Mercator Sailing: Course and Distance

09042018, 07:19 PM
(This post was last modified: 09042018 07:21 PM by Dieter.)
Post: #21




RE: Mercator Sailing: Course and Distance
(09032018 10:10 PM)Gene222 Wrote: Thanks for your comments on the program. I definitely bit off more than I could chew with this program. The revised program is attached. Thank you, the results look good to me. Maybe you can remove the "this check box is not used" part. Unless there is something I haven't realized yet. ;) Finally we got another example of this forum's power: in a collaborative effort we now got a solution that also handles EastWest courses that even some online calculators don't calculate correctly. Dieter 

09052018, 05:46 PM
(This post was last modified: 09112019 12:12 AM by Gene222.)
Post: #22




RE: Mercator Sailing: Course and Distance
FYI. The book "The Calculator Afloat" was written by H. H. Shufeldt and Kenneth E Newcomer. A review of the book (below) was printed in the December 1980 HP Key Notes. It says Newcomer worked for HP and developed the HP65 Navigation Pac. I never bought the Nav Pac for my HP41, but I eventually did buy the book.


09222018, 11:37 PM
Post: #23




RE: Mercator Sailing: Course and Distance
(08122018 05:13 PM)Dieter Wrote:(08102018 03:08 AM)Eddie W. Shore Wrote: Latitude 1: 102° 54’ 16” W = 102.9044444444° I always get latitude and longitude mixed up. Going by the book's examples (pg. 78), north and west were entered as positives. 

09222018, 11:39 PM
Post: #24




RE: Mercator Sailing: Course and Distance
(08242018 07:21 PM)Gene222 Wrote: Two weeks and no response. I guess Eddie is not following his own post. My apologizes for not following subscribing to the program posts I put up; something I will do from now on. I appreciate all the comments and modifications. Eddie 

09102022, 03:17 PM
Post: #25




RE: Mercator Sailing: Course and Distance
(08262018 07:18 AM)Dieter Wrote: Hint: the expression ln(tan(45°+x/2)) in the "book" formula is equivalent to artanh(sin(x)). FYI, atanh(sin(x)) = asinh(tan(x)) = gd^{1}(x) = x + x^3/6 + x^5/24 + ... https://en.wikipedia.org/wiki/Gudermannian_function The Secret Connection between Hyperbolic and Trigonometric Functions 

12212022, 08:31 PM
Post: #26




RE: Mercator Sailing: Course and Distance
(08312018 05:46 AM)Dieter Wrote:(08312018 02:15 AM)Gene222 Wrote: I see what I am doing wrong. The course is 270 (due west) on a Mercator map. I was looking a polar map. I guess starpath.com online Mercator calculator was right. Dieter, Thank you for this. Using your equations (in Excel) for MP and dLon when MP=0, namely: MP = 60*180/PI()*(ATANH(SIN(RADIANS(Lat)))0.081819190842622*ATANH(0.081819190842622*SIN(RADIANS((Lat))))) dLon = Distance/(COS(RADIANS(Lat))*(10.081819190842622^2*SIN(RADIANS(Lat)^2))/(10.081819190842622^2)) and an e value per WGS84, I get a strange dLon value when traveling E/W along the equator. For a course of either 090 or 270 and a distance of 600nm I calculate a dLon value of 595.98337. Shouldn't this value be 600 (i.e., 10 degrees of Lon)? Thanks in advance for your assistance. Vadim 

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