04-28-2023, 10:06 PM
Fred_B,
You most certainly can wind up with a DR and resulting AP that are a long way from where you actually were. However the resulting LOP is not entirely "bad" although it is not as "good" as it could be.
The azimuth line through the AP toward or away from the geographic position (GP) of the observed body is actually along a great circle track. The compass direction along great circle tracks changes constantly, so a very long intercept (a) implies that the azimuth line plotted on your approximately Mercator plotting sheet should show as a slight curve. Usually the amount of this curvature is very slight because we deliberately keep the intercept short but in an example such as you have suggested with 3 degrees of longitude difference it should curve to a small extent.
Also the Sumner line we plot as a LOP is really a circle of position, though it is usually not a great circle - so if your final fix is way out on one or more of your Sumner lines then this too will exhibit small errors because it really should be a curve. This situation is more acute for high observed altitudes since the true circle of position would have a smaller radius and exhibit more curvature.
When any of your plotted lines start to look extra long then it is good procedure to take the resulting fix as an updated DR. Redo the AP and sight reductions from that spot. Chances are the updated new fix will only differ from the first by a handful of miles, but it should be more accurate.
Since the math doesn't care where you say to start from there is no absolute requirement to have your AP long. within 30' of your DR. To say that it MUST BE SO would be incorrect. However on exams where you have to MATCH the examiner's answer you have to start from the SAME AP that the examiner used - and that is pretty much ALWAYS within 30' of longitude from the stated DR. If you use a different AP than the examiner used you will get a different azimuth and intercept than he did.
Peter
You most certainly can wind up with a DR and resulting AP that are a long way from where you actually were. However the resulting LOP is not entirely "bad" although it is not as "good" as it could be.
The azimuth line through the AP toward or away from the geographic position (GP) of the observed body is actually along a great circle track. The compass direction along great circle tracks changes constantly, so a very long intercept (a) implies that the azimuth line plotted on your approximately Mercator plotting sheet should show as a slight curve. Usually the amount of this curvature is very slight because we deliberately keep the intercept short but in an example such as you have suggested with 3 degrees of longitude difference it should curve to a small extent.
Also the Sumner line we plot as a LOP is really a circle of position, though it is usually not a great circle - so if your final fix is way out on one or more of your Sumner lines then this too will exhibit small errors because it really should be a curve. This situation is more acute for high observed altitudes since the true circle of position would have a smaller radius and exhibit more curvature.
When any of your plotted lines start to look extra long then it is good procedure to take the resulting fix as an updated DR. Redo the AP and sight reductions from that spot. Chances are the updated new fix will only differ from the first by a handful of miles, but it should be more accurate.
Since the math doesn't care where you say to start from there is no absolute requirement to have your AP long. within 30' of your DR. To say that it MUST BE SO would be incorrect. However on exams where you have to MATCH the examiner's answer you have to start from the SAME AP that the examiner used - and that is pretty much ALWAYS within 30' of longitude from the stated DR. If you use a different AP than the examiner used you will get a different azimuth and intercept than he did.
Peter