The post tackles a common assumption in rope work: that a smaller-radius device — a carabiner, mallion rapide, or belay device — produces more friction on a rope than a larger one, since the rope is thought to have more internal resistance as the radius decreases. To find out if this holds up, the team ran friction tests comparing stainless steel mallion rapides at 12mm, 10mm, 8mm, and 7mm, all using the same 8mm static rope. The results are checked against the Capstan Equation, which doesn’t include radius as a factor in the first place.
The Problem
- Many claim that a smaller radius device will produce more friction when a rope runs around it.
- The usual reason stated is ‘the rope has greater internal friction with decreasing radius’.
- This seems logical.
- HOWEVER, is this statement true?
What we are covering
1. The WHAT
Testing the friction. Does the radius of a device matter?
2. The WHY
The theory of how friction works when a rope slides around a cylinder?
3. The HOW
A principle for friction and a practical example
Context
Devices?
By device, I mean anything we use to manually apply friction, for example, a:
- carabiner,
- mallion rapide,
- belay device,
- abseil device,
- lowering device
- or even a friction hitch.
How much friction?
Practically, for abseiling and lowering, it’s about having the right amount of friction to allow smooth, controlled movement of the load (or yourself).
“Friction: Not too much, not too little, just right.”
1. The What
Testing the friction
Now, let’s test the friction coefficient to understand if there is any difference between small and large diameter rapides.
- The known load (L) is 0.1kN, which is the normal force (N), acting at 90 degrees to the rapide, and
- The hand on the other side pulls down on the rope and measures the frictional force (F) with the load cell.
Stainless Steel Rapides
The stainless steel mallion rapides used for testing are:
- Peguet Oval Screw Links – 12mm, 10mm, 8mm, 7mm
Rope
The rope used for testing is:
Sterling Canyon Lux 8mm
- Type: Static rope
- Core: Spectra & Polypropylene
- Sheath: Technora & Polyester
- MBS: 24.2kN
- Weight: 41.2g/m
- Elongation @136kg: 3.9%
The Results
- The load (or normal force – N) is 0.1kN
- I am pulling the load down with a frictional force (F) of 0.2 kN on the other side.
- Friction coefficient (u) is calculated by dividing the frictional force (F) by the normal force (N) OR u=F/N
- Therefore, the coefficient of friction is .2/.1= 2.
I have to pull 2x the load to get it moving, or there is 50% more friction - The coefficient of friction is the same for the 12, 10, 8, and 7mm mallion rapides with the same 8mm static rope.
Does the radius of a device matter?
Q. Does a smaller-radius device have more friction?
A. No, it has the same friction as a larger radius device
For the flexible ropes and a range of sizes we use in rope work, e.g., climbing, caving, canyoning, and rescue.
For many of you, this may be counterintuitive. Let’s dive into theory to understand The Why behind the results.
The Why
Friction when a rope slides around a cylinder?
Where the rope is tensioned (T) differently at each end due to friction.
- The T Load (output) is greater than T Hold. (input)
- Friction is created by the rope and the cylinder rubbing against each other, as well as the rope wrapping around the cylinder.
- For example, for an abseil device, lowering device, or friction hitch to be effective, we need the tension we are holding in our hand (T Hold) to be significantly less than the load’s tension (T Load).
The load could be
- a person abseiling or rappelling,
- a person being lowered, or
- a rescuer being lowered with a patient (with or without a stretcher).
For a given load and a rope running around a cylinder, the main things that influence friction are
- The coefficient of friction,
- The contact angle (θ), and, to a lesser extent,
- The pretension.
1. Coefficient of friction:
- It reflects how “sticky” or “slippery” two materials are when they come into contact.
- It depends on the materials involved (e.g., rope composition, cylinder surface finish) and on conditions such as lubrication or contamination.
- The higher the coefficient of friction, the more force you need to slide one surface over the other.
2. Contact angle:
- The cumulative angle of wrap, or contact angle (θ), around the cylinder.
- If the rope is wrapped halfway around a cylinder, it has an angle of wrap of 180 degrees.
3. Pretension
- The maximum pretension before the rope travels around the friction device or hitch, i.e. the amount you can hold in your hand–grip strength T Hold.
- The amount of tension you can hold affects the friction outcome in a wrap or device, as it increases the frictional force.
- HOWEVER, the coefficient of friction and the contact angle have a much greater (exponential) influence on friction than pretension.
According to the theory
- According to the theory, the cylinder’s radius does not affect the amount of friction (where the rope is flexible and non-elastic).
- Some of you may have started thinking of an extreme example to disprove this theory.
- Rather than doing this, I encourage you to stop for a moment, consider what the theory means, and develop your own thinking.
- The theory I have been discussing is known as the Capstan Equation.
- It was developed by a renowned Swiss Mathematician and a German Engineer over 300 years ago.
The Capstan Equation
T load is the output tension
T hold is the input tension
𝜇 is the coefficient of static friction
𝜃 is the contact angle in radians.
e Euler’s number, approx. equal to 2.71828
The Euler number is the base of the natural logarithm and exponential function. This means that, in theory, the coefficient of friction and the contact angle have a much greater (exponential) influence on friction than pretension (T hold).
The radius of the cylinder is not in the equation.
The How
Conclusions
- There is no evidence that the bending of the rope around a smaller radius increases the coefficient of friction in the standard equipment we use for rope work.
- In the context of a flexible rope running around a carabiner, a friction hitch, an abseil device or a lowering device, the radius has little to no effect on the coefficient of friction.
Principle
Therefore, based on the theory and evidence, the only way to increase the friction of a rope in a device once you start operating is to:
Increase the contact angle, i.e. the cumulative amount of wrapping. That is more wrapping or wraps
Once you start operating, all other parameters are already set:
- CoF (coefficient of friction) – rope, device and conditions
Pretension – your grip strength
Example
- An example of this is a Munter Hitch, as shown below, from lower to higher friction (left to right) and from the least wrapping to the greatest wrapping of the rope.
Video
For more detailed information:
Rope Rescue & Rigging Field Guide (3rd edition)
for cave, canyon, alpine and rock
Provides easy-to-reference practical reminders on essential field techniques for teams and individuals training and responding to rope rescue incidents. 200+ pages, 250+ drawings, A6 size, waterproof paper
Disclaimer
SUMMARY: This post is not an instructional guide. Use at your own risk. We assume no responsibility or liability for any errors or omissions. Any testing undertaken was under controlled conditions with a limited set of equipment. The views, information, or opinions expressed in the post are solely those of the author. For the full disclaimer, click HERE
