With all due respect, a Line of Position is more than just a straight line on a map.
No. That's all it is. The term refers to a line drawn as the result of doing an observation. The ideal is to get two LOPs to cross. Then you know that you are almost certainly at the point of intersection (or nearby, at any rate).
"A line indicating a series of possible positions of a craft, determined by observation or measurement. Also known as position line" (
Sci-Tech Dictionary).
A Line of Position is not a "fix." The "fix" comes from having Lines of Position cross each other.
When Fred Noonan shot the sun on the morning of July 2nd and put a 157/337 line on his map, he could be sure that he was somewhere on that line.
But Fred didn't tell us the time at which he made that observation. The terminator swept out that line all across a very large region of the Pacific that morning. With the knowledge of what time he observed the sun, plus knowledge of his altitude, plus some tables, plus some calculations,
FRED could draw a line on his charts and say, "We were on that line at such-and-such a time this morning. Now I all have to do is dead-reckon to a parallel
Line of Position drawn through Howland Island. When we reach that advanced LOP, which I have drawn on my chart to aid dead-reckoning, then we will know that it is time to turn north or south."
Note that both LOPS are 337-157. That's because they are parallel. You can't tell one apart from the other by the compass headings that define them.
Without Fred sending us his chart and without any record of WHEN he made the sun observation,
we are ignorant of something
he knew.
From the information that his two LOPs were 337-157,
we cannot say how far apart their were on his chart.
What we could know is how big a range in the South Pacific would have a 337-157 line drawn by the terminator between night and day on 2 June 1937. The angle of the line drawn by the terminator changes with one's location at the time of the observation because the earth is a globe, not a circle, and the line between night and day is curved around that globe.
We can (and do), of course, surmise that AE's transmissions about being 200 and 100 miles from Howland give us some idea of when Fred drew the two LOPs on his charts and started counting down the distance from one to the other. But that extra information is not encoded by saying, "The dawn LOP on my chart and the advanced LOP that I drew through Howland is 337-157."
Realistically, the "line" might be as much as ten miles wide in an East/West sense and he couldn't know for sure where on the line he was in a North/South sense, but it was better than a dead-reckoning guess.
I never said it was a guess. What I said was that from the information given that their advanced LOP was 337-157, we do not know where they were when Fred took the dawn observation.
He knew (if his watch was keeping good time);
we don't know.
Go ask a navigator where the line 337-157 is in the Pacific. He will tell you that is everywhere and nowhere. Any time you're flying, you can turn to a heading of 337 or 157.
Go to What is the significance of Earhart’s statement “We are on the line 157/337”? for a good explanation of Line of Position.
Go to
Marine Navigation courses: Lines of Position to see how lines drawn on a chart lead to a fix.
Go to
Lines of Position to see how such lines are drawn on charts from observation of celestial bodies.
"Lines of position are constructed on a geographic map from observational data and indicate the observer’s position. For complete determination of a position, it is necessary to construct at least two lines of position, whose intersection corresponds to the unknown location. Here, to ensure a reliable determination, both lines of position must intersect at an angle that is not too acute—at least 30°. If the lines of position have several, usually two, points of intersection, it is not difficult to select the necessary point, since the approximate location of the point of observation is usually known. For the same reason, observers often restrict themselves to constructing only a short segment near the approximate position of the observer rather than an entire line of position. This segment is replaced with the tangent to the line of position.
"Lines of position are used extensively in navigation and aviation to determine the position of a ship or aircraft from the observed altitudes of two celestial bodies. This method was first published by the American sailor T. Sumner in 1843. Such celestial lines of position are called Sumner lines. A convenient, simple method of calculating and constructing these curved lines on a map was demonstrated in 1849 by the Russian sailor M. A. Akimov. Since the late 19th century, celestial lines of position have been calculated and constructed by an even more convenient method proposed by the French sailor M. St.-Hilaire in 1875."
Source:
The Great Soviet Encyclopedia.