Weighted catenary

Aweighted catenary (also flattened catenary, was defined by William Rankineastransformed catenary^[1] and thus sometimes called Rankine curve^[2]) is a catenary curve, but of a special form. A "regular" catenary has the equation

${\displaystyle y=a\,\cosh \left({\frac {x}{a}}\right)={\frac {a\left(e^{\frac {x}{a}}+e^{-{\frac {x}{a}}}\right)}{2}}}$

for a given value of a. A weighted catenary has the equation

${\displaystyle y=b\,\cosh \left({\frac {x}{a}}\right)={\frac {b\left(e^{\frac {x}{a}}+e^{-{\frac {x}{a}}}\right)}{2}}}$

and now two constants enter: a and b.

• 1 Significance
• 2 Examples
• 3 References
• 4 External links and references
  • 4.1 General links
  • 4.2 On the Gateway arch
  • 4.3 Commons

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