THE SAILOR’S ASTRO NAVIGATION PRIMERSAMPLE EXCERPTS (C) M.D 2016WWW.MLDEB.COM/NAV.HTML FOR COMPLETE EDITION

Imago MundiBabylonian 6thC ADPera Museum Istanbul

Beatus Mappa Mundi 11thC ADHereford Cathedral England

British Admiralty Chart 1784Inverness Firth, Published 1919

Survey “The Principal Triangulation of Britain” Datum

British Admiralty Chart 1078Inverness Firth, Published 1977

Surveyed OSGB36 Datum (Pre WGS84 GPS)

THE BASIC IDEA FOR ASTRONAVIGATION

A N Y U N I Q U E L O C A T I O N O N E A R T H C A N B E S P E C I F I E D B Y A L A T I T U D E A N D L O N G I T U D E . U S I N G T H I S I N F O R M A T I O N W E C A N T E L L

T H E C U R R E N T L O C A T I O N A R O U T E T O A N O T H E R P O I N T O F I N T E R E S T

A T Y P I C A L L O N G I T U D E A N D L A T I T U D E G R A T I C U L E

(F I G .3) I S F O R M E D B Y U N W R A P P I N G A M E R C A T O R O R T H E T R A N S V E R S E ME R C A T O R P R O J E C T I O N . T H I S P R O V I D E S T H E R E F E R E N C E S Y S T E M A T T H E E D G E O F AD M I R A L T Y N A V A L C H A R T S

FIGURE 2 LATITUDE AND LONGITUDE SPECIFYING A UNIQUE LOCATION ON EARTH

AS T R O N O M I C A L O B J E C T S A L S O H A V E P O S I T I O N A L I N F O R M A T I O N . TH E I R P O S I T I O N S H A V E B E E N R E C O R D E D I N D E T A I L F O R T H O U S A N D S O F Y E A R S B Y A S T R O N O ME R S A T O B S E R V A T O R I E S . IN T H E 17T H C TH E I R P L A C E S I N O R B I T W E R E D E F I N E D M A T H E M A T I C A L L Y B Y J O H A N N E S K E P P L E R A N D E X P L A I N E D B Y N E W T O N . C A S S I N I A N D L A G R A N G E P R O D U C E D W H A T W E W O U L D R E C O G N I S E T O D A Y A S T A B L E S O F A S T R O N O MI C A L P O S I T I O N A L I N F O R M A T I O N .

TO D A Y A N A S T R O N O MI C A L O B J E C T S P O S I T I O N I S L O C A T E D W I T H G H A /DE C

GHA I S U S E D L I K E L O N G I T U D E

DEC I S U S E D L I K E L A T I T U D E

KN O W I N G T H E O B J E C T S P O S I T I O N F O R A N Y T I M E O F T H E Y E A R W E C A N T A K E A S P H E R I C A L B E A R I N G O F I T (C A L L E D A C I R C L E O F E Q U A L A L T I T U D E ) A N D O B T A I N O U R L I N E O F P O S I T I O N R E L A T I V E T O T H E O B J E C T . LA T E R O N Y O U W I L L S E E H O W W E C O R R E C T T H I S B E A R I N G F R O M AP T O T R U E P O S I T I O N B Y TR A N S L A T I N G T H E C I R C L E A L O N G T H E A Z I M U T H L I N E . W H A T E V E R M E T H O D I S U S E D T O F I N D Y O U R P O S I T I O N , S I D E S , D I S T A N C E S A N D A N G L E S O F A S P H E R I C A L T R I A N G L E A R E B E I N G C A L C U L A T E D U S I N G T H E 3D/S P H E R I C A L V E R S I O N O F T H E C O S I N E R U L E .

F IGURE 3 LATITUDE & LONGITUDE AS A SYSTEMATIC GRATICULE

DEC AND GHA F IX POSITION OF SUN ALTITUDE OF SUN CREATES A SPHERICAL BEARING LINE CALLED A CIRCLE OF EQUAL ALTITUDE.WHEN PLOTTED ON A MAP ONLY A LOCAL TANGENT STRAIGHT LINE SEGMENT IS USED

TWO BEARING LINES REQUIRED TO FIX POSITIONWhen using a map one bearing will produce a line of position. A second bearing is required to fix the position. Likewise in astronavigation, using spherical trigonometry, one measured altitude is only sufficient to produce a line of position. A second altitude either from the same object at different times of the day or from another object is required to produce a fix.

