What is good GM? GM = KM - KG The ideal GM or ideal stability is a GM having a minimum stability consistent with safety. The rolling period is the time in seconds for a ship to complete a full roll cycle, to port and starboard and return upright.
Relation of GM to rolling period Rolling period Formula in English Units of feet T= a fully natural rolling period in seconds B = beam of the vessel in feet = square root of GM in feet Rolling period Formula in metric units of meters T= a fully natural rolling period in seconds B = beam of the vessel in meters = square root of GM in meters
Example 1 Your vessel’s beam is 80 feet and its calculated GM is 3 feet. What is the natural rolling period of the vessel? Solution. Your vessel’s beam is 32. 2 meters and its observed natural rolling period is 20 seconds. What is the approximate GM of your vessel if it returns to its original position when it comes to rest. Solution.
Stiff and tender of ships The ship have a comparatively large GM and short time period, and will roll quickly – and perhaps violently – from side to side. This condition is said to be stiff and such a condition is not desirable The ship have a comparatively small GM and long time period, and will not to tend to return so quickly to the initial position. This condition is said to be tender and such a condition is not desirable Tender ship Tr= 30 -35 Stiff ship Tr = 8 to 10 seconds Comfortable ship Tr = 20 to 25 seconds
Effect of negative GM on vessels A negative GM means that the vessel does not have any initial stability The name for an inclination due to negative GM is angle of loll. Differences between Angle of list and angle of loll
Movement of M with transverse inclination BM is the radius of circle The movement of M is negligible
Breadth of the water plane increase I Breadth of the water plane decrease
Standard long form from method Trim and stability booklet for single screw cargo vessel for SS American Mariner in appendix A. Basic sections: 1. Operating instructions 2. Principle characteristics of the vessel : maximum seasonal drafts, light ship weight, KG and LCG 3. Trimming table 4. Hydrostatic properties: for assumed condition of no trim, list or hull deflection
Mean draft MT 1 LCB LCF Total displacement TPI Transverse KM
5. Table of free surface corrections and tank capacities 6. Gain in GM by ballasting. 7. Required GM curve. 8. Loading table 9. Summary of all categories including the light ship weight
Solve a practical problem Example 1 You are loading logs in bulk. Loading is stopped near the completion of loading for a draft check and a rolling test. Your vessel’s displacement is 32, 500 metric tons, and as result of the draft check, the vessel has 1, 100 metric tons of cargo deadweight available. The rolling test resulted in a 22 second rolling period. Your vessel’s KM is 10. 5 meters; beam is 24 meters; depth is 13 meters, and height of cargo on deck is 7 meters. No. 2 double –bottom tanks port and starboard have KG of 1. 2 meters and are empty with a capacity of 800 metric tons
What is the approximate GM of your vessel if during the rolling test? If the required GM is 0. 85 meters, which way do you need to move G? What is the vessel’s KG at the time of the rolling test? What will be the gain in GM and the shift of G if NO. 2 double-bottom tanks port and starboard are ballasted? After No. 2 double-bottom tanks port and starboard are ballasted, how many metric tons of logs can be loaded at a height of 21 meters above the keel to sail with a minimum required GM of 0. 85 meters.