Question

Calculate the distance between these waypoints using Mercator sailing:
Distance= Dlat/ Cos course
Tan Co= DLO/DMP
MP= 79.15.logtan7(lat/2+45)-23.4sinlat

Solve for DMP

Initial position (A) Lat 32°17.6’ S, Long 007°14.6’W
Final position (B)Lat 29°12.3’ S, Long 001°38.4’ E

Answer 1

First, convert the latitude and longitude values from degrees, minutes, and seconds to decimal degrees:

A Latitude: -32 - (17.6/60) = -32.2933°
A Longitude: -7 - (14.6/60) = -7.2433°

B Latitude: -29 - (12.3/60) = -29.2050°
B Longitude: 1 + (38.4/60) = 1.6400°

Next, calculate the difference in latitude (Dlat):
Dlat = B Latitude - A Latitude = (-29.2050) - (-32.2933) = 3.0883°

Calculate the difference in longitude (DLO):
DLO = B Longitude - A Longitude = (1.6400) - (-7.2433) = 8.8833°

Calculate the course correction (Co):
Co = DLO / DMP
DMP = DLO / Co

Next, calculate the tangent of Co:
Tan Co = DLO / DMP
=> Tan Co = 8.8833 / DMP

Rearrange the equation to solve for DMP:
DMP = 8.8833 / Tan Co

Finally, use the given formula to calculate DMP:

MP = 79.15 * log(tan(Lat/2 + 45)) - 23.4 * sin(Lat)

For point A:
MP_A = 79.15 * log(tan((32.2933/2) + 45)) - 23.4 * sin(32.2933) = 103.8392

DMP_A = 8.8833 / Tan Co

For point B:
MP_B = 79.15 * log(tan((29.2050/2) + 45)) - 23.4 * sin(29.2050) = 99.1302

DMP_B = 8.8833 / Tan Co

The distance between the waypoints using Mercator sailing is calculated by subtracting the two MP values:

Distance = MP_B - MP_A = 99.1302 - 103.8392 = -4.7090


Note: The negative value indicates that the course is in the opposite direction.