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3. VERIFICATION OF NEW APPROXIMATE FORMULAE
3.1 Application for Model Ships
Comparison between simulation results using new approximate formulae and measured results are made to validate accuracy of the formulae. Principal particulars of the model ships are provided in Table 1.
Table 1 Principal particulars of model ships
| |
L(m) |
B(m) |
d(m) |
Cb |
| Ship A |
2.5 |
0.4294 |
0.1402 |
0.8194 |
| Ship B |
2.5 |
0.4194 |
0.1403 |
0.6978 |
| Ship C |
2.5 |
0.4479 |
0.1135 |
0.8123 |
| Ship D |
2.5 |
0.4077 |
0.1696 |
0.831 |
| Ship E |
2.5 |
0.4355 |
0.1573 |
0.80023 |
| Ship F |
2.5 |
0.4350 |
0.1629 |
0.5717 |
| Ship G |
3.5 |
0.6344 |
0.21109 |
0.8045 |
| Ship H |
2.5 |
0.4082 |
0.1714 |
0.7727 |
| Ship I |
3.5 |
0.6344 |
0.21109 |
0.8018 |
| Ship J |
2.5 |
0.500 |
0.1050 |
0.8232 |
| Ship K |
2.5 |
0.500 |
0.1832 |
0.820 |
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Fig.2 provides port & starboard turning trajectories and time histories of speed drop ratio U/U0(U0: initial speed), drift angle β, non-dimensional angular velocity r' and heading angle Ψ.
Symbols in the figure indicate model test results and lines show results of numerical simulation. Results for Ship A with full load condition are shown in Fig.2(i), Ship B with ballast even condition are shown in Fig.2(ii) and Ship C with ballast 1% trim condition are shown in Fig.2(iii). Both predicted and measured time histories also agree well for these different loading conditions.
Fig.3 presents comparison of simulated and measured results for δ-r', β, U/U0. Good agreement is found for these results roughly. This means availability of this new approximate formulae for accurate ship manoeuvring motion at any rudder angle.
Fig.4 and Fig.5 show time histories of the normal force acting on rudder FN, in turning motion. There seems good agreement between predicted and measured results, especially at initial steepness.
δ-r' curves in steady turning motion are provided in Fig.6 (Ship G) and Fig.7 (Ship I). Both results are agreed well. Ship G and Ship I have almost same principal particulars and common fore hull but they have different aft hull shape, that is Ship G has 'V' form sections and Ship I has 'U' form sections in aft hull. Therefore inherent characteristics of course stability of both ships are quite different.
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