Trans RINA, Vol 152, Part A2, Intl J Maritime Eng, Apr-Jun 2010


Figure 3


Simulation of 15/5 Zigzag at 5 knots – Axisymmetric body


Figure 5 Para-


Effect of variation in mathematical model on


trajectory simulation for axisymmetric body θO


Model 1 Model 2


Model 3 (fully linear)


Table 2


meters of Zigzag → (Difference from Model 3 values given in %) 2.40 2.91 6.28 9.44 19.14 11.1%


(deg)


zO (m)


3.6% 33.1% te (sec) tc (sec) 2.6% 3.1% 2.16 2.81 6.12 9.16 td (sec) 1.1%


2.95 3.74 5.76 9.66 20.86 36.6%


5.9% 5.5% 10.1% 18.94


Effect of variation in mathematical model on


trajectory simulation results (15/5 zigzag at 5 kts) for axisymmetric body.


Figure 4 Simulation of 15/5 Zigzag at 5 knots –


SUBOFF body Parameter


Overshoot pitch angle (θO); degrees


Overshoot change of depth (zO); metres


Time to reach execute (te); seconds


Time to check pitch (tc); seconds Time


depth (td); seconds


Table 1 for


15/5 zigzag at 5 mathematical model


Parameters estimated by trajectory simulation knots


using strictly linear to check


Axisym- metric body


SUBOFF body


2.16 11.43 2.81 26.34


6.12 18.96


9.16 45.48 18.94 74.94


Examining the results shown in Table 2, it is seen that changing the mathematical model from strictly linear to non-linear terms causes variation in parameter values in the range of 1 to 37% for the manoeuvre and the body considered. In the sequel, the significance of this level of uncertainty will be examined in light of the other uncertainties in the manoeuvring prediction process.


5. VALUES OF HYDRODYNAMIC COEFFICIENTS


The main unknowns in the procedure of prediction of manoeuvring characteristics are the numerous HDC’s. It is desirable that once the geometry of the vessel is defined in the early stages of the design, these derivatives are estimated by empirical methods based on similar vessels, or other methods, so that necessary checks can be made as to whether the design satisfies the various manoeuvring requirements.


As described in Section 3, the choice of mathematical


model dictates which HDCs that need to be evaluated. Of the 36 first-order HDC’s possible, many can be neglected


A - 76 ©2010: The Royal Institution of Naval Architects


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