1、 GUIDE FOR THE ASSESSMENT OF PARAMETRIC ROLL RESONANCE IN THE DESIGN OF CONTAINER CARRIERS SEPTEMBER 2004 Guide to Color Coding Used in Online Version of the Rules The following summarizes the colors corresponding to Rule Changes, Corrigenda items and editorial changes in the Rules files which are a
2、vailable for download. Rule Changes: NOTICE NO. 1 June 2008 (effective 1 June 2008) Corrigenda: CORRIGENDA/EDITORIALS 17 December 2004 Editorials: Editorial Changes Guide for the Assessment of Parametric Roll Resonance in the Design of Container Carriers GUIDE FOR THE ASSESSMENT OF PARAMETRIC ROLL R
3、ESONANCE IN THE DESIGN OF CONTAINER CARRIERS SEPTEMBER 2004 (Updated June 2008 see next page) American Bureau of Shipping Incorporated by Act of Legislature of the State of New York 1862 Copyright 2004 American Bureau of Shipping ABS Plaza 16855 Northchase Drive Houston, TX 77060 USA Updates June 20
4、08 consolidation includes: September version plus Notice No. 1, Corrigenda/Editorials ABSGUIDE FOR THE ASSESSMENT OF PARAMETRIC ROLL RESONANCE IN THE DESIGN OF CONTAINER CARRIERS .2004 iii Foreword Foreword The main purpose of this Guide is to supplement the Rules and the other design and analysis c
5、riteria 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 fol
6、lowing) 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 e
7、ndangered 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. If criteria and requirements included in this Guide are satisfied, ABS may assign an optional class notation as recogn
8、ition of safety performance in relation to parametric roll resonance. ABS welcomes comments and suggestions for improvement of this Guide. Comments or suggestions can be sent electronically to rddeagle.org. This Page Intentionally Left Blank ABSGUIDE FOR THE ASSESSMENT OF PARAMETRIC ROLL RESONANCE I
9、N THE DESIGN OF CONTAINER CARRIERS .2004 v Table of Contents GUIDE FOR THE ASSESSMENT OF PARAMETRIC ROLL RESONANCE IN THE DESIGN OF CONTAINER CARRIERS CONTENTS SECTION 1 Introduction 1 1 Parametric Roll Resonance in Longitudinal Waves.1 1.1 General .1 1.2 Stability in Longitudinal Waves .1 1.3 Roll
10、Motions in Calm Water.2 1.4 Physics of Parametric Roll Resonance .3 1.5 Influence of Roll Damping .5 1.6 Amplitude of Parametric Roll.6 1.7 Influence of Ahead Speed and Wave Direction.7 1.8 Definitions .8 1.9 Nomenclature8 FIGURE 1 Profile of Waterline in Wave Trough (Solid) vs. Calm Water (Dotted)
11、1 FIGURE 2 Profile of Waterline in Wave Crest (Solid) vs. Calm Water (Dotted) 2 FIGURE 3 Undamped Small Roll Motions in Calm Water.2 FIGURE 4 Parametric Roll Resonance .3 FIGURE 5 Development of Parametric Roll Resonance; Case 1: Ship Encounters Roll Disturbance when Stability is Increasing4 FIGURE
12、6 Development of Parametric Roll Resonance; Case 2: Ship Encounters Roll Disturbance when Stability is Decreasing5 FIGURE 7 Successively Decreasing Roll Amplitudes due to Roll Damping in Calm Water5 FIGURE 8 Change of Instantaneous GM Value with Increasing Heel Angle7 FIGURE 9 Development of Paramet
13、ric Roll 7 FIGURE 10 Coordinate System for Hydrostatic Calculations .9 FIGURE 11 Definition of the Draft i-th Station with j-th Position of the Wave Crest 10 FIGURE 12 Definition of the Offsets at i-th Station with j-th Position of the Wave Crest 10 vi ABSGUIDE FOR THE ASSESSMENT OF PARAMETRIC ROLL
14、RESONANCE IN THE DESIGN OF CONTAINER CARRIERS .2004 SECTION 2 Parametric Roll Criteria. 11 1 General 11 2 Susceptibility Criteria .13 2.1 Design Wave.13 2.2 Stability in Longitudinal Waves13 2.3 Ahead Speed.16 2.4 Application of Susceptibility Criteria 16 3 Severity Criterion for Parametric Roll Res
15、onance in Head Seas .17 TABLE 1 Wave Heights.13 FIGURE 1 Diagram Showing Selection of Wave Length and Ahead Speed .12 FIGURE 2 Change of Stability in Longitudinal Wave 15 FIGURE 3 GM as a Function of Wave Crest Position.15 FIGURE 4 Restoring Moment as a Function of Wave Position and Heel Angle.19 FI
16、GURE 5 Restoring Term as a Function of Time and Heel Angle 19 SECTION 3 Numerical Simulations 21 SECTION 4 Mitigation of Parametric Roll Resonance 23 1 Operational Guidance23 2 Anti-Rolling Devices.23 FIGURE 1 Example of Polar Diagram and Color Scale 24 SECTION 5 Optional Class Notation 25 TABLE 1 O
17、ptional Class Notations .25 APPENDIX 1 Sample Calculations 27 TABLE 1 Particulars of a Sample Container Carrier .27 TABLE 2 Conditions for Sample Calculations.28 TABLE 3 Calculation of GM Value for Different Positions of Wave Crest along Ship Hull (Simplified Method 2/2.2)28 TABLE 4 Sample Results f
18、or Susceptibility Criteria29 TABLE 5 GZ Curves for Different Positions of Wave Crest 31 TABLE 6 Sample Results for Forward Speed Calculations 32 TABLE 7 Sample Input Data for Integration of Roll Equation.33 TABLE 8 Amplitude of Parametric Roll in Degrees.34 ABSGUIDE FOR THE ASSESSMENT OF PARAMETRIC
