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Introduction Corrections to Sextant Time Finding GHA and Declination Assumed Position and Local Hour Angle Computed Altitude and Azimuth Interpolation Altitude Intercept Using Position Plotting Sheets Plotting Lines of Position
FINDING G.P . "GEOGRAPHIC POSITION"
(GHA and Declination)
IF YOU know THE DATE AND EXACT TIME IN THE ZONE OF GREENWICH (GMT), YOU can determine THE GEOGRAPHICAL POSITION (G.P.) OF THE SUN, MOON, VENUS, MARS, JUPITER, SATURN, OR ANYONE OF FIFTY SEVEN STARS. ALL YOU DO IS LOOK UP THE GHA AND DECLINATION OF THE BODY YOU WANT IN THE NAUTICAL ALMANAC. THE ONLY ARITHMETIC INVOLVED IS ADDING SOME NUMBERS.
THE PROBLEMS EXPERIENCED IN FINDING GHA’S AND DECLINATIONS ARE ALMOST ALWAYS THE SAME.
SO ARE THE SOLUTIONS.
1. MISTAKES IN ADDITION: THEY HAVEN'T HAD MUCH PRACTICE ADDING DEGREES AND MINUTES, AND TEND TO TREAT THEM LIKE DOLLARS AND CENTS. THE PRACTICE YOU'VE ALREADY HAD ADDING AND SUBTRACTING HOURS AND MINUTES SHOULD HAVE YOU AT LEAST PART OF THE WAY OVER THAT HUMP.
2. LOSING THEIR PLACE IN THE ALMANAC, OR LOOKING IN THE WRONG PLACE: THE CURE FOR THIS IS TO ADOPT A SET ROUTINE AND FOLLOW THE SAME PROCEDURE EVERY TIME UNTIL IT BECOMES A HABIT. TWO OPENINGS OF THE ALMANAC ARE ALL YOU EVER NEED TO GET A GHA AND DECLINATION. TAKE DOWN ALL THE INFORMATION YOU'RE GOING TO NEED FROM THE FIRST PAGE YOU CONSULT, GO TO THE OTHER PAGE AND TAKE OUT THE INFORMATION YOU NEED FROM IT, AND THEN CLOSE THE BOOK AND DO THE ARITHMETIC. IT'S THE FLIPPING BACK AND FORTH IN THE BOOK THAT CAUSES THE TROUBLE.
3. FORGETTING WHAT TO LOOK UP NEXT: USE A WORKFORM.
THE BULK OF THE NAUTICAL ALMANAC, SOME 250 PAGES, CONSISTS OF WHAT ARE CALLED "DAILY PAGES." EACH PAIR OF PAGES (LEFT AND RIGHT HAND) SHOWS THE INFORMATION NEEDED TO GET THE GHA AND DECLINATION OF THE SUN, MOON, FOUR PLANETS AND THE STARS FOR EVERY WHOLE HOUR OF GMT FOR THREE DATES. THERE IS OTHER INFORMATION, SOME OF WHICH WE'LL GET TO LATER, AND SOME WE WON'T NEED AT ALL. YOU MAY WANT TO HAVE A LOOK AT THE 1981 NAUTICAL ALMANAC EXCERPTS TO SEE HOW A COMPLETE SET OF DAILY PAGES IS LAID OUT. IN THIS CHAPTER, WE'RE GOING TO LOOK AT ONE THING AT A TIME, IT'S EASIER THAT WAY.
YOU'LL SEE INFORMATION IN THE ALMANAC WHICH WE IGNORE. IF IT ISN'T MENTIONED, YOU MAY IGNORE IT TOO. ASTRONOMERS ALSO USE THE ALMANAC AND IT’S SOMETIMES USED FOR EXTREMELY PRECISE LAND SURVEY TECHNIQUES, SO IT CONTAINS SOME DATA NOT NEEDED BY A SEA-GOING NAVIGATOR. FIRST, LET'S WORK WITH THE SUN. ALL THE DATA NEEDED TO GET THE GHA AND DECLINATION OF THE SUN FOR THE WHOLE HOUR OF GMT IS IN THE LEFT-HAND COLUMN OF THE RIGHT HAND DAILY PAGE.
TO GET THE FEEL OF THE SUN COLUMN, LOOK UP THESE GHA'S AND DECLINATIONS AND CHECK YOUR ANSWERS.
