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5. PREDICTED MANOEUVRING MOTION
Using the above-mentioned formulas to estimate hydrodynamic derivatives and coefficients, manoeuvring ship motions can be predicted by the computer simulation. The mathematical model is from eq.(l) to (9) in principle. For ship model F that has a flapped rudder, the mathematical model of rudder normal force eq.(7) is replaced to the Yoshimura's formula [7]. The estimated derivatives and coefficients are listed in Table 3. Simulated ship motions are shown in Fig.13 and Fig.14 with ship model A, C, D and F.
Table 3 Estimated hydrodynamic derivatives and coefficients using eq.(10)-eq.(16)
| Ship Model |
A |
B |
C |
D |
E |
F |
| Hull derivatives |
|
|
|
|
|
|
| X'ββ |
0.0069 |
-0.0526 |
0.0069 |
0.0139 |
-0.0305 |
0.0157 |
| X'βr-m'y |
-0.1872 |
-0.1238 |
-0.1665 |
-0.1921 |
-0.1571 |
-0.3418 |
| X'rr |
-0.0010 |
-0.0010 |
-0.0010 |
-0.0513 |
-0.0666 |
-0.0054 |
| X'ββββ |
0.0231 |
0.4692 |
0.0231 |
-0.0295 |
0.3041 |
-0.0426 |
| Y'β |
0.5692 |
0.5433 |
0.4797 |
0.7634 |
0.8515 |
0.9830 |
| Y'r-m'x |
0.0439 |
0.0452 |
0.0390 |
0.1325 |
0.1803 |
0.0850 |
| Y'βββ |
1.2000 |
1.2000 |
1.2000 |
1.2000 |
1.2000 |
1.2000 |
| Y'ββr |
-0.0172 |
-0.0172 |
-0.0172 |
0.7644 |
1.0019 |
0.0513 |
| Y'βrr |
0.4297 |
0.4297 |
0.4297 |
0.5748 |
0.6189 |
0.4424 |
| Y'rrr |
-0.0210 |
-0.0210 |
-0.0210 |
0.0097 |
0.0190 |
-0.0183 |
| N'β |
0.1455 |
0.1322 |
0.1186 |
0.0374 |
0.0066 |
0.2256 |
| N'r |
-0.0697 |
-0.0706 |
-0.0633 |
-0.0680 |
-0.0666 |
-0.0666 |
| N'βββ |
0.3000 |
0.3000 |
0.3000 |
0.3000 |
0.3000 |
0.3000 |
| N'ββr |
-0.4334 |
-0.4334 |
-0.4334 |
-0.6009 |
-0.6518 |
-0.4481 |
| N'βrr |
0.0169 |
0.0169 |
0.0169 |
0.0281 |
0.0315 |
0.0179 |
| N'rrr |
-0.0069 |
-0.0069 |
-0.0069 |
-0.0181 |
-0.0215 |
-0.0079 |
| Interactions |
|
|
|
|
|
|
| 1-tR |
0.857 |
0.86 |
0.862 |
0.857 |
0.856 |
0.825 |
| αH |
0.058 |
0.046 |
0.041 |
0.057 |
0.062 |
0.314 |
| ε |
0.971 |
0.951 |
0.941 |
0.969 |
0.977 |
1.176 |
| κ |
0.551 |
0.573 |
0.583 |
0.553 |
0.546 |
0.383 |
| l'R |
-0.957 |
-0.976 |
-0.984 |
-0.959 |
-0.952 |
-0.774 |
| γR |
0.439 |
0.421 |
0.413 |
0.437 |
0.443 |
0.610 |
|
Fig.13 |
Comparisons of spiral characteristic measured and predicted.
mark ○ : observed by free-running tests
dotted bold line: prediction by the proposed hydrodynamic coefficients
dotted thin line: prediction by the originally measured coefficients |
(Ship model A)
(Ship model C)
(Ship model D)
(Ship model F)
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