125:. As the ship heels over, the centre of gravity generally remains fixed with respect to the ship because it just depends on the position of the ship's weight and cargo, but the surface area increases, increasing BMφ. Work must be done to roll a stable hull. This is converted to potential energy by raising the centre of mass of the hull with respect to the water level or by lowering the centre of buoyancy or both. This potential energy will be released in order to right the hull and the stable attitude will be where it has the least magnitude. It is the interplay of potential and kinetic energy that results in the ship having a natural rolling frequency. For small angles, the metacentre, Mφ, moves with a lateral component so it is no longer directly over the centre of mass.
513:
the wave. An overly stiff vessel rolls with a short period and high amplitude which results in high angular acceleration. This increases the risk of damage to the ship and to cargo and may cause excessive roll in special circumstances where eigenperiod of wave coincide with eigenperiod of ship roll. Roll damping by bilge keels of sufficient size will reduce the hazard. Criteria for this dynamic stability effect remain to be developed. In contrast, a "tender" ship lags behind the motion of the waves and tends to roll at lesser amplitudes. A passenger ship will typically have a long rolling period for comfort, perhaps 12 seconds while a tanker or freighter might have a rolling period of 6 to 8 seconds.
460:
be applied to the vessel without causing it to capsize. The point of deck immersion is the angle at which the main deck will first encounter the sea. Similarly, the downflooding angle is the angle at which water will be able to flood deeper into the vessel. Finally, the point of vanishing stability is a point of unstable equilibrium. Any heel lesser than this angle will allow the vessel to right itself, while any heel greater than this angle will cause a negative righting moment (or heeling moment) and force the vessel to continue to roll over. When a vessel reaches a heel equal to its point of vanishing stability, any external force will cause the vessel to capsize.
671:, the centre of buoyancy, and the loss of waterplane area - thus a loss of the waterplane moment of inertia - which decreases the metacentric height. This additional mass will also reduce freeboard (distance from water to the deck) and the ship's downflooding angle (minimum angle of heel at which water will be able to flow into the hull). The range of positive stability will be reduced to the angle of down flooding resulting in a reduced righting lever. When the vessel is inclined, the fluid in the flooded volume will move to the lower side, shifting its centre of gravity toward the list, further extending the heeling force. This is known as the free surface effect.
20:
73:
340:
470:) to at least 120° of heel, although many sailing yachts have stability limits down to 90° (mast parallel to the water surface). As the displacement of the hull at any particular degree of list is not proportional, calculations can be difficult, and the concept was not introduced formally into naval architecture until about 1970.
351:
The metacentric height is an approximation for the vessel stability at a small angle (0-15 degrees) of heel. Beyond that range, the stability of the vessel is dominated by what is known as a righting moment. Depending on the geometry of the hull, naval architects must iteratively calculate the center
177:
of the ship moves laterally. It might also move up or down with respect to the water line. The point at which a vertical line through the heeled centre of buoyancy crosses the line through the original, vertical centre of buoyancy is the metacentre. The metacentre remains directly above the centre of
689:
The significance of this effect is proportional to the cube of the width of the tank or compartment, so two baffles separating the area into thirds will reduce the displacement of the centre of gravity of the fluid by a factor of 9. This is of significance in ship fuel tanks or ballast tanks, tanker
459:
There are several important factors that must be determined with regards to righting arm/moment. These are known as the maximum righting arm/moment, the point of deck immersion, the downflooding angle, and the point of vanishing stability. The maximum righting moment is the maximum moment that could
303:
Stable floating objects have a natural rolling frequency, just like a weight on a spring, where the frequency is increased as the spring gets stiffer. In a boat, the equivalent of the spring stiffness is the distance called "GM" or "metacentric height", being the distance between two points: "G" the
512:
specify minimum safety margins for seagoing vessels. A larger metacentric height on the other hand can cause a vessel to be too "stiff"; excessive stability is uncomfortable for passengers and crew. This is because the stiff vessel quickly responds to the sea as it attempts to assume the slope of
137:
For example, when a perfectly cylindrical hull rolls, the centre of buoyancy stays on the axis of the cylinder at the same depth. However, if the centre of mass is below the axis, it will move to one side and rise, creating potential energy. Conversely if a hull having a perfectly rectangular cross
685:
In tanks or spaces that are partially filled with a fluid or semi-fluid (fish, ice, or grain for example) as the tank is inclined the surface of the liquid, or semi-fluid, stays level. This results in a displacement of the centre of gravity of the tank or space relative to the overall centre of
818:
Technically, there are different metacentric heights for any combination of pitch and roll motion, depending on the moment of inertia of the waterplane area of the ship around the axis of rotation under consideration, but they are normally only calculated and stated as specific values for the
322:
An ideal boat strikes a balance. Very tender boats with very slow roll periods are at risk of overturning, but are comfortable for passengers. However, vessels with a higher metacentric height are "excessively stable" with a short roll period resulting in high accelerations at the deck level.