ON THE NEXT PAGE YOU SEE THE INCREMENTS AND CORRECTIONS TABLE FOR 43 MINUTES PAST THE HOUR THAT IS, "ANY HOUR" OF GMT. IT'S ACTUALLY FOUR COMPLETE TABLES FOR THAT 43RD MINUTE.
THE EXTREME LEFT COLUMN BREAKS THE MINUTE INTO 60 SECONDS. THE NEXT THREE COLUMNS SHOW HOW MUCH GHA WILL INCREASE IN 43 MINUTES AND SO MANY SECONDS FOR THE SUN AND PLANETS, ARIES, AND THE MOON. YOU'LL BE USING ARIES WHEN WE GO TO WORK ON STARS, BUT FOR NOW WE'RE CONCENTRATING ON THE SUN.
THE THREE COLUMNS TO THE RIGHT OF THE VERTICAL DOUBLE LINE ARE USED TO GET THE AMOUNT OF CHANGE OF DECLINATION FOR 43 MINUTES PAST THE HOUR. THIS OFTEN CONFUSES PEOPLE, SO LOOK AT IT CAREFULLY. IT’S REALLY ONE LIST. IT COULD BE PRINTED IN A SINGLE COLUMN IF YOU HAD A BIG ENOUGH SHEET OF PAPER. YOU ENTER THIS TABLE WITH THE NUMBER UNDER "v" OR "d", AND USE THE NUMBER UNDER "corr" (STANDS FOR "CORRECTION"). THE NUMBER YOU ENTER WITH IS THE "d" NUMBER AT THE BOTTOM OF THE SUN'S DECLINATION COLUMN ON THE DAILY PAGE. THE "corr" IS APPLIED TO THE DECLINATION FOR THE WHOLE HOUR. WHETHER YOU ADD OR SUBTRACT THE CORRECTION DEPENDS ON WHETHER DECLINATION WAS INCREASING OR DECREASING AT THE WHOLE HOUR.
WHEN USING THE TABLE TO GET THE "v" OR "d" CORRN YOU DO NOT NEED TO WORRY ABOUT THF SECONDS OF TIME. USE THE MINUTE OF TIME TO FIND THE RIGHT PAGE, THEN USE THE "v" OR "d" "INDEX NUMBER" TO GET THE CORRECTION TO DECLINATION.
NOW THAT YOU'VE HAD A TOUR OF PARTS OF THE ALMANAC USED TO FIND THE GHA AND DECLINATION OF THE SUN, IT'S TIME TO START PUTTING SOME PIECES TOGETHER.
THE FIRST THING YOU NEED IS A WORK FORM. HERE IS A GOOD ONE.
GHA AND DEC (SUN)
1 GHA (HR)
2 + m & s ____________
3 GHA
4 DEC (HR) N S
5 d + - _____________
6 DEC
THE NUMBERS TO THE LEFT AREN'T PART OF THE FORM, BUT LINE NUMBERS TO HELP YOU FOLLOW THIS TRANSLATION.
LINE 1: THE GHA OF THE SUN FOR THE WHOLE HOUR OF GMT WHICH YOU FIND ON THE DAILY PAGE.
LINE 2: THE INCREASE OF GHA OF THE SUN FOR THE MINUTES AND SECONDS OF GMT PAST THE HOUR, WHICH YOU FIND ON THE INCREMENTS AND CORRECTIONS PAGE.
LINE 3: THE TOTAL OF 1 AND 2.
LINE 4: THE DECLINATION OF THE SUN FOR THE WHOLE HOUR OF GMT WHICH YOU FIND ON THE DAILY PAGE. THE "N S" IS TO REMIND YOU TO NOTICE WHETHER DECLINATION IS NORTH OR SOUTH--AND TO LABEL IT.
LINE 5: NOTE THE "d" NUMBER AT THE BOTTOM OF THE DECLINATION COLUMN ON THE DAILY PAGE. ENTER THE NUMBER JUST TO THE RIGHT OF THE "d" IN THE WORK FORM. DO NOT PUT IT IN THE COLUMN WHERE YOU MIGHT ACCIDENTALLY INCLUDE IT IN THE TOTAL, HOWEVER.
WHAT GOES IN THE COLUMN IS THE NUMBER YOU FIND UNDER .CORR~R IN THE INCREMENTS AND CORRECTIONS PAGE.
