Empirical Breaking Strengths of Single Prusiks of Four Diameters on 11 mm Static Rope

Thomas Evans

Western Washington University, Geology Department, 516 High Street, Bellingham, WA 98225,

cavertevans@gmail.com

Introduction:

Breaking strength data from slow pull or dynamic loading of prusiks are readily available through

internet searches (Bavaresco 2002, Gommers 2012, Heald 2009, Kharns 2008, Kovach 2009, Lyon 2001,

Moyer 1998, 2000, Sheehan 2004), and as such, prusik behavior should be well known to most riggers.

However, accessing the raw or processed data from many of these tests is difficult, or impossible, and

when such data are available, they are published in grey literature. Grey literature is composed of papers

that could be removed at any time and are not permanently archived for availability to future generations

of riggers. In addition, this literature often has small enough sample sizes that results are anecdotes that

do not inform the reader of the variability in component breaking strengths. While such testing is

incredibly useful, the lack of a permanent record as well as the small sample sizes (anecdotes) means

ideas about prusik behavior are largely unsupported lore (“old riggers’ tales”).

A rigorous understanding of prusik strength and behavior is crucial for making decisions upon

which human lives literally hang in the balance. As such, research is needed that breaks prusiks in

sufficient quantities to observe the variability in breakage strength and behavior. This research must be

coupled with publication in a permanent archive so the community has access to the data to form their

own opinions. This necessity was recognized by attendees of the 2012 International Technical Rescue

Symposium (ITRS), and when surveyed, there was a request for additional prusik testing (Evans and

Stavens 2012b).

Prusiks can be used in a variety of functions (rope grab, progress capture device, belay, personal

climbing system, etc.). Only one function was tested in this study to limit the number of variables involved

in the investigation. Here the focus is the properties of individual prusiks experiencing a slow pull on a

static rope. This is equivalent to the use of a single prusik as a progress capture device or rope grab in a

haul system. In this configuration, the prusik is often assumed to have twice the rated cord strength. This

assumption seems reasonable because, when tied, a prusik has two strands running from the hitch to an

attachment point (an anchor, haul system, etc.). If the system behaves this way, the prediction is that

when prusiks are pulled to failure they will fail at near twice the cord breaking strength. For example, a

prusik made from 8 mm cord with a rated strength of 13.4 kN should have a breaking strength of ~26.8

kN, which is greater than the knotted strength of an 11 mm static rope (about 27 kN without a knot and

about 19 kN with a knot assuming ~30% strength loss). This prediction can be tested by rigging prusiks in

the manner of function, then pulling them to failure on a static rope. Consequently, the null hypothesis

tested here is that prusiks should break at or above twice the rated cord breaking strength when pulled on

a static rope.

Given the lack of archived data, detailed reporting of test conditions, and ambiguity in the strength

of prusiks in their manner of function, this study has the following goals:

1. Measure and calculate the average breaking strengths of prusiks of different diameters on 11 mm

static rope

2. Report the range of breaking strengths of prusiks of different diameters on 11 mm static rope

3. Report prusik breakage mechanism(s) during a slow pull scenario

4. Record observations of the range of behaviors during prusik breakage

5. Test the null hypothesis that prusiks are approximately twice as strong as the single stranded

cord breaking strength.

Accumulating and reporting these data are important because it provides the raw information for

static system safety factor (SSSF) analyses, and enables informed system engineering by showing the

variability in the average values used. Ultimately SSSF analysis should include average component

strengths, the variability in their breaking strengths, and contextual information based on the system

geometry. In addition, these data can be used to determine if our assumptions of how system

components operate are valid, thus determining if we are rigging based on faulty assumptions.

This empirical data set was gathered by slow pulling prusiks made of Pigeon Mountain Industries

(PMI) cordage in four diameters (5, 6, 7, and 8 mm) on 11 mm EZ Bend and 11.4 mm Isostatic rope.

Materials and Methods:

All new and unused rope and cordage was generously donated by Pigeon Mountain Industries.