181:
In the diagram above, the two Bs show the centres of buoyancy of a ship in the upright and heeled conditions. The metacentre, M, is considered to be fixed relative to the ship for small angles of heel; however, at larger angles the metacentre can no longer be considered fixed, and its actual
128:
The righting couple on the ship is proportional to the horizontal distance between two equal forces. These are gravity acting downwards at the centre of mass and the same magnitude force acting upwards through the centre of buoyancy, and through the metacentre above it. The righting couple is
720:
There is also a similar consideration in the movement of the metacentre forward and aft as a ship pitches. Metacentres are usually separately calculated for transverse (side to side) rolling motion and for lengthwise longitudinal pitching motion. These are variously known as
311:
of the boat and the volume of the boat. (The inertia resistance is a quantified description of how the waterline width of the boat resists overturning.) Wide and shallow hulls have high transverse metacentres, whilst narrow and deep hulls have low metacentres . Ignoring the
120:
is the point where the lines intersect (at angle φ) of the upward force of buoyancy of φ ± dφ. When the ship is vertical, the metacentre lies above the centre of gravity and so moves in the opposite direction of heel as the ship rolls. This distance is also abbreviated as
63:
of rolling of a hull, with very large metacentric heights being associated with shorter periods of roll which are uncomfortable for passengers. Hence, a sufficiently, but not excessively, high metacentric height is considered ideal for passenger ships.
330:
and the metacentre is very large in order to resist the heeling effect of the wind on the sails. In such vessels, the rolling motion is not uncomfortable because of the moment of inertia of the tall mast and the aerodynamic damping of the sails.
319:"G", is the center of gravity. "GM", the stiffness parameter of a boat, can be lengthened by lowering the center of gravity or changing the hull form (and thus changing the volume displaced and second moment of area of the waterplane) or both.
694:
loop can be established, in which the period of the roll is equal or almost equal to the period of the motion of the centre of gravity in the fluid, resulting in each roll increasing in magnitude until the loop is broken or the ship capsizes.
133:
of the angle of heel, hence the importance of metacentric height to stability. As the hull rights, work is done either by its centre of mass falling, or by water falling to accommodate a rising centre of buoyancy, or both.
597:
76:
Initially the second moment of area increases as the surface area increases, increasing BM, so Mφ moves to the opposite side, thus increasing the stability arm. When the deck is flooded, the stability arm rapidly
483:
The metacentre has a direct relationship with a ship's rolling period. A ship with a small GM will be "tender" - have a long roll period. An excessively low or negative GM increases the risk of a ship
831:
once it has been built. This can also be done when a ship or offshore floating platform is in service. It can be calculated by theoretical formulas based on the shape of the structure.
138:
section has its centre of mass at the water line, the centre of mass stays at the same height, but the centre of buoyancy goes down as the hull heels, again storing potential energy.
453:
797:
758:
267:
834:
The angle(s) obtained during the inclining experiment are directly related to GM. By means of the inclining experiment, the 'as-built' centre of gravity can be found; obtaining
390:
655:
686:
gravity. The effect is similar to that of carrying a large flat tray of water. When an edge is tipped, the water rushes to that side, which exacerbates the tip even further.
37:
As long as the load of a ship remains stable, G is fixed (relative to the ship). For small angles, M can also be considered to be fixed, while B moves as the ship heels.
227:
521:
463:
Sailing vessels are designed to operate with a higher degree of heel than motorized vessels and the righting moment at extreme angles is of high importance.
400:
is the displacement. Because the vessel displacement is constant, common practice is to simply graph the righting arm vs the angle of heel. The
316:, wide and shallow means that the ship is very quick to roll, and narrow and deep means that the ship is very hard to overturn and is stiff.
