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ASTRO NAV - THE DETAILS

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STAGES OF OBTAINING A POSITION LINE FROM A SUN SIGHT

THE INTERCEPT METHOD

These notes are intended to be used to support study on an RYA Ocean Shorebased Course. They are not meant to be a text book substitute but to help master the basics of getting position lines from sights using a pro forma and the Air Nav Sight Reduction Tables . 

ARITHMETIC

Note that only simple arithmetic (adding and subtracting) is required. Remember there are 60  minutes in a degree and that minutes are divided into tenths (decimals) not seconds.  

53 deg. 15.3 mins. plus 12 deg. 48.8 mins. equals 66 deg. 04.1 mins.

58 deg. 14.2 mins. minus 17 deg. 57.3 mins. equals 40 deg. 16.9 mins. 

If your arithmetic is rusty lay out the above sums on a piece of paper and check your answers. This is as hard as it gets.

PRO FORMAS 

Look at my pro formas and then design your own. You will learn a lot by doing this and have a reference to remind you of the various rules to be applied.     

Please E Mail me with any comments or suggestions - E Mail Ian Crowson  

THE END PRODUCT - THE FIX BUT FIRST THE POSITION LINE

A single sun sight will give us a position line. This position line when run forward or back to another will result in a fix.  

The run is the direction and distance sailed from the time of morning sight to the time of the noon sight. (like a DR) If there is tidal stream or current this would be applied as in an EP.

 

I will cover the method of getting a noon (meridian) latitude later.

In order to keep the process as simple as possible lets break it down into four stages: sextant work, nautical almanac, sight reduction, and intercept/plotting.  

SUMMARY OF THE FOUR STAGES.  Study these to understand the whole process. In my experience of teaching astro nav many people lose track of big picture whilst working on the details.

Ian Crowson April 2008

THE FOUR STAGES OR WORK AREAS.

1. Sextant

Hs > index error > dip > altitude correction > Ho

 

2. Nautical Almanac

Find position of sun at exact time of sight:

a. take GHA apply assumed longitude to get LHA                                       

b. extract declination.                                               

 

3. Sight Reduction Tables

Enter tables with assumed latitude, declination, and LHA       ........extract Hc and Zn (azimuth or bearing of sun)

 

4. Intercept/plotting

Ho & Hc gives intercept.   Zn gives bearing of sun/direction of intercept. Plotting gives a a position line.

Now the details:

1. Sextant work

Getting the Ho

The sextants job is to measure the angle of the sun above the visual horizon. A number of corrections are applied to the angle measured with the sextant (Hs) to get the true altitude (Ho) of the sun above the celestial horizon. (*note below) The Ho is required to calculate the intercept.

The angle measured by the sextant is the Hs. The exact time in UT the sight is taken is noted.

The true altitude is known as the Ho.

CORRECTIONS -  Hs to Ho -  In order of application

1. Index error - individual to a particular sextant **

2. Dip -  this depends on the height of observer above sea level. ***

              .......... apply corrections for index error and dip and then apply: ........

3. Altitude Correction from table in Nautical Almanac ****

 

Notes.  

*The celestial horizon runs through the center of the earth. It is a plane constructed at right angles to a vertical line dropped from the position of the observer to the center of the earth.  

**Index error. A small index error (say up to 6’) is normal on most sextants. The error is due is the index mirror being slightly misaligned. It shows as a step on the horizon when viewed through a sextant set to zero degree/minutes. Rule: if error off the arc add it on to Hs, if on the arc take it off Hs.  

The sextant is an instrument and requires adjustments before use. Please refer elsewhere for details of these important adjustments. However do not constantly adjust the correct index error as you will wear the adjustment screws.

***Dip. Dip depends on the height of the observer above sea level. This correction allows for the difference between the visual horizon and terrestrial horizon. The correction for dip is found in a table in the nautical almanac and is always subtractive.

