At 1830 ZT, vessel is at Lat. 14˚ 25’ S, Long. 112˚ 37’ W. She heads 180˚ T at the speed of 18 knots. What will be her DR position be at midnight?
To calculate the DR (Dead Reckoning) position of the vessel at midnight, we need to determine the vessel's distance and direction of travel during the time period from 1830 ZT to 0000 ZT.
First, let's convert the vessel's initial position from degrees and minutes to decimal degrees.
Latitude: 14° 25' S = -14.4167°
Longitude: 112° 37' W = -112.6167°
Next, let's calculate the vessel's distance traveled. We know the vessel's speed is 18 knots and the time period is 6.5 hours (from 1830 to midnight).
Distance = Speed x Time
Distance = 18 knots x 6.5 hours
Distance = 117 nautical miles
Now, let's determine the vessel's direction of travel. The vessel is heading 180° T (true).
To calculate the DR position, we need to convert the true direction to a compass direction (magnetic) by applying the appropriate magnetic variation. Let's assume the magnetic variation is 10° East (varies depending on the location and changes over time).
Compass direction (magnetic) = True direction - Magnetic variation
Compass direction = 180° T - 10° (approximately)
Compass direction ≈ 170°
Now, using the distance and direction, we can calculate the change in latitude and longitude to calculate the DR position.
Change in Latitude = Distance x sin(Compass direction)
Change in Latitude = 117 nm x sin(170°)
Change in Latitude = 117 nm x -0.342
Change in Latitude ≈ -40 nm
Change in Longitude = Distance x cos(Compass direction)
Change in Longitude = 117 nm x cos(170°)
Change in Longitude = 117 nm x -0.940
Change in Longitude ≈ -110 nm
Finally, let's add the changes in latitude and longitude to the initial position to obtain the DR position.
Latitude (DR) = Initial Latitude + Change in Latitude
Latitude (DR) = -14.4167° - 40 nm
Latitude (DR) ≈ -14.72° S
Longitude (DR) = Initial Longitude + Change in Longitude
Longitude (DR) = -112.6167° - 110 nm
Longitude (DR) ≈ -113.52° W
Therefore, the vessel's DR position at midnight will be approximately Lat. 14° 43’ S, Long. 113° 31’ W.