stability criteria (cr)

1992-2009 Napa Ltd. All rights reserved.

NAPA Online Manuals 2009.1Stability Criteria (CR)



Table of Contents1 Purpose . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

2 Scope of the subsystem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

3 Stability criteria . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2

4 Calculation and output . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34.1 Intact stability criteria . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

4.1.1 Calculation methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34.1.2 Checking of loading conditions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44.1.3 GM and KG limit curves . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44.1.4 Minimum GM and maximum KG values . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44.1.5 Output . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

4.1.5.1 Limit curve . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44.1.5.2 Criterion table . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54.1.5.3 Loading condition table . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54.1.5.4 Min. GM and max. KG table . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54.1.5.5 Summary lists. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54.1.5.6 Loading condition check plot. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54.1.5.7 Minimum GM check plot . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54.1.5.8 Openings, freeboard, margin line and special points . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

4.2 Damage stability criteria . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54.2.1 Calculation methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54.2.2 Checking of damage cases . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64.2.3 GM and KG limit curves . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64.2.4 Output . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

4.2.4.1 Limit curve. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74.2.4.2 Criterion table. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74.2.4.3 Loading condition table. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74.2.4.4 Min. GM and max. KG table . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74.2.4.5 Summary lists. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74.2.4.6 Criterion check plot . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74.2.4.7 Minimum GM check plot . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74.2.4.8 Openings, freeboard, margin line and special points. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

5 Data concepts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85.1 Stability criterion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85.2 Criterion group . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85.3 Heeling moment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85.4 Opening . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95.5 Freeboard deck edge . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95.6 Bilge line . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95.7 Special point . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95.8 Margin line . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9

6 Connections to other subsystems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9

7 Restrictions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

8 General . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

9 Definition functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119.1 Criteria . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11



9.1.1 Maximum righting lever . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 149.1.1.1 Examples. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

9.1.2 Maximum heeling angle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 169.1.2.1 Examples. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18

9.1.3 Minimum area . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 189.1.3.1 Examples. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19

9.1.4 Minimum GM . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 199.1.4.1 Examples. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20

9.1.5 Position of maximum GZ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 209.1.5.1 Example. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20

9.1.6 Angle of downflooding . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 219.1.6.1 Example. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21

9.1.7 Range of stability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 219.1.7.1 Examples. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22

9.1.8 Angle of vanishing stability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 229.1.8.1 Example. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22

9.1.9 Reserve to downflooding . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 229.1.9.1 Example. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23

9.1.10 Reserve to immersion of freeboard . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 239.1.10.1 Example. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23

9.1.11 Area ratio in wind and rolling condition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 249.1.11.1 Example. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24

9.1.12 Area ratio in wind condition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 249.1.12.1 Example. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25

9.1.13 Reserve dynamic stability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 259.1.13.1 Example. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25

9.1.14 Dynamic stability arm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 259.1.14.1 Example. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26

9.1.15 GZ/MOM ratio . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 269.1.15.1 Example. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26

9.1.16 Reserve to immersion of margin line . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 269.1.17 MINGZ - Minimum reserve to C*Sin(heel). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 269.1.18 Crane criteria. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27

9.1.18.1 Example. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 279.2 Using of macros in criteria calculation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 289.3 Criterion group . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 319.4 Heeling moments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32

9.4.1 Moments independent of loading conditions and damage cases . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 329.4.1.1 Constant moment. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 339.4.1.2 Shape cosine. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 339.4.1.3 Shape cosine to the power of two. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 339.4.1.4 Polygon. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 339.4.1.5 Smooth curve. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 349.4.1.6 Expression. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 349.4.1.7 Macro. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34

9.4.2 Moments dependent on loading conditions and damage cases. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 349.4.2.1 Wind moment. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 359.4.2.2 Wind moment by IMO. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 359.4.2.3 Wind moment by USSR Rules. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 369.4.2.4 Wind moment for MODUs. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 369.4.2.5 Turning moment. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 379.4.2.6 Turning moment by IMO. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 379.4.2.7 Turning moment by USSR Rules. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 379.4.2.8 Passenger moment. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 389.4.2.9 Moment by load shift. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38



9.4.2.10 Moment by grain shift. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 399.4.3 Combined moment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39

9.5 Opening . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 399.6 Freeboard deck edge . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 409.7 Bilge line . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 409.8 Special point . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 409.9 Margin line . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41

10 Output functions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4110.1 Arguments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4110.2 Listing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47

10.2.1 GM and KG limit curves . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4710.2.2 Criterion table . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4910.2.3 Loading condition table . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5010.2.4 Minimum GM and maximum KG table . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5110.2.5 Summary list . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5210.2.6 GZ Curves. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5310.2.7 Openings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5410.2.8 Freeboard . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5510.2.9 Margin line . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5710.2.10 Special points . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5810.2.11 Lateral profile . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5910.2.12 Auxiliary listing commands . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60

10.3 Plotting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6110.3.1 Plotting according to macro . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6110.3.2 Minimum GM and maximum KG limit curves . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6110.3.3 Loading condition check plot . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6410.3.4 Criterion check plot . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6510.3.5 Minimum GM check plot . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6810.3.6 Profile check plot . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69

10.4 Forced calculation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6910.5 Assigning variables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70

10.5.1 Variables related to output lists . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7010.5.2 Variables related to hydrostatics and stability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7510.5.3 Variables related to intermediate results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77

11 Administrative functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80

12 Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8012.1 IMO Resolution A.749(ES.IV) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81

12.1.1 5.1. (a) Area under the GZ curve. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8112.1.2 5.1 (b) Righting lever GZ. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8112.1.3 5.1 (c) Position of the maximum righting arm. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8112.1.4 5.1 (d) Metacentric height. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8112.1.5 5.2 (a) Crowding of passengers. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8112.1.6 5.2 (b) Turning. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82

12.2 IMO Resolution A.562(14) (weather criterion) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8212.3 IMO Resolution A.649(16) (1989 MODU CODE) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8212.4 USSR Register of Shipping . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82

12.4.1 2.1 Weather criterion. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8212.4.2 2.2 Curve of statical stability. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8312.4.3 3.1 Passenger ships. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83

12.5 US Coast Guard . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8412.5.1 Weather criterion. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84

12.6 Norwegian Maritime Directorate . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84



12.6.1 Mobile offshore units. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8412.7 See-Berufsgenossenschaft (SBG) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8412.8 US Navy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85

13 CR Commands. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8513.1 Commands for definitions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8513.2 Arguments - intact criteria. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8713.3 List output - intact criteria. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9813.4 Graphic output - intact criteria. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10413.5 Auxiliary functions - intact criteria. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10913.6 Arguments - damage criteria. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11213.7 List output - damage criteria. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12313.8 Graphic output - damage criteria. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12913.9 Auxiliary functions - damage criteria. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133

