25. Fiber rope cable properties

The identification tag for this tutorial is PDS-AAP. Pregenerated input files for this tutorial are found in the folder named PDS-AAP in the provided tutorial input files.

25.1. Tutorial overview

This tutorial covers:

  • Determining DCableSegment feature properties for fiber rope

25.2. Synthetic fiber rope

Note

  • Synthetic ropes, made from polyester, Dyneema, nylon or copolymer materials are frequently used for a variety of mooring and marine applications. For example, a high strength Dyneema rope used in mooring applications is Amsteel-Blue; the manufacturer provides properties for this rope online (found here) that can be used to set the cable properties in the DCableSegment feature in ProteusDS.
  • The following tutorial reviews how to set DCableSegment feature properties for a 3/4 inch Amsteel-Blue rope, the properties of which are given in Fig. 25.1.
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Fig. 25.1 Amsteel-Blue rope properties.

25.3. Size and buoyancy using specific gravity

Note

  • Many fiber ropes do not have a uniform circular cross section, and/or they may effectively contain small air gaps that entrain water when used in subsea applications. The DCableSegment feature properties must be set in ProteusDS to ensure that the mass and buoyancy properties are set to correctly model the effective wet weight and mass in air per unit length of the rope.
  • The $Diameter property is always used to specify the nominal diameter for ropes and cables; this diameter is used for drag and added mass calculations.
  • For a 3/4” nominal diameter rope, the $Diameter is 0.01905 m.

Note

  • The mass per unit length in air can be found in the rope specifications. The mass per unit length for 3/4” Amsteel-Blue rope is given as 19.8 kg/100 m.
  • The $Density property is used with $Diameter to set the mass of the rope in ProteusDS. Based on the mass per unit length, the $Density can be determined using the following equation:

\(\rho = \frac{4M_l}{\pi d^2}\)

where \(M_l\) is the mass per unit length in air in kg/m and \(d\) is the nominal diameter in m.

  • Using this equation, the $Density is calculated to be 694.7 kg/m3.

Note

  • The $BuoyancyDiameter property is used to set the distributed buoyancy force per unit length of the cable. In the case of a fiber rope which entrains water, the $BuoyancyDiameter value would be smaller than the nominal diameter. In the case of a solid pipe, the $BuoyancyDiameter would be equal to the $Diameter.
  • If the $BuoyancyDiameter property is not specified, ProteusDS will use the nominal diameter (the $Diameter property) to calculate buoyancy.
  • To calculate the $BuoyancyDiameter for the 3/4 inch Amsteel-Blue rope requires that either the rope mass per unit length in water, or the specific gravity of the rope material is provided. For the Dyneema fiber used in Amsteel-Blue the specific gravity is 0.98.
  • To calculate buoyancy diameter, use the equation from the ProteusDS User Manual:
\(d_b = \sqrt{\frac{4 M_l}{\pi \cdot 1000 \cdot SG_{cm}}}\)
  • Using this equation, the $BuoyancyDiameter is calculated to be 0.016 m.

25.4. Size and buoyancy using weight per unit length in water

Note

  • It is common for manufacturers to provide the mass and weight per unit length in water. For example, the 113 mm DeepRope Polyester rope data sheet can be found here on page 36, as shown in Fig. 25.2. When provided, these properties should be used to calculate the $BuoyancyDiameter of a cable.
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Fig. 25.2 DeepRope rope properties.

  • For the 113 mm DeepRope, the $Diameter property sets the nominal diameter. For a 113 mm rope it is 0.113 m.
  • Using the provided mass in air (8.80 kg/m) and the nominal diameter, the $Density can be calculated using the equation presented above. The $Density is calculated to be 877 kg/m3.

Note

  • To calculate buoyancy diameter with known mass per unit length in air and mass per unit length in water, an equation from the ProteusDS User Manual is used:

\(d_b=\sqrt{\frac{4(M_l - M_w)}{\pi\rho_w}}\)

where \(M_l\) is the mass per unit length in air in kg/m, \(M_w\) is the apparent mass per unit length in water in kg/m, \(d\) is the nominal diameter in m, and \(\rho\) is the density of water in kg/m3.

  • Using this equation, with a mass per unit length in water of 2.11 kg/m and a water density of 1025 kg/m3 (for saltwater), the $BuoyancyDiameter is calculated to be 0.0912 m.

Note

  • Often various weights in water are provided by the manufacturer for different rope tensions. Use the value that is closest to the expected tension of the rope in the simulation. If the tension is unknown, use one value and readjust the cable properties after running some preliminary simulations.

25.5. Mechanical properties

Note

  • The axial stiffness of fiber ropes can be calculated using the elongation properties provided by the manufacturer.
  • For the 3/4” Amsteel-Blue rope, the percent elongation is given as 0.96% at 30% of the maximum breaking load.
  • The axial stiffness can be calculated using an equation from the ProteusDS User Manual:
\(EA = \frac {100 F_{\zeta}}{\zeta}\)
  • \(\zeta\) is the percent elongation at an applied load of \(F_{\zeta}\) (in N).
  • Taking 30% the minimum strength provided of 58000 lbs, or 258e3 N gives a \(F_{\zeta}\) of 77.4e3 N. Using the equation yields an axial stiffness $EA of 8.063e6 N.

Note

  • The flexural stiffness $EI and torsional stiffness $GJ are negligible in fiber rope and can be assumed to be zero for many applications.
  • Fiber rope has low effective compressive elasticity, therefore the compressive elasticity property $CE may be assumed to be 0 or very low.

25.6. Drag and added mass properties

  • The added mass coefficient $CAc for most ropes and cables can be 1.0, represented as long cylinders.
  • The drag coefficient $CDc for fiber rope can be approximated as 1.5.
  • The tangential drag coefficient $CDt can be left as the default value of 0.01 for all ropes.

Note

  • The rope properties for a 3/4 inch Amsteel-Blue rope may be set as:
// Axial Rigidity
$AxialRigidityMode 0
$EA 8.952E6

// Fluid loading
$CDc 1.5
$CDt 0.01
$CAc 1

// Mechanical
$EI1 0
$EI2 0
$GJ 0
$Diameter 0.01905
$BuoyancyDiameter 0.016
$Density 694.7
$AxialDampingMode 1
$AxialReferenceDampingRatio 0.5
$BCID 0
$TCID 0
$CE 0

// Strain Limit
$ElongationLimitMode 0