19、ROLL RESONANCE IN THE DESIGN OF CONTAINER CARRIERS .2004 vii FIGURE 1 Lines of Sample Container Carrier 27 FIGURE 2 Calculation of GM Value for Different Positions of Wave Crest along Ship Hull (Simplified Method 2/2.2)29 FIGURE 3 GZ Curves for Different Positions of Wave Crest 30 FIGURE 4 Solution
20、of the Roll Equation for V1and = 0.1.34 APPENDIX 2 Sample Polar Diagrams.35 FIGURE 1 Sample Polar Diagram.35 FIGURE 2 Sample Polar Diagram Full Load, Sea State 9.36 FIGURE 3 Sample Polar Diagram Full Load, Sea State 8.37 FIGURE 4 Sample Polar Diagram Full Load, Sea State 7.37 FIGURE 5 Sample Polar D
21、iagram Partial Load, Sea State 9 38 FIGURE 6 Sample Polar Diagram Partial Load, Sea State 8 38 FIGURE 7 Sample Polar Diagram Partial Load, Sea State 7 39 APPENDIX 3 Criteria for Parametric Roll of Large Containerships in Longitudinal Seas 41 This Page Intentionally Left Blank ABSGUIDE FOR THE ASSESS
22、MENT OF PARAMETRIC ROLL RESONANCE IN THE DESIGN OF CONTAINER CARRIERS .2004 1 Section 1: Introduction SECTION 1 Introduction 1 Parametric Roll Resonance in Longitudinal Waves 1.1 General Parametric roll resonance in longitudinal (head and following) seas is observed as a significant amplification of
23、 roll motions, which may become dangerous to the ship, its cargo and crew. This phenomenon is related to the periodic change of stability as the ship moves in longitudinal waves at a speed when the ships wave encounter frequency is approximately twice the rolling natural frequency and the damping of
24、 the ship to dissipate the parametric roll energy is insufficient to avoid the onset of a resonant condition. 1.2 Stability in Longitudinal Waves If a ship is located in a wave trough, the average waterplane width is significantly greater than in calm water. The flared parts of the bow and stern are
25、 more deeply immersed than in calm water and the wall-sided midship is less deep. This makes the mean, instantaneous waterplane wider than in calm water with the result that the metacentric height (GM) is increased over the calm water value. (See Section 1, Figure 1) FIGURE 1 Profile of Waterline in
26、 Wave Trough (Solid) vs. Calm Water (Dotted) In contrast to the above, when the wave crest is located amidships, the waterplane at the immersed portions of the bow and stern are narrower than in calm water. Consequently, the average waterplane is narrower and the GM is correspondingly decreased in c
27、omparison to calm water (see Section 1, Figure 2). As a result, the roll restoring moment of the ship changes as a function of the waves longitudinal position along the ship. Section 1 Introduction 2 ABSGUIDE FOR THE ASSESSMENT OF PARAMETRIC ROLL RESONANCE IN THE DESIGN OF CONTAINER CARRIERS .2004 F
28、IGURE 2 Profile of Waterline in Wave Crest (Solid) vs. Calm Water (Dotted) 1.3 Roll Motions in Calm Water When a ship is in calm water, any disturbance in transversal (as from a wind gust) will lead to roll motions. When the roll equilibrium is disturbed, the hydrostatic restoring moment acts to opp
29、ose the instantaneous roll angle and tends to return the ship back to the upright position. Because of inertia, the ship does not stop at the instant when the equilibrium angle is reached but continues to roll at a progressively slower velocity until a maximum roll angle is reached. At this point, t
30、he excess roll restoring moment causes the ship to begin to right itself. Once upright, inertia causes the ship to continue to roll. As before, the restoring moment works against further motion and it stops at some roll angle. The restoring moment then again pushes the ship back to the equilibrium,
31、and again, because of inertia, the ship cannot stop at the equilibrium point and the motion cycle is repeated. The period of such roll oscillations in calm water is known as the “natural roll period” and is related to ship stability and mass distribution. The corresponding roll frequency is called t
32、he “natural frequency”. A sample of such a free roll oscillation is shown in Section 1, Figure 3. FIGURE 3 Undamped Small Roll Motions in Calm Water 0 5 10 15 20 25 30 35 4010.50.51If a ship sailed on a course exactly perpendicular to the crests of head or following seas, there would be no waveinduc
33、ed heeling moment. However, the ship may experience a very small roll disturbance from some external or internal cause (in reality, roll disturbances can always exist, e.g., wind). Normally, when the roll equilibrium is disturbed in the absence of a wave excitation moment, the ship rolls with its na
34、tural roll frequency and the motion time history is similar to that shown in Section 1, Figure 3 Time, s Roll, deg Period T Section 1 Introduction ABSGUIDE FOR THE ASSESSMENT OF PARAMETRIC ROLL RESONANCE IN THE DESIGN OF CONTAINER CARRIERS .2004 3 1.4 Physics of Parametric Roll Resonance As describe
