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5.2 Pure yaw motion
As no rotating arm facility is available, all results for pure yawing are based on harmonic PMM yaw tests.
Compared to the acceleration derivative of lateral force due to yawing, testing parameters frequency and yaw amplitude have a significant influence on the velocity dependent lateral force Y'(γ) both for full and slender ships.
Fig. 14 |
Influence of frequency and yaw amplitude on non-dimensional lateral force Y'(γ) for the tanker. |
In figure 14 the tabular models of individual test runs (Fn= 0.033) are compared for the tanker at the two available water depths. At 50% UKC the difference between the models based on runs at small frequency/small yaw amplitude or large frequency/large yaw amplitude is noticeable but small. At 20% UKC, on the other hand, the test parameters affect the resulting lateral force. The centrifugal force, -mur, proportional to the ship's mass m is added to the figures of Y'(γ).
The influence of the test parameters can partly be explained based on the sinkage measured during harmonic yaw tests. Maximum sinkage occurs at maximum yaw velocity or yaw rate angle and increases with decreasing water depth and increasing frequency and yaw amplitude (figure 15).
Moreover, the involved test parameters during pure yaw tests with slender ships influence both the magnitude and the sign of the lateral force Y'(γ) at small yaw rate angles.
Fig. 15 |
Net UKC during harmonic yaw tests at under keel clearances of 20 and 50% |
Fig. 16 |
Influence of frequency and yaw amplitude on non-dimensional lateral force Y'(γ) for the container carrier (see table 4 for test parameters). |
Table 4 Test parameters for container carrier
| Run |
UKC |
Fn |
ΨA |
ω’ |
| DAGA02 |
20% |
0.033 |
35° |
4.5 |
| DAGA06 |
20% |
0.033 |
15° |
2.3 |
| DAGB05 |
20% |
0.049 |
35° |
3.4 |
| DAGB11 |
20% |
0.049 |
35° |
2.3 |
| DAGC02 |
20% |
0.065 |
35° |
2.7 |
| DCGA06 |
7% |
0.033 |
15° |
2.3 |
| DCGB03 |
7% |
0.049 |
30° |
2.3 |
| DCGC01 |
7% |
0.065 |
25° |
2.7 |
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With increasing frequency (ω'>3) the centrifugal force increases with the hydrodynamic lateral force Y'(γ) even at yaw rate angles around zero degrees. As the water depth to draught ratio decreases to very shallow water (UKC of 7%), hydrodynamic force Y'(γ) is opposite to the centrifugal force line so that hydrodynamic force and centrifugal force neutralise each other.
Contrary to the lateral force, the yawing moment is scarcely influenced by the test parameters during pure yaw tests. Tabular models during individual test runs (Fn = 0.033;ω' = 3.8; ΨA = 35°) for the tanker and the container carrier are shown in figure 17. Similar to the lateral force due to pure swaying, the difference between non-dimensional yawing moment N'(Y) at 20% UKC for slender and full ships is small.
Four quadrants tabular models for the tanker at an UKC of 20% of the ship's draught are illustrated in figure 18. Values at 90° yaw rate angle are based on oscillating tests around Ψ-axis (zero forward velocity) which are affected by memory effects caused by the ship going through his own wake. Therefore, 90° values were calculated based on the first cycle of oscillating tests during which memory effects are restricted.
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