690:
cargo tanks, and in flooded or partially flooded compartments of damaged ships. Another worrying feature of free surface effect is that a
1047:
352:
of buoyancy at increasing angles of heel. They then calculate the righting moment at this angle, which is determined using the equation:
59:. A larger metacentric height implies greater initial stability against overturning. The metacentric height also influences the natural
846:
can be found. So KM and GM become the known variables during inclining and KG is the wanted calculated variable (KG = KM-GM)
509:
500:. It also puts the vessel at risk of potential for large angles of heel if the cargo or ballast shifts, such as with the
357:
113:. When a ship is at equilibrium, the centre of buoyancy is vertically in line with the centre of gravity of the ship.
999:
970:
950:
504:. A ship with low GM is less safe if damaged and partially flooded because the lower metacentric height leaves less
49:) is a measurement of the initial static stability of a floating body. It is calculated as the distance between the
1040:
1316:
914:
842:
by experiment measurement (by means of pendulum swing measurements and draft readings), the centre of gravity
1326:
1311:
1075:
141:
When setting a common reference for the centres, the molded (within the plate or planking) line of the keel (
1321:
1281:
699:
414:
763:
724:
1260:
871:
233:
1481:
1476:
1466:
1033:
606:
628:
1181:
827:
The metacentric height is normally estimated during the design of a ship but can be determined by an
326:
Sailing yachts, especially racing yachts, are designed to be stiff, meaning the distance between the
1223:
1127:
991:
984:
942:
191:
1117:
285:
934:
1264:
1228:
1132:
1122:
293:
8:
1306:
876:
680:
1440:
1367:
1255:
1207:
861:
622:
488:
96:
83:
1419:
1471:
1056:
995:
966:
946:
935:
910:
691:
308:
101:
50:
1014:
1080:
505:
466:
Monohulled sailing vessels should be designed to have a positive righting arm (the
408:— see diagram): the horizontal distance between the lines of buoyancy and gravity.
1096:
1342:
1286:
1070:
828:
327:
304:
centre of gravity of the boat and "M", which is a point called the metacentre.
1460:
1352:
1347:
1176:
866:
1414:
1202:
1112:
909:. New York: Society of Naval Architects and Marine Engineers. p. 827.
592:{\displaystyle T={\frac {2\pi \,(a_{44}+k)}{\sqrt {g{\overline {GM}}}}}\ }
1186:
495:
88:
1405:
856:
706:
614:
501:
1430:
1400:
1148:
667:
If a ship floods, the loss of stability is caused by the increase in
484:
60:
1025:
19:
1445:
1395:
1390:
1385:
1380:
174:
715:
1435:
1410:
1375:
1171:
698:
This has been significant in historic capsizes, most notably the
516:
The period of roll can be estimated from the following equation:
313:
339:
625:
about the longitudinal axis through the centre of gravity and
16:
Measurement of the initial static stability of a floating body
1424:
986:
Desirable and
Undesirable Characteristics of Offshore Yachts
508:. For this reason, maritime regulatory agencies such as the
394:
Where RM is the righting moment, GZ is the righting arm and
347:: a notional lever through which the force of buoyancy acts
277:
130:
72:
288:
of the waterplane around the rotation axis in metres, and
182:
location must be found to calculate the ship's stability.
129:
proportional to the metacentric height multiplied by the
87:
is at the centre of mass of the volume of water that the
145:) is generally chosen; thus, the reference heights are:
766:
727:
631:
524:
417:
360:
236:
194:
35:(M) with ship upright and heeled over to one side.
983:
791:
752:
649:
591:
447:
384:
307:Metacentre is determined by the ratio between the
261:
221:
173:When a ship heels (rolls sideways), the centre of
300:is the distance from the keel to the metacentre.
1458:
716:Transverse and longitudinal metacentric heights
1041:
276:is the centre of buoyancy (height above the
981:
1048:
1034:
975:
941:. London: Conway Maritime Press. pp.
1203:Panama Canal/Universal Measurement System
990:. New York, London: W.W.Norton. pp.
928:
926:
540:
185:It can be calculated using the formulae:
105:of the ship is commonly denoted as point
904:
478:
338:
91:displaces. This point is referred to as
71:
18:
932:
900:
898:
896:
894:
892:
1459:
1248:
923:
674:
1055:
1029:
819:limiting pure pitch and roll motion.
448:{\displaystyle GZ=GM\cdot \sin \phi }
889:
792:{\displaystyle {\overline {GM_{L}}}}
753:{\displaystyle {\overline {GM_{T}}}}
662:
67:
510:International Maritime Organization
262:{\displaystyle BM={\frac {I}{V}}\ }
13:
1017:Technical computer program support
965:Ship Stability. Kemp & Young.
