# Climbing Ropes

Length: 3 weeks (introductory lecture, independent study and presentations)

Level: 2nd year Sports and Materials Science course

Aims: To consider polymeric fibre and rope production, and to gain a broad picture of the area, including environmental effects on rope durability and wear.

Key skills: Group working, presentation skills, independent research.

Assessment: Group report and presentation.

This is a group-based case study on the materials in rope-based sports, with web searches for specific product details, and presentation of the findings. This exercise requires you to consider polymeric fibre and rope production, and mechanics-of-materials related to sports activities. The problem is how to make rock climbing a safe activity. Ropes are used to protect climbers who fall off a rock face. 50 metres of rope has to be carried to the rock face, so its mass must be moderate. The rope must affordable and it must survive several years of use.

Session 1

Sport and some mechanics background

Short video clip of rock climbing

Group allocation (5-6 members)

Brainstorming in groups on design criteria for climbing ropes

Session 2

Independent study and research

Session 3

Presentations

• What are the design criteria for a climbing rope?
• Why are ropes made from multiple fibres and not a single rod like structure?

Work through the following exercise to help your explanation. If a polymer were in the form of a solid rod of diameter D, this would have 2nd moment of area I

If the solid rod is replaced by n fibres, the total cross sectional area A of polymer must be kept constant, so the rope has constant tensile failure load. Each fibre has diameter

d = D / ,

Why is the expression for d correct?

So has a 2nd moment of area

In a bent rope, as there is no bonding between the fibres, these act as separate ‘beams’, so the total 2nd moment of area is the sum of that of individual fibres (consider bending a stack of plastic rulers which are free to slide over each other)

Show how the following diameters affect I by substituting typical values of D = 12mm and d = 0.05. Use the above to justify your answer in the report.

• Describe how the filaments are produced

Assessment

Each group must submit a single written report addressing the above tasks and summarising the main findings and conclusions drawn. The report is to be 1500 words long (about 4 pages) not including diagrams. Each group must also give a 10 minute presentation (40% of the case study mark). Ensure you introduce who you are and the main areas of your talk. Finish with a slide showing the main conclusions. Click for tips on presentations and reports.

Resources