PMI 11 mm EZ Bend and PMI 11.4 mm Isostatic were the two static ropes used and 5, 6, 7, and 8 mm

PMI accessory cord used to tie prusiks. The rope was cut in to 89 cm (35 inch) lengths, fused on both

ends, and one end tied with a bowline with a Yosemite tie off. Bowline loops were tied as short as

possible, yielding a rope length of ~30 cm (12 in) for each sample. The 5, 6, 7, and 8 mm cord was cut in

to 79 cm (31 in), 91 cm (36 in), 104 cm (41 in), and 114 cm (45 in) lengths respectively. Cordage ends

were fused then prusik loops tied using a double fisherman knot.

Numerous short lengths of rope and cord were donated. To eliminate the effects of which piece of

rope and cord a sample came from, each piece of rope and cord was assigned a number. An attempt was

made to evenly distribute prusiks from a given piece of cordage across the different pieces of rope.

However, because it was not possible to obtain an even distribution of prusiks from each piece of cord on

pieces of each rope, these data may be biased based on the pieces of rope or cordage used. To see a

list of the characteristics of each rope donated, see Table 1a, and for a list of the characteristics of each

length of cordage donated, see Table 1b. In Tables 1a and 1b, each length of rope or cordage is given a

number so when breaking strengths are reported, the piece of rope or cordage used can be correlated

with which original length it came from.

Three-wrap prusik hitches were tied on lengths of rope with the fisherman knot out of the prusik

hitch, and then tightened hard by hand. Lengths of rope were attached to a motionless fixed anchor with a

½ inch diameter screw link, and the prusiks were connected to a hydraulic ram and a load cell with a ½

inch diameter screw link (Figure 1). The assemblies were photographed and pulled to failure with a slow

pull (12.5 cm/min) using the hydraulic ram.

The results were divided into populations with data divided by rope type and diameter of prusik

used. For each combination of rope (EZ Bend or Isostatic) and cord diameter (5, 6, 7, or 8 mm), which is

eight different combinations, descriptive statistics were calculated including: average, standard deviation,

maximum, minimum, and range of breaking strengths in kilonewtons (kN) and pounds (lbs). Average

breakage strength results with 1 sigma error bars were plotted versus cordage diameter and cordage

cross sectional area, and a linear correlation coefficient calculated for each data set.

Results:

Note: Everyone is welcome to the data and encouraged to utilize it. Data tables are posted on the

ITRS web page in pdf format, and available in Excel format via e-mail request to the author.

Quantitative Results

Table 2 reports the breaking strength for each sample, and reports the average, standard

deviation, maximum, minimum, and range of breaking strengths in kilonewtons (kN) and pounds (lbs) for

each sample population. Table 2 is divided into sub-tables so that each rope and cordage combination

are viewed separately (for a total of 8 different combinations). The average breaking strength of 8 mm

prusiks on 11 mm EZ Bend was 15.46 kN (N=24) with a standard deviation of 0.74 kN, maximum of 17.52

kN, minimum of 14.17 kN, and a range of 3.35 kN. For 7 mm prusiks on 11 mm EZ Bend the average

breaking strength was 12.36 kN (N=27) with a standard deviation of 0.47 kN, maximum of 13.48 kN,

minimum of 11.42 kN, and a range of 2.06 kN. For 6 mm prusiks on 11 mm EZ Bend the average

breaking strength was 9.61 kN (N=30) with a standard deviation of 0.52 kN, maximum of 10.50 kN,

minimum of 8.63 kN, and a range of 1.89 kN. For 5 mm prusiks on 11 mm EZ Bend the average breaking

strength was 8.07 kN (N=43) with a standard deviation of 0.61 kN, maximum of 9.11 kN, minimum of 6.50

kN, and a range of 2.61 kN. Broadly the results were similar for prusiks on Isostatic rope. The average

breaking strength of 8 mm prusiks on 11.4 mm Isostatic rope was 15.59 kN (N=20) with a standard

deviation of 0.54 kN, maximum of 16.76 kN, minimum of 14.77 kN, and a range of 1.99 kN. For 7 mm

prusiks on 11.4 mm Isostatic the average breaking strength was 13.57 kN (N=20) with a standard

deviation of 0.69 kN, maximum of 14.79 kN, minimum of 12.45 kN, and a range of 2.34 kN. For 6 mm

prusiks on 11.4 mm Isostatic the average breaking strength was 9.73 kN (N=20) with a standard deviation

of 0.49 kN, maximum of 10.72 kN, minimum of 8.94 kN, and a range of 1.78 kN. For 5 mm prusiks on

11.4 mm Isostatic the average breaking strength was 8.29 kN (N=19) with a standard deviation of 0.72

kN, maximum of 9.26 kN, minimum of 6.89 kN, and a range of 2.37 kN.