F IGURE 4 2D SCENARIO: DETERMINING POSITION WITH 1 AND 2 MEASUREMENTS

SO WHY IS DEC CONSTANTLY CHANGING?S I M P L E

1° / DAY ORBIT1’ / HOUR ROTATIONASSOCIATED FACTOR TIME

T H E S E A R E B A S I C A P P R O X I M A T I O N S W H I C H L A C K T H E P R E C I S I O N R E Q U I R E D B Y A S T R O N A V I G A T I O N . A C C U R A T E V A L U E S A R E U S U A L L Y F O U N D I N A N A L M A N A C O R B Y C O M P U T E R

T I M E , R O T A T I O N A N D O R B I T A R E C O N N E C T E D T H I S A F F E C T S GHA A N D LHA U S E D I N S O L V I N G F O R LO N G I T U D E . L E T ’S H A V E A L O O K A T T I M E , O F T I M E

FIGURE 11 ANGULAR AND TIME MEASURES

THE INTERCEPT TECHNIQUE A G R A P H I C A L R E S O L U T I O N O F P O S I T I O N P U B L I S H E D I N 1873 B Y A D M I R A L M A R C Q D E B L O N D E

D E ST . H I L A I R E A N D T H E B A S I S F O R A L L M O D E R N N A V I G A T I O N A L M E T H O D S I N C L U D I N G GPS. A N O T H E R M E T H O D , T H E S U M N E R M E T H O D W A S A L R E A D Y I N E X I S T E N C E , P U B L I S H E D 1843 B U T I T I S M O R E C O M P L I C A T E D I N T H A T I T P R E S E N T S D I F F E R E N T M E T H O D S D E P E N D I N G O N T H E D A T A Y O U A R E W O R K I N G W I T H .

TAKING A SIGHTING OF THE SUN A C O M P L E T E S U N S I G H T I N G R E Q U I R E S T H E E X A C T D A T E A N D T I M E O B T A I N E D F R O M A N

A C C U R A T E W A T C H A N D T H E A L T I T U D I N A L A N G L E O F T H E S U N O B T A I N E D F R O M A M A R I N E S E X T A N T . T H E M O S T P R A C T I C A L M E T H O D I S D E S C R I B E D B E L O W

O S E T T H E I N D E X M I R R O R S H A D E S – N E V E R L O O K T H R O U G H T H E T E L E S C O P E A T T H E S U N D I R E C T L Y .

O P I C K U P Y O U R S E X T A N T A N D I N T H E S A M E H A N D T H E S T O P W A T C H

O S T A R T Y O U R S T O P W A T C H W H E N Y O U R W R I S T W A T C H E S S E C O N D H A N D R E A C H E S 12/0. M A K I N G A N O T E O F T H E H O U R S & M I N U T E S .

O M O V E T H E S E X T A N T ’ S I N D E X A R M U N T I L T H E S U N C O M E S I N T O V I E W I N T H E R I G H T P O R T I O N O F T H E T E L E S C O P E I M A G E .

O T U R N T H E M I C R O ME T E R G U A G E S L O W L Y A D V A N C I N G T H E I N D E X A R M F O R W A R D U N T I L T H E L O W E R E D G E O F T H E S U N I N T H E T E L E S C O P E I M A G E I S B R O U G H T D O W N T A N G E N T W I T H T H E HO R I Z O N I N T H E L E F T P O R T I O N O F T H E T E L E S C O P E I M A G E . A T T H I S I N S T A N T U S E T H E S T O P W A T C H T O M A R K T H E E L A P S E D S E C O N D S .

STEP 3B HOLDING THE SEXTANT WITH THE INDEX MIRROR NEAR YOUR EYE LOOK TOWARD THE INDEX SCALE . YOU WILL SEE TWO PARTS SPLIT ACROSS THE EDGE OF THE INDEX MIRROR. THE PART ON THE RIGHT IS THE ACTUAL IMAGE WHEN VIEWED AND THE PART TO THE LEFT IS AN IMAGE CREATED BY THE MIRROR ASSEMBLY. IF THE ARC OF THE INDEX APPEARS TO BE UNBROKEN (IN THE SAME PLANE) THEN, AS IN THIS CASE NO LATERAL CORRECTION IS REQUIRED. OTHERWISE THIS INDICATES THE MIRRORS ARE NO LONGER IN PARALLEL ALIGNMENT AND YOU WILL NEED TO USE THE ADJUSTING SCREWS SITUATED BESIDE EACH MIRROR TO BRING THEM BACK INTO A PARALLEL ALIGNMENT