14 CR Service Functions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 136

15 Dredger Calculations. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14215.1 Geometry. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14215.2 Purpose definitions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14315.3 Intact stability calculations. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14415.4 Intact stability criteria. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 144

15.4.1 The criteria according to 6.1.3. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14415.4.2 The weather criterion according to 6.1.4. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14515.4.3 The criteria according to 6.1.2.2 c. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 145

15.5 Variable displacement method and permeabilities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14615.6 Damage stability calculations (Reg. 25-1 amended and modified by DR67: 6.2.1, 6.2.2 and 6.2.3). . . . . . . 14615.7 The load lines. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 146

16 Offshore Structures Stability (OSS). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14916.1 General. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 149

16.1.1 Reference system parameters. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15016.2 Modelling. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 150

16.2.1 The Calculation Object. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15116.2.2 Calculation Sections and Shell Thickness. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15116.2.3 The Compartment Arrangement. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15216.2.4 The Wind Model. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15216.2.5 Using general geometric transformations. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 153

16.3 Creating the Wind Model. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15416.3.1 Geometric Objects. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15416.3.2 Wind Model Tables. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 159

16.4 Calculation Procedure - Intact Stability. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16116.4.1 Loading Conditions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16116.4.2 Wind Moment Definition. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 162

16.4.2.1 Wind Moment from Wind Tunnel Tests. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16316.4.3 Relevant Criteria. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16316.4.4 Azimuth angle for stability axis. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16316.4.5 Wind Model. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16316.4.6 Local Loading Conditions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16316.4.7 Calculation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 163

16.5 Calculation Procedure - Damage Stability. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16416.5.1 Damage Cases. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16416.5.2 Wind Moment Definition. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16416.5.3 Relevant Criteria. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16416.5.4 Wind Model. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 165



16.5.5 Local Initial Conditions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16516.5.6 Calculation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 166

16.6 Calculation Output. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16616.6.1 Wind Model and Area Exposed to Wind. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 166

16.6.1.1 Detailed Wind Moment. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16716.6.2 Moments and Stability. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16816.6.3 Criteria Check. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16816.6.4 Assigning Variables. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 168

17 DNV Verified Criteria. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 168


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1 Purpose The stability criteria subsystem CR covers the functions related to handling of intact stability criteria and damage stabilitycriteria. The purpose of the subsystem is to:n calculate the minimum GM and the maximum KG as a function of draught and trim, which assures compliance with

the relevant intact stability criterian calculate for a selected set of damage cases the minimum GM and the maximum KG as a function of draught and

trim, which assures compliance with the relevant damage stability criterian check whether the loading conditions meet the requirements of the relevant intact stability criterian check whether the damage cases meet the requirements of the relevant damage stability criteria.

The main functions of the subsystem aren definition of intact and damage stability criterian definition of data related to the stability criteria, for example, heeling momentsn calculation of the minimum GM and maximum KG limit curves as a function of draught or trim and relevant intact

criterian calculation of the minimum GM and maximum KG limit curves for a set of damage cases as a function of draught

or trim and relevant damage criterian testing of compliance of the loading conditions with the relevant intact criterian testing of compliance of the damage cases with the relevant damage criterian output of results as alphanumeric and graphic representation.

All these functions are installed in the task CR. The functions related to the intact stability criteria are performed inthe environment INTACT (prompt CR_I.) and the functions related to the damage stability criteria are performed in theenvironment DAMAGE (prompt CR_D.). If CR is entered from the loading condition subsystem LD, the environmentINTACT is assigned and if CR is entered from the damage stability subsystem DA, the environment DAMAGE isassigned. Entering CR from the TASK-level assigns the environment INTACT but the environment may be changed toDAMAGE and back to INTACT by the command ENV. The environments are so separate that the arguments assigned inone environment are not changing arguments in the other environment and the intact stability criteria and damage stabilitycriteria are independent in the different environments. All the criterion types and the properties of the criteria are availablein both environments.

See also NAPA User Meeting workshop papers about stability criteria.

2 Scope of the subsystemMost intact and damage stability criteria published by the classification societies and authorities are covered by thesubsystem. For example, the following regulations, and regulations equivalent to these, can be handled:n SOLAS 90n IMO Resolution A.749(ES.IV)n IMO weather criterion, Resolution A.562(14)n IMO MODU CODE, Resolution A.649(16)n MARPOLn IBC Code (Resolution MSC.4(48))n IGC Code (Resolution MSC.6(48))n SOLAS 1974, Carriage of Grainn US Coast Guard, October 1, 1990 (partly)


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n US Navyn Rules of the USSR Register of Shipping, 1990 (partly)n Norwegian Maritime Directorate, Regulations for Mobile Offshore Units,1991n Norwegian Petroleum Directorate, 1990n Det Norske Veritasn Department of Energy (Brit.), Offshore Installationsn The Merchant Shipping Regulations (Brit.), 1984n SBG (German), 1984n Rahola.

Because all the central aspects of the criteria are given as parameters, the criteria equivalent to those appearing in the aboveregulations, i.e. the criteria which differ from the criteria of the above regulations only in respect of some parameter(s)(e.g. a different height, range, area, area ratio etc.), may be easily defined. There is also a wide range of possibilities todefine own criteria only by changing parameters and combining criteria in different ways.

3 Stability criteriaA stability criterion is a rule defining the minimum or maximum accepted value for one property (quantity) calculatedfrom the righting lever curve, e.g. the maximum height of the GZ curve within some interval range. A criterion is an intactstability criterion, if it is defined in the environment INTACT and the source of the GZ curve is intact stability. A criterionis a damage stability criterion, if it is defined in the environment DAMAGE and the source of the GZ curve is damagestability. The following criteria, or equivalent quantities, may be calculated:n Maximum height of the GZ curve. The minimum accepted value for the maximum of the curve may be a constant

value or it may depend on other properties of the GZ curve by an equation. The calculation of height may alsobe limited to some range of heeling angles or to a given position. If there is a moment connected to the criterion,maximum height means the maximum residual lever.

n Steady equilibrium heeling angle due to a heeling moment. The maximum heeling angle may be a constant value orit may depend on some properties of the loading condition or damage case, e.g. angle of downflooding.

n Area under the GZ curve. The minimum accepted area may be a constant value or it may depend on other propertiesof the GZ curve by an equation. Calculation of the area may be limited to a range of heeling angles. If there is amoment connected to the criterion, area means the area between the GZ curve and the moment arm curve.

