Catenary Formula

For those who have asked me how much anchor rode is necessary for proper scope, here is the
Catenary Mathematical Description

The equation (up to translation and rotation) of a catenary in Cartesian coordinates has the form:

where cosh is the hyperbolic cosine function.


The scaling factor a can be interpreted as the ratio between the horizontal component of the tension on the chain (a constant) and the weight of the chain per unit of length.


The Whewell equation for the catenary is:



Differentiating gives:



and eliminating
gives the Cesàro equation:


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