By E. C. Tupper
''..a transparent and concise advent to the topic, giving a great clutch of the fundamentals of naval architecture.''
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Additional info for Introduction to Naval Architecture
Introduction to Naval Architecture. 00005-9 © 2013 Eric Tupper. Published by Elsevier Ltd. All rights reserved. 63 64 Introduction to Naval Architecture In waves the ship’s underwater form and the waterline shape will be constantly changing. It will be acted on by wave and wind forces. Because many of these forces are cyclic in nature their periods relative to the natural frequencies of the ship’s motion are important and resonance may greatly magnify the resulting motions. In trying to meet the aim of surviving an accident, the above uncertainties apply to the conditions at the time of the incident.
It is convenient to choose the origin to be at the base of y1 to simplify the algebra but the results would be the same wherever the origin is taken. 3 Simpson’s first rule. y2 h 2h 36 Introduction to Naval Architecture Now the three ordinates defining the curve are: y 0 5 a0 2 a 1 h 1 a2 h2 2 a3 h3 y 1 5 a0 y 2 5 a0 1 a 1 h 1 a2 h2 1 a3 h3 It would be convenient to be able to express the area of the figure as a simple sum of the ordinates each multiplied by some factor to be determined. Assuming that A can be represented by: A 5 Fy0 1 Gy1 1 Hy2 then: A 5 ðF 1 G 1 HÞa0 À ðF À HÞa1 h 1 ðF 1 HÞa2 h2 À ðF À HÞa3 h3 5 2a0 h 1 2a2 h3 =3 These equations are satisfied by: F 5 H 5 h=3 and G 5 4h=3 Hence: A5 h ðy0 1 4y1 1 y2 Þ 3 This is known as Simpson’s First Rule or 3 Ordinate Rule.
The calculated draughts at each section can be set upon the Bonjean curves and the immersed areas read off. The immersed volume and position of the centre of buoyancy can be found by approximate integration. For equilibrium, the centre of gravity and centre of buoyancy must be in the same vertical line and the position of the centre of gravity follows. Using the density of water in which the ship is floating, the displacement can be determined. 13 a ship is shown upright and at rest in still water.