n Height of metacenter (GM). The minimum height may be a constant value or it may depend on some properties ofthe ship and loading condition or damage case.

n Position of the maximum of the GZ curve. If there is a moment connected to the criterion, position of the maximummeans the position of the maximum residual lever.

n Angle of downflooding.n Range of positive stability. If there is a moment connected to the criterion, range is calculated from the first

intercept to the second intercept of the GZ curve and the moment arm curve.n Angle of vanishing stability. If there is a moment connected to the criterion, angle of vanishing stability means the

angle of the second intercept of the GZ curve and the moment arm curve.n Reserve to downflooding. The reserve is calculated from the angle of steady equilibrium.n Reserve to immersion of the freeboard. The reserve is calculated from the angle of steady equilibrium.n Reserve to immersion of the margin line. The reserve is calculated from the angle of steady equilibrium.n Ratio between the area under the GZ curve and the area under the moment arm curve. Calculation of the areas may

be limited to different ranges of the heeling angles.n Ratio between the height of the GZ curve and the height of the moment curve.n Height of the dynamic stability curve at a given angle.

The minimum and maximum accepted values of the quantities defined by the criteria are called requirements of thecriteria. A requirement is a constant value valid for all loading conditions or damage cases or it may depend on the loading


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condition or damage case or properties of the GZ curve. Often the actual value of the requirement is not known beforethe criterion is applied to the loading condition or damage case.

The property (quantity) corresponding to the requirement and calculated from the actual GZ curve of the loading conditionor damage case is called an attained value of the loading condition or damage case.

Comparison of the attained value with the requirement defines the status of the loading condition or damage case withrespect to the criterion. The status indicates whether the loading condition or damage case meets the requirement or not.

The GM value, by which the loading condition or damage case meets the requirement and where any lesser value of GMthe requirement is no more met, is called the minimum GM which is in compliance with the criterion. The KG value, bywhich the loading condition or damage case meets the requirement and where any greater value of KG the requirement isno more met, is called the maximum KG which is in compliance with the criterion. There is one to one correspondencebetween the minimum GM and maximum KG values by the formula KM = KG + GM.

For intact stability criteria, the requirements, attained values, status indicators, minimum GM values and maximum KGvalues are stored as standard quantities in the run time memory of the subsystem. For damage stability criteria, therequirements, attained values, status indicators, minimum GM values and maximum KG values are stored as standardquantities in the secondary database (unit 4). For the detailed list of the quantities, see the CR.2 part of these documents.The criteria are identified by names. One may study several criteria of the same type at the same time. The relevant criteriaare chosen by referring to their names. There is no restrictions on number or types of criteria which may be relevantsimultaneously.

A group of criteria is a named set of criteria which may be handled together. It is practical to collect criteria which belongto the same regulation or rule to the same group.

The criteria may refer to heeling moments provided it has some sense. For example, the angle of downflooding has nothingto do with moments.

The set of relevant criteria must be defined and selected by the user according to the regulations and authority.

4 Calculation and output

4.1 Intact stability criteriaThere may be one or several loading conditions under investigation at the same time. A loading condition is eithera condition defined in the loading condition subsystem LD or a condition defined by the floating position of the ship(draught, trim, GM). The latter loading conditions are often called local loading conditions because their GZ curves andother stability data are calculated locally in CR using its arguments and calculation modes. The GM (KG) limit curvesare calculated for a set of local loading conditions (variable draught, constant trim or alternatively variable trim, constantdraught) and the compliance check is usually done for the loading conditions of LD.

4.1.1 Calculation methods

The GZ curve is taken as such from the loading condition of LD or the curve is calculated for the local loading conditionfor the hull, draught and trim as arguments (initial heeling angle is assumed to be zero). In the previous case, the effectof the free liquid surfaces is included in the GZ curve and taken into account as it was specified in LD. In the latter case,the effect of the free liquid surfaces is not taken into account.

Calculation of the GZ curves for the local loading conditions may be carried out by the free trim method or by the fixedtrim method. The calculation methods or arguments of the loading conditions fetched from LD are not possible to changein CR.

The calculation of criteria may be carried out in the presence of heeling moments or without any heeling moment. Themoments are linked to the criteria.


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The minimum GM (maximum KG) which assures compliance with the criteria is calculated from the GZ curve by aniterative method varying GM in the equation GZ = MS + GM*sin(heel). Iteration is terminated when any lesser valueof GM (greater value of KG) within the given tolerance does not any more satisfy the requirement. The minimum GM(maximum KG) may be calculated for a local loading condition or for a loading condition of LD. In the latter case, duringiteration all other aspects of the loading condition but GM (KG) are assumed to be unchanged. The maximum KG valuesare always calculated by help of the minimum GM values; first the program calculates the minimum GM and then appliesthe equation MAXKG = KM - MINGM.

4.1.2 Checking of loading conditions

Checking of the loading condition means that the program examines whether the loading condition is in compliance withthe relevant criteria or not. The loading condition is checked by calculating the quantities defined by the criteria andcomparing them with the requirements. The loading condition is in compliance with the criteria if all the relevant criteriaare met simultaneously .

Both kinds of loading conditions may be checked: loading conditions of LD and local loading conditions.

All calculated quantities (requirements and attained values) are stored in a run time data description.

4.1.3 GM and KG limit curves

The minimum GM (maximum KG) limit curve is the minimum GM (maximum KG) which is in compliance with therelevant criteria as a function of draught or trim. The limit curve is formed by calculating the individual limit curves forall relevant criteria and combining the curves to one overall maximum or minimum curve ensuring that the intersectionpoints between the individual curves are properly taken into account.

Only local loading conditions are used for limit curve calculation. The local loading conditions define the argumentdraughts or trims for the curve and the corresponding minimum GM or maximum KG values are calculated by the iterativemethod described above.

The GM (KG) limit curves can be permanently stored in the data base to be used in other subsystems.The previous chapter presented how to check loading conditions. Another way to check whether the loading conditionmeets the requirements of the relevant criteria, is to compare the corrected GM (KG) of the loading condition with thecorresponding GM (KG) value of the limit curve. Because the GM (KG) limit curve is calculated without any effect offree liquid surfaces and (usually) the loading condition contains free surfaces taken into account by various rules, thiscomparison is not always exact; there is some inaccuracy area on both sides of the limit curve. It may happen that the GMof the loading condition is below the limit curve but comparison of requirements and attained values results status OK. Ifthere is any doubt about reliability of the limit curve check, use status check. The status check is always reliable.

4.1.4 Minimum GM and maximum KG values

In addition to the minimum GM and maximum KG limit curves, there is also a possibility to calculate minimum GM andmaximum KG values for loading conditions of LD. These data are stored in a run time data description.

