What’s in this post?
This post is about the theory and testing behind why making a piece of webbing into a sling is 2x the strength of a single strand. We address the specific question about tension on a single section of sling around a carabiner at the end and draw vectors to show what happens at the anchor connections. We use sling strength evidence; load cells to show the tension on the strands compared to the load and slow pull testing supporting the theory that a sling (or loop) is 2x the strength of a single strand.
The sling strength problem
The question landed in my inbox recently:
How is a loop of rope (or sling) theoretically twice as strong as a single strand?
At the end of the loop (i.e. where it goes around a carabiner), isn’t there a point where it’s a single strand?
The rope (or sling) must be under equal tension from either side, thus at the top, bearing the entire load on this single strand?
It’s a good question, and over the years, plenty of people have tried to convince me the answer is yes, that a sling can only be as strong as the single strand at the top.
If that were true, a sling sewn from 16mm nylon webbing rated at 12.5kN would break somewhere close to 12.5kN. We pulled five of them to failure on a slow pull rig. They broke at an average of 26.09kN.
So whatever is happening at the top of that carabiner, the webbing there is not carrying the full load. In this post, I’ll explain why, using vectors, show what load cells read on each side of a loaded sling, and walk through the slow pull test results, including the ones that didn’t come out exactly double and what that tells us.
A quick note on the sling label. The sewn sling in the photo is marked 22kN, which is less than double the 12.5kN webbing rating. The 22kN figure is the minimum strength EN 566 requires a sewn sling to meet. It’s a certification threshold, not a measure of how much the sling actually holds, so it doesn’t contradict the 2x figure.
1. Sling strength theory
To keep the theory clean, assume the connections at both ends are frictionless, the sling is one continuous loop with no extra wraps, and the webbing doesn’t stretch.
What tension do the strands hold?1
- In the case of a sling (shown below), the tension on each side must be equal, or the sling would rotate around the anchor connection.
- As two strands share the load, the tension on each side is half the load (or the load (L) divided by 2 = L÷2).
- If the tension on each strand is L÷2, and x is the breaking strength of a single strand, then the sling increases the ‘strength’ of the system by 2x over a single strand.
Note: The breaking strength of the webbing does not change. The tension in each strand changes, hence the relationship between tension and sling strength.
What about the one strand at the top?
The thing that confuses people (and is the question at the beginning) is the idea that there is one strand at the anchor connection (e.g. carabiner) at the top.
Let’s think about this logically.
- The sling is a continuous round sling.
- There are two strands sharing the load. The tension on each side is half the load (or the load divided by 2 = L÷2).
- The tension on any part of the sling cannot get above half at any point (L÷2) as it is continuous (with the given parameters), even at the top and the bottom.
Try this exercise:
- Rig a sling on an anchor with a small load.
- Choose a point on the left-hand strand and right halfway between the two anchors.
- Do you agree these two points must share half the load (L÷2)? They must be right. How could they not be? There are two strands.
- Holding these two points, move them to the top and bottom.
- The two points have changed position to the top and bottom, however, must have the same tension (with the given parameters).
- Now move these two points back to their original position. Again they have the same tension as before.
What happens at the anchor connections?
While the sling is continuous and has half the load at any point, we need to transfer this back onto the anchor connection. We can use vectors or, more specifically, vector addition in the same direction to demonstrate what is happening.
Vectors and vector addition overview
A vector is a quantity acting on an object with both magnitude (size) and direction. A vector can be drawn as an arrow with a head and a tail. The vector arrow shows the direction and its length the size. All we need to do is set a scale.
When we have two vectors (components) acting on an object in the same direction, we can add them head-to-tail to get the sum (resultant).
Let’s go through some rigging examples using vectors to demonstrate how the tension is transferred back to the anchor connection (carabiner) from the sling.
Note: I have only drawn the vectors on the anchor end for examples 1-3. The vectors on the load end are the same magnitude, just pointing in the opposite direction: for every action, there is an equal and opposite reaction
One strand
- There is one strand; therefore, this has only one vector: the load = 100.
Two separate strands
- There are two side-by-side strands equally loaded; therefore, this has 2 components. A 50-component vector on the left strand (red) and a 50-component vector on the right strand (blue)
- These vectors are added tip-to-tail on the anchor.
- This makes a 100 resultant vector (green) on the anchor. We can add the component vectors together as they are going in the same direction (or 50 + 50 = 100)
Continuous sling
The continuous sling almost has the same explanation as example 2 above.
- There are two strands equally loaded (equalised through the top and bottom anchor connection) therefore this has 2 component vectors. A 50-component vector on the left strand (red) and a 50-component vector on the right strand (blue).
- These component vectors are added tip to tail on the carabiner.
- This makes a 100 resultant vector (green) on the carabiner – but not anywhere on the sling. The tension on the sling cannot get above 50 at any point (L÷2) as it is continuous. The tension is even everywhere on the sling (with the given parameters above).
