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Mercator Sailing: Course and Distance
09-04-2018, 07:19 PM (This post was last modified: 09-04-2018 07:21 PM by Dieter.)
Post: #21
RE: Mercator Sailing: Course and Distance
(09-03-2018 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 East-West courses that even some online calculators don't calculate correctly.

Dieter
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09-05-2018, 05:46 PM (This post was last modified: 11-10-2018 07:20 PM 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 HP-65 Navigation Pac. I never bought the Nav Pac for my HP-41, but I eventually did buy the book.

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09-22-2018, 11:37 PM
Post: #23
RE: Mercator Sailing: Course and Distance
(08-12-2018 05:13 PM)Dieter Wrote:  
(08-10-2018 03:08 AM)Eddie W. Shore Wrote:  Latitude 1: 102° 54’ 16” W = 102.9044444444°
Longitude 1: 43° 21’ 16” N = 43.3544444444°
Latitude 2: 106° 3’ 8” W = 106.0522222222°
Longitude 2: 42° 4’ 30” N = 42.075°

Results:

Course: 5.782390957°

Distance: 189.832588 mi

Eddie, I think you confused latitudes and longitudes here. There are no latitudes > 90°.

I also wonder how you get these results. For the given data I get a distance of 159,03 nmi and a course of 61,14° Southwest (241,14° true course). This matches the result of an online calculator where I checked the results.

Finally, what sign convention does your program use? Are West and South positions entered with negative sign?

Dieter

I always get latitude and longitude mixed up. Going by the book's examples (pg. 78), north and west were entered as positives.
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09-22-2018, 11:39 PM
Post: #24
RE: Mercator Sailing: Course and Distance
(08-24-2018 07:21 PM)Gene222 Wrote:  Two weeks and no response. I guess Eddie is not following his own post.

I bought Calculator Afloat in the late 80s or early 90s to learn more about geodetic calculations. It's a good book, but it does not go into much detail about the signage for the latitude and longitude calculations. You perform the calculations first then mentally apply the proper signage to the results.

I modified Eddie's program where South latitudes and West longitudes must be entered as negative numbers in degrees, but I ran into a problem when the two points have the same latitude, such as

Lat 40 N, Long 25 W
Lat 40 N, Long 30 W

In this case, the course and distance equations give division by zero error messages. How do you calculate the course and distance on a parallel?

Code:
EXPORT MERCATOR()
BEGIN
// EWS 2018-08-10
// The Calculator Afloat

HAngle:=1; // degrees
LOCAL L1,L2,λ1,λ2,M1,M2;
LOCAL C,D;

INPUT({L1,λ1,L2,λ2},"Mercator",
{"L1:","λ1:","L2:","λ2:"},
{"Latitude 1 in degrees, +N, -S",
"Longitude 1 in degrees, +E, -W",
"Latitude 2 in degrees, +N, -S",
"Longitude 2 in degrees, +E, -W"});

M1:=7915.7045*LOG(TAN(45+L1/2))
-23.2689*SIN(L1);
M2:=7915.7045*LOG(TAN(45+L2/2))
-23.2689*SIN(L2);

LOCAL m,DLo,l,θ;
DLo:=(λ2-λ1)*60; //difference in longitude in minutes
m:=(M2-M1);      //difference in meridional parts in minutes
θ:=ATAN(DLo/m);  //course in degrees relative to North (+ or -) or South (+ or -)
l:=(L2-L1)*60;   //difference in latitude in minutes

IF DLo>=0 AND m>=0 THEN
  C:=θ;
END;

IF DLo<0 AND m>=0 THEN 
  C:=360+θ; 
END;

IF DLo<0 AND m<0 THEN
  C:= 180+θ;
END;

IF DLo>=0 AND m<0 THEN
  C:=180+θ;
END;

D:=ABS(l/COS(θ));

RETURN {C,D};

END;

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
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