****The altitude correction includes the corrections for refraction, semi-diameter and parallax. This correction is found in a table in the Nautical Almanac.

Refraction is the bending of the suns rays as they enter the earths atmosphere and varies with altitude.

The correction for semi-diameter allows for the normal practice of bringing lower limb (bottom) of the sun down to the horizon rather the middle.

Parallax allows for the difference in view points between the observed position of the sun (actually as viewed from sea level) and that from the center of the earth. This is a very small correction in the case of the sun which is a long way from earth but greater in the case of the moon which is relatively near.

Ian Crowson May 2008

PRO-FORMA

 CONVERTING SEXTANT ALTITUDE (Hs) TO TRUE ALTITUDE (Ho)

 

DATE…………………….       HT. OF EYE…………    INDEX ERROR…………..

WATCH TIME        …………..

CORRECTION      …...……..

             GMT     __________

            …………………..         Hs - SEXTANT ALTITUDE - FROM SEXTANT

   +/-     …………………..        INDEX ERROR (- IF ON THE ARC)

   =       _____________

   -        ………………….          DIP (HEIGHT OF EYE)  (ALWAYS  - (FROM CORRECTION TABLE IN NA)       

   =       _____________          APPARENT ALTITUDE (FROM CORRECTION TABLE IN NA)  

  +/-      ………………….          ALTITUDE CORRECTION (FROM CORRECTION TABLE IN NA)

 

   =       _____________          Ho - TRUE ALTITUDE  

 Ian Crowson  2001

 

2. Nautical Almanac

Getting the Exact Position of the Sun at Time of Sight

The almanac contains the exact positions of the sun, moon, planets or stars for every second of the year.

  Declination and GHA > assumed longitude > LHA  

Using the Nautical Almanac you can find the position of the sun at exact time of sight. The sun's position is given as declination, this is how far north of south it is. How far the sun is west of Greenwich (the Prime Meridian) is given as Greenwich Hour Angle -  GHA

Select the correct column in the almanac for the sun! You are looking for the GHA of the sun for the exact time of your sight. The GHA is given for every hour of each day. Use the yellow pages at the back to get the GHA for the minutes and seconds.

Apply assumed longitude to GHA, minus west or plus east, to obtain LHA.

Note LHA must be a whole degree if you intend to use sight reduction tables. Doctor EP longitude by as little as possible to get an assumed longitude which when added (east) or subtracted (west) from GHA results in a whole degree of LHA.  Take note of your assumed longitude  as this is used when plotting intercept.

Take declination from daily pages for exact time of sight. Interpolate between hour figures to get increment for min/sec. Note to add/subtract depending on if declination is increasing or decreasing.

3. Sight Reduction

Getting the Hc and Zn  

The RYA Course uses AP 3270 Sight Reduction Tables for Air Navigation Vols.  II & III.  Volume II latitudes 0 – 39 degrees north or south. Volume III latitudes 40 – 89 degrees north or south. Volumes II & III are limited to celestial objects whose declination (angle above or below the celestial equator) is less than 29 degrees. This is good enough for the sun, moon, planets and some stars. Volume 1 covers the stars.

Enter tables with assumed latitude, declination and LHA     ........extract Hc and Zn (azimuth - bearing of sun)

To enter the tables latitude and LHA must be whole degrees.

Your DR/EP latitude becomes the assumed latitude by rounding it to the nearest whole degree.

Look for the page in the tables for your latitude, degree of declination (taking note if declination  is same or contrary to latitude)  and find LHA down one side. Follow down from declination and across from LHA and extract Hc And Z and d. Take d to correction page/loose card and enter with d and minutes of declination. Add correction to Hc. Take Z and apply rule top left corner for  northern lat, bottom left for southern latitude to get Zn (azimuth /true bearing of sun from assumed position.)

Northern Lat:  LHA > 180 deg. A = Zn.   LHA < 180 deg. Zn = 360 - Z

Southern Lat.  LHA > 180 deg. Zn = 180 deg. - Z.   LHA< 180 deg. Zn = 180 + Z  

The tables have full instructions.

