Author

Topic: Computed DR positions

David Burch

posted February 17, 2004 11:52 PM
This question from Bill.
"What formula should I be using to convert course, speed,and distance traveled to arrive at the correct dr pos.?"
This was brought up in light of a USCG test question, but it does have general applicability.
From: Starpath, Seattle, WA


David Burch

posted February 18, 2004 12:05 AM
the formulas and procedures for doing this are outlined in detail in Bowditch, which is online in full (...although the most recent editions are not as detailed as the older ones for some of the navigation techniques.)
Please see that for the time being, and as soon as i get a moment i will put our own fomulas up here for comparison... they are of course the same, but notation is a key.
To prepare for this, you need a very simple calculator that does trig functions... no programing (programable calculators are not allowed in the test room). You can also do sin and cos using the windows caluclator (change "view" to scientific).... but best to get your own that you will use in the test room or onboard and get used to it.
Then play with it to the point that you can solve these examples:
sin 23.45° = 0.3979
cos 126.3° = 0.59201
sin 6° 49.7' = 0.11889
cos 68° 05.7' = 0.373068
We only need sin and cos.
By the way, there is a very brief but useful review of trig definitions in the Radar Trainer program. Open the Tutorial and do a search on "math solutions."
From: Starpath, Seattle, WA


David Burch

posted February 20, 2004 10:46 PM
As soon as someone posts that "I have my calculator and have done the above examples and i want to know about this and am ready to go on with this topic" then post a reply here like that and we will do it. david
From: Starpath, Seattle, WA


Bill Brucato

posted February 21, 2004 07:24 AM
I have my calculator and I can perform the above calculations correctly. Ok, shoot! Bill
From: Celestial Navigation Home/Online


David Burch

posted February 26, 2004 09:33 PM
We have some articles on this subject with a longer discussion, but they are old and i can't find the files any more, but for now here are the basics:
From (Lat1, Lon1) you run a dist D along true course C, and then your new (Lat2, Lon2) are figured from
Lat2 = Lat1 ± dLat and Lon2 = Lon1 ± dLon
where
dLat = D x cos C
dLon = D x sin C / cos Lat.
For relatively short runs (under 50 miles or so) you can use Lat = Lat1; for longer runs you do better to use Lat = mid lat = Lat1 + (Lat2  Lat1)/2
Note the formulas have in them a ±. There is a way to formulate this with signs so that you could always use +, and then have sign conventions on S and E that will turn the dLat or dLon negative appropriately.
But that is generally more confusing than simply to sketch an intersection that shows your (Lat1, Lon1) position and then a course line from that in the right direction. Then simply decide from the picture if dLat and dLon are + or  from inspection. Then disregard the sign result of your compuation (+ or ) and apply the correction in the right way. In other words, if dLat comes out negative but you are in a north lat headed northerly, just disregard the sign, since you know your lat is getting bigger.
You will have to convert deg and min to decimal degrees for this.
Note that some very inexpensive calculators have a function that is very handy for this conversion—you type in 25.19 (for 25° 19') press the magic button and you get 25+19/60 = 25.3167. This type of calculator is the kind to have for the USCG test. It might be called dd.mm >> dd.dd or some such thing.
You can practice this DR procedure this way:
Go to exercise 6.6 on page 68. It lists 6 Lat1, Lon1 positions along with 6 courses taken from those positions.
Then look at the answers to 6.6 on page A9. That lists 3 separate distances run from each of these positions along with the Lat2, Lon2 you reach after each run.
Use the above procedure to see that you can compute these final positions. As i recall, i computed all of those positions using this procedure.
Have at it. Before you get done with the series you will be expert at the process. They start in each of the 4 global quadrants and go off in various directions. Try some in each combination. david
From: Starpath, Seattle, WA


