MIT 2 996 - Quiz: Hydrostatic, Small and Large Angle Stability

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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, φc 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: φc 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 A.Heeling Moment(10 deg) = NmB.Heel angle φC =degC.Exact Righting Moment(25 deg) = NmD.Sinkage = mE.Heel angle = degResults 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 0.47CT=m, which is achieved considering the weight of the canoe body and the keel, find the waterline length , the waterline beam WLLWLB, the canoe body volume C∇, the canoe body displacement (consider salt water with density C∆1025ρ= Kg/m3), the block coefficient C , and the prismatic coefficient BPC . B. Determine the waterplane area , the transverse moment of inertia IWPAXX of the waterplane, the vertical center of buoyancy VCBC, and the metacentric height GMC for the canoe body. The vertical center of gravity of the canoe body VCGC 0.1 m above DWL. Position XSect. Area ASCenter Z0Y0 @ DWL[m][m2][m] [m]Station 06.40 0.000 0.000 0Station 15.12 0.113 -0.092 0.347Station 23.84 0.384 -0.139 0.773Station 32.56 0.736 -0.171 1.187Station 41.28 1.080 -0.191 1.53Station 50 1.308 -0.197 1.763Station 6-1.28 1.338 -0.194 1.828Station 7-2.56 1.175 -0.178 1.774Station 8-3.84 0.830 -0.134 1.655Station 9-5.12 0.370 -0.074 1.379Station 10-6.4 0.000 0.000 0 Table 2 Canoe Body data.C. Let’s now add a keel to the design (for simplicity the rudder is neglected). The data for the lead-filled keel are given in Table 3. Mass4015.0 kg∆374.45 kgVolume0.365m3LCB0.462 mVCB-1.784 mVCG-1.784 mKeel Data Table 3 Keel Data. Now for the appended boat, calculate the total displacement , the vertical position of the center of gravity VCGTot∆Tot, the vertical position of the center of buoyancy VCBTot, and the metacentric height GMTot. D. Report your results in the following table ∆C KgCBAWP m2VolC m3CP∆Tot KgTC mIXX m4VolTot m3LWL mVCGC mVCBTot mBWL mGMC mGMTot mVCBC mResults Table 4


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MIT 2 996 - Quiz: Hydrostatic, Small and Large Angle Stability

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