My apologies if this post is a little long, but if selecting an AP in the Eastern longitudes has you confused this might get to the heart of the reason why. I try to be complete in my discourse because browsers seem to pass through here looking for answers, and they may not be fully up to speed on the past conversations and rhetoric.
AhHa!
I now SEE a big source of confusion regarding Assumed Positions to which I was previously oblivious! It all started for me with the thread “LHA in Eastern Longitudes?”
https://thenauticalalmanac.com/Forum/sho...hp?tid=243
The problem I now see is that many students are studying TO THE RATING TEST, not to the underlying principles and the practical final plotted line of position (LOP.)
Let me explain:
I was reading older posts in this forum. One very popular thread in particular was "Celestial Problem I Can Not Solve." https://thenauticalalmanac.com/Forum/sho...hp?tid=190 It was here that I realized that in at least three of the celestial problems offered in the referenced video http://www.seasources.net/youtube%20vide...uction.mp4 the student was NOT EXPECTED to plot the problem as a final LOP, instead only expected to find the true azimuth (Zn) and intercept (a) that are the correct answer to the problem.
Naturally most humans have the approach of "I don't want a lecture on theory here - just show me a quick way to get the right answer..." And of course this is more so if the student is not a fan of celestial navigation for any reasons, not the least of which is he or she may be of the opinion that celestial is totally obsolete.
In this special case for the EXAM you DO NOT NEED to know the precise longitude of the Assumed Position (AP) since you will not be plotting the result. You only need the AP latitude (easy); the declination of the body (you look that up and use it as found); and the Local Hour Angle (LHA) for which, rigorously speaking, you need the correct AP longitude.
...but...
By a "short cut" you can get the same LHA that was used for the solution, ...well, most of the time. If all you want is the right answer on the test and don't care about the LOP or to expend the time and effort necessary to fully understand what you are doing, the short cut certainly seems enticing.
An aside: I do not hold any "short cutters" in poor regard. I presume that if they are studying for one of these exams they have got a heck of a lot of other stuff to learn besides celestial, and all of that is in addition to seeing to all their other daily responsibilities. Since celestial may seem like an arcane backwater of that total body of knowledge a "quick fix" certainly is attractive. Also celestial can be confusing to learn and anyone who didn't know that this was a kind of short cut could easily be enticed by seeing a simpler way to do things. -- Myself included.
Let's examine how the short cut works by first looking at West longitude dead reckoning (DR) position:
The LHA is the difference in longitude between your AP and the Greenwich Hour Angle (GHA) of the observed body. All hour angles are ALWAYS measured ONLY westward so the GHA of the body is how far west its geographic position (GP) is from the Greenwich meridian.
Your own longitude is how far west YOU are from the Greenwich meridian.
To get the LHA, which is how far west the body's GP was from YOU, you subtract your DR longitude from the GHA of the body.
If you are using a calculator or an electronic app you can use your DR and the GHA of the body complete with their minutes and tenths as found. The resulting LHA will probably have some minutes and tenths in its result. You can use that LHA along with its minutes and tenths in the electronic app or calculator solution. The results will be an azimuth (Z); a true azimuth (Zn); and an intercept distance in nautical miles (a); to be plotted directly from your DR.
However the test uses tables to do the sight reduction. Usually Pub 229 for USCG. These tables and many others such as Pub. 249 require that you enter them with a whole degree of AP latitude and an AP longitude that results in a whole degree of LHA. You do not enter them with your DR position. Instead you “deliberately take up” a “position of convenience” nearby to where you are which we call and “Assumed Position.” Here “assumed” means “deliberately taken up.”
The reason for the "whole degrees" thing is just for compactness of the tables. It eliminates the huge number of possible solutions that would exist between every whole degree demarcation, making the printed books of tables physically small enough to carry aboard. It has NOTHING to do with the math. The math doesn't care about whole degrees at all.
In order to get the same answer as the exam you need the whole degree latitude and whole degree LHA that THE EXAM WRITER used to enter Pub. 229. If you use these, even with an app, a calculator, or different type of tables, you will come to their same answer - which is the immediate goal - even if you don't actually know what an AP is or how the heck they got one.
