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Simpson's rules are used to calculate the volume of lifeboats, [6] and by surveyors to calculate the volume of sludge in a ship's oil tanks. For instance, in the latter, Simpson's 3rd rule is used to find the volume between two co-ordinates. To calculate the entire area / volume, Simpson's first rule is used. [7]
Ship stability is an area of naval architecture and ship design that deals with how a ship behaves at sea, both in still water and in waves, whether intact or damaged. Stability calculations focus on centers of gravity , centers of buoyancy , the metacenters of vessels, and on how these interact.
In the diagram above, the two Bs show the centres of buoyancy of a ship in the upright and heeled conditions. The metacentre, M, is considered to be fixed relative to the ship for small angles of heel; however, at larger angles the metacentre can no longer be considered fixed, and its actual location must be found to calculate the ship's stability.
The formula above is obtained by combining the composite Simpson's 1/3 rule with the one consisting of using Simpson's 3/8 rule in the extreme subintervals and Simpson's 1/3 rule in the remaining subintervals. The result is then obtained by taking the mean of the two formulas.
For US waters, the US Code of Federal Regulations require ships and their masters to calculate UKC based on the ship's deepest navigational draft. 33 CFR 157.450 The regulations require the master to discuss the UKC calculation with the maritime pilot as the ship approaches US ports/waters. 33 CFR 157.450
Used mainly to determine the minimum water depth for safe passage of a vessel and to calculate the vessel's displacement (obtained from ship's stability tables) so as to determine the mass of cargo on board. Draft, Air – Air Draft/Draught is the distance from the water line to the highest point on a ship (including antennas) while it is ...
The stability conditions of watercraft are the various standard loading configurations to which a ship, boat, or offshore platform may be subjected. They are recognized by classification societies such as Det Norske Veritas , Lloyd's Register and American Bureau of Shipping (ABS).
A basic tool for calculating a vessel's stability is a static stability diagram, which plots the angle of heel on the horizontal axis and the righting lever (GZ) on the vertical axis. (see metacentric height for details). If the static stability curve never crosses the x-axis, the boat is not stable upside-down.