Catenary
Subject
A Catenary is the natural curve generated by a cable or chain (with zero bending stiffness and infinite axial stiffness) when strung between two fixed points.
Whilst the theory used for the analysis of a Catenary is strictly valid for cables with zero bending stiffness and infinite axial stiffness, you can also use it to obtain approximate configurations in cables that exhibit a resistance to bending, if sufficiently long.
As with many of our calculators you could use the catenary calculator for preanalysis and optimisation work instead of expensive and timeconsuming analytical software.
For instance, you could use Catenary to configure closely, say, a small diameter pipeline (relative to water depth) hung off a vessel or platform in fairly still water limiting the expensive and timeconsuming analytical software to final analysis.
Calculator
The catenary calculator includes two calculation options:
1) Fx,Fy: calculates the distance between each end of the catenary based upon the force applied to its free end
2) x,y: calculates the forces in each end of the catenary based upon the distance to its free end
Local Properties can be found for any point on the catenary with respect to its anchored end using either calculation option
For help using this calculator, including its internal selfchecking facility, see Technical Help
Catenary Calculator  Options
Fx,Fy & x,y
One end of the cable is anchored and the other end is free to move. Either you apply a force (Fx,Fy) to the free end or you move it to a specified position relative to the anchor (x,y). Catenary will provide the properties of the resulting catenary along with an image of its configuration.
You enter: 
and the catenary calculator will provide: 


horizontal force in catenary: Fx1000

axial tension in catenary at '1': F₁

vertical force in catenary at '1': Fy₁

axial tension in catenary at '2': F₂

vertical force in catenary at '2': Fy₂

axial tension in catenary at 'p': Fᵨ

vertical force in catenary at 'p': Fyᵨ

radius in catenary at '1' [°]: R₁

slope in catenary at '1' [°]: θ₁

horizontal distance from '1' to '2': x₂

vertical distance from '1' to '2': y₂

radius in catenary at '2': R₂

slope in catenary at '2' [°]: θ₂

length of catenary from '1' to 'ℓ': Lℓ

horizontal distance from '1' to 'ℓ': xℓ

vertical distance from '1' to 'ℓ': yℓ

radius in catenary at 'ℓ': Rℓ

horizontal distance from '1' to 'p': xᵨ

vertical distance from '1' to 'p': yᵨ

radius in catenary at 'p': Rᵨ

slope in catenary at 'p' [°]: θᵨ

A coordinate listing is also provided for further processing in your preferred spreadsheet

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