Table 3 is a synopsis of the cordage cross sectional area, rated breaking strength, average,

standard deviation, maximum, minimum, and range of measured breaking strengths of all prusiks tied on

11 mm EZ Bend. Table 4 is a similar synopsis of the cordage cross sectional area, rated breaking

strength, average, standard deviation, maximum, minimum, and range of measured breaking strengths of

all prusiks tied on 11.4 mm Isostatic rope. Both tables are supplied as summaries to ease comparison of

prusik breaking strengths of different diameters on different rope types.

Generally prusiks broke ~2 kN stronger than the rated breaking strength of the cordage, but far

short of twice the rated cord breaking strength. In all cases the minimum breaking strength was greater

than the rated cord breaking strength. Otherwise, the standard deviations were small, as were the

breaking strength ranges, suggesting that new cordage behavior is remarkably consistent.

To visually depict the comparison between rated cord breaking strength and prusik strength,

Figure 2 plots cord diameter versus breaking strength, including rated strengths and data from both

Isostatic and EZ Bend ropes. Figure 3 plots the same information but transformed by plotting the cross

sectional area of cordage versus breaking strength. It is readily observed that prusiks on both the

Istostatic and EZ Bend rope fail above their rated strength (by ~2 kN), but significantly less than twice the

rated cord strength.

Observational Results

It is noticeable that prusiks were, on average, slightly stronger on the 11.4 mm Isostatic rope than

the 11 mm EZ Bend (Figures 2 and 3), which may suggest that rope diameter also influences prusik

breaking strength. However, while there is a visual difference in the prusik breaking strengths on 11.4 and

11 mm ropes, the difference is small and doubtfully practically significant. It is unclear at this time if this is

an important effect, or not, however, it does suggest that prusik breaking strength is not only a function of

the cordage diameter but of the rope diameter as well. This means there is no one breaking strength for a

given prusik diameter.

Prusiks failed in one of three ways. In nearly all prusik failures (196 out of 203, or 96.6%), the

cordage broke in the same place: where the cordage entered the prusik hitch right under the bridge

(Figure 4). In all cases, the strand that broke was the strand closest to the prusik anchor (the upper strand

in Figure 1). When observing the freshly broken cordage ends they were warm or hot to the touch and

some were partially fused, suggesting some form of compression and heating was involved in failure. It is

unclear if this strand broke because it did not have a knot in it (presumably because knots stretch under

load thus reducing tension in the knotted limb of a prusik), or if the strand closest to the prusik anchor

bears more of the load, or that portion of the hitch is compressed the most (thus causing failure). All

prusik hitches were tied the same way around the rope (with the knot bearing limb toward the rope

anchor), so the present data set cannot be used to answer that question. Six out of twenty-four (25%) 8

mm prusiks tied on EZ Bend rope never broke, but the mantle of the rope failed by breaking and slipping

down the core (Figure 5). Mantle failure suggests that the 8 mm prusiks were near the strength of partial

rope failure. This means that the 8 mm prusiks may be nearly strong enough to make the rope the weak

link in the system when rigged in this configuration. One prusik, tied from 5 mm diameter cord on EZ

Bend rope, broke where the prusik bight connected to the anchor at the screw link (Table 2D).

Discussion and Conclusions:

The measurements reported here are only applicable to single prusiks pulling on a rope relatively

slowly. In other words, these data are not applicable to prusiks in use as a belay in a dynamic event (e.g.,

tandem triple-wrap prusik belay), but are applicable to prusiks used as a component of a haul system or

as a progress capture device.

Prusik breaking strengths were higher than the rated strength of a single strand of cordage by

about 2 kN. However, the breaking strengths were not double the breaking strength of the cordage as has

been suggested by some. Rather, the breaking strengths appear to be the strength of one strand of cord

including the additional the manufacturer’s engineered safety factor. This means that for static system

safety factor (SSSF) calculations, instead of using double the cordage strength, as is common practice,

we must use the single strand cordage strength.