WHILE YOU'RE LOOKING AT THE DAILY PAGE, SEE WHETHER DECLINATION IS INCREASING OR DECREASING, SO YOU'LL KNOW WHETHER TO ADD OR SUBTRACT THE DECLINATION CORRECTION. CIRCLE THE APPROPRIATE SIGN.
LINE 6: THE TOTAL OF 4 AND 5.
AND NOW FOR A STEP-BY-STEP DEMONSTRATION
PROBLEM: FIND THE GHA AND DECLINATION OF THE SUN FOR 09-37-26 GMT ON 3 NOVEMBER 1981.
STEP 1. MAKE THE WORKFORM:
STEP 2. FIND THE 3 NOVEMBER DAILY PAGE IN THE ALMANAC AND COPY THE INFORMATION FROM THAT PAGE IN THE FORM.
STEP 3. FIND THE 37 MINUTE INCREMENTS AND CORRECTIONS TABLE AND FILL IN THE INFORMATION FROM THAT PAGE FOR 37 MINUTES AND 26 SECONDS OF GHA AND A "d" CORRECTION FOR 0.8.
STEP 4. DO THE ARITHMETIC.
AND YOU HAVE THE ANSWERS.
EXPERIENCE SHOWS THAT THE GREAT MAJORITY OF MISTAKES ARE MADE BY COPYING WRONG DATA FROM THE ALMANAC AND TABLES. THIS ROUTINE HELPS TO AVOID MANY OF THEM. GET ALL THE DATA YOU NEED FROM A GIVEN PAGE WHILE IT'S IN FRONT OF YOU. IT SAVES FLIPPING BACK AND FORTH AND GETTING LOST. COPYING NUMBERS FROM THE BOOK IS ONE KIND OF MENTAL ACTIVITY. DOING ARITHMETIC IS ANOTHER. CONCENTRATE ON ONE JOB AT A TIME. DOUBLE CHECK EVERY BIT OF THE WORK EVERY TIME. SECONDS SPENT ON THIS CAN SAVE HOURS OF WORK IN THE LONG RUN. WHEN YOU REALIZE YOU'VE MADE A MISTAKE, IT USUALLY SAVES TIME TO START OVER FROM SCRATCH RATHER THAN SEARCHING THROUGH YOUR WORK TRYING TO FIND THE MISTAKE. TRUE STORY: SKIPPER OF A VESSEL HAD SHOT MORNING STARS AND WAS ABOUT HALF FINISHED WORKING THEM OUT WHEN THE WATCH CALLED HIM TO THE WHEELHOUSE FOR SOMETHING. LATER HE WENT BACK TO THE CHART TABLE AND RESUMED THE CALCULATIONS FROM WHERE HE HAD LEFT OFF. WHEN HE WAS FINISHED, THE RESULTS WERE RIDICULOUS AND HE REALIZED HE'D MADE A MISTAKE. HE LOST MOST OF THE MORNING AND A GOOD DEAL OF HIS REPUTATION AS A PATIENT AND PIOUS MAN SEARCHING FOR THE MISTAKE. {IT TURNED OUT THAT THE WIND HAD TURNED A FEW PAGES OF HIS OPEN BOOK OF TABLES AND HE HAD TAKEN PART OF THE DATA FROM THE WRONG PAGE). HAD HE REMEMBERED TO SCRAP THE WRONG WORK AND START AGAIN FROM THE TOP, HE COULD HAVE BEEN DONE IN TWENTY MINUTES AND HAD A LOT MORE FUN THAT DAY.
FOR PRACTICE, USE YOUR 1981 ALMANAC AND THE PROCEDURES RECOMMENDED ABOVE FINDING THE GHA AND DECLINATION OF THE SUN.
