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 Dead Reckoning (DR) position at midnight, we need to consider the vessel's initial position and its course and speed over time.
Given:
Initial position: Latitude 14˚ 25’ S, Longitude 112˚ 37’ W
Course: 180˚ T
Speed: 18 knots
First, let's convert the initial position to decimal degrees:
Latitude: 14 degrees 25 minutes S = -14.4167 degrees
Longitude: 112 degrees 37 minutes W = -112.6167 degrees
To calculate the vessel's DR position at midnight, we need to determine the distance traveled and the change in latitude and longitude based on the course and speed.
Since the vessel maintains a course of 180˚ T (true) for 5.5 hours (from 1830 ZT to midnight), the total distance traveled can be calculated using the formula: Distance = Speed × Time
Distance = 18 knots × 5.5 hours
Distance = 99 nautical miles
To determine the change in latitude, we need to calculate the distance traveled in minutes of latitude. Since 1 nautical mile of latitude is equal to 1 minute, the change in latitude can be calculated as follows:
Change in Latitude = (Distance / 1 nm) × (1 latitude minute / 1 nm)
Change in Latitude = (99 nm) × (1 latitude minute / 1 nm)
Change in Latitude = 99 latitude minutes
To determine the change in longitude, we need to calculate the distance traveled in minutes of longitude. The distance varies depending on the latitude. Since the initial latitude is 14˚ 25’ S, we need to multiply the distance traveled by the cos(14.4167) to find the change in longitude in minutes. The formula is as follows:
Change in Longitude = (Distance / 1 nm) × (1 longitude minute / cos(latitude))
Change in Longitude = (99 nm) × (1 longitude minute / cos(14.4167))
Using a calculator, we get:
Change in Longitude = 90.74 longitude minutes
Now, we can calculate the final DR position at midnight by adding the change in latitude and longitude to the initial position:
Final Latitude = Initial Latitude + Change in Latitude
Final Latitude = -14.4167 degrees + 99 latitude minutes (converted to degrees)
Final Latitude = -14.4167 degrees + 1.65 degrees
Final Latitude = -12.7667 degrees
Final Longitude = Initial Longitude + Change in Longitude
Final Longitude = -112.6167 degrees + 90.74 longitude minutes (converted to degrees)
Final Longitude = -112.6167 degrees + 1.51 degrees
Final Longitude = -111.1067 degrees
Therefore, the DR position at midnight will be approximately:
Latitude: 12˚ 46’ S
Longitude: 111˚ 6’ W
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