Question:hard
During a captive maneuvering model test of a ship with a rudder, which ONE or MORE of the following coefficients can be calculated using an oblique towing test (straight line test with a drift angle)?
During a captive maneuvering model test of a ship with a rudder, which ONE or MORE of the following coefficients can be calculated using an oblique towing test (straight line test with a drift angle)?
Show Hint
Ask which coefficients need the yaw rate to be nonzero, since an oblique towing test always keeps yaw rate at zero.
Updated On: Jul 28, 2026
- \(Y_v\) and \(Y_{vvv}\)
- \(N_v\) and \(N_{vvv}\)
- \(Y_{v\delta\delta}\) and \(N_{v\delta\delta}\)
- \(N_{r\delta\delta}\) and \(N_{vr\delta}\)
Show Solution
The Correct Option is A, B, C
Solution and Explanation
Step 1: Fix what an oblique towing test physically does.
The model is towed on a straight track at a set drift angle so it has a sway velocity \(v\) but the carriage path is a straight line, which means the yaw rate \(r = 0\) for the entire run. The rudder angle \(\delta\) can be set and held fixed for each run.
Step 2: List what varies during the test.
Across a set of runs the test sweeps drift angle (hence \(v\)) and can also sweep the fixed rudder angle \(\delta\). It never sweeps \(r\), since the carriage itself does not rotate during a run.
Step 3: Sort the four coefficient pairs by whether they contain \(r\).
\(Y_v, Y_{vvv}, N_v, N_{vvv}\) depend only on \(v\), so they come straight out of the drift angle sweep. \(Y_{v\delta\delta}, N_{v\delta\delta}\) depend on \(v\) and \(\delta\), both of which the test controls, so they can be fitted too. \(N_{r\delta\delta}, N_{vr\delta}\) both contain \(r\), a variable this test structurally cannot change, so they are unreachable here.
Final Answer:
Only the coefficients free of yaw rate, in options A, B and C, can be found from an oblique towing test. \[ \boxed{\text{A, B and C}} \]
The model is towed on a straight track at a set drift angle so it has a sway velocity \(v\) but the carriage path is a straight line, which means the yaw rate \(r = 0\) for the entire run. The rudder angle \(\delta\) can be set and held fixed for each run.
Step 2: List what varies during the test.
Across a set of runs the test sweeps drift angle (hence \(v\)) and can also sweep the fixed rudder angle \(\delta\). It never sweeps \(r\), since the carriage itself does not rotate during a run.
Step 3: Sort the four coefficient pairs by whether they contain \(r\).
\(Y_v, Y_{vvv}, N_v, N_{vvv}\) depend only on \(v\), so they come straight out of the drift angle sweep. \(Y_{v\delta\delta}, N_{v\delta\delta}\) depend on \(v\) and \(\delta\), both of which the test controls, so they can be fitted too. \(N_{r\delta\delta}, N_{vr\delta}\) both contain \(r\), a variable this test structurally cannot change, so they are unreachable here.
Final Answer:
Only the coefficients free of yaw rate, in options A, B and C, can be found from an oblique towing test. \[ \boxed{\text{A, B and C}} \]
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