385:{\displaystyle RM=GZ\cdot \Delta }
379:
14:
1493:
907:Principles of Naval Architecture
650:{\displaystyle {\overline {GM}}}
982:Rousmaniere, John, ed. (1987).
334:
55:
23:Ship stability diagram showing
1008:
959:
822:
560:
541:
487:in rough weather, for example
1:
1076:Length between perpendiculars
937:Seamanship in the age of sail
883:
168:
784:
745:
642:
578:
473:
7:
1261:Twenty-foot equivalent unit
872:Limit of positive stability
849:
468:limit of positive stability
10:
1498:
1208:Thames measurement tonnage
1020:accessed 20 December 2006.
678:
607:gravitational acceleration
164:– to Transverse Metacentre
1366:
1335:
1299:
1282:Builder's Old Measurement
1274:
1241:
1216:
1195:
1182:Compensated gross tonnage
1164:
1157:
1141:
1128:Load line (Plimsoll Line)
1105:
1089:
1063:
702:Herald of Free Enterprise
615:added radius of gyration
222:{\displaystyle KM=KB+BM}
178:buoyancy by definition.
1358:Metacentric height (GM)
1081:Length at the waterline
905:Comstock, John (1967).
658:is the stability index.
455:at small angles of heel
152:– to Centre of Buoyancy
1224:Gross register tonnage
933:Harland, John (1984).
793:
754:
651:
593:
449:
386:
348:
263:
223:
158:– to Centre of Gravity
78:
38:
1317:Standard displacement
1265:Intermodal containers
794:
755:
679:Further information:
652:
594:
479:GM and rolling period
450:
387:
342:
286:second moment of area
264:
224:
75:
22:
1229:Net register tonnage
1133:Under keel clearance
764:
725:
629:
522:
415:
358:
234:
192:
1327:Normal displacement
1312:Loaded displacement
877:Weight distribution
681:Free surface effect
675:Free surface effect
343:Distance GZ is the
1322:Light displacement
1256:Deadweight tonnage
789:
750:
647:
623:radius of gyration
589:
445:
382:
349:
309:inertia resistance
259:
219:
97:naval architecture
84:centre of buoyancy
79:
53:of a ship and its
43:metacentric height
39:
29:centre of buoyancy
1482:Vertical position
1477:Ship measurements
1467:Geometric centers
1454:
1453:
1415:§ Neopanamax
1396:Handymax/Supramax
1295:
1294:
1237:
1236:
1057:Ship measurements
1015:U.S. Coast Guard
787:
748:
692:positive feedback
663:Damaged stability
645:
588:
584:
583:
581:
292:is the volume of
258:
254:
102:centre of gravity
68:Different centres
51:centre of gravity
25:centre of gravity
1489:
1246:
1245:
1162:
1161:
1050:
1043:
1036:
1027:
1026:
1021:
1012:
1006:
1005:
989:
979:
973:
963:
957:
956:
940:
930:
921:
920:
902:
798:
796:
795:
790:
788:
783:
782:
781:
768:
759:
757:
756:
751:
749:
744:
743:
742:
729:
656:
654:
653:
648:
646:
641:
633:
598:
596:
595:
590:
586:
585:
582:
577:
569:
564:
563:
553:
552:
532:
454:
452:
451:
446:
399:
391:
389:
388:
383:
268:
266:
265:
260:
256:
255:
247:
228:
226:
225:
220:
1497:
1496:
1492:
1491:
1490:
1488:
1487:
1486:
1457:
1456:
1455:
1450:
1362:
1331:
1291:
1270:
1233:
1212:
1191:
1153:
1137:
1101:
1085:
1059:
1054:
1024:
1013:
1009:
1002:
980:
976:
964:
960:
953:
931:
924:
917:
903:
890:
886:
881:
852:
825:
807:, or sometimes
777:
773:
769:
767:
765:
762:
761:
738:
734:
730:
728:
726:
723:
722:
718:
683:
677:
665:
634:
632:
630:
