Rope/Wire wizard

The wizard will generate an Axisymmetric cross-section.

The different options are

  • Steel wire

  • Nylon rope

    • Linear

  • Polyester:

    • Linear

    • Bilinear

Input:

  • Rope diameter in [mm]: d

All regression equations below take \(d\) in mm, consistent with the reference catalogues and the wizard input.

1. Steel Wire

1.1. Cross-section properties

  • Mass coefficient: \(m_{coeff}=m_{air}\)

  • Weight in air (dry mass):

    • The mass is calculated based on the regression line equation fitted to a 6-strand rope with a steel core (Dyform DB2K®) from Bekaert catalogue (Bridon® Advanced Rope Solutions and Services for the offshore energy industry).

\[m_{air}=0.0044886d^2+0.0062887d-0.23\,\text{[kg/m]}\]

  • External cross sectional area:

\[A_{ext}=\frac{1}{\rho_{sw}} (m_{air}-m_{water} )\,\text{[m^2]}\\ \rho_{sw}= 1025\,\text{[kg/m^3]}\\ m_{water}=0.0039795d^2-0.0059931d+0.2306\,\text{[kg/m]}\]

1.2. Capacity properties

The MBL is calculated based on the regression line equation fitted to a 6-strand rope with a steel core (Dyform DB2K®) from Bekaert catalogue.

  • Tension capacity:

\[\mathrm{MBL} = 0.5 d^2 + 50 d - 2000\,\text{[kN]}\]

1.3. Hydrodynamic force coefficients

  • Load formulation is Morison

  • Input code: Nondimensional coefficients

Quadratic drag coefficient with respect to d

\(CQ_{x}\)

\(CQ_{y}\)

Spiral rope without plastic sheathing (DNV-OS-E302)

0.0

1.6

  • Added mass in tangential direction: \(C_{Ax}=0.0\)

  • Added mass in normal direction: \(C_{Ay}=1.0\)

  • Linear drag coefficient in tangential direction: \(C_{Lx}=0.0\)

  • Linear drag coefficient in normal direction: \(C_{Ly}=0.0\)

1.4. Linear stiffness model

Stiffness is taken from DNV-OS-E302 for Spiral rope (1.13*10^11 N/m^2 corresponding to nominal diameter of the steel wire rope). Please note modification would be needed based on individual wire ropes.

\[EA = 1.13 \cdot 10^{11} \cdot \pi \cdot \frac{(d/1000)^2}{4}\,\text{[N]}\]

2. Nylon Rope

2.1. Cross-section properties

  • Mass coefficient: \(m_{coeff}=m_{air}\)

  • Weight in air (dry mass):

    • The values are calculated based on the regression line equation fitted to Nylon mooring line from Bekaert catalogue (Mooring for floating offshore wind).

\[m_{air}=0.00043447d^2+0.024064d-0.5579 [kg/m]\]

  • External cross sectional area:

\[A_{ext}=\frac{1}{\rho_{sw}} (m_{air}-m_{water} )\,\text{[m^2]}\\ \rho_{sw}= 1025 kg/m^3\\ m_{water}=0.000044249d^2+0.005959d-0.1296\,\text{[kg/m]}\]

2.2. Capacity properties

  • Tension capacity:

\[MBL=0.21601303072d^2+0.8403498d-82.13225\,\text{[kN]}\]

2.3. Hydrodynamic force coefficients

  • Load formulation is Morison

  • Input code: Nondimensional coefficients

Quadratic drag coefficient with respect to d

\(C_{Qx}\)

\(C_{Qy}\)

Fiber rope

0.1

1.6

  • Added mass in tangential direction: \(C_{Ax}=0.0\)

  • Added mass in normal direction: \(C_{Ay}=1.0\)

  • Linear drag coefficient in tangential direction: \(C_{Lx}=0.0\)

  • Linear drag coefficient in normal direction: \(C_{Ly}=0.0\)

2.4. Linear stiffness model

Stiffness is either 10MBL (lowerBound) or 30MBL (upperBound). Please note that stiffness is assumed to be similar to polyester fiber rope however Nylon offers lower stiffness characteristics than polyester.

3. Polyester rope

3.1. Cross-section properties

  • Mass coefficient: \(m_{coeff}=m_{air}\)

  • Weight in air (dry mass):

    • The mass is calculated based on the regression line equation fitted to Bridon Superline Polyester for Permanent Mooring (Bridon fibre rope catalogue).

\[m_{air}=0.0007 d^2-0.0088d+0.489\,\text{[kg/m]}\]

  • External cross sectional area:

\[A_{ext}=\frac{1}{\rho_{sw}} m_{air} (1-r_{air}^{sub})\,\text{[m^2]}\\ \rho_{sw}= 1025 kg/m^3\\ r^{sub}_{air}=\frac{m_{sub}}{m_{air}}=0.25\\\]

where \(r^{sub}_{air}\) is the ratio between submerged weight to weight in air (dry mass).

4. Capacity properties

The MBL is calculated based on the regression line equation fitted to Bridon Superline Polyester for Permanent Mooring (Bridon fibre rope catalogue).

  • Tension capacity:

\[MBL=0.2658d^2+4.9392d-654.74\,\text{[kN]}\]

4.1. Hydrodynamic force coefficients

  • Load formulation is Morison

  • Input code: Nondimensional coefficients

Quadratic drag coefficient with respect to d

\(C_{Qx}\)

\(C_{Qy}\)

Fiber rope

0.1

1.6

  • Added mass in tangential direction: \(C_{Ax}=0.0\)

  • Added mass in normal direction: \(C_{Ay}=1.0\)

  • Linear drag coefficient in tangential direction: \(C_{Lx}=0.0\)

  • Linear drag coefficient in normal direction: \(C_{Ly}=0.0\)

4.2. Linear stiffness model

Linear model has stiffness based on ABS upper-lower bound stiffness model based, i.e., for maximum offset (10MBL) and line tension (30MBL) calculation

4.3. Bi-linear model (Static-dynamic stiffness model)

Will create an axisymmetric cross section with Tension-elongation input for axial stiffness.

Relative elongation and axial force are selected based on ABS curve. The static and dynamic stiffnesses are 10MBL and 30MBL with mean tension of 40% MBL according to ABS