Using small position plotting sheets, we can plot a fix from celestial observations, then transfer the fix to our chart. Our plotting sheets are worksheets to minimize the amount of writing on our charts.
To plot a line of position, we first locate the assumed position for the sight on the plotting sheet. This assumed position will tell us the correct central meridian and central parallel to use. Since the AP Lat s always a whole degree, we can choose this value for the central parallel. The central meridian can be the nearest whole or half degree of longitude to he AP Long. Remember on the scale of longitudes at the bottom of the sheet
to mark the horizontal line that corresponds to your latitude. On this scale you will measure only longitude. Latitude and distance are measured on the central meridian.
Mark the central meridian of your plotting sheet 50° W, central parallel 30° N. With this information, we see that at 1700, the Moon has a true azimuth of 200°. Plot the AP, put a circle around the point. From the AP, we will draw this bearing line (a dashed line) TOWARD 200° (since the intercept is labelled toward) for a distance of 10 nautical miles, measured on the central meridian. After making a mark on our dashed line 10 n.m. away from the AP, we draw a line perpendicular to the azimuth line such that the perpendicular line goes through this mark. This last line is our line of position or LOP.
To figure the the LOP, the navigator can use a right angle triangle against the parallel rulers or another triangle or he can add or subract 90° from the Zn to get the bearing of the LOP and plot this line independntly from the plotting of the bearing line. The LOP has an azimuth of 200° ± 90° = 290° or 110°.
For the 1700 sun sight, again plot the AP for the Sun, from this point plot AWAY from 301° by 8.3 nautical miles, make a mark here and draw a perpendicular line to the azimuth line through this mark. At this LOP and the LOP of the Moon, draw a circle. This is the position of the ship or the FIX. Label it 1700 FIX and record its latitude and longitude.
The lines of position are labelled with the time of sight in four digits above the line, the body observed below the line 1700 Moon.
The assumed positions are labelled AP 1 or AP 2, in the order with which the sights are taken. Some navigators label them AP Sun, AP Moon.
For a fix, you need at least two lines of position, preferably three.
If possible, for a two body fix, the bearings of the bodies should be close to 90° apart, making the LOP's cross also at near 90°. With this situation, there is a minimum of error of the fix even if there is a small error in the sextant reading or sight reduction. If two LOPs crossed at an angle of only 20°, and the bearing of one of the lines was off by one degree, the resulting error in the fix would be greater than if the bodies were 90° apart.
For a three body fix, the bodies should be close to 60° apart or 120° apart, these numbers are obtained by dividing 180° or 360° by the number of bodies observed. This will make a point fix if your sights are perfect.One line of position will never give you a fix.
A course should always be plotted from your an EP, let us this example of the following sight.
Body Sun
AP Lat. 45 N Long 160-25 E
"a" 8.0 Towards
Zn 145 degrees
ZT 1030
The 1030 DR of 44° 40' N, 160° 20' E. From 1030, the ship will proceed on course 040° at a speed of 10 knots.
After plotting the 1030 Sun LOP and the 1030 DR, the 1030 EP is obtained by drawing a dashed perpendicular line to the LOP through the 1030 DR. Where the perpendicular line crosses the LOP, make a point with a square around it and label it 1030 EP. This is the best estimate you can make with the information at hand of your position. You should proceed from your DR and not from your EP.
Two special cases of the use of one line of position.
1) Observing a body dead ahead or dead astern (its LOP will be perpendicular to your course line)
The line of position checks on your speed. If the LOP lies ahead of your DR of the same time, then your ship is going faster than you estimated. If the LOP lies behind your DR of the same time, your ship is going slower than you estimated. Every position on that LOP would be behind your DR.
2) Observing a body abeam (its LOP will be parallel to your course line)
In this case, the line of position checks on your course. If the LOP lies to the north of your course line, this shows that your ship is being set to the northward. If the LOP lies to the south of the course line, this shows that your ship is being set southward.
Lines of position from piloting procedures, radionavigation, and celestial navigation maybe crossed with each other to give a fix. We can treat the celestial lines of position as straight lines even though they are actually parts of circles.
We assumed that both the Sun and Moon sight were taken at the same time. However, most times this is not the case. If two bodies were observed twenty minutes apart and the ship was proceeding on course during these twenty minutes, we have to advance the earlier sight to the later time. The advancing is made to the time of the last sight in some cases the navigator may wish to retard a line to obtain a fix for an earlier time.
To advance a LOP, we need to know the course and speed of the ship. Lets say that our 1600 DR is 19° 40' N, 60° 00' w. Course is 080°, speed 10 knots. The Moon is observed at 1600 and we want to advance it to 1630 when we will observe the Sun. The AP is 20° N, 60° 05' W. Zn = 125°, the intercept is 20' T. We can plot our 1600 Moon LOP as usual, using a plotting'sheet with central parallel 20° N, central meridian 60° W. To advance the 1600 Moon to 1630, we mark where the 1600 Moon crosses our course line. From this point we measure off how far the ship has traveled in the 30 minutes in the direction of the course. In this case, the ship will travel 10 nautical miles in one hour, therefore 5 nautical miles in 30 minutes. Through the point on the course line 5 nautical miles from the crossing of the 1600 Moon, draw a new line of position parallel to the old one. 1600-1630 Moon
Remember to always measure the advance along the course line in the direction of travel. To retard the same line, the procedure would be the same except that the line would be retarded in the direction opposite that of travel. Remember to measure this 5 nautical mile distance from the distance scale on the central meridian. If the LOP is perpendicular to your course line, an distance it will reflect maximum movement in your LOP.
In some cases, the LOP will not cross with the course line as you have plotted it on your plotting sheet. Just plot a new course line (same direction) at a different spot on your plotting sheet where it will cross with the LOP. Then advance your line.
It will sometimes be the case that a line of position will have to be advanced over a time period when a course and/or speed change are involved. There are two methods by which this may be done. If we have the situation where from the 1000 DR the vessel proceeds on course 045° at speed of 20 knots. At 1100, course is changed to 355°, speed to 23 knots. A sight of the Sun is taken at 1015 and must be advanced to 1200 when another sight is taken.
Method l involves figuring a course made good (CMG) and distance made good (DMG) of the vessel between the two sight times. The DR is plotted for these two times (1015 and 1200) and a line drawn between the two points. The distance between the DR is the distance made good, the bearing of the line the course made good. This line may need to be extended to cross with the 1015 LOP. The LOP is then advanced along this line by the amount designated by DMG. The advanced LOP is labeled.
Method 2 is a two or more stepped method. First the 1015 LOP is advanced to the time of course and/or speed change (in this case 1100). The 1015-1100 LOP is plotted. Where this LOP crosses the course line is the starting point for the second step. The LOP is advanced along the new course and/or speed until the next sight time or until course or speed are changed again.
This method can be rather long when many course and speed changes are involved. I like to use Method l for most cases.
When a fix is obtained by advancing a line of position more than 30 minutes, the fix is called a running fix, labeled R. FIX. This type of fix is not as accurate as a fix obtained by sighting bodies almost because the R. FIX is subject to the ship's errors in 90 course and speed. Most times during the day you have no other choice than observing the Sun at intervals of an hour or more and advancing the earlier sight to the later one to obtain a position. Just remember that your ship probably is not at the position labeled R. FIX although this point is as good an estimate. I hope to have forms and plotting sheets on here so its easier to follow along.
