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Where RM is the righting moment, GZ is the righting arm and Δ is the displacement. Because the vessel displacement is constant, common practice is to simply graph the righting arm vs the angle of heel. The righting arm (known also as GZ — see diagram): the horizontal distance between the lines of buoyancy and gravity. [2]
The vessel is in normal operational configuration. The hull is not breached in any compartment. The vessel will be expected to meet various stability criteria such as GMt (metacentric height), area under the GZ (righting lever) curve, range of stability, trim, etc.
The normal distribution, also called the Gaussian or the bell curve. It is ubiquitous in nature and statistics due to the central limit theorem : every variable that can be modelled as a sum of many small independent, identically distributed variables with finite mean and variance is approximately normal.
Simpson's rules are a set of rules used in ship stability and naval architecture, to calculate the areas and volumes of irregular figures. [1] This is an application of Simpson's rule for finding the values of an integral, here interpreted as the area under a curve.
This is a list of Wikipedia articles about curves used in different fields: mathematics (including geometry, statistics, and applied mathematics), ...
In fluid dynamics, the Graetz number (Gz) is a dimensionless number that characterizes laminar flow in a conduit. The number is defined as: [1] = where D H is the diameter in round tubes or hydraulic diameter in arbitrary cross-section ducts
Angle of loll is the state of a ship that is unstable when upright (i.e. has a negative metacentric height) and therefore takes on an angle of heel to either port or starboard.
In sailing, the limit of positive stability (LPS) or angle of vanishing stability (AVS) is the angle from the vertical at which a boat will no longer stay upright but will capsize, becoming inverted, or turtled.