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Square–cube Law
The square–cube law (or cube–square law) is a mathematical principle, applied in a variety of scientific fields, which describes the relationship between the volume and the surface area as a shape's size increases or decreases. It was first described in 1638 by Galileo Galilei in his ''Two New Sciences'' as the "...ratio of two volumes is greater than the ratio of their surfaces". This principle states that, as a shape grows in size, its volume grows faster than its surface area. When applied to the real world, this principle has many implications which are important in fields ranging from mechanical engineering to biomechanics. It helps explain phenomena including why large mammals like elephants have a harder time cooling themselves than small ones like mice, and why building taller and taller skyscrapers is increasingly difficult. Description The square–cube law can be stated as follows: Represented mathematically: A_2=A_1\left(\frac\right)^2 where A_1 is the origina ...
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Galileo Galilei, Discorsi E Dimostrazioni Matematiche Intorno A Due Nuove Scienze, 1638 (1400x1400)
Galileo di Vincenzo Bonaiuti de' Galilei (15 February 1564 – 8 January 1642) was an Italian astronomer, physicist and engineer, sometimes described as a polymath. Commonly referred to as Galileo, his name was pronounced (, ). He was born in the city of Pisa, then part of the Duchy of Florence. Galileo has been called the "father" of observational astronomy, modern physics, the scientific method, and modern science. Galileo studied speed and velocity, gravity and free fall, the principle of relativity, inertia, projectile motion and also worked in applied science and technology, describing the properties of pendulums and "hydrostatic balances". He invented the thermoscope and various sector (instrument), military compasses, and used the telescope for scientific observations of celestial objects. His contributions to observational astronomy include telescopic confirmation of the phases of Venus, observation of the Galilean Moons, four largest satellites of Jupiter, obse ...
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Expander Cycle
The expander cycle is a power cycle of a bipropellant rocket engine. In this cycle, the fuel is used to cool the engine's combustion chamber, picking up heat and changing phase. The now heated and gaseous fuel then powers the turbine that drives the engine's fuel and oxidizer pumps before being injected into the combustion chamber and burned. Because of the necessary phase change, the expander cycle is thrust limited by the square–cube law. When a bell-shaped nozzle is scaled, the nozzle surface area with which to heat the fuel increases as the square of the radius, but the volume of fuel to be heated increases as the cube of the radius. Thus beyond approximately 300 kN (70,000 lbf) of thrust, there is no longer enough nozzle area to heat enough fuel to drive the turbines and hence the fuel pumps. Higher thrust levels can be achieved using a bypass expander cycle where a portion of the fuel bypasses the turbine and or thrust chamber cooling passages and goes directly to the ma ...
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King Kong
King Kong is a fictional giant monster resembling a gorilla, who has appeared in various media since 1933. He has been dubbed The Eighth Wonder of the World, a phrase commonly used within the franchise. His first appearance was in the novelization of the 1933 film ''King Kong (1933 film), King Kong'' from RKO Pictures, with the film premiering a little over two months later. Upon its initial release and subsequent re-releases, the film received universal acclaim. A sequel quickly followed that same year with ''Son of Kong, The Son of Kong'', featuring Little Kong. Toho produced ''King Kong vs. Godzilla'' (1962) featuring a giant Kong battling Toho's Godzilla and ''King Kong Escapes'' (1967), a film loosely based on Rankin/Bass Animated Entertainment, Rankin/Bass' ''The King Kong Show'' (1966-1969). In 1976, Dino De Laurentiis produced a King Kong (1976 film), modern remake of the original film directed by John Guillermin. A sequel, ''King Kong Lives'', followed a decade later fea ...
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Godzilla
is a fictional monster, or '' kaiju'', originating from a series of Japanese films. The character first appeared in the 1954 film ''Godzilla'' and became a worldwide pop culture icon, appearing in various media, including 32 films produced by Toho, four American films and numerous video games, novels, comic books and television shows. Godzilla has been dubbed the "King of the Monsters", a phrase first used in ''Godzilla, King of the Monsters!'' (1956)'','' the Americanized version of the original film. Godzilla is an enormous, destructive, prehistoric sea monster awakened and empowered by nuclear radiation. With the nuclear bombings of Hiroshima and Nagasaki and the '' Lucky Dragon 5'' incident still fresh in the Japanese consciousness, Godzilla was conceived as a metaphor for nuclear weapons. Others have suggested that Godzilla is a metaphor for the United States, a giant beast woken from its slumber which then takes terrible vengeance on Japan. As the film series expan ...
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Allegory
As a literary device or artistic form, an allegory is a narrative or visual representation in which a character, place, or event can be interpreted to represent a hidden meaning with moral or political significance. Authors have used allegory throughout history in all forms of art to illustrate or convey complex ideas and concepts in ways that are comprehensible or striking to its viewers, readers, or listeners. Writers and speakers typically use allegories to convey (semi-)hidden or complex meanings through symbolic figures, actions, imagery, or events, which together create the moral, spiritual, or political meaning the author wishes to convey. Many allegories use personification of abstract concepts. Etymology First attested in English in 1382, the word ''allegory'' comes from Latin ''allegoria'', the latinisation of the Greek ἀλληγορία (''allegoría''), "veiled language, figurative", which in turn comes from both ἄλλος (''allos''), "another, different" ...
