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1349_notes - MANEUVERING AND CONTROL OF MARINE VEHICLES...

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MANEUVERING AND CONTROL OF MARINE VEHICLES Michael S. Triantafyllou Franz S. Hover Department of Ocean Engineering Massachusetts Institute of Technology Cambridge, Massachusetts USA Maneuvering and Control of Marine Vehicles Latest Revision: November 5, 2003 Michael S. Triantafyllou and Franz S. Hover c
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Contents 1 KINEMATICS OF MOVING FRAMES 1 1.1 Rotation of Reference Frames . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.2 Differential Rotations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 1.3 Rate of Change of Euler Angles . . . . . . . . . . . . . . . . . . . . . . . . . 4 1.4 Dead Reckoning . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 2 VESSEL INERTIAL DYNAMICS 5 2.1 Momentum of a Particle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 2.2 Linear Momentum in a Moving Frame . . . . . . . . . . . . . . . . . . . . . 6 2.3 Example: Mass on a String . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 2.3.1 Moving Frame Affixed to Mass . . . . . . . . . . . . . . . . . . . . . 8 2.3.2 Rotating Frame Attached to Pivot Point . . . . . . . . . . . . . . . . 8 2.3.3 Stationary Frame . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 2.4 Angular Momentum . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 2.5 Example: Spinning Book . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 2.5.1 x -axis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 2.5.2 y -axis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 2.5.3 z -axis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 2.6 Parallel Axis Theorem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 2.7 Basis for Simulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 3 NONLINEAR COEFFICIENTS IN DETAIL 13 3.1 Helpful Facts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 3.2 Nonlinear Equations in the Horizontal Plane . . . . . . . . . . . . . . . . . . 15 3.2.1 Fluid Force X . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 3.2.2 Fluid Force Y . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16 3.2.3 Fluid Moment N . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17 4 VESSEL DYNAMICS: LINEAR CASE 17 4.1 Surface Vessel Linear Model . . . . . . . . . . . . . . . . . . . . . . . . . . . 17 4.2 Stability of the Sway/Yaw System . . . . . . . . . . . . . . . . . . . . . . . . 18 4.3 Basic Rudder Action in the Sway/Yaw Model . . . . . . . . . . . . . . . . . 20 4.3.1 Adding Yaw Damping through Feedback . . . . . . . . . . . . . . . . 21 4.3.2 Heading Control in the Sway/Yaw Model . . . . . . . . . . . . . . . . 21 4.4 Response of the Vessel to Step Rudder Input . . . . . . . . . . . . . . . . . . 22 4.4.1 Phase 1: Accelerations Dominate . . . . . . . . . . . . . . . . . . . . 22 4.4.2 Phase 3: Steady State . . . . . . . . . . . . . . . . . . . . . . . . . . 22 4.5 Summary of the Linear Maneuvering Model . . . . . . . . . . . . . . . . . . 23 4.6 Stability in the Vertical Plane . . . . . . . . . . . . . . . . . . . . . . . . . . 23 i
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5 SIMILITUDE 23 5.1 Use of Nondimensional Groups . . . . . . . . . . . . . . . . . . . . . . . . . 23 5.2 Common Groups in Marine Engineering . . . . . . . . . . . . . . . . . . . . 25 5.3 Similitude in Maneuvering . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27 5.4 Roll Equation Similitude . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29 6 CAPTIVE MEASUREMENTS 30 6.1 Towtank . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30 6.2 Rotating Arm Device . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30 6.3 Planar-Motion Mechanism . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30 7 STANDARD MANEUVERING TESTS 33 7.1 Dieudonn´ e Spiral . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33 7.2 Zig-Zag Maneuver . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33 7.3 Circle Maneuver . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34 7.3.1 Drift Angle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34 7.3.2 Speed Loss . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34 7.3.3 Heel Angle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34 7.3.4 Heeling in Submarines with Sails . . . . . . . . . . . . . . . . . . . . 35 8 STREAMLINED BODIES 35 8.1 Nominal Drag Force . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35 8.2 Munk Moment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35 8.3 Separation Moment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36 8.4 Net Effects: Aerodynamic Center . . . . . . . . . . . . . . . . . . . . . . . . 37 8.5 Role of Fins in Moving the Aerodynamic Center . . . . . . . . . . . . . . . . 37 8.6 Aggregate Effects of Body and Fins . . . . . . . . . . . . . . . . . . . . . . . 38 8.7 Coefficients Z w , M w , Z q , and M q for a Slender Body . . . . . . . . . . . . . . 39 9 SLENDER-BODY THEORY 39 9.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39 9.2 Kinematics Following the Fluid . . . . . . . . . . . . . . . . . . . . . . . . . 40 9.3 Derivative Following the Fluid . . . . . . . . . . . . . . . . . . . . . . . . . . 41 9.4 Differential Force on the Body . . . . . . . . . . . . . . . . . . . . . . . . . . 41 9.5 Total Force on a Vessel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42 9.6 Total Moment on a Vessel . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43 9.7 Relation to Wing Lift . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44 9.8 Convention: Hydrodynamic Mass Matrix A . . . . . . . . . . . . . . . . . . 44 10 PRACTICAL LIFT CALCULATIONS 44 10.1 Characteristics of Lift-Producing Mechanisms . . . . . . . . . . . . . . . . . 44 10.2 Jorgensen’s Formulas . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45 10.3 Hoerner’s Data: Notation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46 10.4 Slender-Body Theory vs. Experiment . . . . . . . . . . . . . . . . . . . . . . 47 10.5 Slender-Body Approximation for Fin Lift . . . . . . . . . . . . . . . . . . . . 48 ii
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11 FINS AND LIFTING SURFACES 49 11.1 Origin of Lift . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49 11.2 Three-Dimensional Effects: Finite Length . . . . . . . . . . . . . . . . . . . . 49 11.3 Ring Fins . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50 12 PROPELLERS AND PROPULSION 50 12.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50 12.2 Steady Propulsion of Vessels . . . . . . . . . . . . . . . . . . . . . . . . . . . 51 12.2.1 Basic Characteristics . . . . . . . . . . . . . . . . . . . . . . . . . . . 52 12.2.2 Solution for Steady Conditions . . . . . . . . . . . . . . . . . . . . . 54 12.2.3 Engine/Motor Models . . . . . . . . . . . . . . . . . . . . . . . . . . 54 12.3 Unsteady Propulsion Models . . . . . . . . . . . . . . . . . . . . . . . . . . . 56 12.3.1 One-State Model: Yoerger et al. . . . . . . . . . . . . . . . . . . . . . 56 12.3.2 Two-State Model: Healey et al. . . . . . . . . . . . . . . . . . . . . . 56 13 ELECTRIC MOTORS 57 13.1 Basic Relations
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