4.1.5 Output

All calculated quantities are stored in a run time description for making it possible for the user to make lists by the helpof the standard table output and diagram output functions of NAPA. The subsystem produces also a set of standard listsand plots:

4.1.5.1 Limit curve

The overall minimum GM (maximum KG) limit curve as a function of draught or trim and relevant criteria may be plottedor printed. In addition to the overall minimum (maximum), the minimum GM (maximum KG) limit curves of all individualcriteria may be added to the plot. If desired, a selected set of loading conditions can be marked in the plot.


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4.1.5.2 Criterion table

A criterion table shows, for a single loading condition, all the relevant criteria and their requirements, the correspondingvalues attained by the loading condition and a status indicator showing whether the criterion is met or not.

One listing command produces as many tables as there are selected loading conditions.

4.1.5.3 Loading condition table

A loading condition table shows the names of the loading conditions, the determining criteria and their requirements, thecorresponding values attained by the loading conditions and a status indicator showing whether the criterion is met or not.

4.1.5.4 Min. GM and max. KG table

The min. GM and max. KG table shows, for all selected loading conditions, the minimum GM and maximum KG valueswhich are in compliance with the relevant criteria.

4.1.5.5 Summary lists

The summary lists offer a quick look at the central results of CR: minimum GM, maximum KG and status. The summarylists are two dimensional tables showing the selected quantities as function of loading condition and criterion, draughtand criterion, trim and criterion or draught and trim.

4.1.5.6 Loading condition check plot

For every loading condition, one can plot, the GZ curve of the loading condition combined with a drawing which showsthe properties required by the criteria.

One plotting command produces as many plots as there are selected loading conditions.

4.1.5.7 Minimum GM check plot

This plot is similar to the loading condition check plot, but it is based on the GZ curve which is drawn for the minimumGM which is in compliance with the relevant criteria.

4.1.5.8 Openings, freeboard, margin line and special points

These tables show how the relevant openings, the freeboard deck edge, the margin line and the special points are situatedrelative to the waterline in different loading conditions.

4.2 Damage stability criteriaThere may be one or several initial conditions (loading conditions) and damage cases under investigation at the same time.An initia l condition is either a condition defined in the damage stability subsystem DA or a condition defined by thefloating position of the ship (draught, trim, GM) before flooding. The latter initial conditions are often called local initialconditions because they are defined and stability data are calculated locally in CR using its arguments. All calculationand output functions may be carried out either for a set of local initial conditions or initial conditions defined in DA andfor any set of selected damage cases.

4.2.1 Calculation methods

The GZ curves are taken as such from the precalculated results of DA or they are calculated in CR if precalculated resultsare not up-to-date or initial conditions are local ones.


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Calculation of the GZ curves is always based on actual calculation modes and arguments of CR. Recalculation of the GZcurves is initiated if these settings are changed since the last calculation of the results in CR or DA. It may happen thatrecently calculated results i DA are immediately recalculated in CR because of different calculation modes or argumentsin CR or DA.

The calculation of criteria may be carried out in the presence of heeling moments or without any heeling moment. Themoments are linked to the criteria.

The minimum GM (maximum KG) which assures compliance with the criteria is calculated from the GZ curve by aniterative method varying GM in the equation GZ = MS + GM*sin(heel). Iteration is terminated when any lesser valueof GM (greater value of KG) within the given tolerance does not any more satisfy the requirement. The maximum KGvalues are always calculated by help of the minimum GM values; first the program calculates the minimum GM and thenapplies the equation MAXKG = KM - MINGM.

4.2.2 Checking of damage cases

Checking of the damage cases means that the program examines whether the damage case is in compliance with therelevant criteria or not in all stages and phases of the damage case. The damage case is checked by calculating the quantitiesdefined by the criteria and comparing them with the requirements. The damage case is in compliance with criteria if allthe relevant criteria are met simultaneously in all stages and phases of the damage case.

All calculated results related to the stability criteria are stored in the auxiliary data base (unit 4). Retrieving the storedresults initiates a comprehensive up-to-date check of results. If the hydrostatic results of the damage case are youngerthan the stored results of criteria, results of the damage case are out-of-date or any argument of CR is changed, the storedresults are rejected.

4.2.3 GM and KG limit curves

The minimum GM (maximum KG) limit curve is the minimum GM (maximum KG) which is in compliance with therelevant criteria as a function of draught or trim calculated for a selected set of damage cases. The limit curve is formedby calculating the individual limit curves for all combinations of relevant criteria and damage cases and combining thecurves to one overall maximum or minimum curve ensuring that the intersection points between the individual curvesare taken properly into account.

Both local initial conditions and initial conditions of DA may be used for limit curve calculation. The initial conditionsdefine the argument draughts or trims for the curve and the corresponding minimum GM or maximum KG values arecalculated by the iterative method described above.

The GM (KG) limit curves can be permanently stored in the data base to be used in other subsystems.The previous chapter presented how to check damage cases. Another way to check whether the damage cases meetthe requirements of the relevant criteria, is to compare the corrected GM (KG) of the actual loading condition with thecorresponding GM (KG) value of the limit curve calculated for the specified set of damage cases. Because the GM (KG)limit curve may be calculated without any effect of free liquid surfaces and the actual loading condition may containfree surfaces taken into account by various rules, this comparison is not always exact; there is some inaccuracy area onboth sides of the limit curve. It may happen that GM of the loading condition is below the limit curve but comparisonof requirements and attained values results status OK. If there is any doubt about reliability of the limit curve check, usestatus check. The status check is always reliable.

In the output of the calculation the minimum corrected GM (MINGM) and minimum uncorrected GM (MINGM0) shouldbe quite self-explanatory. In general the MINGM should be used because the GM of the loading conditions used to checkcompliance is the corrected GM. If the initial condition has a GM reduction GMRED, either calculated from the liquid shiftor given explicitly, the difference between the MINGM and MINGM0 is GMRED. I.e. MINGM is the primary calculatedinformation and MINGM0 is derived based on GMRED.

Regarding MAXKG, the maximum KG, this is the "uncorrected" MAXKG i.e. it can be compared to the MINGM0.To take into account the possible effect of the free surface correction in the initial condition, the quantity MAXKGL


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("MAXKG Liquid") should be used instead of MAXKG in the output. MAXKGL is the "virtual maximum KG correctedfor free surfaces" that reflects the same limiting stability value as MINGM.

4.2.4 Output

All calculated quantities are stored in a run time description for making it possible for the user to make lists by the helpof the standard table output and diagram output functions of NAPA. The subsystem produces also a set of standard listsand plots.

