What is the necessary rate of turn ,for a vessel that moves with a speed of 25 miles per hour to complete a 90 degrees turn ,starting the turn 1 mile prior of the way point of altering course?
Radius of turn = 1 mile
How long is the ship turning to turn 1/4 of a circle?
circumference = 2 pi r = 2 pi miles
so the ship travels pi/2 miles while turning.
speed = 25 mph assume constant
time = distance / rate = (pi/2)/25 = pi/50 hours
so the ship turns 90 degrees in pi/50 hours 1432 degrees/hour
times 1 hour/60 minute = 24 degrees/minute
times 1 minute/60 seconds = 0.4 degrees/second
To determine the necessary rate of turn for a vessel, we need to consider the vessel's speed, the desired angle of turn, and the distance from the starting point of the turn to the waypoint.
Given:
- Vessel speed: 25 miles per hour
- Angle of turn: 90 degrees
- Distance from the starting point of the turn to the waypoint: 1 mile
To calculate the necessary rate of turn, we can use the formula:
Rate of Turn = Speed / Distance
1. Convert the vessel speed to nautical miles per hour (since nautical miles are commonly used in marine navigation). 1 nautical mile is equal to 1.15078 miles.
25 miles per hour * (1 nautical mile / 1.15078 miles) = 21.7 nautical miles per hour
2. Convert the distance from miles to nautical miles.
1 mile * (1 nautical mile / 1.15078 miles) = 0.87 nautical miles
3. Substitute the values into the formula to calculate the rate of turn.
Rate of Turn = 21.7 nautical miles per hour / 0.87 nautical miles
Rate of Turn ≈ 24.94 degrees per minute
Therefore, the necessary rate of turn for the vessel to complete a 90-degree turn, starting 1 mile prior to the waypoint, is approximately 24.94 degrees per minute.