Application FormulaeApplication 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/mm2) |
| εb | = Rope Elongation at Break (%) |
| h | = Distance of Fall to End of Unelongated Rope (m) |
| K | = Spring Constant (N/m) |
| KE | = Kinetic Energy (Joules) |
| l | = Rope Length (m) |
| m | = Mass of Load (kg) |
| PE | = Potential Energy (Joules) |
| SE | = Stored Energy (Joules) |
| T | = Tension in Rope (kg) |
| w | = Rope Weight (kg/m) |
See also:
Rope Design (fibre ropes and steel wire ropes)
TTI provides a complete consultancy service in the field of ropes and cables.
Software
Fibre Rope Modeller, modelling program for rope design and performance prediction
Papers
Computer Modelling of Large, High-Performance Fiber Rope Properties
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
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Falling Load (Straight Line Approximation)
Absorbing Kinetic Energy (e.g. Moving Ship)
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
Spring
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Strumming (Violin String)
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
where
Deflection at any point
Rope length
Inclined Span
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.
Coefficient of Friction on a Traction Winch
where:
T1 = High Tension
T2 = Low Tension
µ = Coefficient of Friction
α = Wrap Angle in
Radians