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Simpson's Rules (ship Stability)
Simpson's rules are a set of rules used in ship stability and naval architecture, to calculate the areas and volumes of irregular figures. This is an application of Simpson's rule for finding the values of an integral, here interpreted as the area under a curve. Simpson's 1st rule Also known as the 1–4–1 rule (after the multipliers used ). : \text = \frac( a + 4b + c). Simpson's 2nd rule Also known as the 1–3–3–1 rule, Simpson's second rule is a simplified version of Simpson Rule, Simpson's 3/8 rule. : \text = \frac 8 (a + 3b + 3c + d). Simpson's 3rd rule Also known as the 5–8–1 rule, SImpson's third rule is used to find the area between two consecutive ordinates when three consecutive ordinates are known. : \text = \frac h (5a + 8b - c ). This estimates the area in the left half of the figure for Simpson's 1st Rule while using all three pieces of data. Use of Simpsons rules Simpson's rules are used to calculate the volume of lifeboat (shipb ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Naval Architecture
Naval architecture, or naval engineering, is an engineering discipline incorporating elements of mechanical, electrical, electronic, software and safety engineering as applied to the engineering design process, shipbuilding, maintenance, and operation of marine vessels and structures. Naval architecture involves basic and applied research, design, development, design evaluation (classification) and calculations during all stages of the life of a marine vehicle. Preliminary design of the vessel, its detailed design, construction, trials, operation and maintenance, launching and dry-docking are the main activities involved. Ship design calculations are also required for ships being modified (by means of conversion, rebuilding, modernization, or repair). Naval architecture also involves formulation of safety regulations and damage-control rules and the approval and certification of ship designs to meet statutory and non-statutory requirements. Main subjects The word "vessel" in ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Area
Area is the quantity that expresses the extent of a region on the plane or on a curved surface. The area of a plane region or ''plane area'' refers to the area of a shape A shape or figure is a graphics, graphical representation of an object or its external boundary, outline, or external Surface (mathematics), surface, as opposed to other properties such as color, Surface texture, texture, or material type. A pl ... or planar lamina, while ''surface area'' refers to the area of an open surface or the boundary (mathematics), boundary of a solid geometry, three-dimensional object. Area can be understood as the amount of material with a given thickness that would be necessary to fashion a model of the shape, or the amount of paint necessary to cover the surface with a single coat. It is the two-dimensional analogue of the length of a plane curve, curve (a one-dimensional concept) or the volume of a solid (a three-dimensional concept). The area of a shape can be measured by com ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Volumes
Volume is a measure of occupied three-dimensional space. It is often quantified numerically using SI derived units (such as the cubic metre and litre) or by various imperial or US customary units (such as the gallon, quart, cubic inch). The definition of length (cubed) is interrelated with volume. The volume of a container is generally understood to be the capacity of the container; i.e., the amount of fluid (gas or liquid) that the container could hold, rather than the amount of space the container itself displaces. In ancient times, volume is measured using similar-shaped natural containers and later on, standardized containers. Some simple three-dimensional shapes can have its volume easily calculated using arithmetic formulas. Volumes of more complicated shapes can be calculated with integral calculus if a formula exists for the shape's boundary. Zero-, one- and two-dimensional objects have no volume; in fourth and higher dimensions, an analogous concept to the normal volu ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Simpson's Rule
In numerical integration, Simpson's rules are several approximations for definite integrals, named after Thomas Simpson (1710–1761). The most basic of these rules, called Simpson's 1/3 rule, or just Simpson's rule, reads \int_a^b f(x) \, dx \approx \frac \left (a) + 4f\left(\frac\right) + f(b)\right In German and some other languages, it is named after Johannes Kepler, who derived it in 1615 after seeing it used for wine barrels (barrel rule, ). The approximate equality in the rule becomes exact if is a polynomial up to and including 3rd degree. If the 1/3 rule is applied to ''n'' equal subdivisions of the integration range 'a'', ''b'' one obtains the composite Simpson's 1/3 rule. Points inside the integration range are given alternating weights 4/3 and 2/3. Simpson's 3/8 rule, also called Simpson's second rule, requires one more function evaluation inside the integration range and gives lower error bounds, but does not improve on order of the error. If the 3/8 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Integral
