Home Page      Software Downloads   Free Samples    Maritime Links    Web Rings   Contact SeaSources

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

PLOTTING LINES OF POSITION

   YOU MAY RECALL, FROM AN EARLIER DISCUSSION, THAT WITH A LARGE ENOUGH CHART AND A VERY LARGE PAIR OF DIVIDERS YOU COULD PLOT THE G.P. OF THE BODY ON THE CHART, AND DRAW A CIRCLE WITH A RADIUS EQUAL TO ZENITH DISTANCE, OR 90° MINUS Ho, WITH THE G.P. AS ITS CENTER. YOUR POSITION WOULD LIE SOMEWHERE ON THAT CIRCLE, SO IT WOULD BE A LINE OF POSITION (LOP).   VIEW IMAGE 18

   WE RARELY PLOT THE LINE OF POSITION THIS WAY IN PRACTICE. TO HAVE THE G.P. AND THE VESSEL CLOSE ENOUGH TO BE ON THE SAME CHART OR PLOTTING SHEET, Ho WOULD HAVE TO BE CLOSE TO 90°, AND IT IS VERY DIFFICULT TO GET AN ACCURATE SEXTANT OBSERVATION OF A BODY NEARLY OVERHEAD.

     YOU DO DRAW A SMALL PART OF THE ARC OF THAT CIRCLE. THE RADIUS OF THE CIRCLE IS SO LARGE --AS MUCH AS 4000 MILES--THAT THE CURVATURE OF THE ARC ISN'T EVEN NOTICEABLE. THE SHORT ARC OF THE CIRCLE YOU USE FOR A LINE OF POSITION “LOP” CAN BE REPRESENTED AS A STRAIGHT LINE WITH NO SERIOUS ERROR.

   THAT STRAIGHT LINE IS A TANGENT OF THE CIRCLE, OR A LINE THAT TOUCHES THE CIRCLE AT ONE POINT. A RADIUS DRAWN FROM THE CENTER OF THE CIRCLE TO THE POINT WHERE THE TANGENT TOUCHES THE CIRCLE WILL BE AT A RIGHT OR 90° ANGLE TO THE TANGENT. VIEW IMAGE 19

   EVEN THOUGH YOU CAN'T PLOT THE G.P. ON THE CHART AND DRAW THE COMPLETE RADIUS, YOU CAN DRAW PART OF IT. WHEN YOU USED 229, YOU FOUND THE COMPUTED ALTITUDE (Hc) OF THE BODY, AND ITS AZIMUTH, (Zn) OR TRUE BEARING FROM THE ASSUMED POSITION TO THE G.P. A STRAIGHT LINE DRAWN FROM THE ASSUMED POSITION “A.P.” IN THE DIRECTION OF THE Zn IS PART OF THE RADIUS. THE LINE OF POSITION “LOP” MUST LIE AT RIGHT ANGLES TO IT. VIEW IMAGE 20

     IF YOU HAD ACTUALLY BEEN AT THE A.P. WHEN YOU MADE THE OBSERVATION, THE LOP WOULD PASS THROUGH THE A.P. AT RIGHT ANGLES TO THE RADIUS OF THE CIRCLE. IT WILL BE MORE CONVENIENT TO CALL THE PART OF THE RADIUS YOU DRAW FROM THE A.P. THE “AZIMUTH LINE.”  VIEW IMAGE 21

   YOU'LL PROBABLY NEVER SEE THAT HAPPEN.   Hc WOULD HAVE TO EQUAL Ho, WHICH WOULD GIVE YOU AN ALTITUDE INTERCEPT (a) OF ZERO. THE ODDS ARE GREATLY AGAINST THAT HAPPENING BECAUSE YOU CHOSE THE A.P. TO AVOID INTERPOLATION FOR LATITUDE AND LHA. THE INTERCEPT (a), THE DIFFERENCE BETWEEN Hc AND Ho, IS THE DISTANCE IN MILES FROM THE A.P ALONG THE AZIMUTH LINE TO THE POINT WHERE THE LOP CROSSES THE AZIMUTH LINE. THAT DISTANCE WILL BE MEASURED FROM THE A.P. IN THE DIRECTION OF THE Zn IF (a)  IS NAMED "TOWARD" (HO GREATER THAN HC), OR IN THE OPPOSITE DIRECTION IF (a)  IS NAMED "AWAY" (Hc GREATER THAN Ho) VIEW IMAGE 22    VIEW IMAGE 23