FINDING THE GHA AND DECLINATION OF A STAR IS A LITTLE DIFFERENT, BUT NO HARDER THAN FOR THE SUN. THE DECLINATION IS PRACTICALLY A GIFT. LOOK AT THE FAR RIGHT COLUMN ON ANY LEFT-HAND DAILY PAGE OF THE ALMANAC. THE FIFTY-SEVEN STARS ARE LISTED ALPHABETICALLY ALONG WITH "S.H.A." AND DEC. WE'LL DEAL WITH THE SHA IN A MOMENT. THE DECLINATION GIVEN ON THE PAGE IS USED AS GIVEN. NO INCREMENTS OR CORRECTIONS, NO ARITHMETIC. THE DECLINATION OF THE STARS CHANGES SO SLOWLY THAT ONE ENTRY IS GOOD FOR ALL THREE DATES SHOWN ON A GIVEN DAILY PAGE. SINCE THE ALMANAC LISTS FIFTY-SEVEN STARS, IT WOULD BE IMPOSSIBLE TO GIVE EACH STAR ITS OWN GHA COLUMN LIKE THE ONE FOR THE SUN AND KEEP THE BOOK A REASONABLE SIZE. INSTEAD, THE GHA SOLUTIONS FOR ALL STARS ARE BASED ON A REFERENCE POINT ON THE CELESTIAL SPHERE CALLED "ARIES". ONCE YOU FIND THE GHA OF ARIES, YOU SIMPLY ADD TO IT THE SHA LISTED FOR THE STAR. THE RESULT IS THE GHA FOR THAT STAR. LOOK AT THE LEFT COLUMN ON ANY LEFT-HAND DAILY PAGE AND YOU'LL SEE A GHA COLUMN FOR ARIES ARRANGED JUST LIKE THE ONE FOR THE SUN. THE GHA OF ARIES FOR THE WHOLE HOUR OF GMT COMES FROM HERE. THE INCREASE OF GHA FOR THE MINUTES AND SECONDS PAST THE HOUR COMES FROM THE ARIES COLUMN IN THE INCREMENTS AND CORRECTIONS TABLES. IT IS EXACTLY THE SAME PROCEDURE AS FINDING GHA OF THE SUN EXCEPT FOR USING A DIFFERENT COLUMN. SINCE MOST NAVIGATORS USE THE SUN MORE THAN THEY DO THE STARS, A VERY COMMON MISTAKE IS TO LOOK IN THE SUN COLUMN OUT OF HABIT WHEN THE ARIES COLUMN SHOULD BE USED. THE S.H.A. STANDS FOR "SIDEREAL HOUR ANGLE." IT IS THE ANGLE WESTWARD FROM ARIES TO THE STAR. THEREFORE, GHA ARIES + SHA STAR = GHA STAR. YOU ALWAYS ADD THE TWO.
QUITE OFTEN THE SUM OF THE GHA ARIES AND THE SHA OF THE STAR IS MORE THAN 360° . WHEN THAT HAPPENS, SIMPLY SUBTRACT 360°. YOU SHOULD KNOW A SYMBOL OFTEN USED FOR ARIES. YOU WON'T SEE IT MUCH IN THIS BOOK BECAUSE IT ISN'T ON A TYPEWRITER, BUT IT OFTEN APPEARS IN PRINTED WORKS. IT LOOKS LIKE THIS:
IN ASTROLOGY, ARIES IS THE RAM. DOESN'T THE SYMBOL REMIND YOU OF A HEAD-ON VIEW OF ONE OF THOSE SHEEP WITH THE CURLED BACK HORNS?
THE PROCEDURE FOR FINDING THE G.P. OF A STAR IS AN EVEN SWAP WITH THAT OF FINDING IT FOR THE SUN. YOU DO ONE EXTRA ADDITION IN THE GHA PART (AND SOMETIMES HAVE TO SUBTRACT 360° FROM THAT SUM), BUT THE DECLINATION FROM THE DAILY PAGE COMES FINISHED AND READY TO USE.
AS YOU WORK THIS COURSE IT'S LIKELY YOU'LL MEET SOMEONE WHO BELIEVES AN OLD MYTH THAT THE STARS ARE HARDER TO WORK WITH THAN THE SUN. IF YOU BELIEVE HIM, IT MIGHT SLOW YOUR PROGRESS. LET'S KNOCK THAT MYTH IN THE HEAD RIGHT NOW. IT IS TRUE THAT YOU NEED QUITE A LOT OF PRACTICE WITH A SEXTANT TO BE ABLE TO GET A ROUND OF USEABLE STAR SIGHTS IN A SHORT PERIOD OF TWILIGHT.
WITH THE SUN, YOU HAVE PLENTY OF TIME. MOST BEGINNING NAVIGATORS DO GET BETTER RESULTS FROM THEIR SUN OBSERVATIONS. FROM THIS, THEY CONCLUDE THAT THERE IS SOMETHING MYSTERIOUS AND DIFFICULT ABOUT THE SOLUTION OF STAR SIGHTS. NOT AT ALL. THE PAPERWORK FOR THE STARS IS NO MORE COMPLICATED THAN THAT FOR THE SUN.
