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Response Amplitude Operator
In the field of ship design and design of other floating structures, a response amplitude operator (RAO) is an engineering statistic, or set of such statistics, that are used to determine the likely behavior of a ship when operating at sea. Known by the acronym of ''RAO'', response amplitude operators are usually obtained from models of proposed ship designs tested in a model basin, or from running specialized CFD computer programs, often both. RAOs are usually calculated for all ship motions and for all wave headings. Usage RAOs are effectively transfer functions used to determine the effect that a sea state will have upon the motion of a ship through the water, and therefore, for example, whether or not (in the case of cargo vessels) the addition of cargo to the vessel will require measures to be taken to improve stability and prevent the cargo from shifting within the vessel. Generation of extensive RAOs at the design phase allows shipbuilders to determine the modifications t ...
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Shipbuilding
Shipbuilding is the construction of ships and other floating vessels. It normally takes place in a specialized facility known as a shipyard. Shipbuilders, also called shipwrights, follow a specialized occupation that traces its roots to before recorded history. Shipbuilding and ship repairs, both commercial and military, are referred to as "naval engineering". The construction of boats is a similar activity called boat building. The dismantling of ships is called ship breaking. History Pre-history The earliest known depictions (including paintings and models) of shallow-water sailing boats is from the 6th to 5th millennium BC of the Ubaid period of Mesopotamia. They were made from bundled reeds coated in bitumen and had bipod masts. They sailed in shallow coastal waters of the Persian Gulf. 4th millennium BC Ancient Egypt Evidence from Ancient Egypt shows that the early Egyptians knew how to assemble planks of wood into a ship hull as early as 3100 BC. Egyptian potte ...
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Added Mass
In fluid mechanics, added mass or virtual mass is the inertia added to a system because an accelerating or decelerating body must move (or deflect) some volume of surrounding fluid as it moves through it. Added mass is a common issue because the object and surrounding fluid cannot occupy the same physical space simultaneously. For simplicity this can be modeled as some volume of fluid moving with the object, though in reality "all" the fluid will be accelerated, to various degrees. The dimensionless added mass coefficient is the added mass divided by the displaced fluid mass – i.e. divided by the fluid density times the volume of the body. In general, the added mass is a second-order tensor, relating the fluid acceleration vector to the resulting force vector on the body. Background Friedrich Bessel proposed the concept of added mass in 1828 to describe the motion of a pendulum in a fluid. The period of such a pendulum increased relative to its period in a vacuum (even after ac ...
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Cambridge University Press
Cambridge University Press is the university press of the University of Cambridge. Granted letters patent by Henry VIII of England, King Henry VIII in 1534, it is the oldest university press A university press is an academic publishing house specializing in monographs and scholarly journals. Most are nonprofit organizations and an integral component of a large research university. They publish work that has been reviewed by schola ... in the world. It is also the King's Printer. Cambridge University Press is a department of the University of Cambridge and is both an academic and educational publisher. It became part of Cambridge University Press & Assessment, following a merger with Cambridge Assessment in 2021. With a global sales presence, publishing hubs, and offices in more than 40 Country, countries, it publishes over 50,000 titles by authors from over 100 countries. Its publishing includes more than 380 academic journals, monographs, reference works, school and uni ...
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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 ...
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Ship Design
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 ...
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Imaginary Unit
The imaginary unit or unit imaginary number () is a solution to the quadratic equation x^2+1=0. Although there is no real number with this property, can be used to extend the real numbers to what are called complex numbers, using addition and multiplication. A simple example of the use of in a complex number is 2+3i. Imaginary numbers are an important mathematical concept; they extend the real number system \mathbb to the complex number system \mathbb, in which at least one root for every nonconstant polynomial exists (see Algebraic closure and Fundamental theorem of algebra). Here, the term "imaginary" is used because there is no real number having a negative square. There are two complex square roots of −1: and -i, just as there are two complex square roots of every real number other than zero (which has one double square root). In contexts in which use of the letter is ambiguous or problematic, the letter or the Greek \iota is sometimes used instead. For example, ...
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Harmonic Oscillator
In classical mechanics, a harmonic oscillator is a system that, when displaced from its Mechanical equilibrium, equilibrium position, experiences a restoring force ''F'' Proportionality (mathematics), proportional to the displacement ''x'': \vec F = -k \vec x, where ''k'' is a positive coefficient, constant. If ''F'' is the only force acting on the system, the system is called a simple harmonic oscillator, and it undergoes simple harmonic motion: sinusoidal oscillations about the equilibrium point, with a constant amplitude and a constant frequency (which does not depend on the amplitude). If a frictional force (Damping ratio, damping) proportional to the velocity is also present, the harmonic oscillator is described as a damped oscillator. Depending on the friction coefficient, the system can: * Oscillate with a frequency lower than in the Damping ratio, undamped case, and an amplitude decreasing with time (Damping ratio, underdamped oscillator). * Decay to the equilibrium p ...
