the
    >>>> refraction at low altitudes may, in extreme atmospheric conditions,
    >>>> differ
    >>>> considerably from the mean values used in the tables".
    >>>> Bennett's empirical formula was, presumably, optimised to achieve an
    >>>> acceptable fit for positive angles of altitude and took no account
    >>>> of
    >>>> negative angles, and there's no reason to expect it to fit the
    >>>> observed
    >>>> refraction in that region.
    >>>> What I would conclude from all this is that there's no point in
    >>>> seeking
    >>>> extreme accuracy for such low-angle refraction predictions, positive
    >>>> or
    >>>> negative.. Where Marcel says-
    >>>>> In the mean time I also found the source code of a BASIC program to
    >>>>> calculate refraction by integration. The program was described in
    >>>>> Sky &
    >>>>> Telescope of March 1989. Without having the original article, I
    >>>>> transcribed
    >>>>> the program into the language with which I am working at the
    >>>>> moment,
    >>>>> i.e. in
    >>>>> Pascal/Delphi. A comparison of the refraction values, either from
    >>>>> the
    >>>>> table
    >>>>> 6 or those from Bennett, with those of the program show that those
    >>>>> depend
    >>>>> substantially of the selected refraction index of air. The problem
    >>>>> of
    >>>>> calculating the refraction becomes now a problem of calculating a
    >>>>> realistic
    >>>>> refraction index for air,  which depends on the wavelength,
    >>>>> temperature,
    >>>>> humidity.
    >>>> It strikes me that (as Fred Hebard has indicated) such corrections
    >>>> for
    >>>> wavelength and humidity are sufficiently small to be neglected, and
    >>>> to be
    >>>> overwhelmed, at low angles of altitude, by the unpredictable
    >>>> layering of
    >>>> temperature gradients in the air. Any such integration is only as
    >>>> good as
    >>>> the data that is available to feed into it, varying from one day to
    >>>> the next.
    >>>> Marcel added-
    >>>>> All this investigations done so far are for refraction values for
    >>>>> APPARENT
    >>>>> negative altitudes. For my program I need however also the
    >>>>> "inverse",
    >>>>> i.e.
    >>>>> the calculation of the refraction for physical, TRUE negative
    >>>>> altitudes,which has not been tuched so far.
    >>>> Well, I touched on it, in my last posting, in quoting the refraction
    >>>> at the
    >>>> tangent point (which corresponds to zero degrees true altitude) to
    >>>> be, at
    >>>> sea level, about 29 minutes, and not 34 minutes (which is the
    >>>> adopted
    >>>> mean
    >>>> value for refraction at zero degrees apparent altitude).
    >>>> George.
    >>>> ===============================================================
    >>>> Contact George at george@huxtable.u-net.com ,or by phone +44 1865
    >>>> 820222,
    >>>> or from within UK 01865 820222.
    >>>> Or by post- George Huxtable, 1 Sandy Lane, Southmoor, Abingdon, Oxon
    >>>> OX13
    >>>> 5HX, UK.

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