WHAT ABOUT WORKING WITH THE MOON AND PLANETS? WE WON'T DISCUSS THEM IN THIS BOOK BEYOND THIS PAGE. THE COAST GUARD DOESN'T REQUIRE IT FOR YOUR LICENSE ENDORSEMENT, AND THE SOLUTION FOR GHA AND DECLINATION IS A BIT MORE COMPLICATED. BUT AFTER YOU HAVE THAT EXAM BEHIND YOU AND GET TO SEA YOU MIGHT FIND IT VERY USEFUL TO BE ABLE TO USE THE MOON AND PLANETS. BY THEN YOU WILL UNDERSTAND CELESTIAL NAVIGATION WELL ENOUGH TO FIGURE THEM OUT FROM THE DIRECTIONS IN THE ALMANAC. SAVE THAT FOR LATER WHEN YOU HAVE SOME SPARE TIME. BUT HERE'S A LITTLE HINT. EVEN IF YOU DIDN'T KNOW THAT THE PLANETS REQUIRE AN EXTRA CORRECTION AND WORKED A PLANET SIGHT EXACTLY AS YOU DO THE SUN, YOUR LINE OF POSITION WOULDN'T BE OFF MORE THAN TWO OR THREE MILES.
REMEMBER THIS, THOUGH, TO SAVE YOU THE TROUBLE EXPERIENCED BY A STUDENT IN ONE OF OUR RECENT CLASSES. HE GOT A TEST QUESTION REQUIRING A FIX USING VENUS. HE DIDN'T KNOW HOW TO WORK PLANETS, SO HE GOT UPSET AND BLEW THAT ONE AND RETURNED MORE THAN A LITTLE UPSET WITH THE INSTRUCTOR. HE'D HAVE BEEN FINE IF HE HAD JUST READ THE QUESTION. THE GHA AND DECLINATION WERE GIVEN IN THE PROBLEM. DIDN'T NEED TO USE THE ALMANAC AT ALL AND THE REMAINDER OF THE SOLUTION FOR A PLANET IS THE SAME AS FOR ANY OTHER BODY.
THE PROCEDURE FOR FINDING GHA AND DEC. OF A STAR IS SO MUCH LIKE THE PROCEDURE FOR THE SUN THAT YOU DON'T NEED A STEP-BY-STEP DEMONSTRATION.
HERE IS THE WORKFORM:
FOLLOW THE SAME PROCEDURE AS FOR THE SUN. TAKE ALL THE DATA YOU NEED FROM THE DAILY PAGE, FILL IN THE FORM, AND CHECK IT. THEN GO TO THE INCREMENTS AND CORRECTIONS TABLES, TAKE OUT THE " m & s " VALUE FROM THE ARIES COLUMN, THEN DO THE ARITHMETIC. REMEMBER, THERE IS NO "d" OR "Corrn" TO WORRY ABOUT.
THE DECLINATION IS TAKEN STRAIGHT FROM THE DAILY PAGE AND DOES NOT NEED TO BE CORRECTED.
FOR PRACTICE, FIND THE GHA AND DECLINATION OF THESE STARS:
ANSWERS
TO REVIEW THE STEPS OF THE SIGHT REDUCTION PROCESS WE HAVE STUDIED THUS FAR, WE HAVE:
1. TAKEN A SEXTANT READING (HS) AND CORRECTED IT TO AN OBSERVED ALTITUDE (HO).
2. CHANGED THE TIME THAT WE TOOK THE SEXTANT READING TO GMT SO WE COULD USE THE NAUTICAL ALMANAC.
3. USED THE NAUTICAL ALMANAC TO FIND THE GHA AND DECLINATION OF THE CELESTIAL BODY.
AND WHERE HAS IT GOTTEN US? WE ARE NOW TO THE POINT WHERE WE CAN PUT AWAY THE NAUTICAL ALMANAC AND USE ANOTHER PUBLICATION. IN ORDER TO USE THAT PUBLICATION, HOWEVER, WE NEED AN "ASSUMED POSITION" FOR OUR BOAT. THIS ASSUMED POISTION WILL BE NEAR THE BOAT'S DR POSITION AT THE TIME OF THE SIGHT. IT IS NECESSARY TO DO THIS STEP TO MAKE LIFE A LITTLE EASIER WHEN WE LOOK UP NUMBERS IN THE NEXT PUBLICATION. LET'S NOW DISCOVER HOW TO FIND AN ASSUMED POSITION.
