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Troposkein
{{Short description, Momentum curve of a rope In physics and geometry, the troposkein is the curve an idealized rope assumes when anchored at its ends and spun around its long axis at a constant angular velocity. This shape is similar to the shape assumed by a skipping rope, and is independent of rotational speed in the absence of gravity, but varies with respect to rotational speed in the presence of gravity. The troposkein does not have a closed-form representation; in the absence of gravity, though, it can be approximated by a pair of line segments spanned by a circular arc (tangential to the line segments at its endpoints). The form of a troposkein can be approximated for a given gravitational acceleration, rope density and angular velocity by iterative approximation. This shape is also useful for decreasing the stress experienced by the blades of a Darrieus vertical axis wind turbine A vertical-axis wind turbine (VAWT) is a type of wind turbine where the main ro ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Physics
Physics is the natural science that studies matter, its fundamental constituents, its motion and behavior through space and time, and the related entities of energy and force. "Physical science is that department of knowledge which relates to the order of nature, or, in other words, to the regular succession of events." Physics is one of the most fundamental scientific disciplines, with its main goal being to understand how the universe behaves. "Physics is one of the most fundamental of the sciences. Scientists of all disciplines use the ideas of physics, including chemists who study the structure of molecules, paleontologists who try to reconstruct how dinosaurs walked, and climatologists who study how human activities affect the atmosphere and oceans. Physics is also the foundation of all engineering and technology. No engineer could design a flat-screen TV, an interplanetary spacecraft, or even a better mousetrap without first understanding the basic laws of physic ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Geometry
Geometry (; ) is, with arithmetic, one of the oldest branches of mathematics. It is concerned with properties of space such as the distance, shape, size, and relative position of figures. A mathematician who works in the field of geometry is called a ''geometer''. Until the 19th century, geometry was almost exclusively devoted to Euclidean geometry, which includes the notions of point, line, plane, distance, angle, surface, and curve, as fundamental concepts. During the 19th century several discoveries enlarged dramatically the scope of geometry. One of the oldest such discoveries is Carl Friedrich Gauss' ("remarkable theorem") that asserts roughly that the Gaussian curvature of a surface is independent from any specific embedding in a Euclidean space. This implies that surfaces can be studied ''intrinsically'', that is, as stand-alone spaces, and has been expanded into the theory of manifolds and Riemannian geometry. Later in the 19th century, it appeared that geometries ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Rope
A rope is a group of yarns, plies, fibres, or strands that are twisted or braided together into a larger and stronger form. Ropes have tensile strength and so can be used for dragging and lifting. Rope is thicker and stronger than similarly constructed cord, string, and twine. Construction Rope may be constructed of any long, stringy, fibrous material, but generally is constructed of certain natural or synthetic fibres. Synthetic fibre ropes are significantly stronger than their natural fibre counterparts, they have a higher tensile strength, they are more resistant to rotting than ropes created from natural fibres, and they can be made to float on water. But synthetic ropes also possess certain disadvantages, including slipperiness, and some can be damaged more easily by UV light. Common natural fibres for rope are Manila hemp, hemp, linen, cotton, coir, jute, straw, and sisal. Synthetic fibres in use for rope-making include polypropylene, nylon, polyesters (e.g. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Angular Velocity
In physics, angular velocity or rotational velocity ( or ), also known as angular frequency vector,(UP1) is a pseudovector representation of how fast the angular position or orientation of an object changes with time (i.e. how quickly an object rotates or revolves relative to a point or axis). The magnitude of the pseudovector represents the ''angular speed'', the rate at which the object rotates or revolves, and its direction is normal to the instantaneous plane of rotation or angular displacement. The orientation of angular velocity is conventionally specified by the right-hand rule.(EM1) There are two types of angular velocity. * Orbital angular velocity refers to how fast a point object revolves about a fixed origin, i.e. the time rate of change of its angular position relative to the origin. * Spin angular velocity refers to how fast a rigid body rotates with respect to its center of rotation and is independent of the choice of origin, in contrast to orbital angular ve ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Skipping Rope
