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Calculator Description
Catenary Calculator v1


Calculator for the properties of a catenary


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 pre-analysis and optimisation work instead of expensive and time-consuming 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 time-consuming analytical software to final analysis.


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 self-checking 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 at '2': Fx
  • vertical force at '2': Fy₂
  • or
  • horizontal distance from '1' to '2': x₂
  • vertical distance from '1' to '2': y₂
  • and
  • total length of catenary from '1' to '2': L
  • weight per unit length of catenary: w
  • distance along catenary from '1' to 'p': p
  • 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 co-ordinate listing is also provided for further processing in your preferred spreadsheet

Check minimum system requirements

Price: £19.50

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