The vast majority of prusiks rigged in the configuration tested here break at a strand under the

prusik bridge. This location appears to be the most constricted portion of the hitch, suggesting this may

be the weakest point regardless of prusik diameter. Most notably, the knot in the prusik is not the weakest

point. The weakest point is the strand most compressed under the prusik bridge. This is a similar result to

those of Evans et al. (2012) which demonstrated that knots in the limbs of webbing anchors with four

strands were not the weakest point but webbing that was constricted or smashed was consistently the

weak point in the system.

For 8 mm cord on 11 mm rope it appears that some prusiks are nearly as strong as the mantle.

So when pulling an 8 mm prusik on an 11 mm rope, it is possible for the rope mantle to fail before the

prusik does. This means that additional prusik strength (e.g., by adding multiple prusiks) may not provide

additional system strength increase because the rope mantle will be the weakest link. Further

investigation is warranted to identify the factors involved in prusik/mantle interactions.

Prusik strength is proportional to cordage diameter and cross sectional area (as expected).

However, prusik strength increased slightly on ropes with a larger diameter, but the difference is probably

not statistically or practically significant. This indicates, however, that there is not a single reportable

prusik strength for a given prusik cord diameter. Ultimately this means that when calculating SSSF’s it is

necessary to factor in both variability and the specific conditions under which the prusik is rigged (e.g.

rope diameter).

A notable result is that although we expect prusiks to break at twice the rated cord strength, this

does not happen, which is a similar conclusion from recent webbing research (Evans and Stavens 2011,

Evans et al. 2012, Evans 2013). It appears that a paradigm shift is needed to encompass these new

results. When software (e.g., webbing or cordage) is doubled, but travels through a connector (e.g.,

carabiner or screw link) the strength is not doubled. This has significant ramifications for SSSF

calculations.

Generally we need more research in to how systems are operating, because recent testing has

shown that the results are not as expected. In addition to observational and small scale empirical studies

(Evans and Stavens, 2012a, Evans 2010), we need studies with larger sample sizes to partially constrain

and capture the variability in the systems and equipment. Within the confines of prusiks we need dynamic

testing of tandem triple-wrap prusik belays with large numbers of samples to constrain variability in

system behavior.

Acknowledgements:

This study would not have been possible without the generous donations from PMI, and for the

support of Loui McCurley who facilitated acquisition of rope and cordage on short notice. Dr. Mike Berry

(Montana State University) provided lab space, time on equipment, and the use of numerous pieces of

equipment (load cell, hydraulic ram, and data acquisition hardware and software). Dave Hutchinson

designed and built the testing rig used. Ladean McKittrick provided logistical and mechanical support, as

well as paying for the shipping for cordage. Sherrie McConaeghey purchased the screw links used in all

tests. Sarah Truebe provided valuable assistance in editing the final document, though any errors remain

solely my own.

Literature Cited:

Bavaresco, Paolo, 2002, Ropes and Friction Hitches used in Tree Climbing Operations, http://www.paci.com.au/downloads_public/knots/14_Report_hitches_PBavaresco.pdf

Evans, Thomas, 2013, Empirical Observation of Anchor Failure Points in Old and Retired Webbing, International Technical Rescue Symposium, Albuquerque, New Mexico, November 7-10, 2013, 11 pages

Evans, Thomas, Stavens, Aaron, McConaughey, Sherrie, 2012, Causal Mechanisms of Webbing Anchor Interface Failure and Failure Modes, International Technical Rescue Symposium, Seattle, Washington, November 1-3, 2012, 17 pages

Evans, Thomas, Stavens, Aaron, 2012a, Basic Research Methods for Technical Rescue Science, International Technical Rescue Symposium, Seattle, Washington, November 1-3, 2012, 7 pages

Evans, Thomas, Stavens, Aaron, 2012b, Implementing Example Research Methods at ITRS 2012 and Their Results, International Technical Rescue Symposium, Seattle, Washington, November 1-3, 2012, 14 pages

Evans, Thomas, Stavens, Aaron, 2011, Empirically Derived Breaking Strengths for Basket Hitches and Wrap Three Pull Two Webbing Anchors, Proceedings of the International Technical Rescue Symposium, Fort Collins, Colorado, November 3-6, 2011, 8 pages