For western DR positions you subtract your AP longitude from the GHA of the body. To do this rigorously you first determine the GHA of the body including the minutes and tenths. Then you append those same minutes and tenths of the GHA to the whole degree of your longitude to get an AP longitude. In real life you will need this EXACT AP longitude later for plotting, so you would not short cut. But for the EXAM you don't plot so all you need is the LHA as a whole degree – and it has to be the same one the exam writer used or your answer will be different.
Here you can see if you simply ignore the minutes and tenths of BOTH the GHA and the DR when you subtract the DR longitude degrees from the GHA degrees you (usually) get the right answer. ... More on"usually" later.
When in eastern longitudes things change a bit. Here you must add how far east of the Greenwich meridian you are to how far west the GP of the body was from the Greenwich meridian to determine how far west the body's GP meridian is from YOUR meridian.
All the above discussion regarding using calculators or apps still applies. The math does NOT need a whole degree of anything, but the tables, and the exam question answer based on using the tables, DO need a whole degree AP latitude and a whole degree LHA. The whole degree latitude part is easy - just round the DR latitude to the nearest degree. The whole degree LHA is a little trickier.
Rigorously speaking since you will be ADDING your AP longitude to the GHA of the body the minutes and tenths of your contrived AP must sum with the minutes and tenths of the GHA to equal exactly 60.0' which is one whole degree.
EXAMPLE: GHA 34° 40.0' DR lon 15° 32.5' E and 34° 40.0' + 15° 32.5 E = 50° 12.5'
this doesn't give a whole degree LHA so instead you contrive an AP longitude of 15° 20.0' E.
Then 34° 40.0' GHA
+ 15° 20.0 E AP lon (contrived so LHA will comeout to a whole degree)
49° 60.0'
=> 50° 00.0' LHA for use with Tables after you carry over the 60.0'
The RIGOROUS result for LHA will ALWAYS have the format of a trailing " 60.0' "
and this will ALWAYS increase the degree value by ONE WHOLE DEGREE.
It is this trailing 60.0' that Chris Nolan mentions in his teaching video when he comments " ... how many times have I forgotten to add that 1 degree?" https://youtu.be/X6VokWcuonU?t=204 but if you watch that segment carefully you will clearly see that he isn't short-cutting. He actually derives the proper AP longitude rigorously. What he “forgets” is to to carry over the 60.0'
The trailing “ 60.0' ” is also the basis of the shortcut method that says: "add the whole degrees of the DR to the whole degrees of the LHA and then add 1 degree to that result."
Looking at the above example if we do the following we get the LHA for the exam question, though it leaves us without knowing the longitude of the AP necessary for plotting and therefore in real life would be useless - but it WILL get the correct answer for the exam ... most of the time.
It isn't the "correct" way to do it. It is NOT based on either the mathematical requirements nor on good practice, nor a requirement for the tables. Its just a trick, but it can work...for the exam ... but not for actual navigation because you don't have a real AP longitude from which to start your plot. You skipped that step and went directly to finding the LHA.
Short Cut Version:
34° LHA degrees
+ 15° E DR degrees
+ 1° short cut "add one degree"
50° LHA
Next: About that "...most of the time"
Examiners want you to pick an AP longitude within 30.0' of longitude to your DR. Sometimes the above shortcut won't do that, and if you have not applied the rigorous method you may not be aware of that flaw because you never actually derived the AP longitude.
Suppose that in the above example the DR longitude had been 15° 52.5' E instead of 15° 32.5' E ? Using the short cut still would have a result of 50° for LHA. However employing the rigorous approach the AP longitude of 15° 20.0'E is now 32.5' of longitude away from the DR longitude – too far for the examiner! Here the "correct" AP longitude is adjusted to be 16° 20.0' E bringing the AP longitude to 27.5 minutes of longitude from the DR. It also changes the LHA to 51° In this case the short cut gets you the wrong answer for the exam!
All of that rigorous adjusting to make the AP longitude within 30.0' of the DR longitude makes essentially NO DIFFERENCE to the resulting LOP in real life AFTER PLOTTING, but may make a small difference in the results for Z and Zn values, and it WILL make a big difference in the intercept length leading you to the wrong answer for the exam.
If you used the short cut for exams and your Zn looks pretty good but your intercept is way off, try adjusting the LHA by one degree. Or better yet just take the extra minute to derive your AP longitude the rigorous way - it's really not that difficult.
My conclusion is that learning how to use the short cut is no easier than learning the rigorous method;
That the short cut confuses students because the do not realize it is just a trick; That the short cut is useless in real life because you don't have an AP longitude from which to base your plots; And because of these reasons the short cut, like most short cuts in learning, is not a better choice in the end.
