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
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
To calculate the distance between waypoints A and B using Mercator sailing, we need to determine the following values:
A: Initial position
A_lat = 32°17.6' S
A_long = 007°14.6' W
B: Final position
B_lat = 29°12.3' S
B_long = 001°38.4' E
1. Convert the latitude and longitude from degrees, minutes, and seconds (DMS) to decimal degrees (DD):
A_lat_DD = -32.2933° (approx.)
A_long_DD = -7.2433° (approx.)
B_lat_DD = -29.2050° (approx.)
B_long_DD = 1.6400° (approx.)
2. Calculate the difference in latitude (Dlat) and difference in longitude (DLO):
Dlat = B_lat_DD - A_lat_DD = -2.0883° (approx.)
DLO = B_long_DD - A_long_DD = 8.8833° (approx.)
3. Convert the course angle from degrees to radians:
Course = atan(DLO / Dlat) = atan(8.8833° / -2.0883°) ≈ -1.3330 radians
4. Calculate the distance (DMP) using the given formula:
MP = 79.15 * log(tan((A_lat_DD / 2) + 45°)) - 23.4 * sin(A_lat_DD)
MP ≈ 79.15 * log(tan((-32.2933° / 2) + 45°)) - 23.4 * sin(-32.2933°)
MP ≈ 79.15 * log(tan(56.8533°)) - 23.4 * sin(-32.2933°)
MP ≈ 79.15 * log(1.3586) - 23.4 * sin(-32.2933°)
MP ≈ 79.15 * 0.3098 - (-16.3569)
MP ≈ 24.5 + 16.3569
MP ≈ 40.8569
Distance = Dlat / cos(Course) = -2.0883° / cos(-1.3330 radians)
Distance = -2.0883° / cos(-1.3330)
Distance ≈ 1.7304
The distance between waypoints A and B using Mercator sailing is approximately 1.7304 nautical miles.
To calculate the distance between the waypoints A and B using Mercator sailing, we will follow the provided formulas:
1. Calculate the difference in latitude (Dlat) between the two waypoints:
Dlat = LatB - LatA
Given:
LatA = 32°17.6’ S = -32.2933°
LatB = 29°12.3’ S = -29.2050°
Dlat = -29.2050° - (-32.2933°)
= 3.0883°
2. Calculate the cosine of the course (Cos course):
Cos course = cos(course)
Since the course is not provided, we cannot calculate the cosine of the course. Please provide the course to proceed further.
Please provide the course value in order to continue the calculation.
To calculate the distance between the waypoints A and B using Mercator sailing, we will use the given formulas:
1. Distance = Dlat / Cos course
2. Tan Co = DLO / DMP
3. MP = 79.15 * log(tan((lat / 2) + 45)) - 23.4 * sin(lat)
Let's break down the steps to get the answer:
Step 1: Calculate the values for Dlat and DLO.
Dlat = LatB - LatA = 29°12.3' - (-32°17.6') = 32°17.6' + 29°12.3' = 61°29.9'
DLO = LongB - LongA = 1°38.4' E - 7°14.6' W = 1°38.4' + 7°14.6' = 8°53'
Step 2: Calculate the course (Co) using the formula Tan Co = DLO / DMP.
Before calculating Co, we need to find the value for DMP using the formula MP = 79.15 * log(tan((lat / 2) + 45)) - 23.4 * sin(lat).
For this, we first need to convert the latitude values from degrees and minutes to degrees:
LatA = -32°17.6' = -32.2933°
LatB = -29°12.3' = -29.2050°
Now, let's calculate MP for the initial position (A):
MP(A) = 79.15 * log(tan((LatA / 2) + 45)) - 23.4 * sin(LatA)
= 79.15 * log(tan(((-32.2933 / 2) + 45)) - 23.4 * sin(-32.2933)
Using a scientific calculator, calculate the MP(A):
MP(A) = 64.607
Step 3: Calculate the course (Co).
Tan Co = DLO / DMP
Co = atan(DLO / DMP)
Plug in the values:
Co = atan(8°53' / 64.607)
Co ≈ 0.131 radians
Step 4: Calculate the distance.
Distance = Dlat / cos(course)
Distance = 61°29.9' / cos(0.131)
Distance ≈ 719.3 nautical miles
Therefore, the distance between the waypoints A and B using Mercator sailing is approximately 719.3 nautical miles.