Guide for the Assessment of Parametric Roll Resonance in the Design of Container Carriers/Руководство по оценке параметрического резонанса бортовой качки в проектировании контейнерных судов

Издание на английском языке
The main purpose of this Guide is to supplement the Rules and the other design and analysis criteria that ABS issues for the classification of container carriers in relation to parametric roll resonance phenomenon.
The Guide contains a brief description of the physical phenomenon of parametric roll resonance, which may cause an excessive roll of a containership in longitudinal (head and following) waves. The Guide also contains a description of criteria used to determine if a particular vessel is vulnerable to parametric roll (susceptibility criteria) and how large these roll motions might be (severity criteria). Recommendations are given for further actions if a ship is found to be endangered by the possibility of parametric roll, including numerical simulations and a model test. Means of mitigation of consequences of the parametric roll are briefly considered.
The August 2024 edition adds enhanced requirements for the numerical simulation of parametric roll. Subsection 4/1 adds the requirements for digital onboard operational guidance. Subsection 4/2 adds guidelines on the simulation of polar diagrams considering the anti-rolling tank (ART) effect. If criteria and requirements included in this Guide are satisfied. ABS may assign an optional class notation as recognition of safety performance in relation to parametric roll resonance.

Contents
Section 1 Introduction
1 Parametric Roll Resonance in Longitudinal Waves
1.1 General
1.2 Stability in Longitudinal Waves
1.3 Roll Motions in Calm Water.
1.4 Physics of Parametric Roll Resonance
1.5 Influence of Roll Damping
1.6 Amplitude of Parametric Roll
1.7 Influence of Ahead Speed and Wave Direction
1.8 Definitions.
1.9 Nomenclature
Figure 1 Profile of Waterline in Wave Trough (Solid) vs. Calm Water (Dotted)
Figure 2 Profile of Waterline in Wave Crest (Solid) vs. Calm Water (Dotted)
Figure 3 Undamped Small Roll Motions in Calm Water
Figure 4 Parametric Roll Resonance
Figure 5 Development of Parametric Roll Resonance;Case 1: Ship Encounters Roll Disturbance when Stability is Increasing
Figure 6 Development of Parametric Roll Resonance; Case 2: Ship Encounters Roll Disturbance when Stability is Decreasing
Figure 7 Successively Decreasing Roll Amplitudes due to Roll Damping in Calm Water
Figure 8 Change of Instantaneous GM Value with Increasing Heel Angle
Figure 9 Development of Parametric Roll
Figure 10 Coordinate System for Hydrostatic Calculations.
Figure 11 Definition of the Draft /-th Station with j-th Position of the Wave Crest
Figure 12 Definition of the Offsets at /'-th Station with /-th Position of the Wave Crest
Section 2 Parametric Roll Criteria
1 General
2 Susceptibility Criteria
2.1 Design Wave.
2.2 Stability in Longitudinal Waves
2.3 Ahead Speed
2.4 Application of Susceptibility Criteria.
3 Severity Criterion for Parametric Roll Resonance in Head Seas
Table 1 Wave Heights
Figure 1 Diagram Showing Selection of Wavelength and Ahead Speed
Figure 2 Change of Stability in Longitudinal Wave
Figure 3 GM as a Function of Wave Crest Position
Figure 4 Restoring Moment as a Function of Wave Position and Heel Angle
Figure 5 Restoring Term as a Function of Time and Heel Angle
Section 3 Numerical Simulations
Section 4 Mitigation of Parametric Roll Resonance
1 Operational Guidance
2 Anti-Rolling Devices
Figure 1 Example of Polar Diagram and Color Scale (1 June 2008)