627:
626:
570:
568:
548:
544:
533:
531:
523:
520:
519:
481:
476:
416:
413:
412:
404:(known also as
398:
395:
359:
356:
355:
337:
246:
235:
232:
231:
193:
190:
189:
171:
70:
36:
17:
12:
11:
5:
1495:
1485:
1484:
1479:
1474:
1469:
1452:
1451:
1449:
1448:
1443:
1438:
1433:
1428:
1422:
1417:
1408:
1403:
1398:
1393:
1388:
1383:
1378:
1372:
1370:
1364:
1363:
1361:
1360:
1355:
1350:
1345:
1343:Inclining test
1339:
1337:
1333:
1332:
1330:
1329:
1324:
1319:
1314:
1309:
1303:
1301:
1297:
1296:
1293:
1292:
1290:
1289:
1287:Moorsom System
1284:
1278:
1276:
1272:
1271:
1269:
1268:
1258:
1252:
1250:
1243:
1239:
1238:
1235:
1234:
1232:
1231:
1226:
1220:
1218:
1214:
1213:
1211:
1210:
1205:
1199:
1197:
1193:
1192:
1190:
1189:
1184:
1179:
1174:
1168:
1166:
1159:
1155:
1154:
1152:
1151:
1145:
1143:
1139:
1138:
1136:
1135:
1130:
1125:
1120:
1115:
1109:
1107:
1103:
1102:
1100:
1099:
1093:
1091:
1087:
1086:
1084:
1083:
1078:
1073:
1071:Length overall
1067:
1065:
1061:
1060:
1053:
1052:
1045:
1038:
1030:
1023:
1022:
1007:
1000:
974:
958:
951:
922:
915:
887:
885:
882:
880:
879:
874:
869:
864:
859:
853:
851:
848:
829:inclining test
824:
821:
786:
780:
776:
772:
747:
741:
737:
733:
717:
714:
676:
673:
664:
661:
644:
640:
637:
580:
576:
573:
567:
562:
559:
556:
551:
547:
543:
539:
536:
530:
527:
480:
477:
475:
472:
457:
456:
444:
441:
438:
435:
432:
429:
426:
423:
420:
396:
381:
378:
375:
372:
369:
366:
363:
336:
333:
328:centre of mass
270:
269:
253:
250:
245:
242:
239:
229:
218:
215:
212:
209:
206:
203:
200:
197:
170:
167:
166:
165:
159:
153:
69:
66:
15:
9:
6:
4:
3:
2:
1494:
1483:
1480:
1478:
1475:
1473:
1470:
1468:
1465:
1464:
1462:
1447:
1444:
1442:
1441:VLCC and ULCC
1439:
1437:
1434:
1432:
1429:
1426:
1423:
1421:
1418:
1416:
1412:
1409:
1407:
1404:
1402:
1399:
1397:
1394:
1392:
1389:
1387:
1384:
1382:
1379:
1377:
1374:
1373:
1371:
1369:
1365:
1359:
1356:
1354:
1353:Angle of loll
1351:
1349:
1346:
1344:
1341:
1340:
1338:
1334:
1328:
1325:
1323:
1320:
1318:
1315:
1313:
1310:
1308:
1305:
1304:
1302:
1298:
1288:
1285:
1283:
1280:
1279:
1277:
1273:
1266:
1262:
1259:
1257:
1254:
1253:
1251:
1247:
1244:
1240:
1230:
1227:
1225:
1222:
1221:
1219:
1215:
1209:
1206:
1204:
1201:
1200:
1198:
1194:
1188:
1185:
1183:
1180:
1178:
1177:Gross tonnage
1175:
1173:
1170:
1169:
1167:
1163:
1160:
1156:
1150:
1147:
1146:
1144:
1140:
1134:
1131:
1129:
1126:
1124:
1121:
1119:
1118:Moulded depth
1116:
1114:
1111:
1110:
1108:
1104:
1098:
1095:
1094:
1092:
1088:
1082:
1079:
1077:
1074:
1072:
1069:
1068:
1066:
1062:
1058:
1051:
1046:
1044:
1039:
1037:
1032:
1031:
1028:
1019:
1018:
1011:
1003:
1001:0-393-03311-2
997:
993:
988:
987:
978:
972:
971:0-85309-042-4
968:
962:
954:
952:0-85177-179-3
948:
944:
939:
938:
929:
927:
918:
912:
908:
901:
899:
897:
895:
893:
888:
878:
875:
873:
870:
868:
867:Angle of loll
865:
863:
860:
858:
855:
854:
847:
845:
841:
837:
832:
830:
820:
816:
814:
810:
806:
802:
778:
774:
770:
739:
735:
731:
713:
711:
710:
704:
703:
696:
693:
687:
682:
672:
670:
660:
659:
638:
635:
624:
620:
616:
612:
608:
604:
599:
574:
571:
565:
557:
554:
549:
545:
537:
