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4.3 Yaw motion
Harmonic yaw tests have been executed with positive and negative speed. For full ships the added moment of inertia is rather insensitive to the selected test parameters during harmonic yaw tests. For slender ships the absolute value of the acceleration derivative increases slightly with increasing frequency during harmonic yaw and oscillatory tests. In figure 7 the added moment of inertia N'f is displayed in function of the non-dimensional frequency ω’ for harmonic yaw tests (Fn = 0.033) and oscillatory tests.
For the ship going astern, the added moment of inertia does not differ from the derivative for positive ship's speed both in magnitude and sign.
The selected value of the yaw amplitude has an important influence on the acceleration derivative of lateral force. According to [6] there are indications that conventional PMM yaw tests give more reliable results at high yaw amplitude. In addition, first order harmonic force components measured on fore (F) and aft body (A) proportional to the yaw acceleration (cosine) change in magnitude if the ship is going astern compared to going ahead. If a ship is going ahead, the lateral force proportional to the acceleration is concentrated on the fore body during yaw motion (table 3). Going astern, maximum forces are measured on the aft body. This results in a change of sign for the yaw acceleration derivative of lateral force.
Fig. 7 Added moment of inertia for ship D and E.
Table 3 First harmonic force components (tanker E)
| |
cosine (N) |
sine (N) |
| run |
Fn |
|ω’| |
(F) |
(A) |
(F) |
(A) |
| EGGH08 |
0.016 |
3.34 |
-4.4 |
1.4 |
- 4.3 |
3.9 |
| EGGI02 |
-0.016 |
3.34 |
-1.7 |
3.7 |
-1.8 |
5.0 |
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In [5] the derivative Y'r is regarded as a parameter of small importance. Although the influence of test parameters is neglected in figure 8 by showing mean values during ahead motion, a sensitivity analysis must give a definitive answer about the importance of the acceleration derivative due to yaw and thus the test parameters on ship's manoeuvrability.
Compared to the results of pure yawing tests, the acceleration derivatives of the lateral force and yawing moment are affected by combining yaw and drift, depending on the hull form and the test parameters.
Fig. 8 |
Mean value of yaw acceleration derivative of lateral force Y'rdot based on harmonic yaw tests. |
Fig. 9 |
Influence of drift angle on yaw acceleration derivative of lateral force Y'rdot based on combined yawing and drifting tests. |
Fig.10 |
Influence of drift angle on added moment of inertia N'rdot based on combined yawing and drifting tests. |
According to figure 9 and 10, the influence of a constant drift angle during a harmonic yawing test appears to be more significant for the acceleration derivative of lateral force both for slender and full ships and for the added moment of inertia of slender ships. The effect of drift is most important at low yaw amplitudeΨA and/or low non-dimensional frequency ω'. Nevertheless, the increase of the derivatives is more or less symmetrical for positive and negative drift angles.
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