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Allometry
Allometry is the study of the relationship of body size to shape, anatomy, physiology and finally behaviour, first outlined by Otto Snell in 1892, by D'Arcy Thompson in 1917 in ''On Growth and Form'' and by Julian Huxley in 1932. Overview Allometry is a well-known study, particularly in statistical shape analysis for its theoretical developments, as well as in biology for practical applications to the differential growth rates of the parts of a living organism's body. One application is in the study of various insect species (e.g., Hercules beetles), where a small change in overall body size can lead to an enormous and disproportionate increase in the dimensions of appendages such as legs, antennae, or horns The relationship between the two measured quantities is often expressed as a power law equation (Allometric equation) which expresses a remarkable scale symmetry: : y = kx^a \,\! or in a logarithmic form: : \log y = a \log x + \log k\,\! or similarly \ln y = a \ln x ...
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Terminal Velocity
Terminal velocity is the maximum velocity (speed) attainable by an object as it falls through a fluid (air is the most common example). It occurs when the sum of the drag force (''Fd'') and the buoyancy is equal to the downward force of gravity (''FG'') acting on the object. Since the net force on the object is zero, the object has zero acceleration. In fluid dynamics an object is moving at its terminal velocity if its speed is constant due to the restraining force exerted by the fluid through which it is moving. As the speed of an object increases, so does the drag force acting on it, which also depends on the substance it is passing through (for example air or water). At some speed, the drag or force of resistance will equal the gravitational pull on the object (buoyancy is considered below). At this point the object stops accelerating and continues falling at a constant speed called the terminal velocity (also called settling velocity). An object moving downward faster than ...
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Lift (force)
A fluid flowing around an object exerts a force on it. Lift is the component of this force that is perpendicular to the oncoming flow direction. It contrasts with the drag force, which is the component of the force parallel to the flow direction. Lift conventionally acts in an upward direction in order to counter the force of gravity, but it can act in any direction at right angles to the flow. If the surrounding fluid is air, the force is called an aerodynamic force. In water or any other liquid, it is called a hydrodynamic force. Dynamic lift is distinguished from other kinds of lift in fluids. Aerostatic lift or buoyancy, in which an internal fluid is lighter than the surrounding fluid, does not require movement and is used by balloons, blimps, dirigibles, boats, and submarines. Planing lift, in which only the lower portion of the body is immersed in a liquid flow, is used by motorboats, surfboards, windsurfers, sailboats, and water-skis. Overview A fluid flowing arou ...
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Structural Engineering
Structural engineering is a sub-discipline of civil engineering in which structural engineers are trained to design the 'bones and muscles' that create the form and shape of man-made structures. Structural engineers also must understand and calculate the stability, strength, rigidity and earthquake-susceptibility of built structures for buildings and nonbuilding structures. The structural designs are integrated with those of other designers such as architects and building services engineer and often supervise the construction of projects by contractors on site. They can also be involved in the design of machinery, medical equipment, and vehicles where structural integrity affects functioning and safety. See glossary of structural engineering. Structural engineering theory is based upon applied physical laws and empirical knowledge of the structural performance of different materials and geometries. Structural engineering design uses a number of relatively simple structural c ...
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Aerostats
An aerostat (, via French) is a lighter-than-air aircraft that gains its lift through the use of a buoyant gas. Aerostats include unpowered balloons and powered airships. A balloon may be free-flying or tethered. The average density of the craft is lower than the density of atmospheric air, because its main component is one or more gasbags, a lightweight skin containing a lifting gas (which could be heated air or any gas of lower density than air) to provide buoyancy, to which other components such as a gondola containing equipment or people are attached. Especially with airships, the gasbags are often protected by an outer envelope. Aerostats are so named because they use aerostatic lift which is a buoyant force that does not require movement through the surrounding air mass, resulting in VTOL ability. This contrasts with the heavy aerodynes that primarily use aerodynamic lift which requires the movement of a wing surface through the surrounding air mass. The term has also be ...
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Sloop
A sloop is a sailboat with a single mast typically having only one headsail in front of the mast and one mainsail aft of (behind) the mast. Such an arrangement is called a fore-and-aft rig, and can be rigged as a Bermuda rig with triangular sails fore and aft, or as a gaff-rig with triangular foresail(s) and a gaff rigged mainsail. Sailboats can be classified according to type of rig, and so a sailboat may be a sloop, catboat, cutter, ketch, yawl, or schooner. A sloop usually has only one headsail, although an exception is the Friendship sloop, which is usually gaff-rigged with a bowsprit and multiple headsails. If the vessel has two or more headsails, the term cutter may be used, especially if the mast is stepped further towards the back of the boat. When going before the wind, a sloop may carry a square-rigged topsail which will be hung from a topsail yard and be supported from below by a crossjack. This sail often has a large hollow foot, and this foot is sometimes fil ...
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Clipper
A clipper was a type of mid-19th-century merchant sailing vessel, designed for speed. Clippers were generally narrow for their length, small by later 19th century standards, could carry limited bulk freight, and had a large total sail area. "Clipper" does not refer to a specific sailplan; clippers may be schooners, brigs, brigantines, etc., as well as full-rigged ships. Clippers were mostly constructed in British and American shipyards, although France, Brazil, the Netherlands and other nations also produced some. Clippers sailed all over the world, primarily on the trade routes between the United Kingdom and China, in transatlantic trade, and on the New York-to-San Francisco route around Cape Horn during the California Gold Rush. Dutch clippers were built beginning in the 1850s for the tea trade and passenger service to Java. The boom years of the clipper era began in 1843 in response to a growing demand for faster delivery of tea from China. This continued under the stim ...
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