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Joukowsky Transform
In applied mathematics, the Joukowsky transform (sometimes transliterated ''Joukovsky'', ''Joukowski'' or ''Zhukovsky'') is a conformal map historically used to understand some principles of airfoil design. It is named after Nikolai Zhukovsky, who published it in 1910. The transform is : z = \zeta + \frac, where z = x + iy is a complex variable in the new space and \zeta = \chi + i \eta is a complex variable in the original space. In aerodynamics, the transform is used to solve for the two-dimensional potential flow around a class of airfoils known as Joukowsky airfoils. A Joukowsky airfoil is generated in the complex plane (z-plane) by applying the Joukowsky transform to a circle in the \zeta-plane. The coordinates of the centre of the circle are variables, and varying them modifies the shape of the resulting airfoil. The circle encloses the point \zeta = -1 (where the derivative is zero) and intersects the point \zeta = 1. This can be achieved for any allowable centre p ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Complex Conjugate
In mathematics, the complex conjugate of a complex number is the number with an equal real part and an imaginary part equal in magnitude but opposite in sign. That is, if a and b are real numbers, then the complex conjugate of a + bi is a - bi. The complex conjugate of z is often denoted as \overline or z^*. In polar form, if r and \varphi are real numbers then the conjugate of r e^ is r e^. This can be shown using Euler's formula. The product of a complex number and its conjugate is a real number: a^2 + b^2 (or r^2 in polar coordinates). If a root of a univariate polynomial with real coefficients is complex, then its complex conjugate is also a root. Notation The complex conjugate of a complex number z is written as \overline z or z^*. The first notation, a vinculum, avoids confusion with the notation for the conjugate transpose of a matrix, which can be thought of as a generalization of the complex conjugate. The second is preferred in physics, where ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Conformal Mappings
Conformal may refer to: * Conformal (software), in ASIC Software * Conformal coating in electronics * Conformal cooling channel, in injection or blow moulding * Conformal field theory in physics, such as: ** Boundary conformal field theory ** Coset conformal field theory ** Logarithmic conformal field theory ** Rational conformal field theory * Conformal fuel tanks on military aircraft * Conformal hypergraph, in mathematics * Conformal geometry, in mathematics * Conformal group, in mathematics * Conformal map, in mathematics * Conformal map projection In cartography, a conformal map projection is one in which every angle between two curves that cross each other on Earth (a sphere or an ellipsoid) is preserved in the image of the projection; that is, the projection is a conformal map in the mat ..., in cartography * Conformal prediction, in computer science {{disambig ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
NASA
The National Aeronautics and Space Administration (NASA ) is an independent agencies of the United States government, independent agency of the federal government of the United States, US federal government responsible for the United States's civil list of government space agencies, space program, aeronautics research and outer space, space research. National Aeronautics and Space Act, Established in 1958, it succeeded the National Advisory Committee for Aeronautics (NACA) to give the American space development effort a distinct civilian orientation, emphasizing peaceful applications in space science. It has since led most of America's space exploration programs, including Project Mercury, Project Gemini, the 1968–1972 Apollo program missions, the Skylab space station, and the Space Shuttle. Currently, NASA supports the International Space Station (ISS) along with the Commercial Crew Program and oversees the development of the Orion (spacecraft), Orion spacecraft and the Sp ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hsue-shen Tsien
Qian Xuesen ( zh, s=钱学森; December 11, 1911October 31, 2009; also spelled as Tsien Hsue-shen) was a Chinese aerospace engineer and cyberneticist who made significant contributions to the field of aerodynamics and established engineering cybernetics. He achieved recognition as one of America's leading experts in rockets and high-speed flight theory prior to his deportation to China in 1955. Qian received his undergraduate education in mechanical engineering at National Chiao Tung University in Shanghai in 1934. He traveled to the United States in 1935 and attained a master's degree in aeronautical engineering at the Massachusetts Institute of Technology in 1936. Afterward, he joined Theodore von Kármán's group at the California Institute of Technology in 1936, received a doctorate in aeronautics and mathematics there in 1939, and became an associate professor at Caltech in 1943. While at Caltech, he co-founded NASA's Jet Propulsion Laboratory. He was recruited by the Un ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Right Hand Side
