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Gentlemen,

George refers to anomalous dip that occurs "when the air-layers within a
few feet of the horizon differ in temperature in an unexpected way, and
refract accordingly."  I stumbled into this phenomenon two years ago
comparing sights taken in Maine and the Caribbean.  I was taking
multiple sun sights whenever I could get a clear horizon during our
summer trips among the Maine islands.  Compared to an "assumed position"
from GPS, my sights most frequently indicated an intercept 2-4 nm
"away", which suggested I was under-measuring the altitude by 2' to 4'.
I thought it was my technique or instrument error until I repeated the
same exercise during a week long cruise in the Caribbean.  Those sights
were typically +- 2' either side of truth, showing none of the same bias
toward consistent under-measurement I had experienced in Maine.

I found one possible explanation on pages 424-425 of my 1958 Bowditch
where Sea-air temperature difference correction (S) is discussed in the
chapter on Sextant Altitude Corrections.  Bowditch explains that
standard dip tables assume a standard air density gradient from sea
level up into the sky. That standard gradient is effected by many
factors, including the relative sea-air temperature.

Bowditch states:
"If the water is warmer than the air, the horizon is depressed and dip
is increased.  Under these conditions the measured altitudes are too
great.  Therefore, as a correction to the altitude, the sea-air
temperature difference correction is negative when the water is warmer
than the air.  When the air is warmer, the reverse is true, and the
altitude correction is positive."

Most of my Maine sights were on warm days (75-80�F) on the cold waters
Gulf of Maine (55-60�F), a differential of in the range of 20-25�F.
Bowditch indicates this would result in the measured altitudes being too
small which is exactly what I experienced in the consistent bias of my
Maine sights.  This theory is supported by my Caribbean sights which
displayed no such bias under conditions where sea and air temperatures
were within 10�F of each other.

Bowditch also states that "The effect is greater as the temperature
difference increases." He notes that studies attempting to derive a
correction factor based on the sea-air temperature difference "differ
considerably". However, he summarizes the range of results and reports
"the average of these [studies] is about 0.16' per degree Fahrenheit
(0.28' per degree Celsius).  Thus, the correction is about one-sixth of
a minute per degree Fahrenheit, or one minute per each six degrees."

This rough rule of thumb when applied to my Maine sights (temperature
difference of 30�F) would suggest a correction of about 3' to 4' which
is strikingly consistent with the 2' to 4' bias I experienced in my
Maine sights.

While I won't be measuring sea and air temperature before my next round
of sights, I now keenly aware the potential impact of non-standard
atmospheric conditions on sight accuracy.

Regards,
Arthur

-----Original Message-----
From: Navigation Mailing List
[mailto:NAVIGATION-L@LISTSERV.WEBKAHUNA.COM] On Behalf Of George
Huxtable
Sent: Monday, March 17, 2003 2:53 PM
To: NAVIGATION-L@LISTSERV.WEBKAHUNA.COM
Subject: Re: Sextant Accuracy and anomalous dip.

Fred Hebard wrote-

>The location of my house seems to be settling down to perhaps 0.3 to
>0.4 nautical miles north of its actual location.  All of this with an
>artificial horizon.  One new technique I tried was to preset the
>sextant to the future altitude of a body and then watch the body pass
>through that altitude while listening to the time being counted out.
>
>My general objective is to get these observations as accurate as
>possible, say to within 0.1 or 0.2 miles.  I'm not sure why I have this
>objective, but it persists.
>
>Bill Murdoch mentioned he had never bothered to apply instrument
>corrections to readings taken with his Freiberger, implying that it's
>not necessary to achieve accuracies better than about 1 nautical mile.
>That also seems to be the general opinion here, especially with regard
>to observations from small yachts, where it often is not possible to
>get more accurate.  But how about larger vessels?  Does anybody want to
>defend trying to get accuracies closer than 1 mile?

Comments from George.

Fred has every right to be satisfied with these results. Presumably he
has
rather sharp eyesight. It would be interesting to know how much scatter
there is between Fred's individual measurements of the position of his
house. Is his result of "perhaps 0.3 to 0.4 miles Morth" an average of
many
observations, perhaps? I'm interested in how closely they cluster about
that value.

I am presuming that the artificial horizon used is some form of
reflecting
pool. Altitude measurements made that way on land have several
advantages
over horizon altitudes measured from a boat. Because the doubled
altitude
is measured on the sextant, the effect of sextant calibration (and
other)
errors is halved. With a stable platform underfoot, the observer isn't
being buffeted and his images are steady, so he can use a high-gain
telescope. If a glass cloche is being used as a windbreak, care has to
be
taken over the optical quality of the glass panes used.

The main errors in measuring an altitude at sea arise from deficiencies
in
the sea-horizon that has to be used as a reference: deficiencies that
are
absent in artificial-horizon observations on land.

From a small boat at sea, the horizon is not a steady straight line but
a
succession of overlapping wavecrests, observed from a platform that's
also
heaving up and down, changing the perspective view of the waves and
altering the dip from moment to moment. A big vessel, with its slow and
predictable roll, and its high viewpoint, is MUCH less affected in that
way.

Even in millpond conditions, however, when the small boat loses much of
that disadvantage, there remains a source of error affecting the
horizontality of the horizon, for small vessels and large ones alike.
This
is an old "hobby-horse" of mine, and I hope nobody minds if I trot it
out
for a ride once again.

This error is "anomalous dip", when the air-layers within a few feet of
the
horizon differ in temperature in an unexpected way, and refract
accordingly. It causes dip to vary slightly, in an unpredictable way,
and
it's hard to detect it happening, let alone estimate how much to allow
for.
This effect has nothing to do with the small corrections for refraction,
depending on temperature and pressure, which most almanacs provide.

Changes of dip of a minute or so from the predicted value can be quite
frequent, changes of 2 or 3 minutes can occasionally happen, changes of
5
minutes are possible though very unusual. These can perturb a sextant
altitude by a corresponding amount, and the observer will be completely
unaware that it has happened.

So if you are a sextant-navigator wishing to avoid a dangerous hazard,
how
much room do you allow to consider your vessel safe? Usually the
dip-error
will be within a minute, but it's hardly satisfactory to say that
"usually"
you will miss that dangerous rock. You wouldn't wish to navigate in such
a
way as to hit it "only occasionally". A safety-standard of "almost
never"
is I think the very minimum anyone would accept, and any prudent
navigator
would insist on a better margin even than that. So a navigator without
knowledge of the dip-of-the-moment might be wise to allow a margin of 5
miles or so, to cater for possible anomalous-dip.

Dipmeters have been invented and used in oceanographic survey work. A
crude
but effective dipmeter can be knocked together without great expense. It
requires a view of the horizon in two opposite directions to be visible
simultaneously from somewhere on deck.

There may be a case for a quick check of the dip as a matter of routine
whenever sextant observations are made. The results would probably be
very
boring. Most of the time the dip-error would be well within one
arc-minute.
But on those rare occasions when it was considerably greater, the
navigator
would be forewarned, and could act to correct it. That correction would
allow him a greater reliance on the precision of his sextant
observations.

Anomalous dip seems to be generally disregarded as a hazard to sextant
navigation. However, I think it's worth taking seriously. There's more
stuff about anomalous dip in old archives of this mailing list.

George Huxtable

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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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