Peter
AhHa!
I now SEE a big source of confusion regarding Assumed Positions to which I was previously oblivious! It all started for me with the thread “LHA in Eastern Longitudes?”
https://thenauticalalmanac.com/Forum/sho...hp?tid=243
The problem I now see is that many students are studying TO THE RATING TEST, not to the underlying principles and the practical final plotted line of position (LOP.)
Let me explain:
I was reading older posts in this forum. One very popular thread in particular was "Celestial Problem I Can Not Solve." https://thenauticalalmanac.com/Forum/sho...hp?tid=190 It was here that I realized that in at least three of the celestial problems offered in the referenced video http://www.seasources.net/youtube%20vide...uction.mp4 the student was NOT EXPECTED to plot the problem as a final LOP, instead only expected to find the true azimuth (Zn) and intercept (a) that are the correct answer to the problem.
Naturally most humans have the approach of "I don't want a lecture on theory here - just show me a quick way to get the right answer..." And of course this is more so if the student is not a fan of celestial navigation for any reasons, not the least of which is he or she may be of the opinion that celestial is totally obsolete.
In this special case for the EXAM you DO NOT NEED to know the precise longitude of the Assumed Position (AP) since you will not be plotting the result. You only need the AP latitude (easy); the declination of the body (you look that up and use it as found); and the Local Hour Angle (LHA) for which, rigorously speaking, you need the correct AP longitude.
...but...
By a "short cut" you can get the same LHA that was used for the solution, ...well, most of the time. If all you want is the right answer on the test and don't care about the LOP or to expend the time and effort necessary to fully understand what you are doing, the short cut certainly seems enticing.
An aside: I do not hold any "short cutters" in poor regard. I presume that if they are studying for one of these exams they have got a heck of a lot of other stuff to learn besides celestial, and all of that is in addition to seeing to all their other daily responsibilities. Since celestial may seem like an arcane backwater of that total body of knowledge a "quick fix" certainly is attractive. Also celestial can be confusing to learn and anyone who didn't know that this was a kind of short cut could easily be enticed by seeing a simpler way to do things. -- Myself included.
Let's examine how the short cut works by first looking at West longitude dead reckoning (DR) position:
The LHA is the difference in longitude between your AP and the Greenwich Hour Angle (GHA) of the observed body. All hour angles are ALWAYS measured ONLY westward so the GHA of the body is how far west its geographic position (GP) is from the Greenwich meridian.
Your own longitude is how far west YOU are from the Greenwich meridian.
To get the LHA, which is how far west the body's GP was from YOU, you subtract your DR longitude from the GHA of the body.
If you are using a calculator or an electronic app you can use your DR and the GHA of the body complete with their minutes and tenths as found. The resulting LHA will probably have some minutes and tenths in its result. You can use that LHA along with its minutes and tenths in the electronic app or calculator solution. The results will be an azimuth (Z); a true azimuth (Zn); and an intercept distance in nautical miles (a); to be plotted directly from your DR.
However the test uses tables to do the sight reduction. Usually Pub 229 for USCG. These tables and many others such as Pub. 249 require that you enter them with a whole degree of AP latitude and an AP longitude that results in a whole degree of LHA. You do not enter them with your DR position. Instead you “deliberately take up” a “position of convenience” nearby to where you are which we call and “Assumed Position.” Here “assumed” means “deliberately taken up.”
The reason for the "whole degrees" thing is just for compactness of the tables. It eliminates the huge number of possible solutions that would exist between every whole degree demarcation, making the printed books of tables physically small enough to carry aboard. It has NOTHING to do with the math. The math doesn't care about whole degrees at all.
In order to get the same answer as the exam you need the whole degree latitude and whole degree LHA that THE EXAM WRITER used to enter Pub. 229. If you use these, even with an app, a calculator, or different type of tables, you will come to their same answer - which is the immediate goal - even if you don't actually know what an AP is or how the heck they got one.
For western DR positions you subtract your AP longitude from the GHA of the body. To do this rigorously you first determine the GHA of the body including the minutes and tenths. Then you append those same minutes and tenths of the GHA to the whole degree of your longitude to get an AP longitude. In real life you will need this EXACT AP longitude later for plotting, so you would not short cut. But for the EXAM you don't plot so all you need is the LHA as a whole degree – and it has to be the same one the exam writer used or your answer will be different.