Evans, Thomas, 2010, Science as Applied to Technical Rescue Research, Proceedings of the International Technical Rescue Symposium, Golden, Colorado, November 4-7, 2010, 7 pages

Gommers, Mark, 2012, Knots Study Guide – Knots used for life support, Professional Association of Climbing Instructors, http://paci.com.au.downloads_public/knots/01_Knots.pdf

Heald, Dino, 2009, The Performance of Polypropylene Ropes During Static Applications Including Tensioning and Hauling, http://www.pyb.co.uk/ropetesting

Kharns, Brandon, 2008, Nylon and Polyester Prusik Testing, Proceedings of the International Technical Rescue Symposium, Albuquerque, New Mexico, November 6-10, 2008, 2 pages, http://itrsonline.org/nylon-and-polyester-prusik-testing/

Kovach, Jim, 2009, Fall Factors: Do They Apply to Rope Rescue and Rope Access? Proceedings of the International Technical Rescue Symposium, Pueblo, Colorado, November 5-8, 2009, 8 pages, http://itrsonline.org/fall-factors-do-they-apply-to-rope-rescue-rope-access/

Lyon Equipmet Limited, 2001, Industrial rope access – Investigation into items of personal protective equipment, Contract Research Report 364/2001, Health and Safety Executive, http://www.paci.com.au.downloads_public/knots/09_Tests_Lyon_Friction-hitches.pdf

Moyer, Tom, 1998, SLCo SAR Pull-Test Session – November 1998, http://user.xmission.com/~tmoyer/testing/pull_tests_11_98.html

Moyer, Tom, 2000, MRA Intermountain Recert Pull-Test Session – July, 2000, http://user.xmission.com/~tmoyer/testing/pull_tests_7-00.html

Sheehan, Alan, 2004, Load Testing, http://paci.com.au.downloads_public/knots/08_Tests_OberonSES_29July04.pdf

Figure 1: Pull test apparatus. To the left is a stationary anchor, and to the right is the hydraulic ram with a

load cell (8 mm prusik on 11 mm EZ Bend rope used as an example here).

Figure 2: Cord diameter vs. breaking strength in kN for prusiks broken on EZ Bend and Isostatic rope.

5 6 7 8

y = 2.4905x - 4.8153 R² = 0.9794

y = 2.5734x - 4.9302 R² = 0.9715

5

6

7

8

9

10

11

12

13

14

15

16

17

Ave

rage

Bre

akin

g St

ren

gth

(kN

)

Accessory Cord Diameter (mm)

EZ Bend

Isostatic

Rated Strength (OneStrand)

Figure 3: Cord cross section area vs. breaking strength in kN for prusiks broken on EZ Bend and

Isostatic.

Figure 4: Breakage location for the vast majority of prusiks, the strand closest to the load under the

bridge (gently loaded 8 mm prusik on 11 mm EZ Bend rope depicted here).

y = 0.0613x + 2.9984 R² = 0.9938

y = 0.0629x + 3.1972 R² = 0.9735

5

6

7

8

9

10

11

12

13

14

15

16

17

75 85 95 105 115 125 135 145 155 165 175 185 195 205

Bre

akin

g St

ren

gth

(kN

)

Accessory Cord Area (mm2)

EZ Bend

Isostatic

Rated Strength (OneStrand)

This strand broke, right

under the bridge.

Prusik

Bridge

Figure 5: Mantle failure. The mantle elongated, snapped, and slipped down the rope core (8 mm prusik

on 11 mm EZ Bend rope shown here).

Empirical Breaking Strengths of Single Prusiks in Four Diameters on 11 mm Static Rope Thomas Evans

Western Washington University, Geology Department, 516 High Street, Bellingham, WA 98225, cavertevans@gmail.com

