Catenary equation                          


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A catenary is the natural shape of a freely suspended line.

 

The following figure shows the forces acting on such a catenary line, split up in horizontal and vertical components. The basic working principle of the catenary line is as follows: if the upper end of the line is moved to the right, the line is lift-off more from the seabed, increasing the suspended weight which in turn increases the line tension. Simultaneously the slope of the line becomes less steep, so the horizontal component of the tension becomes larger. These effects combined result in a restoring force against moving away from the anchor point.

 

 

 

 

 

 

 

               Figure c.1.a:Forces on mooring line                Figure c.1.b:Mooringline element

  

The following graph shows that elasticity of mooring lines significantly influences the excursions under loading, therefore the catenary equation that includes elasticity is briefly discussed here.

 

 

 

 

 

 

 

 

                            Figure c.2: Line load-excursion characteristics

  

 

 

 

 

 

 

 

             Figure c.3: Mooring line element with and without axial stretch

After the geometry of the catenary line has been determined based on static equilibria, force equations including elasticity can be derived (for step by step derivations of catenary equations see www.offshoreengineering.org (click button ‘catenary I’ or ‘catenary II’)

 

 

 

 

 

(See also figure “forces on a mooring line” for the meaning of the parameters.)

       

                                                                     

 

 

 

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Last modified: 10/16/06