4.2.4.1 Limit curve

The overall minimum GM (maximum KG) limit curve as a function of draught or trim and relevant criteria may beplotted or printed. In addition to the overall minimum (maximum), the minimum GM (maximum KG) limit curves ofall individual criteria or damage cases may be added to the plot. If desired, a selected set of loading conditions can bemarked to the to the plot.

4.2.4.2 Criterion table

A criterion table shows, initial conditions, damage cases, damage stages, damage phases and listing sides PS and SB asarguments, all the relevant criteria and their requirements, the corresponding attained values, status indicators showingwhether the criterion is met or not, minimum corrected GM values, maximum corrected KG values, minimum uncorrectedGM0 values and maximum uncorrected KG0 values.

4.2.4.3 Loading condition table

A loading condition table shows the names of the loading requirements, the corresponding attained values, determiningdamage cases and a status indicator showing whether all criteria are met in all damage cases.

4.2.4.4 Min. GM and max. KG table

The min. GM and max. KG table shows, for all initial conditions, damage cases, stages, phases and sides, the minimumGM and GM0 and maximum KG and KG0 values which are in compliance with the relevant criteria.

4.2.4.5 Summary lists

The summary lists offer a quick look at the central results of CR: minimum GM and GM0, maximum KG and KG0and status. The summary lists are two dimensional tables showing the selected quantities as function of loading (initial)condition and criterion, draught and criterion, trim and criterion, draught and trim, loading (initial) condition and damagecase, draught and damage case, trim and damage case and criterion and damage case.

4.2.4.6 Criterion check plot

For every criterion, one can plot, the GZ curves of the damage cases combined with, a drawing which shows the propertiesrequired by the criteria.

4.2.4.7 Minimum GM check plot

This plot is similar to the criterion check plot, but it is based on the GZ curve which is drawn for the minimum GM whichis in compliance with the relevant criteria.


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4.2.4.8 Openings, freeboard, margin line and special points

These tables show how the relevant openings, the freeboard deck edge, the margin line and the special points are situatedrelative to the waterline in different stages and phases of damage cases.

5 Data conceptsThe subsystem provides means to define, handle and store the following data:n intact stability criterian damage stability criterian intact stability criterion groupsn damage stability criterion groupsn heeling moment curvesn openings for calculation of downfloodingn freeboard deck edges for calculation of residual freeboardn margin linesn bilge linesn special points for checking immersion of certain points in the ship.

5.1 Stability criterionA stability criterion is defined by its type (required property) and corresponding parameter value (requirement). Anexternal moment is connected to the criterion by referring to it by name.

5.2 Criterion groupA criterion group is a named set of stability criteria. The criteria defined by regulations form natural criterion groups.

5.3 Heeling momentMany criteria must be checked in the presence of a heeling moment. There are two ways to define moments. The firstone is to define the moment curve by the help of the regulations giving only few parameters, e.g. name of the lateralprofile curve. The second method is to select the type of the moment curve and give the related moment value(s). Thereare sixteen types of moment curves:

1. constant moment as the ship is heeling2. moment distributed as cosine of the heeling angle3. moment distributed as cosine to a power of two4. polygon5. polygon which is made smooth6. moment by arithmetic expression7. general wind moment8. wind moment by IMO9. wind moment by USSR rules10. wind moment by IMO MODU CODE for ship-shaped hulls11. general turning moment12. turning moment by IMO


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13. turning moment by USSR rules14. passenger moment15. moment caused by shifting of load16. moment caused by grain shift.

5.4 OpeningAn opening is a point in the ship through which downflooding may occur. The openings are used to determine the angleof downflooding and the reserve to downflooding. The user selects the relevant openings.

5.5 Freeboard deck edgeA freeboard deck edge is a curve in the ship used for the calculation of the angle at which the freeboard deck immersesand for calculation of residual freeboard. The freeboard deck edge may be defined by referring to a curve defined in thegeometry subsystem or it may be a height approximation. The height approximation means that the point at the mid frameat a given height is used instead of a whole curve in freeboard calculations.

5.6 Bilge lineSome criteria are depending on the heeling angle at which the bilge comes out of water. A curve called 'bilge line' is usedfor this purpose. The bilge line is simply a reference to a curve defined in the geometry subsystem or a point approximation.The point approximation is either an explicitly given point or the point at the mid frame at which the tangent forms agiven angle with the y-axis.

5.7 Special pointThe immersion angle of a special point is in some criteria used to calculate the maximum allowed heeling angle. Specialpoints are not used when checking angles of downflooding.

5.8 Margin lineA margin line is a curve in the ship used for the calculation of the angle at which the margin line immerses and forcalculation of the reserve to immersion of the margin line.

6 Connections to other subsystemsThe stability criteria subsystem CR works in close connection to the loading condition subsystem LD and damage stabilitysubsystem DA. In the environment INTACT, CR may use loading conditions defined in LD and LD may use intact stabilitycriteria defined in CR for checking whether the loading conditions are in compliance with the intact stability criteria. Inthe environment DAMAGE, CR may use initial conditions and damage cases defined in DA and DA may use damagestability criteria defined in CR for checking whether the damage cases are in compliance with the damage stability criteria.

The GM (KG) limit curves of intact stability are available in DA and the GM (KG) limit curves of damage stability areavailable in LD through the CR subsystem.

All the geometric entities are created in the geometry subsystem (task DEF). Their definition in CR is simply a referenceto the geometric object. The geometric objects used by CR are:n profile to calculate lateral arean freeboard deck edgen bilge linen margin line


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n calculation hull.

The stability criteria subsystem CR may be entered directly from LD or DA or from the TASK level.

If CR is entered from LD, the environment INTACT is assigned and the current loading condition is activated forcalculation and output. All commands of CR are available except the command that changes the environment. The controlis returned to LD by the command END or LD.

CR may be entered in two ways from DA. If an output command of DA concerns stability criteria, the program calls CR,assigns the environment DAMAGE, copies all necessary arguments, LQ's, TOO's, PQ's and POO's from DA, performsthe output command and returns back to DA. The permanently stored arguments of damage stability criteria remainunchanged. If the damage stability subsystem is entered from DA by the command CR, the program goes to the subsystemCR, assigns the environment DAMAGE, copies all necessary arguments, LQ's, TOO's, PQ's and POO's from DA and waitsfor commands of CR (all available except the one which changes the environment). If some argument is now changedby an explicit command, it will be stored permanently in the data base. The control is returned to DA by the commandEND or DA.

Both environments and all functions of CR are accessed from the TASK level by calling CR. The environment is selectedby the specific command ENV. The default environment is INTACT. Running CR in this way, no argument is copiedfrom other subsystems, but control is fetched from the permanently stored argument sets or explicitly given argumentcommands.

