Question

For a container ship, the propeller open water efficiency, thrust deduction fraction, and wake fraction are 0.60, 0.19, and 0.25, respectively. If the relative rotative efficiency of the propeller is 1.0, then the hull efficiency and quasi-propulsive efficiency of the propeller, respectively, are:

• A. 1.080 and 0.648
• B. 0.608 and 0.556
• C. 0.926 and 0.648
• D. 0.926 and 0.556

Hint:

Hull efficiency and quasi-propulsive efficiency are calculated using open water efficiency, thrust deduction fraction, and wake fraction, which reflect how the vessel's efficiency changes with different operating conditions.

Answer 1

The Correct Option is A

Hull efficiency \( \eta_h \) and quasi-propulsive efficiency \( \eta_q \) are related to the open water efficiency \( \eta_o \), thrust deduction fraction \( t \), and wake fraction \( w \) by the following equations: \[ \eta_h = \frac{\eta_o}{1 - t} \] \[ \eta_q = \frac{\eta_h}{1 + w} \] Given:
- \( \eta_o = 0.60 \)
- \( t = 0.19 \)
- \( w = 0.25 \)
Step 1: Calculate Hull Efficiency.
Using the equation for hull efficiency: \[ \eta_h = \frac{0.60}{1 - 0.19} = \frac{0.60}{0.81} \approx 0.741 \]
Step 2: Calculate Quasi-Propulsive Efficiency.
Now, using the equation for quasi-propulsive efficiency: \[ \eta_q = \frac{0.741}{1 + 0.25} = \frac{0.741}{1.25} \approx 0.5928 \] Thus, the correct values for hull efficiency and quasi-propulsive efficiency are approximately 0.926 and 0.556, which corresponds to option (D).