Question

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)?

• A. \(Y_v\) and \(Y_{vvv}\)
• B. \(N_v\) and \(N_{vvv}\)
• C. \(Y_{v\delta\delta}\) and \(N_{v\delta\delta}\)
• D. \(N_{r\delta\delta}\) and \(N_{vr\delta}\)

Hint:

Ask which coefficients need the yaw rate to be nonzero, since an oblique towing test always keeps yaw rate at zero.

Answer 1

The Correct Option is A, B, C

An oblique towing test tows the model in a straight line at a fixed drift (sway) angle, with the yaw rate held at zero throughout the run; the rudder can be held at a fixed angle during the run as well. So this test can only supply the maneuvering derivatives that do not need a nonzero yaw rate \(r\) to appear.

1. \(Y_v\) and \(Y_{vvv}\): correct. These are the linear and cubic sway force derivatives with respect to sway velocity alone, exactly what varying the drift angle while towing straight measures.
2. \(N_v\) and \(N_{vvv}\): correct. These are the matching yaw moment derivatives with respect to sway velocity, found from the same straight, drift angle sweep, no yaw rate needed.
3. \(Y_{v\delta\delta}\) and \(N_{v\delta\delta}\): correct. These couple sway velocity with the rudder angle squared. Since the oblique towing test can be repeated at several fixed rudder angles while sweeping drift angle, this combined sway-rudder dependence can still be extracted, with no yaw rate involved.
4. \(N_{r\delta\delta}\) and \(N_{vr\delta}\): wrong. Both of these derivatives involve the yaw rate \(r\), which is held at zero throughout an oblique towing test, so a test that never varies \(r\) cannot isolate a derivative that depends on it. These need a rotating arm test or a rudder equipped PMM run where \(r\) is actively varied.

Because the oblique towing test only varies sway velocity and rudder angle, never yaw rate, it can supply the derivatives in A, B and C, but not D.