Paul,
First thank you for your question. I know this is initially a point of confusion for many and I worried that no questions meant I did not explain it very well! Full disclosure: It confused the heck out of me when I was trying to learn it!
I go into the rigorous approach a bit more including an example in the thread titled "LHA in Eastern Longitudes" There is a link to that thread above but I'm working on a mobile device and its not getting the link here - sorry.
For finding an AP longitude from an eastern longitude DR by the rigorous method:
subtract the minutes and tenths of the GHA as found from 60.0'
append those resulting minutes to the whole degree of DR longitude to get AP longitude
add the AP longitude to the GHA getting a result with trailing 60.0' for LHA
carry over the trailing 60.0' as one degree to the LHA
for examinations: check that the resulting AP longitude is less than 30.0' from DR longitude
example: GHA 18 54.2' DR long. 20 12.1E DR latitude 15 54.2'N
start with 60.0' - 54.2' = 05.8' so the 05.8'' is what we append to our DR long degrees for our AP longitude. That result is an AP longitude of 20 05.8'E
Now we add 18 54.2' to 20 05.8'E = 38 60.0' as LHA
when we carry over the 60.0' as one full degree this updates to 39 00.0' as the LHA
This is an LHA you will find listed in the tables (because they only list whole degrees LHA and lat.)
Here you now have the whole degree LHA needed for most tables (39 00.0') AND an actual AP longitude of a starting point for your plot ( 20 05.8'E )
In this example 20 05.8'E is less than 30.0' of longitude away from the DR longitude of 20 12.0E
Since theDR latitude is 15 54.2'N you set the AP latitude to the nearest whole degree 16 00.0'N
The AP is put down on your chart or plotting sheet at:
16 00.0' N 20 05.8' E and it is from THIS point (not your DR) that you plot in the true azimuth and intercept distance to the line of position.
With a bit of luck the LOP will pass very close to your DR.
Hope this helps. I'm happy to answer any further questions because I'm pretty sure there are more.
Peter
A wrinkle:
H.O. 211 Ageton's tables and its various derivatives including a version in Bowditch as well as The S Tables by Mike Pepperday allow sight reduction and plotting directly from your DR. This is also true of most electronic apps and direct calculation methods.
However since all of them work from any position they ALSO work with traditional AP's per the above discussion. After all the DR is just a position that is somewhat close to where you think you are and in this regard the math and methods don't know the difference from a DR to an AP.
It is only the commonly used tables that require a whole degree LHA and Lat ... not the math.
If you DO use Ageton's or direct calculation then on exams you still must find the traditional AP that the examiner who wrote the question used. When you use that with your DR methods you will get the correct answers for the exam, the same as if you had used Pub. 229 tables.
Therefore you really ought to learn how to properly find the AP even if you do not use it day to day.
Peter
First thank you for your question. I know this is initially a point of confusion for many and I worried that no questions meant I did not explain it very well! Full disclosure: It confused the heck out of me when I was trying to learn it!
I go into the rigorous approach a bit more including an example in the thread titled "LHA in Eastern Longitudes" There is a link to that thread above but I'm working on a mobile device and its not getting the link here - sorry.
For finding an AP longitude from an eastern longitude DR by the rigorous method:
subtract the minutes and tenths of the GHA as found from 60.0'
append those resulting minutes to the whole degree of DR longitude to get AP longitude
add the AP longitude to the GHA getting a result with trailing 60.0' for LHA
carry over the trailing 60.0' as one degree to the LHA
for examinations: check that the resulting AP longitude is less than 30.0' from DR longitude
example: GHA 18 54.2' DR long. 20 12.1E DR latitude 15 54.2'N
start with 60.0' - 54.2' = 05.8' so the 05.8'' is what we append to our DR long degrees for our AP longitude. That result is an AP longitude of 20 05.8'E
Now we add 18 54.2' to 20 05.8'E = 38 60.0' as LHA
when we carry over the 60.0' as one full degree this updates to 39 00.0' as the LHA
This is an LHA you will find listed in the tables (because they only list whole degrees LHA and lat.)
Here you now have the whole degree LHA needed for most tables (39 00.0') AND an actual AP longitude of a starting point for your plot ( 20 05.8'E )
In this example 20 05.8'E is less than 30.0' of longitude away from the DR longitude of 20 12.0E
Since theDR latitude is 15 54.2'N you set the AP latitude to the nearest whole degree 16 00.0'N
The AP is put down on your chart or plotting sheet at:
16 00.0' N 20 05.8' E and it is from THIS point (not your DR) that you plot in the true azimuth and intercept distance to the line of position.
With a bit of luck the LOP will pass very close to your DR.
Hope this helps. I'm happy to answer any further questions because I'm pretty sure there are more.
Peter
A wrinkle:
H.O. 211 Ageton's tables and its various derivatives including a version in Bowditch as well as The S Tables by Mike Pepperday allow sight reduction and plotting directly from your DR. This is also true of most electronic apps and direct calculation methods.
However since all of them work from any position they ALSO work with traditional AP's per the above discussion. After all the DR is just a position that is somewhat close to where you think you are and in this regard the math and methods don't know the difference from a DR to an AP.
It is only the commonly used tables that require a whole degree LHA and Lat ... not the math.
If you DO use Ageton's or direct calculation then on exams you still must find the traditional AP that the examiner who wrote the question used. When you use that with your DR methods you will get the correct answers for the exam, the same as if you had used Pub. 229 tables.
Therefore you really ought to learn how to properly find the AP even if you do not use it day to day.
Peter