Your now have Ho and Hc and the suns azimuth. (Zn)

Ian Crowson May 2008

 

SIGHT REDUCTION USING A POCKET CALCULATOR

This requires a scientific calculator. It should have sin, cos and tan functions and be able to handle degrees and minutes. The Casio fx-83WA which should cost less than £10 is suitable.

1.  Sun Sights. 

A. To find Hc (calculated altitude) (Do this calculation first as the Hc is required to find Azimuth)

Required:   (a) LHA of body   (b) DR Latitude   (c) Declination of body

sin Hc  = 

(cos LHA x cos DR lat x cos dec)  + or - (sin DR lat x sin dec)

Note: use + if lat and dec are same names.

B. To find Azimuth (Zn)

Required:   (a)  DR Latitude   (b) Declination of body   (c) Hc (from first calculation)

cos Az * =  

sin dec +/- (sin Hc x sin DR lat) divided by (cos Hc x cos DR lat)

Note: use + when lat  and dec are of opposite names.

* Remember Az is the azimuth angle. To get Zn (Azimuth) apply the rules:

Northern Lat:  LHA > 180 deg. Azimuth = Azimuth Angle.   LHA < 180 deg. Zn = 360 - Az

Southern Lat.  LHA > 180 deg. Zn = 180 deg. - Az.   LHA< 180 deg. Zn = 180 + Az  

Ian Crowson. Dec 2005

4. Intercept and plotting. 

Using the Ho, Hc and Zn to obtain a Position Line

Plotting on plotting sheets or charts?

Plotting to obtain a fix in an ocean area is done on a plotting sheet rather than the chart which would be too small a scale. Plotting sheets such as the Imray allow a section of a larger scale Mercator chart to be created. Instructions on the sheets. If your are practicing in an area covered by a larger scale chart, say 1:125000 or greater, typical cross channel chart, then plot directly on the chart.

Ho / Hc gives intercept.   Zn gives true bearing of sun/direction of intercept. Plotting gives position line.

Hc - Ho = INTERCEPT AWAY   Ho - Hc = INTERCEPT TOWARDS

Ho is the corrected sextant altitude from your sight.

Hc is the calculated altitude from your AP (assumed position) taken from the sight reduction tables.

The Azimuth is the true bearing of the sun from your assumed position taken from the sight reductions tables.

 

The position line (in red below) is actually a circle around the GP (geographical position) of the sun. The azimuth (bearing of the sun) tells you which part of the circle you are on. The circle is very large (maybe 1500 miles dia.) so the bit we are interested in appears as a straight line.

 Hc - Ho = INTERCEPT AWAY   Ho - Hc = INTERCEPT TOWARDS

Ian Crowson May 2008

MORE TO COME

UNDER DEVELOPMENT - MORE TO FOLLOW:

 

ONE TO ONE TUITION IN ASTRO NAV...........................REVISION FOR OCEAN EXAM......................EMAIL OR PHONE IAN CROWSON

Ian Crowson May 2008

How accurate can I expect to be with   'fixes'  with the Davis Mark 15
once I become competent at using it?

The Davis sextants are capable of accurate work. Being plastic there is more potential for inaccuracies  as the are and micrometer cannot be as finely machine as metal. Here is a link to an article:  http://www.starpath.com/online/celestial/plastic.pdf   David Burch at the StarPath School of Navigation is a leading authority on astro nav. If you have not seen Starpath's Site its worth a visit.
You should be able to get accurate results with practice, especially from the shore. Something you could try is to take a series of sights, say ten over ten minutes noting the time and altitude and then draw a graph which should produce a straight line. Any bum sights would show up as being off the line.This also tests your timing of the sights. Using this method does not require the time intervals between sights to be the same.
regards
Ian Crowson

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UNDER DEVELOPMENT - MORE TO FOLLOW:

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