Section 5 Optional Class Notation
Table 1 Optional Class Notations
Section 6 Surveys
1 Initial Surveys
1.1 Passive Anti-rolling Devices
1.3 Active Anti-rolling Devices
3 Surveys After Construction
3.1 Annual Surveys.
3.3 Special Periodical Surveys
Appendix 1 Sample Calculations
Table 1 Particulars of a Sample Container Carrier
Table 2 Conditions for Sample Calculations
Table 3 Calculation of GM Value for Different Positions of Wave
Crest along Ship Hull (Simplified Method - 2/2.2)
Table 4 Sample Results for Susceptibility Criteria
Table 5 GZ Curves for Different Positions of Wave Crest
Table 6 Sample Results for Forward Speed Calculations
Table 7 Sample Input Data for Integration of Roll Equation
Table 8 Amplitude of Parametric Roll in Degrees
Figure 1 Lines of Sample Container Carrier
Figure 2 Calculation of GM Value for Different Positions of Wave Crest along Ship Hull (Simplified Method - 2/2.2)
Figure 3 GZ Curves for Different Positions of Wave Crest
Figure 4 Solution of the Roll Equation for V1 and ^ = 0.1
Appendix 2 Sample Polar Diagrams3
Figure 1 Sample Polar Diagram
Figure 2 Sample Polar Diagram -Full Load, Sea State 9
Figure 3 Sample Polar Diagram -Full Load, Sea State 8
Figure 4 Sample Polar Diagram -Full Load, Sea State 7
Figure 5 Sample Polar Diagram -Partial Load, Sea State 9
Figure 6 Sample Polar Diagram -Partial Load, Sea State 8
Figure 7 Sample Polar Diagram -Partial Load, Sea State 7
Appendix 3 Criteria for Parametric Roll of Large Containerships in Longitudinal Seas
1
2 Abstract
3 Introduction
4 Physics of parametric roll
4.1 Stability in Longitudinal Waves
4.2 Roll Motions in Calm Water
4.3 Physics of Parametric Resonance
4.4 Influence of Roll Damping
4.5 Influence of Forward Speed and Wave Direction
4.6 Summary
5 Stability in longitudinal seas
5.1 Sample Ship Data
5.2 Spreadsheet Calculation Technique for Wave
Influence on GM.
5.3 Results for the Sample Ship
6 Susceptibility criteria
6.1 Mathieu Equation
6.2 Bounded and Unbounded Solutions of the Mathieu Equation (Ince-Strutt Diagram)
6.3 Approximations to the Ince-Strutt Diagram
6.4 Threshold Problem
6.5 Structure of Susceptibility Criteria
6.6 Frequency Condition of Susceptibility Criteria
6.7 Damping Threshold Condition of Susceptibility Criteria
6.8 Choice of Forward Speed for Susceptibility Criteria.
7 Verification of susceptibility criteria
7.1 Simulation Tools
7.2 Basic Verification
7.3 Boundary Verification
7.4 Sensitivity Verification
8 Amplitude of parametric roll in regular waves
8.1 Influence of Nonlinearity
8.2 Asymptotic Methods
8.3 Numerical Methods
9 Parametric roll in irregular waves
9.1 Influence of Nonlinearity
9.2 Ergodicity
9.3 Probability Distribution
9.4 Review of Probabilistic Methods
9.5 Choice of Wave Height
10 Control of parametric roll
11 Summary of verification of the guide
12 Concluding remarks
13 Acknowledgements
14 References
Table 1 Principal Dimensions of Post-Panamax C11 class container carrier
Table 2 Wave Characteristics
Table 3 Stability changes in waves calculated with simplified (spreadsheet) method
Table 4 Stability changes in waves calculated with EUREKA
Table 5 Frequency condition of Susceptibility Criteria (simplified method)
Table 6 Frequency condition of Susceptibility Criteria (EUREKA) Table 7 Damping threshold condition of Susceptibility Criteria
Table 8 Basic verification of Susceptibility Criteria
Table 9 Summary of numerical results for Boundary verification wave height 13.1 m, displacement 76,400 ton, EUREKA calculations
Table 10 Tanker data
Table 11 Susceptibility Criteria for tanker- first check
Table 12 Susceptibility Criteria for tanker- second check
Table 13 Amplitude of Parametric Roll with Asymptotic Formula
Table 14 Choice of Design Wave Height
Table 15 Summary of verification