7 RestrictionsThe stability criteria subsystem does not providen automatic definition or selection of loading conditions which should be checkedn automatic definition or selection of damage cases which should be checkedn automatic definition or selection of relevant stability criteria.

8 GeneralThere are two preconditions for a successful intact stability criteria run: loading conditions and relevant intact criteria. Asuccessful damage stability criteria run needs three preconditions: initial (loading) conditions, damage cases and relevantdamage criteria. There is always a default set of draughts (trim=0) defining a few local loading or initial conditions. Thereis also always some default set of relevant criteria; the one selected by the user in some earlier run or a default set selectedby the program if the user has never made his own selection. There is never a default set of damage cases unless CR isactivated by a listing command of DA. The shortest useful command sequence in the environment INTACT is:

LIST

In the environment DAMAGE, the shortest way to get output is to give some listing command concerning stability criteriain DA e.g.

LIST DCRT

If an intact stability criteria run concerns only loading conditions defined in LD or a damage stability criteria run is calledfrom DA, no calculation arguments are needed; the calculation hull, heeling angles, calculation method etc. are alreadyselected in LD or DA.

If any of the loading conditions or initial conditions are defined in CR by the floating position of the ship (local condition),requiring calculation of the GZ curve, the calculation arguments hull, heeling angles and calculation method must bedefined. There are always useful default values for all of these arguments and usually there should be no need to changethem.


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Whenever relevant criteria has been selected for the particular ship, the selected set remains in force until a new selectionis done. It should be quite unusual to change the relevant criteria after an initial selection has been made.

The functions of the CR subsystem are divided into three categories:n definition functionsn output functionsn administrative functions.

The following chapters describe in detail all the commands related to the functions of this subsystem.

9 Definition functionsThe purpose of the definition functions is to define data entities and store them in the data base. There are eight differenttypes of data: criteria, criterion groups, heeling moments, openings, freeboard deck edges, bilge lines, special points andmargin lines. The openings and margin lines are common to other subsystems (e.g. DA, LD, STAB). The other data typesare depending on CR and it is not possible to define them elsewhere. All other definitions but criteria and criterion groupsare common in both environments. The criteria and criterion groups are available only in that environment where theywere defined.

Definition tasks are started by the commands CRIT, CGR, MOM, OPE, FRB, BIL, POI and MARG. Definitions areterminated by the explicit command OK or by an upper level command of CR. The command SKIP terminates definitionwithout storing the result in the data base.

9.1 Criteria The criteria are requirements concerning one property of the GZ curve. Because the running environment defines whetherthe criterion becomes intact stability criterion or damage stability criterion and because most of definition data are commonto both types, all what is said in this chapter about definition of criteria is valid for both types of criteria. The exceptions(commands PHA, STA, FIN and PRO) are clearly indicated.The criterion is identified by a name. The program does not make any interpretation concerning the name but the namemust not be the same as the name of any criterion group.

The criterion may be equipped with a descriptive text, which is printed and plotted instead of the definition name, providedthe text is given.

The property of the GZ curve that the criterion is dealing with, is expressed by an obligatory TYPE command. Availabletypes of criterian are:

1. MAXGZ : maximum GZ at least ...2. MINGZ : minimum reserve of GZ curve to C*sin(heel)3. MAXHEEL : maximum heeling angle less than ...4. MINAREA : area under the GZ curve at least ...5. MINGM : GM at least ...6. POSMAX : position of the maximum of the GZ curve at least ...7. DOWNFLD : angle of downflooding at least ...8. RANGE : range of positive part of the GZ curve at least ...9. VSTAB : angle of vanishing stability at least ...10. RESFLD : reserve to downflooding at least ...11. RESFRB : reserve to immersion of the freeboard at least ...12. ARATIO1 : area ratio in wind and rolling condition at least ...13. ARATIO2 : area ratio in wind condition at least ...14. RESDYN : reserve dynamic stability at least ...


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15. DYNARM : lever of dynamic stability at least ...16. GZRATIO : ratio GZ/MOM at some point at least ...17. RESMRG : reserve to immersion of the margin line at least ...18. SSOLAS : probability of survival s acc. to SOLAS II-1, Part B-1.19. MACRO : criterion defined by a macro20. CRANE1 / CRANE2 : crane counter ballasting, area ratio / residual

The required value is given by a compulsory REQ command. The valueis either a constant or, in some connections, anequation. One criterion sets at most one requirement to the GZ curve; if there are several requirements of the same type,there must be also several criteria each corresponding to one requirement. The given requirement may be - (minus sign),meaning that nothing at all is required.

The commands PHA, STA, FIN and PRO are accepted only for damage stability requirements in the environmentDAMAGE. The commands may be given in addition to the compulsory command REQ and they state differentrequirements in different flooding stages. The command REQ defines the requirement that is applied before flooding andin all stages of flooding unless PHA, STA, FIN or PRO states an exception. The command PHA defines the requirement(or -) that is applied during intermediate phases of flooding. The command STA defines the requirement (or -) that isapplied at the end of every intermediate stage. The command FIN defines the requirement (or -) that is applied at the endof the final stage of flooding (before stage PROGRESSIVE, if any). The command PRO defines the requirement (or -)that is applied in the progressive stage of flooding. These commands have exactly the same parameter alternatives thanthe command REQ has.The optional command RANGE limits the calculation heeling angles to a part of the GZ curve, i.e. the quantity is calculatedwithin a smaller range of angles than the total range of the GZ curve. For instance, if one wants to calculate the areaof the GZ curve between 30 and 40 degrees or the maximum height of the curve between the upright and the angle ofdownflooding, the RANGE command is necessary. The form of the command is

RANGE lim1, lim2;

where lim1 and lim2 are the lower and upper limits of the range. The symbol EQ means the angle of the first intercept ofthe GZ curve and the moment curve, or if there is no moment, the first intercept of the GZ curve and heeling angle axis.The symbol EQZ means the angle of the first intercept of the GZ curve and heeling angle axis (zero heeling moment).The angles EQ and EQZ are same if no heeling moment is acting on the ship. The following alternatives are possiblefor the limits:n ANGLE : given angle in degreesn