Here you can see if you simply ignore the minutes and tenths of BOTH the GHA and the DR when you subtract the DR longitude degrees from the GHA degrees you (usually) get the right answer. ... More on"usually" later.
When in eastern longitudes things change a bit. Here you must add how far east of the Greenwich meridian you are to how far west the GP of the body was from the Greenwich meridian to determine how far west the body's GP meridian is from YOUR meridian.
All the above discussion regarding using calculators or apps still applies. The math does NOT need a whole degree of anything, but the tables, and the exam question answer based on using the tables, DO need a whole degree AP latitude and a whole degree LHA. The whole degree latitude part is easy - just round the DR latitude to the nearest degree. The whole degree LHA is a little trickier.
Rigorously speaking since you will be ADDING your AP longitude to the GHA of the body the minutes and tenths of your contrived AP must sum with the minutes and tenths of the GHA to equal exactly 60.0' which is one whole degree.
EXAMPLE: GHA 34° 40.0' DR lon 15° 32.5' E and 34° 40.0' + 15° 32.5 E = 50° 12.5'
this doesn't give a whole degree LHA so instead you contrive an AP longitude of 15° 20.0' E.
Then 34° 40.0' GHA
+ 15° 20.0 E AP lon (contrived so LHA will comeout to a whole degree)
49° 60.0'
=> 50° 00.0' LHA for use with Tables after you carry over the 60.0'
The RIGOROUS result for LHA will ALWAYS have the format of a trailing " 60.0' "
and this will ALWAYS increase the degree value by ONE WHOLE DEGREE.
It is this trailing 60.0' that Chris Nolan mentions in his teaching video when he comments " ... how many times have I forgotten to add that 1 degree?" https://youtu.be/X6VokWcuonU?t=204 but if you watch that segment carefully you will clearly see that he isn't short-cutting. He actually derives the proper AP longitude rigorously. What he “forgets” is to to carry over the 60.0'
The trailing “ 60.0' ” is also the basis of the shortcut method that says: "add the whole degrees of the DR to the whole degrees of the LHA and then add 1 degree to that result."
Looking at the above example if we do the following we get the LHA for the exam question, though it leaves us without knowing the longitude of the AP necessary for plotting and therefore in real life would be useless - but it WILL get the correct answer for the exam ... most of the time.
It isn't the "correct" way to do it. It is NOT based on either the mathematical requirements nor on good practice, nor a requirement for the tables. Its just a trick, but it can work...for the exam ... but not for actual navigation because you don't have a real AP longitude from which to start your plot. You skipped that step and went directly to finding the LHA.
Short Cut Version:
34° LHA degrees
+ 15° E DR degrees
+ 1° short cut "add one degree"
50° LHA
Next: About that "...most of the time"
Examiners want you to pick an AP longitude within 30.0' of longitude to your DR. Sometimes the above shortcut won't do that, and if you have not applied the rigorous method you may not be aware of that flaw because you never actually derived the AP longitude.
Suppose that in the above example the DR longitude had been 15° 52.5' E instead of 15° 32.5' E ? Using the short cut still would have a result of 50° for LHA. However employing the rigorous approach the AP longitude of 15° 20.0'E is now 32.5' of longitude away from the DR longitude – too far for the examiner! Here the "correct" AP longitude is adjusted to be 16° 20.0' E bringing the AP longitude to 27.5 minutes of longitude from the DR. It also changes the LHA to 51° In this case the short cut gets you the wrong answer for the exam!
All of that rigorous adjusting to make the AP longitude within 30.0' of the DR longitude makes essentially NO DIFFERENCE to the resulting LOP in real life AFTER PLOTTING, but may make a small difference in the results for Z and Zn values, and it WILL make a big difference in the intercept length leading you to the wrong answer for the exam.
If you used the short cut for exams and your Zn looks pretty good but your intercept is way off, try adjusting the LHA by one degree. Or better yet just take the extra minute to derive your AP longitude the rigorous way - it's really not that difficult.
My conclusion is that learning how to use the short cut is no easier than learning the rigorous method;
That the short cut confuses students because the do not realize it is just a trick; That the short cut is useless in real life because you don't have an AP longitude from which to base your plots; And because of these reasons the short cut, like most short cuts in learning, is not a better choice in the end.
Peter