• Application Formulae

  • YOU ARE IN TOOLS & GUIDES

  • Application Formulae

    In this section of the website we provide commonly used formulae for a number of rope applications.

    The units used in this section are:

    δl = Rope Elongation (m)
    E.A = Modulus of Elasticty * Area (N)
    εb = Rope Elongation at Break (%)
    h = Distance of Fall to End of Unelongated Rope (m)
    K = Spring Constant (N/m)
    KE = Kinetic Energy (J)
    l = Rope Length (m)
    m = Mass of Load (kg)
    PE = Potential Energy (J)
    SE = Stored Energy (J)
    T = Tension in Rope (N)
    w = Rope Weight (kg/m)

     

    Energy

    Absorbed Energy
    Ropes have to absorb energy if they are to arrest a falling object or prevent an errant vessel from colliding with sensitive equipment. In general the absorbed energy due the rope elongating has to equal the potential or kinetic energy.

    Absorbed Energy is the Area Under the Rope Stress Strain Curve

    Rope Stress Strain 01

    Falling Load (Straight Line Approximation)

    02

    03

    04

    Absorbing Kinetic Energy (e.g. Moving Ship)

    05

    06

    Rope Motion
    Ropes have three characteristic motions. Often the engineer is interested in the ropes behaviour as a spring and sometimes the strumming frequency. For the sake of completeness the rope as a pendulum is also given.

    Pendulum

    07

    Spring

    09 08

    Strumming (Violin String)

    10

    Sag

    Overheads lines are subject to considerable sag and this determines the height of pylons. In most overhead line analysis the following parabolic approximations are used.

    The units used in this section are:
    S = Maximum (Centre) Sag (m)
    t = Horizontal Component of Rope Tension (N)
    W = Rope Weight (N/m) 
    Where x = horizontal position along D 
    Where θ0 = Angle at support

    Level Span

    Level Span

    where

    12


    Deflection at any point

    13

    14

    15

    Rope length

    16

    17

    18

    19

    Inclined Span

    Inclined Span

    21

    22

    23

    24

    25

    26

    27

    28

    29

    30

    31

    Winching

    Ropes lose tension over a pulley or winch and this is limited by the following equation. For a traction winch to work, it is necessary to ensure that the low tension is at least as high as the given in this equation. If it falls below this value the rope will simply slip on the winch.

    Traction Winch

     

    Coefficient of Friction on a Traction Winch

    33

    where: 

    T1 = High Tension
    T2 = Low Tension
    µ = Coefficient of Friction 
    α = Wrap Angle in Radians

      • Optimoor Mooring Analysis Software view
      • Fibre Rope Modeler Rope Design Software view
      • Riser Protection Nets (RPN) Technical Expertise view
      • Expert Witness Marine Accident Investigation view
      • Joint Industry Projects (JIP) Research and Development (R&D) view
      • Rope Service Life Prediction And Replacement Criteria view