Chapter 3 - Dynamics of Marine Vessels

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6 3.2.4 Ballast Systems Assume that the disturbances in heave, roll, and pitch have means <strong>of</strong> zero. Consequently: wr w3, w4, w5 0 and can be written: −Zz 0 −Z 0 −K 0 −Mz 0 −M g zd d d 1 1 1 y1 yn−1 yn −x1 −xn−1 −xn n g∑ Vi w3 i1 n g∑ yiVi w4 i1 n −g∑ xiVi w5 i1 The water volumes V i is found by using the pseudo-inverse: H y H HH −1 y V1 V2 Vn H y −Zzzd−Zd −K d −Mzzd−Md Ivar Ihle – TTK4190 Spring 2006
7 3.2.4 Ballast Systems Example (Semi-Submersible Ballast Control) Consider a semi-submersible b b b b with 4 ballast tanks located at r1 −x, −y, r2 x, −y, r3 x, y,r4 −x, y In addition, yz-symmetry implies that Z Mz 0 H g y 1 1 1 1 −y −y y y x −x −x x −Zzzd −K d −Md H y H HH −1 y V1 V2 V3 V4 1 4g 1 − 1 y 1 x 1 − 1 y − 1 x 1 1 y − 1 x 1 1 y 1 x gA wp 0z d g∇GMT d g∇GML d gA wp 0z d g∇GMT d g∇GML d p 1 + V 1 P P V 4 O y b P P x b p 2 Inputs: zd, d, d + + V 2 P P V 3 p 3 Ivar Ihle – TTK4190 Spring 2006
Page 1 and 2: 1 Chapter 3 - Dynamics of Marine Ve
Page 3 and 4: 3 3.2.4 Ballast Systems Consider a
Page 5: 5 3.2.4 Ballast Systems Conditions
Page 9 and 10: 9 3.2.4 Ballast Systems Automatic P
Page 11 and 12: 11 3.2.4 Ballast Systems Feedback c
Page 13 and 14: 13 3.2.4 Ballast Systems Ivar Ihle
Page 15 and 16: 15 3.3 6 DOF Equations of Motion Bo
Page 17 and 18: 17 3.3.1 Nonlinear Equations of Mot
Page 19 and 20: 19 3.3.2 Linearized Equations of Mo
Page 25 and 26: 25 3.5 Standard Models for Marine V
Page 27 and 28: 27 3.5.1 3 DOF Horizontal Motion Lo
Page 29 and 30: 29 3.5.1 3 DOF Horizontal Motion Fo
Page 31 and 32: 31 3.5.2 Decoupled Models for Forwa
Page 37 and 38: 37 3.5.3 Longitudinal and Lateral M

Chapter 3 - Dynamics of Marine Vessels

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