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HW-4A-2014

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  EMShip [Ship Theory] Home Work 4 Submission date: October 27, 2014 Numerical Values up to 3 decimal places only Units to be clearly noted if required Your answer script should have a clearly spelt Name and ID Question 1:  The GZ’s and angles of heel for a ship of 10,200 tonnes displacement, taken from the cross-curves for which the KG is 6 m, area as follows: GZ (m) 0.12 0.3 0.47 0.53 0.44 0.23 -0.06 θ  (deg) 10 20 30 40 50 60 70 Draw the curve of statical stability when KG = 6.25 m and metacentric height is 0.3 m. Specify the maximum GZ, the angle of maximum GZ and the range of stability. Ans: Max GZ= 0.39 m, Max GZ at 38 o  and range of stability 62 o  Question 2: A wall-sided ship in a certain condition of loading has a negative metacentric height of 76 mm.  The BM at this loading is 3.35 m. Estimate the angle of loll, and determine the positive metacentric height at that angle. Ans: Angle of loll = 12.025 o  and GM (positive) = 155 mm Question 3: A ship wall-sided ship at the waterline has a displacement of 10000 tonnes , a BM of 3 m and a GM of 0.15 m. Determine the angle of heel caused by shifting 100 tonnes transversely across the deck through 15 m. Ans: 21.45 o  Question 4: a)   A box shaped vessel length 100 m, breadth 10 m, depth 5 m displacing 2000 tonnes in FW has KG 4.5 m and is floating in fresh water. Find the initial GM of the barge and the GM after a weight of 500 tonnes is loaded at KG 4.0 m. Find the righting moment at 10 degrees of heel in both cases. b)   A vessel with 7250 displacement of tonnes (SW) has a KM 7.65m and a KG of 6.55m. A weight of 120 tonnes is shifted 2.25m to port and 3.9 m upwards. If the vessel is initially upright, calculate the resulting list.    Ans: Before loading GM 0.667 m, after loading GM 0.183 m, RM 231.647 t-m & 79.444 t-m List to port 2.06 o  Question 5:  The following is an extract from a vessels hydrostatics: Draft (m) TPC (tonne) 7 41.1 8 41.6 9 42.1 10 42.6 11 44.0 12 44.4 13 44.8 14 45.2  The displacement at a draft of 7 m is 14760 tonne. Calculate the displacement at a draft of 14 m and the vertical position of centre of buoyancy (VCB) at this draft if the VCB is 3.75 at the 7 m draft. Ans: ∆∆∆∆  = 45010 tonnes, VCB = 8.328 m above base Question 6: A box shaped vessel of L=55 m, B= 11.2m is floating at a draft of 2.75 m in sea water of ρ  = 1.026 t/m 3 . Find the TPC and MCTC of this vessel at this draft. Ans: TPC = 6.32 t/cm, MCTC =28.967 t-m/cm Question 7:  The water plane of a vessel is parabolic in nature where the length is 20 m and maximum breadth is 8 m at mid-ships. Find the TPC and MCTC at the water plane level. Assume ρ  = 1.025 t/m 3 . Ans: TPC = 1.093 tonne, MCTC = 1.089 t-m
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