534:
528:
525:
517:
514:
511:
507:
506:safety margin
503:
499:
498:
493:
492:
486:
471:
469:
464:
461:
442:
439:
436:
433:
430:
427:
424:
421:
418:
411:
410:
409:
407:
403:
392:
376:
373:
370:
367:
364:
361:
353:
346:
341:
332:
329:
324:
320:
317:
315:
310:
305:
301:
299:
295:
291:
287:
283:
279:
275:
251:
248:
243:
240:
237:
230:
216:
213:
210:
207:
204:
201:
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195:
188:
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183:
179:
176:
163:
160:
157:
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151:
148:
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146:
144:
139:
135:
132:
126:
124:
119:
114:
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108:
104:
103:
98:
94:
90:
86:
85:
74:
65:
62:
58:
57:
52:
48:
44:
34:
30:
26:
21:
1357:
1307:Displacement
1016:
1010:
985:
977:
961:
936:
906:
843:
839:
835:
833:
826:
817:
812:
808:
804:
800:
719:
708:
701:
697:
688:
684:
668:
666:
657:
618:
610:
602:
600:
518:
515:
496:
490:
482:
467:
465:
462:
458:
405:
402:righting arm
401:
393:
354:
350:
345:righting arm
344:
335:Righting arm
325:
321:
318:
306:
302:
297:
294:displacement
289:
281:
273:
271:
184:
180:
172:
161:
155:
149:
142:
140:
136:
127:
122:
117:
115:
110:
106:
100:
92:
82:
80:
54:
46:
42:
40:
32:
28:
24:
1427:(Qatar-max)
1196:Specialized
1187:Net tonnage
823:Measurement
296:in metres.
1461:Categories
1406:Malaccamax
916:9997462556
884:References
857:Kayak roll
502:Cougar Ace
169:Metacentre
118:metacentre
77:decreases.
56:metacentre
33:metacentre
1431:Seawaymax
1401:Handysize
1336:Stability
1165:Worldwide
1149:Air draft
1123:Freeboard
785:¯
746:¯
643:¯
579:¯
538:π
485:capsizing
474:Stability
443:ϕ
440:
434:⋅
380:Δ
377:⋅
31:(B), and
1472:Buoyancy
1446:Yamalmax
1391:Chinamax
1386:Capesize
1381:Baltimax
1242:Capacity
862:Turtling
850:See also
707:MS
705:and the
700:MS
175:buoyancy
1436:Suezmax
1420:Péniche
1411:Panamax
1376:Aframax
1275:Archaic
1249:Current
1217:Archaic
1172:Tonnage
1090:Breadth
709:Estonia
621:is the
613:is the
605:is the
494:or the
491:Captain
314:ballast
284:is the
1368:Limits
1300:Weight
1158:Volume
1142:Height
1064:Length
998:
969:
949:
913:
601:where
587:
397:Δ
272:Where
257:
99:. The
61:period
1425:Q-Max
1113:Draft
1106:Depth
805:GM(l)
801:GM(t)
27:(G),
1413:and
1348:List
1097:Beam
996:ISBN
967:ISBN
947:ISBN
911:ISBN
838:and
811:and
803:and
760:and
617:and
497:Vasa
489:HMS
278:keel
131:sine
116:The
89:hull
81:The
41:The
992:310
813:GMl
809:GMt
611:a44
437:sin
280:),
162:KMT
109:or
95:in
1463::
994:.
945:.
943:43
925:^
891:^
844:KG
840:KM
836:GM
815:.
799:,
712:.
669:KB
609:,
550:44
406:GZ
298:KM
274:KB
156:KG
150:KB
123:GM
111:CG
47:GM
1267:)
1263:(
1049:e
1042:t
1035:v
1004:.
955:.
919:.
779:L
775:M
771:G
740:T
736:M
732:G
639:M
636:G
619:k
603:g
575:M
572:G
566:g
561:)
558:k
555:+
546:a
542:(
535:2
529:=
526:T
431:M
428:G
425:=
422:Z
419:G
374:Z
371:G
368:=
365:M
362:R
290:V
282:I
252:V
249:I
244:=
241:M
238:B
217:M
214:B
211:+
208:B
205:K
202:=
199:M
196:K
143:K
107:G
93:B
45:(
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