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
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.
To calculate the distance between the waypoints (A and B) using Mercator sailing, we need to follow a few steps.
1. Convert the latitude and longitude values from degrees, minutes, and seconds to decimal degrees:
Initial position (A) Lat: 32°17.6' S, Long: 007°14.6' W
Convert 32°17.6' S to decimal degrees: -32.2933°
Convert 007°14.6' W to decimal degrees: -7.2433°
Final position (B) Lat: 29°12.3' S, Long: 001°38.4' E
Convert 29°12.3' S to decimal degrees: -29.2050°
Convert 001°38.4' E to decimal degrees: 1.6400°
2. Calculate the values for Dlat and DLO:
Dlat = LatB - LatA = -29.2050° - (-32.2933°) = 3.0883°
DLO = LongB - LongA = 1.6400° - (-7.2433°) = 8.8833°
3. Calculate the course (Co):
Tan Co = DLO / DMP
Given that Mercator sailing is used, we can rearrange the formula to solve for DMP:
DMP = DLO / Tan Co
4. Calculate the value for Co:
Co = atan(DLO / Dlat)
5. Calculate the distance (Distance) using the formula:
Distance = Dlat / cos(Co)
Let's calculate the values now.
First, calculate the value for Co:
Co = atan(8.8833° / 3.0883°)
Co ≈ 1.6504 radians
Next, calculate the value for DMP:
DMP = DLO / tan(Co) = 8.8833° / tan(1.6504 radians)
DMP ≈ 8.8833° / 2.5479 ≈ 3.4808°
Finally, calculate the distance (Distance):
Distance = Dlat / cos(Co) = 3.0883° / cos(1.6504 radians)
Distance ≈ 3.0883° / 0.4842 ≈ 6.3696°
Thus, the distance between the waypoints A and B using Mercator sailing is approximately 6.3696 degrees.