# MIT 2 996 - Quiz: Hydrostatic, Small and Large Angle Stability (3 pages)

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## Quiz: Hydrostatic, Small and Large Angle Stability

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## Quiz: Hydrostatic, Small and Large Angle Stability

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Pages:
3
School:
Massachusetts Institute of Technology
Course:
2 996 - Advanced Topics in Mechanical Engineering
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13 734 Sailing Yacht Design Fall 2003 October 3rd 2003 Quiz closed book Hydrostatic Small and Large Angle Stability Problem 1 Consider a box shaped barge that is 100 m long 20 m in total breadth 10 m tall and with a draft of 4 m The center of gravity is at amidships and on centerline at a height of 6 m above the keel The barge is floating in water with a mass density of 1025 kg m3 A Determine the heeling moment to heel the barge by 10 degrees B At what angle of heel c does one of the lower long edges of the barge come into contact with the water surface C Determine the exact righting moment of the fluid on the barge based on the actual position of the center of gravity and the center of buoyancy at 25 of heel Hint c is less than 25 which means that the lower corner is out of the water and the immersed shape looks like a triangle D If 106 Kg are placed in the center of the deck of the upright barge how much does the barge sink E If the 106 Kg on the deck are moved 2 m athwartships what is the barge heel angle Report your result in the following table Results A Heeling Moment 10 deg Nm B Heel angle C deg C Exact Righting Moment 25 deg Nm D Sinkage m E Heel angle deg Table 1 Results Problem 2 In this problem you are asked to calculate hydrostatic parameters and small angle stability for a sailing yacht starting from the data in Table 2 which contains the sectional areas AS vertical position of each section Z0 with respect to the DWL a negative value means below and half beam Y0 at DWL for 11 equally spaced stations x is positive forward Do all the integrations with a hand calculator using Simpson s rule A For a canoe body draft TC 0 47 m which is achieved considering the weight of the canoe body and the keel find the waterline length LWL the waterline beam BWL the canoe body volume C the canoe body displacement C consider salt water with density 1025 Kg m3 the block coefficient CB and the prismatic coefficient CP B Determine the waterplane area AWP the transverse

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