- : from the beginning of the curve (lim1) or to the end of the curve (lim2)n EQ : angle of steady equilibrium (first intercept)n EQ+ang : from the equilibrium ang degrees forwardn EQ-ang : from the equilibrium ang degrees backwardn EQ-ROLL : from the equilibrium rolling angle backwardn EQZ : angle of the first intercept, zero momentn EQZ+ang : from EQZ ang degrees forwardn EQZ-ang : from EQZ ang degrees backwardn EQZ-ROLL : from EQZ rolling angle backwardn DYNA : dynamic heeling angle, i.e. the first intercept of the dynamic stability arm (efi)n DYNA+ang : given angle forward from the dynamic heeling anglen DYNA-ang : given angle backward from the dynamic heeling anglen DECKIMM(a1,a2): angle a2 will be used if the freeboard deck edge immerses prior to angle a1, otherwise a1 is

appliedn

-ROLL : from the upright rolling angle backwardn FA : angle of downflooding, unprotected + weathertight openingsn FA/p : fraction 1/p of FA (p>0)n FAUN : angle of unprotected flooding


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n FAUN/p : fraction 1/p of FAUN (p>0)n FAWE : angle of flooding through weathertight openingsn FAWE/p : fraction 1/p of FAWE (p>0)n MAX : angle of position of the max. of the GZ curven MIN(lim,lim,...) : minimum of the values in the parentheses.Note that the rolling angle is available only in connection with the moment curves of IMOWEATHER andUSSRWEATHER. If the range shrinks to one point, the possibilities RANGE angle; and AT angle; (or the samealternatives as in RANGE) may be used instead of writing 'RANGE a,a' where 'a' is the same angle for both limits. Forexample, all three following commands mean that the quantity is calculated at the angle of 30 degrees: AT 30, RANGE30 and RANGE 30,30.

The criteria may be calculated under the influence of a heeling moment (some quantities are not affected by moments,e.g. angle of downflooding). The moment is connected to the criterion by referring to its name asMOM name

Instructions how to plot extra markings in the criterion check drawings (PLD CRT, PLD MGM, PLD DCRT and PLDDMGM) are possible to save in the definition data of the criterion by the commandMRK opt,opt,...;

The options depend on the type of the criterion and they must be selected from the following set:n TH=h : Text height of additional markings. Default that one selected by diagram plotting.n PEN=p : Select pen code for additions, p=logical pen code. Default P1011.n HPEN=p : Select pen code for auxiliary lines (usually horizontal), p=logical pen code. Default P1011.n ID=c : Control for (numeric) identification; c=ON, add standard identification (default); c=OFF, no identification;

c='text', use the given text.n ARROW : Draw pointers as arrows. Default bare line.n U=u : Horizontal coordinate for the starting point of the pointer line. Default: line is vertical.n V=v : Vertical coordinate for the starting point of the pointer line.n FLL= c : Raster code for area filling, c


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ARATIO1 + - - - - - - - + + - + + -ARATIO2 + - - - - - - - + + + + + +RESDYN + - - - - - - - + + - + + -DYNARM + + + + + - - - - - - - - -

The definition is terminated by the command OK; which stores the criterion in the project data base or by the commandSAVE SYSDB; which stores the criterion in the system data base. The definition is skipped by the command SKI; whichterminates the definition task without storing.

As a summary, the general format of the definition data for an intact criterion is

CRI name 'descr. text'; TYPE type;REQ value; RANGE lim1,lim2; MOM name; MRK opt,opt,... OK;

The general format of the definition data for a damage criterion is

CRI name 'descr. text'; TYPE type; REQ value;PHA value; STA value;FIN value; PRO value; ACC value;RANGE lim1,lim2; MOM name; MRK opt,opt,...;OK;

The following chapters contain the detailed description of each criterion and related definition data. Because the TYPE,RANGE and MOM commands are common to all criteria and the commands PHA, STA, FIN, ACC and PRO have exactlythe same parameter alternatives than REQ, only the REQ command is described.

9.1.1 Maximum righting lever

The criterion with the type MAXGZ requires a minimum value for the maximum height of the GZ curve. If the criterionis equipped with the moment arm curve, the maximum height means the maximum residual lever, i.e. the maximumdifference of the GZ curve and the moment arm curve, if not otherwise stated. Note that the maximum may occur atdifferent angles with different moments.

There are four alternatives to give the requirement:


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Constant height

REQ gz;

The required maximum height is equal to the given value gz (m).Height depending on GM

REQ BY GM gm;

The maximum height depends on the given GM value (m) by the equation 0.5*gm*sin(heel). Source: Department ofEnergy.

Height depending on range

REQ BY RANGE gz0, dgz, rng0;

The maximum height depends on the range of the GZ curve so that, if the range is less than rng0, the requirement iscalculated by the equation gz0+(rng0-range)*dgz. If the range is greater than rng0, the value gz0 is used. The parametersof the command are:

gz0 required height for ranges greater than rng0 (m),dgz increment of height per degree (m),rng0 upper range limit (degrees).

Source: SBG.

Height depending on moment arm at steady equilibrium

REQ BY GZE k;

The maximum height depends on the height of the GZ curve at the angle of steady equilibrium (first intercept of the GZcurve and the moment arm curve) by the equation k*gze, wherek dimensionless coefficient,

gze height of the GZ curve at the angle of steady equilibrium (m).The maximum height means here the maximum height of the GZ curve, not the maximum height of the residual lever.

Source: US Navy.

9.1.1.1 Examples

CRI IMOGZ 'Max. GZ by IMO Res. A.749'; TYPE MAXGZ; REQ 0.2; RANGE 30, FA; OK;

CRI MGZ 'Max. GZ by Dep. of Energy'; TYPE MAXGZ; REQ BY GM 0.5; ** h=0.5*0.5*sin(heel); RANGE -,MIN(15,FA,MAX); OK;

CRI GZSBG 'Max. GZ by SBG'; TYPE MAXGZ; REQ BY RANGE 0.2 0.01 60; ** h=0.2+0.01*(60-range);AT 30; OK;

CRI GZUS 'Max. GZ by US Navy';


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TYPE MAXGZ; REQ BY GZE 1.67; ** h=1.67*GZe, i.e. GZe=0.6*h MOM USWIND; OK;

CRI SOLASGZ 'SOLAS 90, passenger ships, residual lever'; TYPE MAXGZ; REQ -; FIN 0.04; MOM GREATEST; OK;

9.1.2 Maximum heeling angle

The criterion with the type MAXHEEL sets a maximum value for the steady equilibrium heeling angle. The angle of thesteady equilibrium is the first intercept of the GZ curve and the moment arm curve or the GZ curve and the heel axis.

There are eight alternatives to define the requirement:

Constant angle

REQ angle;

The maximum heeling angle must not exceed the given value 'angle' (degrees).Angle depending on downflooding

REQ FA;

REQ FAUN;

REQ FAWE;

The maximum angle is equal to the angle of downflooding; FA = angle at which the first unprotected or weathertightopening immerses; FAUN = angle at which the first unprotected opening immerses; FAWE = angle at which the firstweathertight opening immerses.

