# The sling strength problem

This question was sent to me 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 is 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?

I’ve had many people attempt to convince me that a sling got to be only the strength of a single strand, as that’s what’s happening at the top.

Take the sling example above; the manufacturer says a single strand is 12.5kN for this 16mm Nylon tubular webbing. However, the rating on the sewn sling is 22kN (EN566). This breaking strength of 22kN is more than a single strand. What’s up with this? There must be something else going on here.

#### To answer this question, we are covering:

##### 1. Sling strength theory

- Explain the theory behind why making a piece of webbing into a sling is 2x the strength of a single strand (this applies to any cord or rope made into a loop as well).
- Address the specific question at the beginning about the tension on a single section of sling around a carabiner at the end.
- Draw vectors to show what happens at the anchor connections.

##### 2. Sling strength evidence

- Use load cells to show the tension on the strands compared to the load
- Slow pull testing to back up the theory that a loop (or sling) is in fact double the strength of a single strand.

##### 3. Bonus material

- I have attached a download of all the testing. So check that out as well at the end.

# 1. Sling strength theory

## What are the parameters?

So you (we) don’t get distracted by other things, for the exercise, to understand the theory of what’s happening with the sling, let’s assume the following parameters:

- anchor and load connections are frictionless,
- the sling is a continuous round sling without additional wraps, and
- the sling has no stretch.

**What tension do the strands hold?**^{1}

^{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.

### W**hat 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 together to get the sum (resultant). Let’s look at an example below, pushing on an object to the right.

- A 5-component vector (red) and a 7-component vector (blue) act on the object to the right.
- We can add the two vectors together by drawing them head to tail.
- We can now draw a resultant vector from the first vector’s tail to the second’s head and as the vectors are in the same direction, 7+5=12.
- We no longer need the component vectors.

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 action, there is an equal and opposite reaction

**Example 1 Single strand**

- There is a single strand; therefore, this has only one vector: the load = 100.

**Example 2 – Two 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)

**Example 3 – 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).

**Example 4 – Basket hitch single strand**

As someone asked, I decided to add this to the post.

The basket hitch single strand combines the continuous sling at one end and two strands at the other. It almost has the same explanation as examples 2 and 3 above.

- Two strands are equally loaded (equalised through the top 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**at the top (anchor end). These component vectors are added tip to tail on the**load**at the bottom (load end). - This makes a 100 resultant vector (green) on the
**carabiner**AND a 100 resultant vector (green) on the**load**– but not anywhere on the sling. The tension on the sling cannot get above 50 at any point (L÷2) as it is continuous from load to load. The tension is even everywhere on the sling (with the given parameters above).

# 2. Sling strength evidence

If you can’t get your head around the theory how about some hard proof?

### Load cells

In this part of the post, we are using 3 load cells to demonstrate what’s happening with the tension on the sling.

The setup is a bag with 100 kilograms of mass. When we hang this on an anchor we get close to 1kN of force. As Force = Mass x Acceleration, with acceleration being gravity (around 9.81 m/s squared) the force on the load cell here should be in theory 0.98kN. The actual was 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.

Slow pull tests were at 100mm/min. See attached testing report for more information.

**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 |

**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 was lower than 2x. See the testing report for more analysis.

# 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.

For the full disclaimer click HERE