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MIT2_017JF09_p40

# MIT2_017JF09_p40 - 40 METACENTRIC HEIGHT OF A CATAMARAN 40...

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40 METACENTRIC HEIGHT OF A CATAMARAN 164 40 Metacentric Height of a Catamaran Consider the roll stability of a catamaran described as follows: total beam is 6 b , where b is the beam of each hull, the draft is T , and each hull is rectangular in cross-section. 1. What is the distance KM for this section, at small roll angles? You may approximate the area of the ”buoyancy wedges” as the mean height times the width. The differential moment is as follows: 5 5 b 2 θ × dM = 2 × b × ρg dx, 2 2 where the terms separated by the × symbol are for: two wedges, the area enclosed in each wedge (approximation), the moment arm of each wedge, density and gravity and the differential length. We know that ρgd ( KM ) θ = dM , which leads directly to 25 b 2 KM = . 4 T There is an additional term T/ 2 (as in the case of monohulls) but this is very small by comparison for a catamaran. 2. What is KM for a single block of draft T and beam 2 b ?

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MIT2_017JF09_p40 - 40 METACENTRIC HEIGHT OF A CATAMARAN 40...

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