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The two practical properties defining a natural catenary are:ġ) the horizontal force (Fx) in the cable is constant throughout its length, and Ģ) the vertical force (Fy) in the cable at any point is equal to the weight of cable that point is carrying (i.e. Practical Catenary diagram Definition of a Catenary Refer to Tight Catenary below for a definition of the configuration of electricity or anchor cables.įig 2. chain or string), the theory may equally be applied with reasonable accuracy to a cable with inherent bending stiffness if sufficiently long. Whilst a true catenary curve will occur naturally in a cable with zero bending stiffness (e.g. Whilst this curve is a theoretical mathematical shape, it is also something that occurs naturally every time you hang a cord of zero bending stiffness and infinite axial stiffness between any two points ( co-ordinates).ĬalQlata is concerned only with the practical use of this configuration and has therefore tailored this calculator around finding relative co-ordinates, forces & angles at both ends and at any point along its length ( Fig 2). Some of the other relationships between the parameter and the curve are shown in Fig 1 (R is the radius of the curve at point P). a flat catenary has a large parameter and a tall catenary has a small parameter.
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Where 'a' is the curve's parameter (a = Fx / w) and defines the shape of the catenary: i.e. Theoretical Catenary diagram Theoretical CatenaryĪ catenary is a theoretical curve with the x,y relationship: y = a.