   NOTICE THAT IN THE PRECEDING EXAMPLES WE DREW THE AZIMUTH LINES AS DASHED LINES AND THE LOP'S SOLID. THE REASON IS THAT WHEN YOU PLOT THREE OR MORE STARS FROM A.P.'S PRETTY CLOSE TOGETHER, IT WOULD BE EASY TO CONFUSE AZIMUTH LINES WITH LOP'S. THE FIX IS WHERE THE LOP'S CROSS. THE AZIMUTH LINES ARE MERELY USED TO CONSTRUCT THE LOP'S AND HAVE NOTHING TO DO WITH THE FIX. USING DIFFERENT COLORED PENCILS TO DISTINGUISH AZIMUTH LINES FROM LOP'S WOULD BE GREAT IF YOU COULD FIND COLORED PENCILS THAT WILL STAY SHARP. A SHARP PENCIL AND CAREFUL PLOTTING IS VERY IMPORTANT. CONCERNING ACCURACY OF PLOTTING, SOME TOLERANCE HAS TO BE ALLOWED. ON THE USUAL PLOTTING SHEET, A LINE DRAWN WITH A FRESHLY SHARPENED #2 PENCIL MIGHT BE TWO TENTHS OF A MILE WIDE. THE MOST EXPERIENCED NAVIGATOR WHO PLOTS THE SAME FIX TWICE WILL NOT GET EXACTLY THE SAME LATITUDE AND LONGITUDE TWICE. MOST PEOPLE GET UNDULY CONCERNED WHEN THEY’RE ANSWER TO "WHAT IS THE LATITUDE AND LONGITUDE OF THE 1500 FIX?" DOESN'T COME OUT EXACTLY LIKE THE BOOK ANSWER. IN PROBLEMS THAT DON'T INVOLVE DRAWING, YOU SHOULD GET THE BOOK ANSWER. IN THE PRACTICE PLOTTING PROBLEMS, YOU WILL MOST LIKELY DIFFER FROM THE BOOK. WHEN YOU'RE STILL A BEGINNER, BE HAPPY IF YOUR RESULT IS WITHIN TWO OR THREE MILES OF THE BOOK ANSWER. THAT WILL PROVE THAT YOU HAVEN'T MADE ANY GROSS MISTAKES AND THAT YOUR PROCEDURE IS CORRECT. YOUR PLOTTING ACCURACY WILL IMPROVE WITH PRACTICE, BUT NOBODY CAN EVER GET RID OF ALL PLOTTING ERRORS. RELAX AND ENJOY THE PLOTTING EXERCISES. ALLOW YOURSELF A LITTLE "SLOP" AND CONCENTRATE ON PROCEDURE--DRAWING EVERYTHING IN THE RIGHT DIRECTION--AT FIRST. FOR MORE PRACTICE, REWORK -THE SAME EXERCISES ON A FRESH SHEET. WHEN YOUR FIXES START COMING WITHIN A MILE OF THE BOOK ANSWERS, YOUR PLOTTING WORK WILL BE PLENTY GOOD ENOUGH TO PASS A COAST GUARD TEST.

   ANOTHER THING THAT WORRIES STUDENTS UNNECESSARILY IS FINDING A THREE LINE FIX THAT DOESN'T CROSS TO A PINPOINT BUT FORMS A SMALL TRIANGLE.

    IT IS CUSTOMARY TO ASSUME THE FIX IS IN THE CENTER OF THE TRIANGLE, WHICH YOU CAN JUDGE QUITE ACCURATELY BY EYE. NO DOUBT THE PERSON WHO MADE UP THE PROBLEM STARTED WITH A PINPOINT AND WORKED BACKWARDS TO CREATE A PROBLEM, INTENDING FOR YOU TO GET THE SAME PINPOINT. BUT A NORMAL AND PERFECTLY ACCEPTABLE AMOUNT OF PLOTTING ERROR CAN CAUSE YOUR THREE LINES TO FORM A TRIANGLE AS LARGE AS A MILE ON A SIDE. EYEBALL THE CENTER OF YOUR LITTLE TRIANGLE AND GO WITH IT. IT WON'T DIFFER FROM THE AUTHOR'S PINPOINT BY MORE THAN A HALF MILE. THAT WILL BE CLOSE ENOUGH TO PICK OUT THE CORRECT MULTIPLE CHOICE ANSWERS.

    IF, HOWEVER, YOU WIND UP WITH A LARGE TRIANGLE SEVERAL MILES ACROSS, SOMETHING IS WRONG WITH YOUR WORK. ONE OR MORE OF THE LOP'S IS OUT OF PLACE. THERE IS NO WAY TO TELL WHICH IS WRONG. PROBABLY THE QUICKEST WAY TO CORRECT THE MISTAKE IS TO WORK THE WHOLE THING OVER AGAIN ON A FRESH SHEET. GOING OVER YOUR EXISTING WORK TRYING TO FIND A MISTAKE IS USUALLY A WASTE OF TIME. WE ALL TEND TO BELIEVE WHAT WE SEE ON PAPER, ESPECIALLY IF WE PUT IT THERE.. IN NO TIME A MAN CAN CONVINCE HIMSELF THAT HIS OWN WORK IS CORRECT AND THE MISTAKE MUST BE IN THE COAST GUARD (OR BOOK) PROBLEM. THAT'S POSSIBLE, BUT NOT VERY LIKELY.

   HERE ARE FIVE EXERCISES FOR PLOTTING ONE LOP AT A TIME. SET UP ONE OF THE UNIVERSAL PLOTTING SHEETS FOR LATITUDES 27°-30° TO WORK THE PROBLEMS. THE ANSWERS AREN'T THE SORT YOU'LL SEE ON THE TEST. THAT'S JUST A CONVENIENT WAY OF CHECKING TO SEE THAT THE LOP IS IN THE RIGHT PLACE.

 PROCEDURE:  

  1. PLOT THE ASSUMED POSITION.
  2. TAKE THE DIFFERENCE BETWEEN Hc AND Ho TO FIND THE INTERCEPT (a) .THE INTERCEPT IS PROVIDED IN THE EXERCISES.
  3. IF (a) IS TOWARD, DRAW A DASHED AZIMUTH LINE FROM THE A.P. IN THE DIRECTION OF THE Zn. IF (a) IS AWAY, DRAW THE AZIMUTH LINE IN THE OPPOSITE DIRECTION FROM Zn.
  4. FROM THE A.P., MEASURE A DISTANCE IN MILES EQUAL TO (a) ALONG THE AZIMUTH LINE AND MARK THE POINT.
  5. THROUGH THAT POINT, DRAW A SOLID LOP AT RIGHT ANGLES TO THE AZIMUTH LINE. (MAKE THE LOP LONG ENOUGH TO CROSS THE MERIDIAN OR PARALLEL IN THE QUESTION SO YOU CAN CHECK YOUR ANSWER.)