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Re: Why are NA sight reduction tables not
From: Gary LaPook
Date: 2012 Apr 8, 14:16 -0700

The criticism of this standard formula is that it produces an "azimuth angle" in the range of 0 to 90° and so some worry that a navigator might get confused when the azimuth is near east or west. I, for one, don't believe that this is a likely problem for a practical navigator at sea (or in the air) but is only a concern for those working sample problems on dry land. Even if the navigator plotted the azimuth as 89° instead the correct 91° the effect on the resulting LOP would be de minimis (too small to worry about.) We discussed this formula several years ago and George Huxtable argued for using a different formula using the TAN function to produce azimuths without this perceived ambiguity. The formula used by the Power Squadron also eliminates this perceived problem but at the expense of a whole lot more key strokes. This might be better for classroom work but not in the real world:

cos Zc = (sin Dec - (sin Lat * sin Hc)) / (cos Lat * cos Hc)

compared to:

sin A=(cos DEC sin LHA)/cos Hc.

Or restated

sin A = sec Hc cos DEC sin LHA.

(This is easier to use on a calculator. After you derive Hc with the law of cosines formula just take the cosine of it, then the inverse and then continue on with the rest of the formula.)

Since my implementation of the Bygrave method also has the same "ambiguity" I include these rules for resolving it and the first two rules also work for most cases using this simpler formula:

EXPLANATION OF AZIMUTH RULES

In most situations there is no ambiguity as to which 
quarter the Zn lies since you know the approximate direction you are 
looking when you take the sight. The problem arises because the azimuth 
angle is limited to the range of zero to 90 degrees and when the Zn is near 
east or west the correct Zn might fall either 
side of the line so there is an ambiguity in converting from azimuth 
angle to Zn.

One easy rule to apply first is that if the declination is greater than 
the latitude then the azimuth can never be in the opposite semicircle. 
To generalize this rule, if the declination has 
the same name as the latitude and the declination is greater than the 
latitude, then you start with the direction of the elevated pole (the 
nearer pole) when converting from azimuth angle to azimuth (Zn.)

The second rule to apply is that if the declination is contrary then the Zn 
must be in the opposite
 semicircle. To generalize this rule, if the 
declination and the latitude have contrary names then you start with the 
direction of the depressed pole (the further pole) when converting from 
azimuth angle to Zn.

These two rules take care of most of the cases, especially for 
navigators in low latitudes.

The remaining ambiguity concerns situations in which the declination is 
the same name as the latitude but is less than the latitude. In this 
situation the azimuth of the body will be both north and south of the 
east - west line during part of each day. The rules compare "W" 
with latitude to resolve this remaining ambiguity.

So, combining all three rules:

If the declination or if "W" is greater than the latitude then combine 
the azimuth angle with the direction of the elevated pole.
If the declination name is contrary to the name of the latitude or if 
"W" is less than the latitude then
 combine azimuth angle with the 
direction of the depressed pole.

--- On Sun, 4/8/12, Gary LaPook <garylapook@pacbell.net> wrote:

From: Gary LaPook <garylapook@pacbell.net>
Subject: [NavList] Re: Why are NA sight reduction tables not
To: NavList@fer3.com
Date: Sunday, April 8, 2012, 11:36 AM

Are you sure that is the correct formula for finding Azimuth?

The standard formula is
sin A=(cos DEC sin LHA)/cos h.

gl

--- On Sun, 4/8/12, Alexandre E Eremenko <eremenko@math.purdue.edu> wrote:

From: Alexandre E Eremenko <eremenko@math.purdue.edu>
Subject: [NavList] Re: Why are NA sight reduction tables not
To: NavList@fer3.com
Date: Sunday, April 8, 2012, 10:05 AM

Geoffrey,
Thanks.

The formula for the asimuth in NA seems a little
more complicated than the one
taught by PE. I don't know what is the reason for this more complicated
formula.
All Russian books use even simpler formula:
sin A=(cos Lat sin LHA)/cos h.
where A is the asimuth, h is the altitude.
That's what I use.
It requires 3 inputs of angles to the calculator (without memory) while PS
requires 5
and NA requires 6.

There are also modified Russian formulas optimized for the calculator with
one memory cell (like Casio f250), however I do not use them, because
they compute asimuth first and altitude second, while I need
only altitude in most cases for land observations.

Alex.

On Sun, 8 Apr 2012, Geoffrey Kolbe wrote:

>
> At 16:08 08/04/2012, you wrote:
>
>> I would like to follow this discusion,
>> But what is the formula (for the calculator) taught by the Power Squadron?
>> Can anyone give me a link with this formula?
>
> <http://www.akronpowersquadron.com/NauticalTools/SightReduction/SightReduction.shtml>http://www.akronpowersquadron.com/NauticalTools/SightReduction/SightReduction.shtml
>
>
>> (I know two formulas for sight reduction).
>
> Why Alex, there is a world of excitement waiting for you then. ;-)
>
> Geoffrey
>
>
>
>
>
> : http://fer3.com/arc/m2.aspx?i=118813
>
>
>

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