A skipping rope (British English) or jump rope (American English) is a tool used in the sport of skipping/jump rope where one or more participants jump over a rope swung so that it passes under their feet and over their heads. There are multiple subsets of skipping/jump rope, including single freestyle, single speed, pairs, three-person speed (Double Dutch), and three-person freestyle (Double Dutch freestyle). Rope skipping is commonly performed as an exercise or recreational activity, and there are also several major organizations that support jump rope as a competitive sport. Often separated by sex and age, events include hundreds of competitive teams all around the world. In the US, schools rarely have jump rope teams, and few states have sanctioned official events at the elementary school level. In freestyle events, jumpers use a variety of basic and advanced techniques in a routine of one minute, which is judged by a head judge, content judges, and performance judges. In ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Closed-form Expression
In mathematics, a closed-form expression is a mathematical expression that uses a finite number of standard operations. It may contain constants, variables, certain well-known operations (e.g., + − × ÷), and functions (e.g., ''n''th root, exponent, logarithm, trigonometric functions, and inverse hyperbolic functions), but usually no limit, differentiation, or integration. The set of operations and functions may vary with author and context. Example: roots of polynomials The solutions of any quadratic equation with complex coefficients can be expressed in closed form in terms of addition, subtraction, multiplication, division, and square root extraction, each of which is an elementary function. For example, the quadratic equation :ax^2+bx+c=0, is tractable since its solutions can be expressed as a closed-form expression, i.e. in terms of elementary functions: :x=\frac. Similarly, solutions of cubic and quartic (third and fourth degree) equations can be expresse ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Iterated Function
In mathematics, an iterated function is a function (that is, a function from some set to itself) which is obtained by composing another function with itself a certain number of times. The process of repeatedly applying the same function is called iteration. In this process, starting from some initial object, the result of applying a given function is fed again in the function as input, and this process is repeated. For example on the image on the right: :with the circle‑shaped symbol of function composition. Iterated functions are objects of study in computer science, fractals, dynamical systems, mathematics and renormalization group physics. Definition The formal definition of an iterated function on a set ''X'' follows. Let be a set and be a function. Defining as the ''n''-th iterate of (a notation introduced by Hans Heinrich Bürmann and John Frederick William Herschel), where ''n'' is a non-negative integer, by: f^0 ~ \stackrel ~ \operatorname_ ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Darrieus Wind Turbine
The Darrieus wind turbine is a type of vertical axis wind turbine (VAWT) used to generate electricity from wind energy. The turbine consists of a number of curved aerofoil blades mounted on a rotating shaft or framework. The curvature of the blades allows the blade to be stressed only in tension at high rotating speeds. There are several closely related wind turbines that use straight blades. This design of the turbine was patented by Georges Jean Marie Darrieus, a French aeronautical engineer; filing for the patent was October 1, 1926. There are major difficulties in protecting the Darrieus turbine from extreme wind conditions and in making it self-starting. Method of operation In the original versions of the Darrieus design, the aerofoils are arranged so that they are symmetrical and have zero rigging angle, that is, the angle that the aerofoils are set relative to the structure on which they are mounted. This arrangement is equally effective no matter which direction the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Vertical Axis Wind Turbine
A vertical-axis wind turbine (VAWT) is a type of wind turbine where the main rotor shaft is set transverse to the wind while the main components are located at the base of the turbine. This arrangement allows the generator and gearbox to be located close to the ground, facilitating service and repair. VAWTs do not need to be pointed into the wind, which removes the need for wind-sensing and orientation mechanisms. Major drawbacks for the early designs (Savonius, Darrieus and giromill) included the significant torque ripple during each revolution, and the large bending moments on the blades. Later designs addressed the torque ripple by sweeping the blades helically ( Gorlov type). Savonius vertical-axis wind turbines (VAWT) are not widespread, but their simplicity and better performance in disturbed flow-fields, compared to small horizontal-axis wind turbines (HAWT) make them a good alternative for distributed generation devices in an urban environment. A vertical axis wind ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
