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Catenary - Wikipedia
In physics and geometry, a catenary is the curve that an idealized hanging chain or cable assumes under its own weight when supported only at its ends in a uniform gravitational field. The catenary curve has a U-like shape, superficially similar in appearance to a parabola, which it is not. The curve appears in … See more
The word "catenary" is derived from the Latin word catēna, which means "chain". The English word "catenary" is usually attributed to Thomas Jefferson, who wrote in a letter to See more
In free-hanging chains, the force exerted is uniform with respect to length of the chain, and so the chain follows the catenary curve. The same is true of a simple suspension bridge or … See more
The catenary produced by gravity provides an advantage to heavy anchor rodes. An anchor rode (or anchor line) usually consists of chain or … See more
Model of chains and arches
In the mathematical model the chain (or cord, cable, rope, string, etc.) is idealized by assuming that it is so thin that it can be regarded as a curve and that it is so flexible any force of tension exerted by the chain is parallel to … See moreCatenary arches are often used in the construction of kilns. To create the desired curve, the shape of a hanging chain of the desired dimensions is transferred to a form which is then used … See more
Equation
The equation of a catenary in Cartesian coordinates has the form
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If the density of the chain is variable then the analysis above can be adapted to produce equations for the curve given the density, or given the curve to find the density.
Let w denote the … See moreWikipedia text under CC-BY-SA license - bing.com/videosWatch full video
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WEBMar 9, 2024 · The sag is the difference between the height at the end points and the height in the middle. The equation of a catenary is. y = a cosh(t/a) and the length of the catenary between t = −x and t = x is. 2s …
Catenary equations solving for sag given distance and …
WEBMay 21, 2019 · Once you have solved numerically for the value of $a$, the sag can then be calculated as $$\Delta y=y(d/2)-y(0)=a\left(\cosh\frac{d}{2a}-1\right).$$ As a numerical example, let …
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CATENARY - Selux