HP Prime and TI-84 Plus CE: Mercator Sailing Course and
Distance
Introduction
The following program MERCATOR calculates the course direction
and distance in miles given two pairs of latitude (north/south) and longitude
(east/west). Conversion to arc minutes
will be required during calculation.
Formulas Used:
Course:
C = atan ( | λ2 – λ1 | * 60 / | M2 – M1 | )
Where:
M1 = 7915.7045 * log ( tan (45° + L1 / 2 ) ) – 23.2689 * sin
L1
M2 = 7915.7045 * log ( tan (45° + L2 / 2 ) ) – 23.2689 * sin
L2
Direction:
D = | L2 – L1 | * 60 / cos C
HP Prime MERCATOR
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",
"Longitude 1",
"Latitude 2",
"Longitude 2"});
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;
C:=ABS(λ1-λ2)*60;
M:=ABS(M2-M1);
C:=ATAN(C/M);
D:=ABS(L2-L1)*60/COS(C);
RETURN {C,D};
END;
TI-84 Plus CE Program MERCATOR
Degree
Input "LATITUDE
1:",A
Input
"LONGITUDE 1:",B
Input "LATITUDE
2:",C
Input
"LONGITUDE 2:",D
7915.7045*log(tan(45+A/2))-23.2689*sin(A)→E
7915.7045*log(tan(45+C/2))-23.2689*sin(C)→F
abs(D-B)*60→R
abs(F-E)→M
tan^-1(R/M)→R
abs(C-A)*60/cos(R)→S
Disp
"COURSE:",R,"DISTANCE:",S
Example
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
Source:
Henry H. Shufeldt and Kenneth E. Newcomer The Calculator Afloat: A Mariner’s Guide to
the Electronic Calculator Naval Institute Press: Annapolis, Maryland. 1980
I will be taking a few weeks off this August, it will be part
vacation, part math research. I plan to
come back during the week of 8/20/2018. I
may have one more post before the break, especially if a calculator I ordered
comes in time for a review. Anyway, stay
safe, sane, and for those of you in the Northern Hemisphere, cool. Weather wise, this summer has been bonkers.
Eddie
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