2. Sling strength evidence
Load cells showing the tension
The theory says each leg carries half the load, and the two halves add up to the load. Load cells let us check that directly.
We hung a 100kg bag from a sling. Multiply 100kg by gravity (9.81m/s²), and you get a theoretical force of 0.98kN. The load cell at the load read 0.96kN.
The sling is set up with two load cells on each side to demonstrate the tension. We have used pulleys as the connections to minimise friction and a 5mm Dyneema cord tied directly to the load cells to minimise stretch.
In theory, the force on the two load cells as part of the sling should be the same and be half the force displayed on the load.
left strand + right strand = Load
The force on the left is 0.46kN and on the right 0.50kN. Compared to the force on the load is 0.96kN.
0.46kN + 0.50kN = 0.96kN
The slings tension is half the load, all the way around, as it is a continuous sling, even at the top and bottom (with the stated parameters).
As stated previously in the theory section, the breaking strength of the webbing has not changed. The load cells prove the theory that we have halved the tension by sharing it between two strands.
Test data
In this part of the post, we are using slow pull testing to back up the theory that a loop (or sling) is in fact double the strength of a single strand.
Aspiring 16mm Nylon webbing (12.5kN) single strand tied with overhand knots (12mm pins)
- Average Max force (5 tests): 9.57kN (77%)
- Comments: Broke at one of the overhand knots, single strand side
Aspiring 16mm Nylon webbing (12.5kN) sling tied with tape bend (12mm pins)
- Average Max force (5 tests): 20.72kN (83%)
- Comments: Broke at one side of the tape bend
Aspiring 16mm Nylon webbing (12.5kN) single strand sewn loops (12mm pins)
- Average Max force (5 tests): 11.59kN (93%)
- Comments: Broke at one of the stitching blocks, single strand side
Aspiring 16mm Nylon webbing (12.5kN) sling sewn (12mm pins)
- Average Max force (5 tests): 26.09kN (104%)
- Comments: Broke at one side of the stitching block
Aspiring 13mm Dyneema webbing (17kN) single strand sewn loops (12mm pins)
- Average Max force (5 tests): 16.93 (100%)
- Comments: Permanent deformation of webbing on the single strand (4), broke in webbing on the single strand (1)
Aspiring 13mm Dyneema webbing (17kN) sling sewn (12mm pins)
- Average Max force (5 tests): 26.80 (79%)
- Comments: Mostly broke except for a few strands at 12mm pin
Aspiring 13mm Dyneema webbing (17kN) sling sewn (30mm pins)
- Average Max force (5 tests): 29.76 (88%)
- Comments: Permanent deformation in webbing (1), mostly broke except a few strands (1), broke stitching block (2), broke in webbing (1)
Testing Analysis
| Items tested | Tested between | Single strand kN | Sling kN | Multiplication Factor (1DP) |
|---|---|---|---|---|
| 16mm Nylon webbing tied | Both 12mm pins | 9.57 | 20.72 | 2.2 |
| 16mm Nylon webbing sewn | Both 12mm pins | 11.59 | 26.09 | 2.3 |
| 13mm Dyneema webbing sewn | Both 12mm pins | 16.93 | 26.8 | 1.6 |
| 13mm Dyneema webbing sewn | Single strand 12mm pins, Sling 30mm pins | 16.93 | 29.76 | 1.8 |
| Average | 1.9 |
Multiplication Factor
Sling (kN) DIVIDED BY Single Strand (kN) = Multiplication Factor (rounded to 1 decimal place – 1DP)
Theoretically, a sling should be 2x the strength of a single strand. As you can see, the results are close to being a 2x multiplication factor (average 1.9x) from a single strand compared to a sling.
As the breaking strength of the webbing has not changed, the only way for this 2x multiplication factor to occur is for the tension on all parts of the sling has to be half the load.
Testing Notes
- Results with the Nylon 16mm sling (Aspiring) were higher than the stated 22kN (EN566) on the label, as the label reflects the EN sling standard, not the test result.
- Results with the Dyneema 13mm the sling were less than 2x (1.6x). The effect of the tight radius of the 12mm pin in combination with the material (Dyneema) properties (such as lower melting point and lower stretch – compared to Nylon) could be the reason for this not reaching 2x.
- In order to remove the influence of the 12mm pins and to get the Dyneema 13mm sling to break in the webbing, we tested with 30mm pins (for comparative purposes). The effect was to move the failure to either the webbing or the stitching block in between the two 30mm pins and increase the breaking strength of the sling by 2kN, and closer to 2x (1.8x) breaking strength of a single strand.
Conclusions
- First, consider that the tension on the continuous round sling is half the load (L÷2) and equal all the way around.
- Second, consider how the tension is applied back to an anchor connection (carabiner) from a sling using vectors.
- Third, if you can’t get your head around the theory, believe the evidence of the load cells and slow pull testing.
Bonus material
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. Testing 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.
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