Calculate the distance between these waypoints using Mercator sailing:

Question

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

To calculate the distance between the waypoints A and B using Mercator sailing, you can follow the steps below:

1. Convert the latitude and longitude coordinates from degrees, minutes, and seconds (DMS) to decimal degrees (DD).

For position A (initial position):
Latitude: 32°17.6' S = -32.2933°
Longitude: 007°14.6' W = -7.2433°

For position B (final position):
Latitude: 29°12.3' S = -29.2050°
Longitude: 001°38.4' E = 1.6400°

2. Convert the decimal degrees to radians by multiplying them by π/180.

For position A:
Latitude: -32.2933° * (π/180) = -0.563828 rad
Longitude: -7.2433° * (π/180) = -0.126371 rad

For position B:
Latitude: -29.2050° * (π/180) = -0.509699 rad
Longitude: 1.6400° * (π/180) = 0.0286174 rad

3. Calculate the difference in longitude (Δλ) between the two positions.

Δλ = LongitudeB - LongitudeA
Δλ = 0.0286174 rad - (-0.126371 rad)
Δλ = 0.1559884 rad

4. Calculate the distance using the Mercator formula:
DMP = R * Δλ
Where R is the Earth's radius, which is approximately 6,371 km.

DMP = 6,371 km * 0.1559884 rad
DMP = 990.65 km

So, the distance between waypoints A and B using Mercator sailing is approximately 990.65 kilometers.