A weighted catenary is a catenary curve, of a special form, with two constants
A hanging chain is a regular catenary — and is not weighted.
A weighted catenary (also flattened catenary, was defined by William Rankine as transformed catenary[1] and thus sometimes called Rankine curve[2]) is a catenary curve, but of a special form. A "regular" catenary has the equation
for a given value of a. A weighted catenary has the equation
and now two constants enter: a and b.
^Osserman, Robert (February 2010). "Mathematics of the Gateway Arch" (PDF). Notices of the American Mathematical Society. 57 (2): 220–229. ISSN 0002-9920.
^Andrue, Mario (2020). "The arches of the facade of the Palau Güell. Hyphotesis about its conformation" (PDF). fundacionantoniogaudi.org. Antonio Gaudi Foundation. Retrieved 5 January 2024.
A weightedcatenary (also flattened catenary, was defined by William Rankine as transformed catenary and thus sometimes called Rankine curve) is a catenary...
a "weightedcatenary" instead. Its shape corresponds to the shape that a weighted chain, having lighter links in the middle, would form. Catenary arches...
United States. Clad in stainless steel and built in the form of a weightedcatenary arch, it is the world's tallest arch and Missouri's tallest accessible...
A catenary arch is a type of architectural arch that follows an inverted catenary curve. The catenary curve has been employed in buildings since ancient...
particular are of significance to the arch design: parabola itself, catenary, and weightedcatenary. The arches naturally use the inverted (upside-down) versions...
and Company. Momentum theory State function Track transition curve Weightedcatenary themastertons@btinternet.com. "Scottish Engineering Hall of Fame"...
The tallest man-made monument in the U.S., the arch is based on a weightedcatenary design conceived by Finnish American architect Eero Saarinen. In 1967...
too low for the catenary but too high to be optimal for traction motors. The solution to the problem was to use 25 kV AC for the catenary and provide on-board...
of parametric equations, he could automatically derive the shape of the catenary curves through the force of gravity acting on the strings. German architect...
is not an issue, a heavier chain provides better holding by forming a catenary curve through the water and resting as much of its length on the bottom...
separately. Railways generally tend to prefer overhead lines, often called "catenaries" after the support system used to hold the wire parallel to the ground...
is weighted down by hanging chains. In this configuration, the line is suspended in a catenary between two towing vessels. The shape of that catenary (the...
out is never level but also approximates to a parabola. (But see also catenary.) [323] What is the weight of water falling from a bucket hanging on a...
− i ) = 0 {\displaystyle R^{i}f_{*}F(r-i)=0} for all i > 0. catenary A scheme is catenary, if all chains between two irreducible closed subschemes have...
on hooks close to the float, i.e. the shallower hooks on the longline catenary. The WPRFMC response was to amend the FEP and required fishermen on vessels...
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