NavList:

   

Reply

Chuck,

Are you acquainted with the works of Jean Meeus, specifically his
"Astronomical Algorithms"? He has a chapter devoted to Interpolation and
covers the subject somewhat by discussing 3 and 5 variable interpolation,
interpolation with LaGranges method, extremum and zero valued interpolation.
I also draw your attention to "Fundametal Ephemeris Calculations" by Paul
J. Heafner.

HTH

Vic
________________________________________________________

Victor Fraenckel - The Windman                 vfraenc1@nycap.rr.com
KC2GUI                                                      www.windsway.com

      Home of the WindReader Electronic Theodolite
                               Read the WIND

"Victory at all costs, victory in spite of all terror, victory however long
and hard the road may be; for without victory there is no survival."
- Winston [Leonard Spencer] Churchill (1874 - 1965)

Dost thou not know, my son, with how little wisdom the world is governed?
-Count Oxenstierna (ca 1620)

----- Original Message -----
From: "Chuck Taylor" 
To: 
Sent: Friday, September 20, 2002 7:32 AM
Subject: Tables vs. Calculators


| Sight reduction tables have long been widely used by celestial navigators.
Why?
| The formulas for sight reduction by the law of cosines have long been
known. The
| answer is pretty straightforward:  Tables are used to save labor in
performing
| calculations.
|
| One can perform sight reduction by the law of cosines with with a set of
| trigonometric tables (sines, cosines, etc.) and a pencil and paper.
Multiplying
| and dividing 5-digit sines and cosines can be a bit tedious, however.  The
| traditional solution was to use more tables, specifically tables of
logarithms,
| so that multiplication could be converted to addition, and division to
| subtraction.
|
| The next logical step was to combine trigonometric an logarithm tables, so
that
| one could look up, for example, the log-sine of an angle (the logarithm of
the
| sine).  Then came variations on the same theme, such as tables of
haversines and
| log-haversines.
|
| Next came various other sets of tables intended to speed up the process of
sight
| reduction by combining various steps, relieving the navigator of still
more of
| the labor of computation.  Examples include HO 214, Pub 229, Ageton's
Tables,
| and numerous others produced by various hydrographic offices around the
world.
|
| Many of us object to the exclusive use of "black boxes" such as GPS units
on the
| grounds that it takes all the sport out of navigating if all you have to
do is
| turn on the black box and observe your position (either the lat/lon or a
mark on
| a chartplotter). We call it a "black box" because most of us don't fully
| understand how it operates, and we certainly can't duplicate its results
by
| other means such as pencil and paper.
|
| We also believe that it is important to use the traditional methods in
order to
| maintain our skills.  Who knows, the black box may fail some day.
|
| I would argue that tables such as Pub 229 are an early form of "black
box". At
| least many of us treat it as such.  We open to the appropriate page and
extract
| numbers, trusting on faith that they are correct.  How many of us have
tried to
| verify that those numbers are correct?  I have.  I can successfully
reproduce
| the main tables by computer, but I have been stumped at trying to reverse
| engineer the the interpolation tables (difference and
double-second-difference
| tables).  I even asked the folks at NIMA who publish the tables, and they
| couldn't give me a satisfactory answer.  If I can't program it, I don't
trust
| it.
|
| I would be very grateful if one of you could provide me with a set of
algorithms
| to reproduce the various difference and double-second-difference tables in
Pub
| 229.
|
| How can we logically dismiss the use of the "GPS black box" while
simultaneously
| embracing the "Pub 229 black box"?  I'll grant you that the Pub 229 black
box is
| less susceptible to failure due to causes beyond the control of the
navigator,
| but it still has many of the other characteristics of a black box.  (It is
| certainly easier to carry a spare GPS than a spare set of the various
volumes of
| Pub 229.)
|
| To me a calculator is less of a black box than a set of tables.  I can
| reproduce the calculator's results using pencil and paper and a bit of
time and
| effort. I could even reproduce the sines and cosines if I wanted to
trouble
| myself with going through a Taylor series expansion.  Because I can
| independently reproduce  what a calculator does, I trust it.  I don't
trust
| tables that I can't reproduce.  (I do trust the Ageton tables, because
they are
| more easily reproduceable).
|
| In this sense, the use of a calculator is arguably less of a black-box
operation
| than the use of sight reduction tables such as Pub 229.  In that sense I
would
| argue that the use of calculators (programmable or otherwise) is fully in
| keeping with the spirit of traditional navigation.  The calculator simply
does
| what you could do with more time and effort.  There is nothing mysterious
about
| it.  Those who came before us weren't a bit shy about using such
labor-saving
| methods as tables of logarithms.  Why should we be shy about using more
modern
| labor-saving devices?
|
| Chuck Taylor
| Everett, WA, USA
|

   

Reply