A vessel at LAT 18° 54' N, LONG 073° E heads for a destinations at LAT 13° 12', LONG 054° E. Determine the true course and distance by Mercator sailing.
Given:
Postion 1: LAT 18° 54' N, LONG 073° E
Position 2: LAT 13° 12' N, LONG 054° E
What is asked:
Course and distance by Mercator sailing
Solution:
1. Solving for difference in latitude (DLAT)
Lat1 = 18° 54' N
Lat2 = 13° 12' N (same sign, so subtract)
DLAT = 5° 42' S (Sign of DLAT is south because the direction of the ship is going south)
x 60 to convert it into miles
342 miles
2. Solving for the difference in longitude (Dlo)
Long1 = 073° 00' E
Long2 = 054° 00' E (same name: subtract)
Dlo = 19° W (Sign is west because the direction of the ship is westward)
x 60 to convert it into miles
1140 miles
3. Solving for Meridional Parts in each latitude and the difference in meridional parts (DMP). This is the formula in getting meridional parts.
Meridional Parts = (Latitude ÷ 2) + 45 = Tan Log Ans × 7915.7 - Sin latitude × 23.2
So, Lat 18° 54' N = 1147.6 MP
Lat 13° 12' N = 793.8 MP
And to get DMP, we have to subtract the meridional parts because our latitudes are of the same sign.
MP1 = 1147.6
MP2 = 793.8
DMP = 353.8
4. We can now solve for the course. This is the formula in solving course by Mercator sailing.
Tan Course = Dlo
DMP
= 1140
353.8
Course = 72.76°
= S 72.76° W (southwest, that is in the third quadrant. You might ask, why SW? What is the rule in naming? South because that's the sign of your DLAT; and West because that's the sign of your Dlo).
Converting quadrantal form to the new form:
Course = S 72.76° W
+ 180° (because that's in the 3rd quadrant)
True Course = 252.76°
5. Solving now for the distance.
Distance = DLAT
Cosine Course
= 342
Cos 72.76° (not 252.76 to avoid negative answer)
= 1153.9 nautical miles is the distance
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Given:
Postion 1: LAT 18° 54' N, LONG 073° E
Position 2: LAT 13° 12' N, LONG 054° E
What is asked:
Course and distance by Mercator sailing
Solution:
1. Solving for difference in latitude (DLAT)
Lat1 = 18° 54' N
Lat2 = 13° 12' N (same sign, so subtract)
DLAT = 5° 42' S (Sign of DLAT is south because the direction of the ship is going south)
x 60 to convert it into miles
342 miles
2. Solving for the difference in longitude (Dlo)
Long1 = 073° 00' E
Long2 = 054° 00' E (same name: subtract)
Dlo = 19° W (Sign is west because the direction of the ship is westward)
x 60 to convert it into miles
1140 miles
3. Solving for Meridional Parts in each latitude and the difference in meridional parts (DMP). This is the formula in getting meridional parts.
Meridional Parts = (Latitude ÷ 2) + 45 = Tan Log Ans × 7915.7 - Sin latitude × 23.2
So, Lat 18° 54' N = 1147.6 MP
Lat 13° 12' N = 793.8 MP
And to get DMP, we have to subtract the meridional parts because our latitudes are of the same sign.
MP1 = 1147.6
MP2 = 793.8
DMP = 353.8
4. We can now solve for the course. This is the formula in solving course by Mercator sailing.
Tan Course = Dlo
DMP
= 1140
353.8
Course = 72.76°
= S 72.76° W (southwest, that is in the third quadrant. You might ask, why SW? What is the rule in naming? South because that's the sign of your DLAT; and West because that's the sign of your Dlo).
Converting quadrantal form to the new form:
Course = S 72.76° W
+ 180° (because that's in the 3rd quadrant)
True Course = 252.76°
5. Solving now for the distance.
Distance = DLAT
Cosine Course
= 342
Cos 72.76° (not 252.76 to avoid negative answer)
= 1153.9 nautical miles is the distance
P.S. Like what you read? Please click the share button below to share this post to your friends. Sharing is caring...
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This is really helpful! I'm glad I found your blog. Thanks a lot! :D
ReplyDeleteYou're welcome Bryan.
DeleteWhat's the basis of the two constant figures?
Delete*what are
DeleteThis comment has been removed by the author.
ReplyDeleteHi nauta. can you please show me how to use the formula of meridional parts step by step? i've been trying this formula with my calculator for how many times but always came up with the wrong answer. anyway, i'm using casio fx-85ms. S-V.P.A.M. thanks in advance :)
ReplyDeleteHow I wish I could, Kim, but I no longer have my svpam calculator with me. Thanks for visiting this blog.
DeleteKim sky if you know how please tell me.how you do it.
Delete(lat1/2)+45=tan Ans Log Ans x 7915.7 -sin Lat1 x 23.2 that's the formula on how to calculate meridional part!