In mathematics Mathematics is an area of knowledge that includes the topics of numbers, formulas and related structures, shapes and the spaces in which they are contained, and quantities and their changes. These topics are represented in modern mathematics ..., an integral assigns numbers to functions in a way that describes Displacement (geometry), displacement, area, volume, and other concepts that arise by combining infinitesimal data. The process of finding integrals is called integration. Along with Derivative, differentiation, integration is a fundamental, essential operation of calculus,Integral calculus is a very well established mathematical discipline for which there are many sources. See and , for example. and serves as a tool to solve problems in mathematics and physics involving the area of an arbitrary shape, the length of a curve, and the volume of a solid, among others. The integrals enumerated here are those termed definite integrals, which can be int ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Simpson2rule
Simpson most often refers to: * Simpson (name), a British surname *''The Simpsons'', an animated American sitcom **The Simpson family, central characters of the series ''The Simpsons'' Simpson may also refer to: Organizations Schools * Simpson College, in Indianola, Iowa *Simpson University, in Redding, California Businesses *Simpson (appliance manufacturer), former manufacturer and brand of whitegoods in Australia *Simpson Investment Company, an American holding company, formerly a forest products manufacturer *Simpson Manufacturing Company, an engineering firm and building materials producer in the United States *Simpson Performance Products, an American motorsports parts supplier *Simpson Thacher & Bartlett, a law firm * Simpsons (department store), a defunct Canadian department store *Simpsons of Piccadilly, a defunct clothing store in London *Simpson's-in-the-Strand, one of London's oldest traditional English restaurants Places Australia *Simpson, Northern Territory, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Simpson Rule
In numerical integration, Simpson's rules are several approximations for definite integrals, named after Thomas Simpson (1710–1761). The most basic of these rules, called Simpson's 1/3 rule, or just Simpson's rule, reads \int_a^b f(x) \, dx \approx \frac \left[f(a) + 4f\left(\frac\right) + f(b)\right]. In German and some other languages, it is named after Johannes Kepler, who derived it in 1615 after seeing it used for wine barrels (barrel rule, ). The approximate equality in the rule becomes exact if is a polynomial up to and including 3rd degree. If the 1/3 rule is applied to ''n'' equal subdivisions of the integration range [''a'', ''b''], one obtains the #Composite Simpson's 1/3 rule, composite Simpson's 1/3 rule. Points inside the integration range are given alternating weights 4/3 and 2/3. #Simpson's 3/8 rule, Simpson's 3/8 rule, also called Simpson's second rule, requires one more function evaluation inside the integration range and gives lower error bounds, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Lifeboat (shipboard)
A lifeboat or liferaft is a small, rigid or inflatable boat carried for emergency evacuation in the event of a disaster aboard a ship. Lifeboat drills are required by law on larger commercial ships. Rafts (liferafts) are also used. In the military, a lifeboat may double as a whaleboat, dinghy, or gig. The ship's tenders of cruise ships often double as lifeboats. Recreational sailors usually carry inflatable liferafts, though a few prefer small proactive lifeboats that are harder to sink and can be sailed to safety. Inflatable lifeboats may be equipped with auto-inflation (carbon dioxide or nitrogen) canisters or mechanical pumps. A quick release and pressure release mechanism is fitted on ships so that the canister or pump automatically inflates the lifeboat, and the lifeboat breaks free of the sinking vessel. Commercial aircraft are also required to carry auto-inflating liferafts in case of an emergency water landing; offshore oil platforms also have liferafts. Ship-launche ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Sludge
Sludge is a semi-solid slurry that can be produced from a range of industrial processes, from water treatment, wastewater treatment or on-site sanitation systems. For example, it can be produced as a settled suspension obtained from conventional drinking water treatment, as sewage sludge from wastewater treatment processes or as fecal sludge from pit latrines and septic tanks. The term is also sometimes used as a generic term for solids separated from suspension in a liquid; this 'soupy' material usually contains significant quantities of 'interstitial' water (between the solid particles). Sludge can consist of a variety of particles, such as animal manure. Industrial wastewater treatment plants produce solids that are also referred to as sludge. This can be generated from biological or physical-chemical processes. In the activated sludge process for wastewater treatment, the terms "waste activated sludge" and "return activated sludge" are used. In food processing and bevera ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
