LINE OF POSITION
You might not be able nor will you need to plot the whole of a circle of equal altitude. The position is usually within 10 miles and possibly even less than that. With enough of the arc of a circle of equal altitude to cover the limits of a position, this is called a Sumner line of position or just a line of position.
TWO LINES OF POSITION
The best method of establishing two lines of position is by observing two different bodies, although two lines may be obtained from the same body by observations taken at different times. As in piloting, the nearer the two lines approach a right angles to each other, the more accurate is the fix.
When two lines are determined by observing the same body, the first line established is brought forward the distance run on the course steered. For example, if a ship steams 27 miles on course 315 between the first and second observations, her position is on a line parallel with the first one established, but drawn 27 miles away (to scale) on the course line 315. Intersection of the line established by the second observation with the advanced line of the first observation is a fix. The fix may decreases in accuracy, depending on how, far the first line is advanced. You should not advance a time for more than 5 hours of run.
DETERMINING A LINE OF POSITION
You probably have the idea that what you want to find out is which circle of equal altitude you are on, and what this altitude is. To draw such a circle, you would need a chart covering an extensive area, unless the heavenly body's altitude approached 90 degrees. You do not determine the entire circle but only a portion of its arc, so small that it is plotted and regarded as a straight line.
An assumed position (AP) is selected according to the rule of 30' of your DR position for the time of sight. Observation of a star provides sextant altitude. Sextant altitude is then corrected to obtain observed altitude (ho). The star's altitude from the assumed position (called the computed altitude (Hc) and its azimuth angle are determined from tables the azimuth angle is then converted to azimuth.
After selecting an AP, draw the azimuth through the AP. Along the azimuth, measure off the altitude intercept (difference between the observed altitude and the computed altitude). At the end of this measurement, draw a perpendicular line, which is the LOP.
REMEMBER IN FULL SIGHT REDUCTION LHA HAS TO END IN WHOLE DEGREES AND YOUR ASSUMED LONGITUDE HAS TO BE WITH IN 30'
OF YOUR DR LONGITUDE.
You must know whether altitude intercept (a) should be measured from AP TOWARD the star or from AP AWAY from the star. (Frequently, the initials for Coast Guard Academy (CGA) are found to be helpful.) If the computed altitude is greater than the observed altitude, altitude intercept (a) is measured away from the star. (In other words applying the CGA "memory aid," you have computed, greater, away (CGA).)
SELECTING BODIES FOR OBSERVATION
Before going into problems and tables. I should mention few things concerned with selecting astronomical bodies for observation.
Observing two heavenly bodies in rapid succession is the best method of finding two lines of position to establish a fix. Three bodies gives three lines. and these three define the fix more accurately (as in piloting). Accuracy of the fix by intersecting lines of position depends upon the angle between the lines. The nearer this angle approaches 90° the more accurate the fix.
Sights seldom are taken on two or more bodies simultaneously. Instead, the navigator decides which bodies to observe, then takes a round of sights, each one timed exactly. Lines of position are advanced or retarded the amount of the ship's run between the time of observation and the time of the desired fix.
The best situation for lines of position is by observing three bodies would be that are 120° apart in azimuth. The best fix using four bodies would include two north-south lines and two east-west lines of position to form a box. A line perpendicular to the course are best for checking the run. Those lines parallel to it are helpful in deciding the accuracy of the course made good.
For altitude, best results are obtained by observation of bodies whose altitudes are between 15° and 65°
ADVANCING AND RETARDING THE LOP
Several methods may be used to advance a line of position. The most frequent method consists of advancing the AP in the direction of your course and for the distance of the run, and drawing the new LOP. To retard a LOP, just go reciprocal of your course and for the distance run.
