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Re: Abhav sightreduction?
From: Greg Rudzinski
Date: 2012 Aug 1, 11:46 -0700

Here is what the Weem's reduction looks like. (The example is lower limb Sun and 2 meter H.E. right ?)

aLat. 47* N aLon 3*4.5' W
Dec 6*21' S
LHA 45*

5748 56*35.9'
34221 +6*21.0'
______ _________
39969 62*56.9'
Hc23*29'
Ho23*10.5'
int 18.5 away
Z = S49.5W = Az 229.5*

Greg Rudzinski

[NavList] Re: Abhav sightreduction?
From: Gary LaPook
Date: 1 Aug 2012 09:28
Kermit, thanks for giving me an opportunity to see if I can still understand French, I can!

But, rather than try to type a translation myself, I went to Google translate and attach it here. I take no credit or blame for the accuracy of the following translation.

gl
----------------------------------------------------------
The calculations required for the Astro

Method "manual"

using tables and Dieumegard Battle

(For the life table method HO-249, click here)

Tables Dieumegard and Battle were widely used before the appearance of HO-249. It was the formal calculation of the Navy, edited by SHOM under the name "900 Tables". They are sold on navastro.fr.

These tables have the advantage of being relatively small, compared to the massive size and weight of HO-249. Indeed, they may contain a specification of less than 40 pages. However their use is somewhat more complex than the HO-249 and above, they use a relatively sophisticated system that is that unless very maths, we can only use "stupid" without really understanding why the how. This does not change the result, but an intellectual point of view of understanding the system, it's a bit frustrating. This is actually a particular presentation, suitable for navigation, tables of logarithms using the system-versines haversines (Want to know the mathematical details of these tables? Click HERE)

The tables Dieumegard:

Description: These tables are only used for calculating the height calculated using a formula different from the usual formula. They come in the form of 29 tables of numbers, divided into 4 groups:
Table 1 (12 pages) provides a first number (A) from the angle local time;
Table 2 (5 pages) gives a second (B) and a third number (C) from the estimated latitude of the observer and the declination of the star;
Table 3 (pages 6) provides a fourth number (D) from the sum of A + B + C;
Table A (6 pages) gives a fifth digit (E) from our latitude and declination, then the height calculated from the sum D + E.

This shows that, as usual, always calculate the geographical position of the star (point Pg) to determine its declination (Dec.) and hour angle (HA). Always have also estimated position in latitude (L) and longitude (G).
These two positions (star and estimated) give the three parameters still needed:

• The declination of the star in December,
• The AHL Local hour angle of the star = AH + / - Longitude estimated G (if G + is, - if G West)
• The estimated latitude L

See a practical example encrypted to fix ideas:
and here this canvas filled with the following example.

March 4, 1998, you observe the sun at 15h 24min 4s UT, at a height of 22 ° 59 '. Your estimated position is L = 47 ° 29 'N and G = 2 ° 53' W. You look at 2m above sea level Calculate the right height.

We will use the Nautical Almanac Office of Longitudes:
Here is an excerpt from page 04/03/1998
(To see the entire page, click here)
The first column gives the hour UT,
the second, the sun AHvo
and the third its declination.

Calculation of the Declination of the Sun:

At 15h, the variation was 6 ° 21.4 'S. At 16h, it will be 6 ° 20.4 'S. It thus decreases a 'per hour. So we can easily estimate, "the eye", only 15h 24min 4s she was 6 ° 21 'S.

Calculation of the Hour Angle of the Sun:

At 15h, the hour angle was 42 ° 3.5 '. Using interpolation tables provided at the end of the ephemeris, we find that the sun during the 24min additional 4 s, moved from 6 ° 1 '. Its position is 15h 24min 4s thus: 42 ° 3.5 '+ 6 ° 1' = 48 ° 4.5 '

The Sun's position at the instant of observation is thus: 48 ° 4.5 'W 6 ° 21' S, somewhere south of Belem, the Amazon.