Prusik strengths are ‘well known’, but accessing the data from preexisting tests is difficult because the data are not archived. This hinders new riggers from viewing the primary data needed to develop informed decisions. Consequently, the community needs archived freely-accessible testing data. Prusiks can be used for many functions (rope grab, progress capture, belay, etc.), however here only one function was tested to limit variables. Testing focused on individual prusiks experiencing a slow pull on static rope. This is equivalent to use as a progress capture device or rope grab in a haul system. In this configuration, prusik strength is often assumed as twice the rated cord strength. This assumption is reasonable because a prusik has two strands running from the hitch to an attachment. Consequently, the null hypothesis is that prusiks should break at or above twice the rated cord strength. New, unused, rope and cordage was generously donated by Pigeon Mountain Industries (PMI). The two static ropes utilized were PMI 11 mm EZ Bend and PMI 11.4 mm Isostatic, while 5, 6, 7, and 8mm PMI accessory cord was used to tie prusiks. The rope was cut in to 89 cm (35 in) lengths, fused on both ends, and one end tied with a bowline with a Yosemite tie off. Bowline loops were tied as short as possible, yielding a rope length of ~30 cm (12 in) for each sample. The 5, 6, 7, and 8 mm cord was cut in to 79 cm (31 in), 91 cm (36 in), 104 cm (41 in), and 114 cm (45 in) lengths respectively. Cordage ends were fused then prusik loops were tied using a double fisherman knot. Three-wrap prusik hitches were tied on rope lengths with the fisherman knot out of the prusik hitch, and then tightened hard by hand. Rope lengths were attached to a fixed anchor with a ½ inch diameter screw link, and the prusiks were connected to a hydraulic ram and a load cell with a ½ inch diameter screw link. The assemblies were photographed and slowly pulled (12.5 cm/min) to failure. The average breaking strengths of prusiks on 11 mm EZ Bend rope was 15.46 kN (N=24) for 8 mm cord, 12.36 kN (N= 27) for 7 mm cord, 9.61 kN (N=30), and 8.07 kN (N=43) for 5 mm cord. On 11.4 mm Isostatic rope the average breaking strengths of prusiks were 15.59 kN (N=20) for 8 mm cord, 13.57 kN (N=20) for 7 mm cord, 9.73 kN (N=20) for 6 mm cord, and 8.29 kN (N=19) for 5 mm cord. Standard deviations for all populations were around ~0.5 kN, and ranges between 1.78 kN to 3.35 kN. Prusiks failed in one of three ways. In 196 out of 203 (96.6%), the cordage broke where the cord entered the prusik hitch right under the bridge. In all cases the strand that broke was the strand closest to the prusik anchor. Freshly broken cord ends were warm or hot to the touch and some were partially fused, suggesting strand compression was involved in failure. Six out of twenty-four (25%) 8 mm prusiks tied on EZ Bend rope never broke, but the rope mantle failed by breaking and slipping down the core. Mantle failure suggests that the 8 mm prusiks were near the rope mantle strength. One prusik, tied from 5 mm cord on EZ Bend rope, broke where the prusik bight connected to the screw link. Prusik strengths appear to be the strength of one cord strand including the additional manufacturers engineered safety factor. One strand of new 8 mm cord is rated to 13.4 kN, 7 mm cord to 10.7 kN, 6 mm cord to 7.5 kN, and 5 mm cord to 5.8 kN. Generally, prusiks broke ~2 kN stronger than the rated cord strength, but far short of twice the rated cord strength. In all cases, the measured breaking strength was greater than the single strand rated breaking strength, and the weakest point in the prusik was the most constricted strand, not the knot. This has consequences for static system safety factor calculations, because we should be using the single strand cordage strength in calculations not double the cord strength. For 8 mm cord on 11 mm rope, some prusiks are nearly as strong as the mantle. So when pulling an 8 mm prusik on an 11 mm rope, it is possible for the rope mantle to fail before the prusik. The measurements reported here are only applicable to single prusiks pulling on a rope relatively slowly. These data are not applicable to prusiks in use as a belay in a dynamic event (tandem triple wrap prusik belay), but are applicable to prusiks used as a progress capture device or rope grab.

Thomas Evans began caving in 2005 and was instantaneously hooked on vertical caving. As he studied single rope technique for cave access he realized rescue skills are an important part of a rigger’s repertoire, so he started studying rescue material independently and attended trainings through NCRC, BCCR, and ESAR. It was clear through exposure to different rigging instructors that many ideas were propagated in trainings that often had an unknown origin. During graduate school he realized that the skills necessary in the discovery of knew scientific information could and should be applied to technical rescue subjects to improve the quality and quantity of information available to a rigger (both student and teacher alike), and provide a reference that could be cited for why different techniques are used. After stating these ideas at ITRS 2010, he began his own testing program to further the science of technical rescue through targeted analytically robust research.