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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