LINE OF POSITION
In practice, you may neither be able nor will you need to plot the whole of a circle of equal altitude. The position is usually known within 10 miles and possibly even less than that. Inside these limits, the curve of the arc of a circle of equal altitude is hardly perceptible, and the arc is plotted and regarded as a straight line. Such a line, comprising enough of the arc of a circle of equal altitude to cover the probable limits of a position, is called a Sumner line of position or just a line of position.
TWO LINES OF POSITION
The preferable 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 angle 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, obviously 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 progressively decreases in accuracy, depending on how, far the first line is advanced. You should not advance such a time for more than 5 hours of run.
DETERMINING A LINE OF POSITION
At this point you might be entitled to complain that much has been said concerning what a line of position tells you, but very little has been said about how you should determine it in the first place. We are coming to that part now.
You probably have grasped 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. Consequently, you do not determine the entire circle but merely 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 and 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.
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).)
