To find CMG and SMG, allow leeway before allowing current to get CMG and SMG. Course steered 020° (T). Leeway wind NW (to the leeward) + 5°. Then, find the beam bearing of the true... To find CMG and SMG, allow leeway before allowing current to get CMG and SMG. Course steered 020° (T). Leeway wind NW (to the leeward) + 5°. Then, find the beam bearing of the true course steered 020° (T).
Understand the Problem
The question is asking to find the Course Made Good (CMG) and Speed Made Good (SMG) of a vessel navigating under certain conditions. It involves some calculations based on the ship's course, wind direction, and current. The task requires understanding trigonometric angles and vectors in navigation.
Answer
CMG: $040^\circ (T)$, SMG: $11$ knots.
Answer for screen readers
The Course Made Good (CMG) is $040^\circ (T)$ and the Speed Made Good (SMG) is $11$ knots.
Steps to Solve
- Adjust the Course for Leeway
The wind direction is NW, which means it pushes the vessel to the leeward. The leeway allowance is +5°. Thus, the effective course made good (CMG) after allowing for leeway will be:
$$ \text{CMG} = 020^\circ + 5^\circ = 025^\circ (T) $$
- Calculate the Distance Drifted
The vessel is moving at a speed of 10 miles in 1 hour. The distance drifted due to the leeway and current is 3 miles. So first, we plot the points based on the effective course.
- Determine the Current's Course
Extend the line AC and represent the current direction, which yields a drift at a distance of 3 miles (line BC). This total distance gives the position of point F.
- Draw the Course Made Good
Join the lines AC and extend to determine the final course made good. After accounting for the current, the course made good (AC) is observed as:
$$ \text{CMG} = 040^\circ (T) $$
- Calculate Speed Made Good
The speed made good (SMG) is given as 11 knots during travel over the total distance can be observed with the plotted positions.
The Course Made Good (CMG) is $040^\circ (T)$ and the Speed Made Good (SMG) is $11$ knots.
More Information
The CMG takes into account the leeway from the wind and the current's influence on the ship's course. Understanding how to adjust your course using trigonometric concepts is essential in navigation.
Tips
- Miscalculating the angle due to leeway.
- Confusing true headings with magnetic bearings.
- Forgetting to adjust the course for both wind and current effects.
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