In mathematics, LHS is informal shorthand for the left-hand side of an equation. Similarly, RHS is the right-hand side. The two sides have the same value, expressed differently, since equality is symmetric. definition and example of abbreviation More generally, these terms may apply to an or ; the right-hand side is everything on the right side of a |
Tangent
In geometry, the tangent line (or simply tangent) to a plane curve at a given point is, intuitively, the straight line that "just touches" the curve at that point. Leibniz defined it as the line through a pair of infinitely close points on the curve. More precisely, a straight line is tangent to the curve at a point if the line passes through the point on the curve and has slope , where ''f'' is the derivative of ''f''. A similar definition applies to space curves and curves in ''n''-dimensional Euclidean space. The point where the tangent line and the curve meet or intersect is called the ''point of tangency''. The tangent line is said to be "going in the same direction" as the curve, and is thus the best straight-line approximation to the curve at that point. The tangent line to a point on a differentiable curve can also be thought of as a '' tangent line approximation'', the graph of the affine function that best approximates the original function at the given point ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Karman Trefftz Transform
Karman or Kármán is a Hungarian surname. Notable people with the surname include: * Harvey Karman (20th century), inventor of the Karman cannula * Janice Karman (born 1954), American film producer, record producer, singer, and voice artist * József Kármán (1769–1795), sentimentalist Hungarian author * Tawakkol Karman (born 1979), Yemeni journalist, politician, and human rights activist See also * Karman Holdings, an American corporation * Theodore von Kármán (1881–1963), Hungarian-American engineer and physicist **Von Kármán (other) * Josephine de Karman, sister and life-partner of Theodore von Kármán * Karman cannula * Kármán–Howarth equation * Kármán line * Kármán vortex street * Kaman (other) * Karmann * Kerman (other) * Carman (other) * Karma (other) Karma, in several Eastern religions, is the concept of "action" or "deed", understood as that which causes the entire cycle of cause and effect. Karma may al ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Kármán–Trefftz Airfoil
In applied mathematics, the Joukowsky transform (sometimes transliterated ''Joukovsky'', ''Joukowski'' or ''Zhukovsky'') is a conformal map historically used to understand some principles of airfoil design. It is named after Nikolai Zhukovsky, who published it in 1910. The transform is : z = \zeta + \frac, where z = x + iy is a complex variable in the new space and \zeta = \chi + i \eta is a complex variable in the original space. In aerodynamics, the transform is used to solve for the two-dimensional potential flow around a class of airfoils known as Joukowsky airfoils. A Joukowsky airfoil is generated in the complex plane (z-plane) by applying the Joukowsky transform to a circle in the \zeta-plane. The coordinates of the centre of the circle are variables, and varying them modifies the shape of the resulting airfoil. The circle encloses the point \zeta = -1 (where the derivative is zero) and intersects the point \zeta = 1. This can be achieved for any allowable centre po ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Lift (force)
When a fluid flows around an object, the fluid exerts a force on the object. Lift is the Euclidean_vector#Decomposition_or_resolution, component of this force that is perpendicular to the oncoming flow direction. It contrasts with the drag (physics), 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 is defined to act perpendicular to the flow and therefore can act in any direction. If the surrounding fluid is air, the force is called an aerodynamic force. In water or any other liquid, it is called a Fluid dynamics, hydrodynamic force. Dynamic lift is distinguished from other kinds of lift in fluids. Aerostatics, 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 (boat), Planing lift, in which only the lower po ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Coefficient Of Pressure
In fluid dynamics, the pressure coefficient is a dimensionless number which describes the relative pressures throughout a flow field. The pressure coefficient is used in aerodynamics and hydrodynamics. Every point in a fluid flow field has its own unique pressure coefficient, . In many situations in aerodynamics and hydrodynamics, the pressure coefficient at a point near a body is independent of body size. Consequently, an engineering model can be tested in a wind tunnel or water tunnel, pressure coefficients can be determined at critical locations around the model, and these pressure coefficients can be used with confidence to predict the fluid pressure at those critical locations around a full-size aircraft or boat. Definition The pressure coefficient is a parameter for studying both incompressible/compressible fluids such as water and air. The relationship between the dimensionless coefficient and the dimensional numbers is :C_p = where: : p is the static pressure at ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