Calculation of the local Hour Angle (LHA):

Our estimate is West longitude, we must subtract the hour angle of the sun to get the local hour angle AHL:
48 ° 4.5 '- 2 ° 53' = 45 ° 11.5 '

A determination of the figure:

We enter the table with a value of Dieumegard Ahl ie in this case: 45 ° 11.5 '. There are A = 0.5298

Determination of the number B:

With our estimated latitude (47 ° 29'N), one enters the table 2. There are B = 0.1702

Determination of total C:

Also in Table 2 (on another page if necessary), it was placed at C corresponding to the declination of the sun (6 ° 21'S). C = 0.0027

Determination of total D:

We add the three numbers A + B + C: 0.5298 + 0.1702 + 0.0027 = 0.7027.
With this result, we enter inside the table 3 for the number touver D = 0.1983

Determination of total E:

If our Latitude and Declination were of the same name (both N or S), the soustraierait.
But as in our example, they are of opposite (L = 47 ° 29'N, 6 ° = December 21'S), are added. 47 ° 29 '+ 6 ° 21' = 53 ° 50 '
With this value, through the table A, we find the value E = 0.4099

Determination of height calculated:

Then adding these figures D and E: 0.1983 + 0.4099 = 0.6082
With this number you enter inside the table to find A (well. ..) the calculated height: Hc = 23 ° 4 '

Calculation of Intercept:

It first calculates the true altitude by correcting our instrumental height of the correction found in the correction tables.
Hv = 22 ° 59 '+ 11.3' = 23 ° 10.3 '

Then subtracts the calculated height Hc:

Our intercept is thus: 23 ° 10.3 '- 23 ° 4' = 6.3 'or 6.3 million, toward the star.

Tables of Battle:

Description: These tables are used to calculate the Azimuth. That is why they complement each Dieumegard tables (which determine only the calculated height) and are mostly associated. Especially since the user manual of the two tables is very similar. However, as you will see, they are totally independent.

Battle of the tables are presented in the form of 10 tables of numbers divided into two groups:
Table 1 (4 pages) can turn the corner to the pole P and our estimated latitude The first digit in a (m). If P <90 °, is given m the sign -;
Table 2 (6 pages) can turn the declination in December and our estimated latitude L in a second number (n). If D and L are the name (N or S) different, n is given the sign -.
We add m + n.

Finally, the fitted result of this addition and P, it returns in Table 2 to find the value of the azimuth.

So we use always the same three initial parameters: estimated Latitude (L), Local Hour Angle (LHA) and Declination (Dec). We shall not repeat their calculation (see above).

Numerical example:

We will continue with the same example as above.

One must first calculate the angle at the pole P, according to Ahl:
AHL if <180 ° P = AHL
if AHL> 180 ° P = 360 ° - AHL

In our example, the AHL is 45 ° 11.5 'P = 45 ° 11.5'

Determination of the number m:

Using our angle to the pole (P = 45 ° 11.5 ') and our estimated latitude (L = 47 ° 29'N) in Table 1, we find m = - 0.52 (P <90 °, then m negative)

Determination of the number n:

The same is done with the Declination (Dec. 6 = 21 ° S) and our estimated latitude (L = 47 ° 29'N) in Table 2. We find n = - 0.07 (December and L are different name, so no negative)

Determination of the azimuth:

Then added m and n: - 0.52 + - 0.07 = - 0.59.
Using that number with our angle to the pole P, in Table 2, we determine the azimuth Z = 50 °
In this figure, we apply a final calculation
facilitate the drawing of azimuth relative to north:
m + n> 0 m + n <0
Lat. N Lat. S Lat. N Lat. S
AHL> 180 °
(Morning) Zn Zn = Z = 180 - 180 Z = Zn - Zn Z = Z
AHL <180 °
(Afternoon) Zn = 360 - Z Zn Z = 180 + 180 + Zn = Zn = Z 360 - Z

In our case, m + n <0 (- 0.59), our Lat. is N, and AHL <180 ° (it is 45 ° 11.5 '), so Zn = 180 + Z = 180 + 50 = 230 °

We here at the end of calculations. The data we have now are:

Our estimated position: (47 ° 29 'N, 2 ° 53'W)

Intercept (6.3 M, to the star)

and the azimuth (230 °).

Armed with this data, it remains for us to draw our line of position.

Moving to the track on the map ...

Back to Table of Methods
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--- On Wed, 8/1/12, Antoine Couëtte <antoine.m.couette---fr> wrote:

From: Antoine Couëtte <antoine.m.couette---fr>
Subject: [NavList] Re: Abhav sightreduction?
To: NavList---org
Date: Wednesday, August 1, 2012, 8:03 AM

The Abhav method seems (quite) close to the "Tables Bataille" calculations with haversines which have been in official use in the French Navy for (well) over fifty years now.

See http://navastro.free.fr/dieumegard1.htm (I could not find any reference in English, sorry ...)

Kermit
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