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Linear Differential Equation
In mathematics, a linear differential equation is a differential equation that is defined by a linear polynomial in the unknown function and its derivatives, that is an equation of the form :a_0(x)y + a_1(x)y' + a_2(x)y'' \cdots + a_n(x)y^ = b(x) where and are arbitrary differentiable functions that do not need to be linear, and are the successive derivatives of an unknown function of the variable . Such an equation is an ordinary differential equation (ODE). A ''linear differential equation'' may also be a linear partial differential equation (PDE), if the unknown function depends on several variables, and the derivatives that appear in the equation are partial derivatives. A linear differential equation or a system of linear equations such that the associated homogeneous equations have constant coefficients may be solved by quadrature, which means that the solutions may be expressed in terms of integrals. This is also true for a linear equation of order one, with non-con ...
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Boundary Element Method
The boundary element method (BEM) is a numerical computational method of solving linear partial differential equations which have been formulated as integral equations (i.e. in ''boundary integral'' form), including fluid mechanics, acoustics, electromagnetics (where the technique is known as Method of moments (electromagnetics), method of moments or abbreviated as MoM), fracture mechanics, and contact mechanics. Mathematical basis The integral equation may be regarded as an exact solution of the governing partial differential equation. The boundary element method attempts to use the given boundary conditions to fit boundary values into the integral equation, rather than values throughout the space defined by a partial differential equation. Once this is done, in the post-processing stage, the integral equation can then be used again to calculate numerically the solution directly at any desired point in the interior of the solution domain. BEM is applicable to problems for which G ...
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Strip Theory
Strip or Stripping may refer to: Places * Aouzou Strip, a strip of land following the northern border of Chad that had been claimed and occupied by Libya * Caprivi Strip, narrow strip of land extending from the Okavango Region of Namibia to the Zambezi River * Gaza Strip, narrow strip of land along the Mediterranean, in the Middle East * Las Vegas Strip, section of Las Vegas Boulevard South * Strip District, Pittsburgh, a neighborhood in Pittsburgh, Pennsylvania * Sunset Strip, 1.5-mile stretch of Sunset Boulevard in West Hollywood, California, US * Tarfaya Strip (Cape Juby Strip), a strip of land between Morocco and the Western Sahara along the Atlantic ocean * Toledo strip, formerly contested area between Ohio and Michigan; see Toledo War Arts, entertainment, and media Comics * Strip (comics), a comics anthology published by Marvel UK in 1990 * Comic strip, a sequence of drawings arranged in interrelated panels to display brief humor or form a narrative * Sunday strip, a ...
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Ship Motions
Ship motions are defined by the six degrees of freedom that a ship, boat or any other craft can experience. Reference axes The '' vertical/Z axis'', or ''yaw axis'', is an imaginary line running vertically through the ship and through its centre of mass . A yaw motion is a side-to side movement of the bow and stern of the ship. The '' transverse/Y axis'', ''lateral axis'', or ''pitch axis'' is an imaginary line running horizontally across the ship and through the centre of mass. A pitch motion is an up-or-down movement of the bow and stern of the ship. The '' longitudinal/X axis'', or ''roll axis'', is an imaginary line running horizontally through the length of the ship, through its centre of mass, and parallel to the ''waterline''. A roll motion is a side-to-side or port-starboard tilting motion of the superstructure around this axis. Rotational There are three special axes in any ship, called longitudinal, transverse and vertical axes. The movements around them a ...
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Restoring Force
In physics, the restoring force is a force that acts to bring a body to its equilibrium position. The restoring force is a function only of position of the mass or particle, and it is always directed back toward the equilibrium position of the system. The restoring force is often referred to in simple harmonic motion. The force responsible for restoring original size and shape is called the restoring force. An example is the action of a spring. An idealized spring exerts a force proportional to the amount of deformation of the spring from its equilibrium length, exerted in a direction oppose the deformation. Pulling the spring to a greater length causes it to exert a force that brings the spring back toward its equilibrium length. The amount of force can be determined by multiplying the spring constant, characteristic of the spring, by the amount of stretch, also known as Hooke's Law. Another example is of a pendulum. When a pendulum is not swinging all the forces acting on i ...
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