NavList:

   

Reply

Paul Hirose's contributions are always worth taking seriously, though this
time I'm unconvinced by his arguments.

I had written- "An hour angle is nothing else but the longitude of the body,
measured Westerly from Greenwich, 0 to 360. Why don't we measure our
geographical longitudes exactly the same way, so that we simply difference
the longitudes to get local hour angle? Meeus is an astronomer who sets us a
sensible example."

and Paul countered- "First off, "positive west" is odd enough nowadays that
Meeus felt obliged to defend it in a sidebar."

Well, I wasn't arguing that we should choose positive-West just because
Meeus did; but that here's an astronomer, writing for astronomers, providing
us with a respectable example.

Astronomers have more coherent reasons for choosing positive-East than we
navigators do. Nearly everything they measure is referred to the sphere of
"fixed" stars, and on that background almost everything moves Easterly
(everything, that is, ecept for planets making a "retrograde" loop, which
caused such argument). Positions were therefore defined in terms of Right
Ascension (R.A.), measured Easterly from Aries, and times in terms of
sidereal time (and declination, just as it is today). In those coordinates,
stars stayed put (give or take the odd arc-minute in a year). That's still
what is done in the Astronomical Almanac.

Just over 50 years ago, the Nautical Almanac switched to using Greenwich
Hour Angles, and Greenwich Time, and all our astro. positions are defined
with respect to the Earth, and the Greenwich Meridian. So to a navigator,
everything in the sky is whistling round the Earth at very nearly 15 degrees
in every hour, give or take a few minutes, in a Westerly direction. The GHA
is simply the longitude of the spot on Earth directly below the body,
measured Westerly, 0 to 360.

Historically, navigators have always preferred to attach a label, E or W,
rather than a numerical sign, to their longitudes (as for their latitudes,
too), and then established a complex set of rules for adding or subtracting
numbers and labelling the result, depending on whether their labels are the
same or different, and which is numerically greater. Now, we can simply say
"subtract them", being reasonably confident (as they may not have been) that
we know how to handle subtractions of numbers that might be positive or
negative.

One consequence is that hisorically, there's never been an accepted
convention for the signs of N and S, or E and W. In our numerical age, with
calculations and programs working with + or - rather than with such letters,
such a convention is needed. Fortunately, not even the most bloody-minded
Australians have (yet) contended that we should give the Southern hemisphere
a + sign, so at least that one is settled. But in terms of E and W, we have
the worst possible arrangement, of two conventions, both in use, and often
without a clear statement anywhere about which one has been adopted.

In the CD that contains the collection of ION papers on celestial
navigation, some articles have chosen one convention, some the other:
sometimes, the reader has to guess. I haven't attempted a survey to decide
on which is preponderant.

I agree that positive-Easterly fits better with mathematical conventions,
with the standard set of 3 Cartesian axes. So it's the other way round than
a standard graph, conventionally drawn with the x-axis increasing positively
to the right, and the y-axis positive upwards. That's one reason why the
standard computer functions for polar-rectangular conversion need to be
adapted to suit (the other is the way navigators define azimuths).

Paul argues- "With the "positive east" convention it's easier (for me) to
remember how to compute local hour angle: "add everything". That is, LHA =
GHA body + lon and LHA = GHA Aries + SHA star + lon."  That's as may be, but
he is then adding numbers which may have different signs, so he isn't
actually avoiding that (sexagesimal) numerical subtraction. And how does he
readily remember the converse formula, for getting his longitude from where
the body is? And if he wants to know how far East or West of a headland his
craft is (which is solving the same problem) he then has to apply a
different formula, and subtract instead. It just isn't logical, to express
corresponding quantities that represent the same measure in the same units
(Hour angle and longitude) in opposite directions. I can't think of another
example in which it occurs, in science or technology.

George.

contact George Huxtable at george@huxtable.u-net.com
or at +44 1865 820222 (from UK, 01865 820222)
or at 1 Sandy Lane, Southmoor, Abingdon, Oxon OX13 5HX, UK.
----- Original Message -----
From: "Paul Hirose" 
To: "Google nav list" 
Sent: Wednesday, June 11, 2008 10:00 PM
Subject: [NavList 5400] longitude positive west?


--~--~---------~--~----~------------~-------~--~----~
Navigation List archive: www.fer3.com/arc
To post, email NavList@fer3.com
To , email NavList-@fer3.com
-~----------~----~----~----~------~----~------~--~---

   

Reply