**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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content copyright, © 2011-2018. Edward
Shore. Unauthorized use and/or unauthorized
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