DeleteOther formula for DMP = Lat÷2+45=tan=log=×7915.7-23.2sinLAT
Deletedmp=7915.7xlog tan(lat/2 + 45) - 23.2xsinlat
DeleteSir how to solve DMP? can u explain briefly
DeleteHow to divide the latitude? Do I need to convert it first?
Deleteyou can also get the MP by
ReplyDeleteMP=Log Tan (lat / 2 + 45) x 7915.7 - (sinLAT x 23.2689)
Sir the 7915.7 and 23.2689 it is constant?
DeleteYes. Page 5 of Bowditch Volume II, 1981.
Deletehow to compute tan co= dlo
ReplyDeletedmp
using my calculator casio fx 901 thanks
We got the same problem if you know how please tell me.
DeleteWe got the same problem if you know how please tell me.
DeleteTty shift tan x dlo/dmp
DeleteAfter getting the quotient by dividing the DLO and DMP, press shift then Tan.
Deletehi how to compute tan co=dlo/dmp?
ReplyDeleteWe got the same problem.
Deletehi how to compute tan co=dlo/dmp?
ReplyDeleteTo get the course tan needs to be transfered to the right side. so use tan-1 x dlo/dmp
DeleteFind the course and distance from initial position A. latitude 30°00'N longitude 045°00'W final position B. latitude 25°00'N longitude 050°00'W
Deletewhen im try your meridonal part formal im getting the wrong answer please help
ReplyDeleteVery good answer. I have confused to North or South MP and DMP. Thx for your answer:-)
ReplyDeletemy question is how to determine if long is e or w...because sometimes i get confuse about it..pls reply...thank you
ReplyDeletemy question is how to determine if long is e or w...because sometimes i get confuse about it..pls reply...thank you
ReplyDeleteThe name of longitude is given...
DeleteDo you mean how to determine the name of the difference in longitude (dlo)?
The name of your dlo is determined to what direction your ship is going, either east or west.
it depends on the course of the ship, that's my opinion.
DeleteThis comment has been removed by the author.
ReplyDeletewhy north to north answer is south in dlat ?
DeleteThe Dlat is south because your direction is going south. The ship is from 18 deg 54 mins N going to 13 deg 12 min N. Therefore, your Dlat is named south.
DeleteBut, supposing the ship is from 13 deg 12 min N going to 18 deg 54 min N, then your Dlat is north.
sir how about where did you get the 342 miles by converting 60 what is the formula?
ReplyDeletesir asap where did you get to come up the answer of 342 miles is the da dlat and 1140 miles is the dlo, and also the distance is 1153.9?? what formula did you use?
DeleteThank You to this blog..it's really heplful!
ReplyDeleteThank you for the mini lesson....I got that AHA! moment while i was doing my lesson and reading over your blog...Thank you...Oh and I just get my MP from table 5 in Bowditch II ;)
ReplyDeleteHi good day! I need explanation regarding the distance formula. Why did you use the DLAT instead of the DMP? To my understanding if you use DLAT its Plane Sailing not Mercator Sailing anymore.
ReplyDeleteI used the pythagorain formula and we didn't arrive in the same answer... :-(
Handing, moet ik niet meer zelf doen
ReplyDeleteHow to get this Course= S 72.76° W i don't know how get this can you help me please.
ReplyDeleteIn sci calcu, shift tan, then do the division. Then dms
DeleteIn solving dlat and dlo and have different name, do you add them?
ReplyDeletePlease Tell me the quadrants from 1 to 4
ReplyDeleteNE = as it is
DeleteSE = -180
SW = +180
NW = -360
How to compute the meridional parts using sci cal step by step because it always show syntax error :(
ReplyDeleteThis comment has been removed by the author.
ReplyDeleteThis comment has been removed by the author.
DeleteSir please make 2 example per topic to for us to avoid confusion. Thank you sir more power!
ReplyDeleteHow did the dlat turned into 342 my calculator show 325.2? Need help
ReplyDeleteHow to solve dlat if the lat1 long1 course and distance are given??
ReplyDeletesir if the question is a vessel is 065degree T , covering a distance of 254m
ReplyDeletereq.Dlat
p/departure
Dlon
what is the answer
Sir , how you simplify the DMP FORMULA. ?
ReplyDeleteSir ganda naman ng example mu ask ko sana kung my plane at parallel sailing ka thanks sir Godbless you paki email lng sir kung pwede hehehe thanks talaga
ReplyDeleteHere's the example of a parallel sailing on this blog.
Deletehttps://oic-nwreviewer.blogspot.com/2014/03/advancement-of-clock.html?m=1
how can I divide the latitude? Do I need to convert it first?
ReplyDeletehow can I divide the latitude? Do I need to convert it first?
ReplyDeletewhat if same longitude how to get the course and distance ?
ReplyDeletethe course 72.76 deg.. its on the 3rd quadrant, shouldn't you subtract it by 270?
ReplyDeleteWhat should I do if the total of my DLAT 0° 6' ?
ReplyDeleteCan you do plane Sailing?
ReplyDeleteHow to solve plane sailing?
ReplyDelete