REQ FA=res;

REQ FAUN=res;

REQ FAWE=res;

The maximum angle is equal to the angle at which there is left the given reserve (m) to downflooding. For the differencebetween FA, FAUN and FAWE, see above.

REQ FA=*f;

REQ FAUN=*f;

REQ FAWE=*f;

The maximum angle is equal to the angle at which there is the given fraction f of the original reserve to downflooding left.The original reserve is calculated at the upright position. For the difference between FA, FAUN and FAWE, see above.


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REQ FA=


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9.1.2.1 Examples

CRI IMOPASS 'Max. heel by IMO Reg. for passenger ships';TYPE MAXHEEL;REQ 10;MOM IMOPASS;OK

CRI DOWNFLD 'Downflooding not allowed';TYPE MAXHEEL;REQ FA;MOM TURN;OK

CRI USCG 'Max. heeling by USCG for small pass. ships';TYPE MAXHEEL;REQ MIN(14,FRB=*0.5);MOM USCGWIND;OK

CRI MARPOL 'Max. heeling by MARPOL 25/30';TYPE MAXHEEL;REQ BY DECKIMM 25 30;OK

9.1.3 Minimum area

The criterion with the type MINAREA requires a minimum value for the area under the positive part of the GZ curve orthe area between the GZ curve and the moment arm curve.

There are two alternatives to determine the requirement:

Constant value

REQ area;

The minimum area is equal to the given area (m*rad).Area depending on position of max. GZ

REQ BY MAX a0,da,amax0;

The area depends on the position of the maximum of the GZ curve amax so that, if the position of the max. GZ is lessthan amax0, the requirement is equal to a0+da*(amax0-amax). If the position of the max. GZ is greater than amax0, thevalue a0 is used. The parameters of the command are:

a0 area (m*rad),da increment of area per one degree (m*rad),


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amax0 upper limit for the position of the max. GZ (degrees).Source: DNV.

9.1.3.1 Examples

CRI IMOA40 'Area within 0, 40 by IMO'; TYPE MINAREA; REQ 0.09; RANGE 0,MIN(40,FA) OK

CRI DNVAREA 'Area by DNV'; TYPE MINAREA; REQ BY MAX 0.055,0.001,30; ** a=0.055+0.001*(30-max); RANGE 0,MAX; OK

9.1.4 Minimum GM

The criterion with the type MINGM requires a minimum value for GM. GM is calculated at the upright position (= heeling0.0) or at an angle given by the command AT (RANGE). Note that the data item MOM have no effect on the requirementor attained value.

There are three alternatives to give the requirement:

Constant GM

REQ gm;

The minimum GM is equal to the given corrected gm (m).GM depending on lateral area

REQ BY PROF P=p, PROF=(curve,curve,...); GM depends on the lateral area of the ship by the equation GM = P*A*H/(W*tan(T) ), where P is coefficient dependingon the operation of the ship (parameter p in the command), A is the lateral area above the waterline (calc. from the profile),H is the distance from the center of A to the center of the underwater portion of the lateral area, W is the displacementand T is the minimum of 14 degrees or the angle at which 1/2 of the freeboard to the deck edge is immersed.

The parameters of the command are:

P=p parameter describing wind force (t/m2),PROF=(curve,curve,...) (optional) name(s) of curve(s) forming the profile of the ship. The default profile

comes from the arguments of CR.

Source: US Coast Guard, Weather Criterion.

GM depending on limit curve


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REQ BY CURVE t1,gm1 t2,gm2, ...

The minimum GM is defined by interpolating its value from the given polygon for the draught of the loading condition. Thepolygon goes through the points (t1,gm1), (t2,gm2), ... where (t1,t2,... are draughts (m) in ascending order and gm1,gm2,...corresponding GM values (m)). If the draught of the loading condition is outside the range of the polygon, GM of thefirst or last point is used.

REQ BY CURVE DAM=name

Like above but the GM limit curve of damage stability is used.

9.1.4.1 Examples

CRI GMIMO 'Min. GM by IMO'; TYPE MINGM; REQ 0.15; OK

CRI USCG 'Weather crit. by USCG' TYPE MINGM; REQ BY PROF P=0.0608; OK

CRI GMLIM 'Limit curve from DA' TYPE MINGM; REQ BY CURVE DAM=GMLIMIT.DA OK;

9.1.5 Position of maximum GZ

The criterion with the type POSMAX requires a minimum value for the position of the maximum of the GZ curve. Themaximum of the GZ curve occurs at an angle where the tangent of the curve is horizontal. Note that the data items RANGEand MOM have no effect on the requirement or attained value.

REQ angle;

The requirement is equal to the given angle (degrees).

9.1.5.1 Example

CRI POSMAX 'Position of the max. GZ'; TYPE POSMAX; REQ 30; OK


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9.1.6 Angle of downflooding

The criterion with the type DOWNFLD requires a minimum value for the angle of downflooding. Note that the data itemsRANGE and MOM have no effect on the requirement or attained value. Because changing of GM does not change thefloating position of the ship at different heeling angles, there is no minimum GM (maximum KG) which is in compliancewith this criterion; this criterion is used only for checking of loading conditions.

REQ angle;

The minimum immersion angle of the unprotected or weathertight openings is equal to the given angle (degrees).REQ UN=angle;

The minimum immersion angle of the unprotected openings is equal to the given angle (degrees).REQ WE=angle;

The minimum immersion angle of the weathertight openings is equal to the given angle (degrees).

9.1.6.1 Example

CRI DWNFLD 'No downflooding'; TYPE DOWNFLD; REQ 40; OK;

9.1.7 Range of stability

The criterion with the type RANGE requires a minimum value for the range of the positive part of the GZ curve. The rangeis equal to that part of the GZ curve which is to the right from the first intercept of the GZ curve and the horizontal axisor the GZ curve and the moment arm curve and to the left from the second intercept of the GZ curve and the horizontalaxis or the GZ curve and the moment arm curve. If there are more than two intercepts, the range is equal to the greatestcontinuous part.

REQ rng;

The requirement is equal to the given range rng (degrees).


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REQ BY AREA r a l1 l2;

The required range depends on the area under the GZ curve by the equation

requirement = r*a/(area under GZ curve) where r is the given range (degrees) and a the given area (mrad). The optional parameters l1 and l2 are limits for calculationof the area under the GZ curve and they have the same alternatives than the limits in the range command (see RANGE).If l1 and l2 are missing,

stability criteria (cr)

Documents

stability criterion

damage stability criteria

intact stability criteria

minimum gm check plot74

minimum gm check plot54

range of stability

criterion check plot74

criterion table74