STEP 4 PUT AT LEAST THE 1ST TWO SHADES IN PLACE BEFORE VIEWING THE SUN

READING OFF THE MEASURED ALTITUDEREADING DEGREES AND MINUTES

READING FRACTIONAL MINUTES WITH THE VERNIER

A WORKED EXAMPLE FOR THE SUN T H E D A T E I S F R I 18 APR 2014 UTC I S 12:16 A N D A S E X T A N T R E A D I N G H A S P R O D U C E D A N

U N C O R R E C T E D A L T I T U D E M E A S U R E M E N T , HS = 43° 10’ O U R B E S T E S T I M A T E O F P O S I T I O N U P D A T E D W I T H A C O U R S E V E C T O R O F C O M P A S S B E A R I N G I S

T H E A .P . A S A S I M P L I F I E D C A S E A S S U M E W E ’V E N O T L O N G D E P A R T E D I N V E R N E S S M A R I N A . S O O U R AP I S

I N V E R N E S S M A R I N A A T LAT=57° 29’ N & LNG 4° 14’ W. W E W I L L S I G H T T H E S U N L O W E R L I M B A N D U S E T H E C A L C U L A T O R P R O G R A M T O C O M P U T E DIP, R E F R A C T I O N A N D S E M I D I A M E T E R . T H I S P R O D U C E S H C 43⁰ 25’ Z N =179⁰ 54’ & Z D =-2.48 N A U T I C A L M I L E S A W A Y F R O M T H E SU N ’S G.P.

PLOTTING THE INTERCEPT ON A CHART P E R F O R M A S I G H T R E D U C T I O N U S I N G A C A L C U L A T O R O R AL M A N A C T H E N W I T H T H E P L O T T I N G

S O L U T I O N Z N , T O/AW A Y , Z D P R O C E E D L A Y T H E P R O T R A C T O R B A S E A G A I N S T T H E L O N G I T U D I N A L L I N E O F Y O U R AP M E A S U R E T H E S U N ’ S

A Z I M U T H A N G L E Z N (179⁰ 54’ ) . M E A S U R E Z D N A U T I C A L M I L E S T O O R A W A Y F R O M T H E AP. DR A W A L I N E A T 90 D E G R E E S T O T H E A Z I M U T H L I N E . T H I S I S Y O U R 1 S T L O P/BE A R I N G . YO U R L O C A T I O N I S S O M E W H E R E A L O N G T H I S L I N E .

SIGHT REDUCTION USING ALMANAC DATA T H E F O L L O W I N G E X C E R P T F R O M T H E AL M A N A C P U B L I C A T I O N (HMNAO P U B GP 100)

D E S C R I B E S H O W T H E V A R I O U S D A T A I S O B T A I N E D F R O M T H E A L M A N A C A N D U S E D T O O B T A I N A GHA A N D DEC F O R A N Y D A T E A N D T I M E F O R T H E G I V E N Y E A R T H A T E D I T I O N O F T H E A L M A N A C H A S B E E N P U B L I S H E D F O R . O N C E T H E GHA A N D DEC H A S B E E N O B T A I N E D A S I M I L A R P R O C E S S I S U S E D I N T H E S E P A R A T E P U B L I C A T I O N (HMNAO P U B NP303/AP3270) F O R S I G H T R E D U C T I O N T O O B T A I N A P L O T T I N G S O L U T I O N .

FORMS FOR USE WITH AN ALMANAC T H E S E E X A M P L E F O R M S A R E P R O V I D E D B Y T H E A D M I R A L T Y A L A M A N A C O F F I C E F O R P E R F O R M I N G

V A R I O U S S I G H T R E D U C T I O N S .

W H E N M E A S U R I N G O F F T H E TO/A W A Y D I S T A N C E A L O N G Y O U R LOP I T I S I M P O R T A N T T O R E A L I S E T H A T T H E L I N E A R D I S T A N C E R E P R E S E N T E D B Y 1 O I S E Q U I V A L E N T T O 60 N A U T I C A L M I L E S A T T H E LA T I T U D E O F T H E E Q U A T O R O N L Y . A T D I F F E R E N T L A T I T U D E S I T V A R I E S . M O S T A D M I R A L T Y C H A R T S T A K E T H I S I N T O C O N S I D E R A T I O N A N D T A B U L A T E A N A P P R O P R I A T E L I N E A R D I S T A N C E S C A L E . SO M E O T H E R C H A R T S P R I N T A D E V I C E O N T H E C H A R T T O C A L C U L A T E W H A T L I N E A R S C A L I N G T O A P P L Y . O N E E X A M P L E O F T H I S I S A L S O I N C L U D E D H E R E .