35、d earlier, when a ship is sailing in longitudinal (head or following) or nearly longitudinal seas, its stability increases in the wave trough and decreases on the wave crest. If this oscillatory change in stability occurs at approximately twice the natural roll period, roll motions may increase to a
36、 significant, possibly unacceptable, angle as a result of parametric roll resonance. A typical sample time history is shown in Section 1, Figure 4. FIGURE 4 Parametric Roll Resonance 0 10 20 30 40 50 60 70 80 90 100 110 12020101020The most rapid increase of parametric roll motion could be observed w
37、hen the ship experiences an external roll disturbance at the time when the wave crest is moving away from amidships, i.e., the condition of improving or increasing stability, in combination with an encounter frequency approximately twice that of the natural roll frequency. In this situation, the res
38、toring moment tends to accelerate the ship back to equilibrium with a larger-than-calm-water moment because the ship is entering the wave trough where stability is improved. As a result, at the end of the first quarter of the period T, the roll angle is slightly larger than it would be in calm water
39、. See Section 1, Figure 5. At the end of the first quarter period of roll oscillation, the ship reaches a zero-degree roll angle, which is the upright equilibrium attitude, but the roll motion does not stop there because of the roll inertia. During the second quarter of the period, the ship encounte
40、rs a wave crest and its stability is decreased. Meanwhile, the roll motion inertia makes the ship continue to roll. The restoring moment now resists further motion, but with a less-than-calm-water value since ship stability is lessened on the wave crest. As a result, the ship rolls more than it woul
41、d in calm water with the same roll disturbance, consequently, after the second quarter, the increase in roll angle is even greater than after the first quarter. This is shown in Section 1, Figure 5. In the third quarter, the ship enters the wave trough and an increased restoring moment pushes it bac
42、k with an increased force. The situation is analogous to that observed during the first quarter. The observations in the fourth quarter are similar to those in the second quarter, and the roll angle continues to increase, as shown in Section 1, Figure 5. With no further change in wave amplitude and
43、ship speed, this combination of restoring (with a larger-than-calm-water) and resisting the roll (with less-than-calm-water) can cause the roll angle to progressively increase to a large and possibly dangerous level. This constitutes the parametric roll resonance phenomenon. t, s Roll, deg Section 1
44、 Introduction 4 ABSGUIDE FOR THE ASSESSMENT OF PARAMETRIC ROLL RESONANCE IN THE DESIGN OF CONTAINER CARRIERS .2004 FIGURE 5 Development of Parametric Roll Resonance; Case 1: Ship Encounters Roll Disturbance when Stability is Increasing If the ship experiences the roll disturbance while approaching a
45、 wave crest, i.e., when the stability is decreasing, the evolution of parametric roll development is different. The same factors that were increasing roll in the first case now damp the roll motion. When the ship is just disturbed, it approaches a wave crest with its stability decreased and the “pus
46、h back” is made with a smaller moment than in calm water. Once the ship reaches equilibrium, its stability starts to improve and it reaches a less-than-in-calm-water angle at the end of the first period. See Section 1, Figure 6. Such a combination of decreasing and increasing roll restoring moments
47、is capable of significantly decreasing roll. However, this situation does not last long. The changing stability leads to a slight change in the natural period. As a result, the roll in waves lags behind in comparison with the roll in calm water. See Section 1, Figure 6. As can be seen from Section 1
48、, Figure 6, the shifting phase leads to a situation where the ship reaches a peak value of roll angle and as its GM is just about to start to increase. This situation is similar to the conditions considered in the previous case. The two considered sample scenarios represent two extreme possibilities
49、 with the most and least favorable conditions for the development of parametric roll. The real situation is usually somewhere in between. 0 10 20 30 40 50 60 70 80 90 100 110 1201 0.5 0.5 1 1.5 0.5 T T Ship has amplitude roll angle and GM Roll starts to riseChange of GM in Waves Mean Stability in Waves Free RollParametric Roll10 20 30 40 50 60 70 80 90 100 110 120t, s t, s GM Roll angle, degrees Section 1 Introduction ABSGUIDE FOR THE ASSESSMENT OF PARAMETRIC ROLL RESONANCE IN THE DESIGN OF CONTAINER CARRIERS .2004 5 FIGURE 6 Development of Parametric Roll
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