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Prismatic coefficient (C p) is the volume (V) divided by L WL x A x. It displays the ratio of the immersed volume of the hull to a volume of a prism with equal length to the ship and cross-sectional area equal to the largest underwater section of the hull (midship section). This is used to evaluate the distribution of the volume of the underbody.
The total amount of water to be displaced by a moving hull, and thus causing wave making drag, is the cross sectional area of the hull times distance the hull travels, and will not remain the same when prismatic coefficient is increased for the same lwl and same displacement and same speed.
In 1820, the French engineer A. Duleau derived analytically that the torsion constant of a beam is identical to the second moment of area normal to the section J zz, which has an exact analytic equation, by assuming that a plane section before twisting remains planar after twisting, and a diameter remains a straight line.
Hull speed can be calculated by the following formula: where is the length of the waterline in feet, and is the hull speed of the vessel in knots. If the length of waterline is given in metres and desired hull speed in knots, the coefficient is 2.43 kn·m −½.
However, in cases of non-prismatic members, such as the case of the tapered beams or columns or notched stair stringers, the flexural rigidity will vary along the length of the beam as well. The flexural rigidity, moment, and transverse displacement are related by the following equation along the length of the rod, x {\displaystyle x} :
The squat effect is the hydrodynamic phenomenon by which a vessel moving through shallow water creates an area of reduced pressure that causes the ship to increase its draft (alternatively decrease the underkeel clearance of the vessel in marine terms) and thereby be closer to the seabed than would otherwise be expected.
Above – in the momentum equation in conservation form – A, I 1 and I 2 are evaluated at σ = h(x,t). The term g I 1 describes the hydrostatic force in a certain cross section. And, for a non-prismatic channel, g I 2 gives the effects of geometry variations along the channel axis x.
The resulting equation is of fourth order but, unlike Euler–Bernoulli beam theory, there is also a second-order partial derivative present. Physically, taking into account the added mechanisms of deformation effectively lowers the stiffness of the beam, while the result is a larger deflection under a static load and lower predicted ...