Page:Self-righting boat design.pdf/4

 motions, and high values at very large angles of heel (above 90 degrees) result in a violent righting action. The combined requirements of safety and comfort suggest that it should be possible to define an ideal GZ curve, or more realistically an acceptable stability envelope, with minimum values defined by the safety criteria, and maximum values by reference to acceptable motions. It can be proposed the probable form of a stability envelope intended to be used as a design objective. If the objective of a design for stability exercise is to create a vessel that has a GZ curve that lies within a defined envelope, then we have to be able to directly control the shape of the curve. Analysis of the stability of a vessel based on the righting lever arm over the entire range of angles of heel, the GZ curve, has its limits. Despite the limitations of parametric rolling, surf riding, broaching, effects of heave accelerations on the righting moment and the impact of a wave waterline on the behavior of the vessel, it is a valuable model of many aspects of the behavior of a vessel and the sufficiency of the stability of all types of craft.

Reserve stability can be evaluated though a curve of righting arms, also called stability curve, which plots the righting arm GZ, against heel angle. As long as GZ is positive, the boat will self-right. At the angle the GZ turns negative, the boat will capsize. This shows immediately as the range of stability. The curve also shows other important things. The area under the positive portion of the righting arm curve represent the energy required to capsize the boat. The more energy required, the stronger the wind gust and the more sustained it must be to create a capsize. Alternately, the bigger and faster moving the wave must be to capsize the boat. Similarly, the area under the negative side of the curve represents the energy required to re-right a boat once it’s been capsized.

In this case, there are three different ship conditions in the following:

a) A ship with positive GM: In this condition, the center of gravity is below the metacenter point sothatso that [sic] a righting arm will begin to develop as soon as the ship heels over. b) A ship with zero GM: In this condition, the center of gravity coincides with the ship metacenter point, in other words, there is zero distance between two points. That is, there is no internal couple created to return the ship to upright position.