NavList:
A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding
From: Wolfgang Köberer
Date: 2007 Oct 7, 15:13 +0200
Peter Fogg
what’ s really nauseating – by the way
the correct saying is: „ad nauseam” not “ad nauseum” –
is the increasingly vicious tone you have been using against George. If you
want to insult George, please do it without making everybody else on this list read
it. I personally have not understood so far what caused you to use such venomenous
language. It just cannot be just for the fact that George is flogging a dead
horse as you believe. To point that out would be sufficient – and if he
insists the normal reaction would be to delete such messages. Nobody has to
react to what he thinks is “piffle”. And the
picture you are creating of George is ludicrously false as everybody who met
him in person can attest to; I’ m certain some other list members who
know him will subscribe to that.
Which leads to the next topic: On the “old list”
when something came up like this, the former list owner told everybody to cool
down. I haven’t read something like that from Frank yet. This may be
because he has a bone to pick with George, too, for whatever reason. But if he
feels any responsibility apart from technical maintenance of the he should not
lean back and let this escalate.
And now for something completely different:
As I said before: the BBC thing on the history of
navigation is full of mistakes. I just added 2, George pointed out some more. They
are not “minor editing errors”, but show in big parts a fundamental
misunderstanding and/or lack of knowledge of navigation and its history. Now what
is the “educational effectiveness“ of giving
wrong information? Is this list not a place to raise the question of
misinformation which is spread regarding the art and science that the list
members are interested in?
Wolfgang
Dr. Wolfgang Köberer
Wolfsgangstr. 92
D-60322 Frankfurt am Main
Tel: + 49 69 95520851
Fax: + 49 69 558400
e-mail: koeberer@navigationsgeschichte.de
Von:
Gesendet: Samstag, 6. Oktober 2007
13:07
An:
Betreff: [NavList 3361] Azimuth
determination (ad nauseum)
While
some of us have heard all this time and again, its been a couple of years now
since George dragged up last his same tired old objection to the Azimuth Tables
in The Complete On-Board Celestial Navigator,
so we'll go though it all again for the benefit of those who haven't heard it
all before.
The
book devotes quite a bit of attention to the derivation of azimuth, beginning
with:
General
advice on azimuth determination
As long
as the DR is relatively close to the position, intercepts remain short
(remember that the tabular sight reduction method proposed in the book is based
on a single DR, not an assumed position to nearest whole degrees). In
this case the need for accuracy with azimuths is not, generally speaking,
great. Additionally, given the limitations on plotting with great
precision while underway on a small boat, azimuths accurate to within a couple
of degrees are adequate for the purpose.
Indeed,
a corrected compass bearing should give such a reasonably good idea of true
bearing, or at least serve as a check for whatever other method may be used;
indicating gross error if such should occur. Or vice versa.
Redundancy is good on boats.
While
on the subject of estimation of azimuth, the prediction and identification
tables of the book can be used, although since latitude and LHA to the nearest
10 degrees are used: "the accuracy of
azimuths found by this method may not be very high".
For plotting
purposes the book proposes quite a few alternatives:
Azimuth
Tables
Apparently
this simple and quick tabular method of deriving azimuth was popular with
sailing ships in the nineteenth century. This is hardly surprising since the
method:
"…
involves one table with different points of
entry. No interpolation is required, and it is one of the simplest techniques
for finding azimuth with an accuracy of one or two degrees."
Sounds
great, doesn't it? They are great too; they were popular for good reason (and
still are, with people like me who actually use them). Is there a catch? Well,
its a good idea to understand their limitations.
If I
remember the story correctly, these tables are based on the sine formula, and
so tend to become unreliable as the azimuth approaches the prime vertical
– due east and west. Of course the remedy in such cases is obvious
– beware. In practice, in such a case the initial problem can be
choosing which of two similar values to adopt. There is a procedure to
follow for this, but since it compromises the 'quick and simple' appeal of the
tables, I find it altogether simpler to give these tables a miss with azimuths
around prime vertical.
Is that
it? Not quite. The tables are entered with values of whole degrees. George has
rather cleverly discovered that if a carefully contrived combination of half
degree values are used, significant error can be induced. And is still dining
out, from time to time, on this.
A
statistical study has been carried out to analyse and quantify this potential
problem. The results have never been challenged. When 121,677,000 random
combinations of possible values were tested, an azimuth correct to within 2
degrees was generated in 98.8% of the cases. "Very large errors i.e. greater than ten degrees occur in only 0.005% of
the sample. An error in excess of ten degrees up to a maximum of less than 18
degrees is extremely rare." More detail is available at:
http://gbennett.customer.netspace.net.au/
under
'Azimuth Tables'.
The
common sense approach is to beware of entering the tables with a combination of
half degrees, especially when the bearing approaches east and west. Once
the navigator is aware of the extremely rare potential for significant error in
such a combination of circumstances its easy to avoid, via use then of an
alternative method. As Frank says; its a trivial problem, not a major one,
except in George's mind. Although we have gone over all this again and again
and again, generally to deafening silence from George, every so often George
likes to climb back up onto this worn soapbox and moan piously about how
dangerous such potential error could be for the poor navigator. You're pushing
piffle, George. You really should get a life.
Additionally,
in a few succinct words the book explicitly warns the user of the above,
concluding: "When in doubt, use the
Weir diagrams" which are conveniently located on the page
following the azimuth tables.
Weir
Diagrams
Much
like, I should imagine, generations of students of navigation, I have always
thought of them as weird diagrams.
I've
heard that they were popular with the Royal Navy, which used larger coloured
versions than the book, that is limited to line drawings that fit onto the
pages. They work fine, it seems (am unaware of any criticism).
Because they constitute a graphical solution, the accuracy of the derived
azimuth is limited by the skill of the user (this also affects the accuracy of
the plotted LOPs and then fix, with the pencil and paper plots proposed by the
book). I guess that they are also, generally, limited to being accurate to
within a degree or two. Maybe less.
Is this
good enough? Sure it is. It is unrealistic to expect great accuracy
from celestial observations from the deck of a small boat underway. What are
proposed by the book is relatively quick and simple methods that are entirely
appropriate for that environment.
But
hey, you want precision? Drag out that calculator …
Azimuth
via Formulas
Three
are proposed in the book:
The tan formula, which George tells us he
approves of.
The cos formula, which I've been given to
understand suffers when asked to produce azimuths close to due north and south,
and:
The sin formula, which has the aforementioned
inbuilt lack of reliability with azimuths close to east and west.
******************************************************************************************************
Is that
enough about the derivation of azimuth from one slim volume? I would have
thought so. Given all this choice I would have thought disingenuous was
expressing George's obsession with the Azimuth Tables in the mildest terms
possible.
But
wait, there's more:
Amplitude
There's
a formula for this too (and other stuff) although the Azimuth Tables can also
be used to derive amplitude. They're handy tables, those Azimuth Tables.
I wouldn't leave home without them.
A
challenge for George
If you
want to show us what a clever chap you really are George, why don't you take your
favourite tan formula and produce from it a set of tables that will derive
azimuth at least as simply and easily as some creative person has done with the
sin formula. Of course we will expect it to work perfectly in all
circumstances. I should imagine that nothing less would be good enough
for your own high standards, either.
Do that
George and we will be impressed. You will have managed to actually create
something of value, rather than just carping in an increasingly monotonous
fashion from the sidelines about imperfections (and in particular a highly
contrived error) within hugely useful tools that have been regularly used in
the past by real sailing ships over extended periods and are again proposed for
use, quite justifiably, albeit with their warts, for the benefit of us all.
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