APPENDICES

Obtaining GHA & DEC from the Nautical Almanac

Calculating your LHA, GHA

Calculating your Latitude using DEC at Local Mid-Day

Procedure for 3 star fix

Procedure for Sun, Moon, Planets, Stars

Obtaining Hc, d, Z using sight reduction tables NP301/AP3270/Pub.249

Sample plotting sheet

The law of cosines derived for the spherical triangle using vector calculus

Worked example of a sun shot using the intercept method

Worked example of a noon day sight

Time – UTC description

Equipment list

Further resources

CALCULATING LHA FROM GHA

SPHERICAL MATH OF NAVIGATIONAL TRIANGLES TH E FOLLO WIN G R EPR ESEN T T H E C OMP LET E SET OF T RI A NG LES US ED IN SOLV I NG

NA V IGA T IO NA L PR OB LEMS

GE OM E T RY FO R SO LVI N G TH E SP H E RI CA L TR IA N GLE

WORKED EX. DETAILS – INTERCEPT METHODNB .

ROU N DI N G HA S OC CU RR E D IN TH E DE C IM A L SE C ON D S DU E TO DIP, REFR AN D SD AS TH E SE RE S UL TS AR E FR OM A CO M P UT E R .

ALW AY S NOR TH=+, SOU TH=- EAS T=+ WE ST=-

AP AN D DR AR E US UA LLY TA KE N TO M E AN TH E SA M E TH IN G .

HS 43⁰ 10’ ME A S U R E D F R O M S E X T A N T

+/-IC 00’ SU B T R A C T I F “ O N T H E A R C , F O R W A R D O F T H E 0” A D D I F “ O F F T H E A R C , B E H I N D T H E 0” < 0

-DIP -02’ S U B T R A C T

HA 43⁰ 08’ A P P A R E N T A L T I T U D E

-REFR 01’ S U B T R A C T

SD+LL/-UL +16’ A D D W H E N S I G H T I N G L O W E R L I M B O T H E R W I S E S U B T R A C T

HO 43⁰ 22’ OB S E R V E D A L T I T U D E

Zonetime (ZT)

Used in combination with watchtime (WT) Navigation at Sea Divide the world into 24x15⁰ wide zones.

o Each zone is centred on the meridian with the margins at 7.5⁰ either sideo Each zone has a letter Z (Zulu) for Greenwich (J is unused)

GHA FROM ALMANA/COMPUTER 04⁰ 09’DEC FROM ALMANAC/COMPUTER 10⁰ 54’

AP LNG -04⁰ 14’

LHA = GHA – AP LNG -01⁰ 55’ 30”= 04⁰ 09’ + (-04⁰ 14’)RESULT MUST BE IN RANGE 0-360 SO +360

LHA 359⁰ 55’ 30”

o Zones West of Greenwich have a positive delta increment and East have a negative delta increment (which is different to what happens in Timezones)

o Also a practical limitation on applicability with regard to resetting timezone on a vessel every 60nm

o Clock time on larger vessels may also be governed by working regulations

Figure 1 Map of Timezones & Zonetime - Source NIST (for ZT West should be "+" and East should be "-")

Timezones (TZ)

Timezones are mainly used on lando Opposite of ZT have decreasing deltas to the West and increasing deltas to

the Easto May have DST appliedo Practical recognition of applicability in a country-wide context

Eg. Its impractical to reset your watch to a new timezone every 60nm for a road-trip you take.

China, a country that spans a large E-W range for example only has 1 timezone

Watchtime (WT) and practical application on a Sailboat

This is used in conjunction with Zonetime on your Sailboat and is simply the current time on your wristwatch

Before departure it is practical to set your wristwatch to either the ZT of your departure port or the ZT of your arrival port.

This means your watch will be out of synchronization of the “apparent” day but apart from this small inconvenience represents the best solution for astro navigation

E Q U I P M E N T L I S T

SEXT A N T

WA T C H C A L IB RA T ED WIT H A B RO A DC A ST T IMES IGN A L SU C H A S ON SWR OR RA DIO 4

ST OPW A T CH

CA LC ULA T OR/C OMP UT ER

N A VI GA T ION QU ALI T Y PR OT R A C T OR SU C H A S T H E PO RT LA N D

PA RA LLEL RULE

D IV IDER S

ADMIR A LT Y / CH A RT S FOR A REA OF IN T ERES T

CH IN A GR A PH PEN C IL

AR TI ST S PU T T Y ER AS ER