57
Learning from the Forest
Calculating Cable Tension
Subject(s): Science/Math
Grade Level: 9th – 12th
Activity Author: Dr. Leonard Johnson, Univ. of
Idaho
Objectives: To demonstrate the effect of cable
geometry on cable tension and to show the
trigonometric relationship between cable geometry and
cable tension.
Materials Needed: Known weight, tape measure,
small diameter rope or cable, pulley and spring scale.
Background:
The most efficient way to lift and support a load is to lift if vertically. This might be possible
in logging with a helicopter or balloon, but does not work with cable yarding systems. In these
systems, the cable is fixed at both ends and suspended over the operating area and some of the lifting
capacity of the cable is lost to forces acting in the horizontal, rather than the vertical direction.
The lifting capacity of the cable, often called wire rope in logging, is a function of its size …
primarily its diameter. Lifting capacity is directly proportional to the square of the diameter or the end
area of the cable. Depending on the type of steel used to construct the cable and the strength of the
material used in its middle section (core), cable of a given size will have a measured capacity of a
certain number of pounds of breaking strength. A ¾ inch wire rope used as a skyline in logging, for
example, would have a breaking strength of 58,800 pounds. You would not operate a cable up to its
breaking strength, however. A wire rope acts like a spring that stretches under load and returns to its
original shape when the load is released. Just like a spring that is overloaded, however, if the cable is
loaded past what is called its elastic limit, it will not return to its original shape. This occurs at a load
of about half of the breaking strength and will severely weaken the cable for future applications.
Cables are usually operated with a factor of safety to prevent the cable from being stretched beyond its
elastic limit and to guard against sudden dynamic loads that may occur in logging. With a factor of
safety of 3, the effective safe working load of the inch cable would be 58,800/3 or 19,600 pounds.
This would be the value used to plan the number of logs a cable could carry each logging cycle.
Procedure:
1. Use a single cable or rope to lift the known weight vertically. Measure the tension in the cable with
the spring scale. What should the scale read?
2. Now loop the cable or rope through a pulley. Attach the pulley to the load and lift the load
vertically with both ends of the cable. Measure the tension in each of the cable segments
What is the tension in the two halves of the cable? If it is lower, why?
Will the tension be the same throughout the cable?
3. Tie one end with a spring scale to a fixed object. Measure the height of the scale above the floor.
With the weight still tied to the pulley, move a distance of 10 feet from the fixed end of the cable.
Keeping the height of the end of the cable the same as at the fixed end, pull on the cable until the
weight is completely suspended by the cable. Measure the tension in each end of the cable, the
horizontal distance from the weight to the person holding the free end of the cable. Measure the length
of the cable from the fixed end to the weight and the distance of the load above the floor.
Why is the cable tension higher than when the load was lifted vertically?
How much of the load weight is being supported by each end of the cable?
Without direct measurement, determine the amount of vertical deflection of the cable (the
distance from a chord line connecting the end points and the load).
4. Move the free end of the cable back another 10 feet. Repeat the experiment and measurements of
part 3 and calculate the vertical deflection.
What is happening to the tension cable? Why?
