effectiveness of mountaineering manual belay/abseil devices

ORIGINAL ARTICLE

Effectiveness of mountaineering manual belay/abseil devices

W. J. Stronge • Mathonwy Thomas

� International Sports Engineering Association 2013

Abstract Mountaineers and rock climbers use a belay

device to increase tension in the rope that links the belayer

to a falling climber—this rope slows and finally stops the

fall. With a manual (passive) belay device the belayer can

hold a force of several kN although he/she applies a hand

force of only 0.2–0.35 kN on the rope; i.e. the device

increases the hand force by a factor between 5 and 10. This

investigation provides dynamic measurements of force

amplification by various manual belay devices when used

on a range of both wet and dry climbing ropes and it

examines the source of force amplification in these devices.

The force amplification is found to be due to a combination

of friction and distortion of the rope as it traverses around

tight corners within the device. In modern devices, the

tension amplification due to distortion exceeds that due to

friction.

Keywords Belay device � Friction � Amplification

factor � Device comparison � Climbing ropes

1 Introduction

The mountaineering term ‘‘abseil’’ or ‘‘rappel’’ describes a

controlled slide down a rope that is fixed to an anchor at the

top, while ‘‘belay’’ describes a procedure for limiting the

length of fall for a roped climber by either preventing or

controlling the slippage of the rope as it passes through the

belay. In both cases, the belayer/abseiler controls the rate at

which rope passes through the belay/abseil station by

tightening or loosening his/her grip on the ‘‘tail’’ end of the

rope. Since hand strength is normally insufficient to control

rope tensions that can be several times larger than body

weight, a belay/abseil device is typically used as a ‘‘force

multiplier’’ to increase the effective control hand force that

resists flow of the rope through the belay device [1–3]. To

carry less weight, most climbers carry a single device for

both abseiling and belaying.

Manual (passive) belay/abseil devices are designed

such that as the rope extends under a suddenly applied

load, it is required to follow a tortuous route slipping

around small radius corners in the device. As rope passes

through the device, friction between the aluminium

device and the polyamide rope dissipates energy. This

friction amplifies the hand force that restrains slippage of

rope through the device. The first devices were manu-

factured in the 1960s; they were thick aluminium plates

containing a pair of chamfered slots through which a

bight (loop) of rope could be passed (the Sticht plate).

On the back side of the plate, a carabiner was passed

through the loop and this carabiner was attached to the

belayer’s harness. The ‘‘live’’ end of the rope is con-

nected to the lead climber while the ‘‘tail’’ end is grip-

ped by the hand of the belayer. If the lead climber falls,

tension in the rope above the device can be as much as

10 times larger than the weight of the falling climber. To

arrest the fall, this tension must be resisted by the

product of the belayer’s grip on the tail of rope and the

amplification factor of the belay device [4].

The design of belay/abseil devices has undergone

minor changes from that of the original Sticht plate—the

radii of curvature around edges in the device have grown

tighter and V-grooved exit passages have increased

friction by increasing the normal force acting on the

rope. These changes have roughly doubled the

W. J. Stronge (&) � M. Thomas

University of Cambridge, Cambridge, UK

e-mail: [email protected]

Sports Eng

DOI 10.1007/s12283-013-0147-6

amplification of current manual belay devices in com-

parison with the Sticht plate.

Generally, it is believed that manual belay/abseil devi-

ces rely on friction to generate the multiplication in tensile

force in the rope between the ‘‘tail end’’ and the loaded

‘‘live end’’ of the device; i.e. the tensile load required to

induce slippage of the rope through the device is the sum of

friction in the device plus the grip force on the tail of the

rope [5]. If this conjecture is correct and Coulomb’s

coefficient of friction (COF) l is independent of normal

force, then across a device without grooves, the ratio

between the tensile load T1 on the live end and the grip

force T0 on the tail end of the device can be calculated as

T1=T0 ¼ elh;

where h is the sum of the angles through which the rope is

bent within the device. This expression, termed the capstan

or Euler equation, applies to sliding friction between a thin

flexible rope and a cylindrical drum. It describes a tension

ratio that is independent of the radius of curvature around

corners within the device. Minor effects due to elongation

of the rope and a power-law decreasing COF have been

considered by Jung et al. [6]. One question addressed in

this paper is whether surface friction between rope and

device is the only force that resists the rope being drawn

through a belay/abseil device.

2 Devices and ropes that were tested

2.1 Mountaineering/rock climbing ropes

Climbing ropes are required to be strong, elastic, light-

weight, easy to securely knot and have good resistance to

cutting over an edge. They not only hold a fallen climber,

but also bring the falling climber to rest without too large

an acceleration. Thus, they are elastic for tensile forces

somewhat larger than body weight but can suffer perma-

nent damage when required to hold a high load (a leader

fall with a Fall Factor [1.4) [5].

Currently, mountaineering or rock climbing ropes use

kernmantle construction; this has a central core composed

of a bundle of 9–11 cords—each with a large angle of

twist. The direction of twist for half the cords is clockwise

and the other half anti-clockwise so that under tension,

there is no net twist of the core. This core is contained

within a woven sheath which provides protection against

abrasion, dirt, uv-damage, etc. Dynamic climbing ropes are

made of Polyamide 6/6, a type of nylon.

Ropes for use in wet conditions can be purchased with

either the sheath or both core and sheath composed of fil-

aments that have been chemically treated to reduce water

absorption. Those with a treated sheath are termed ‘‘dry’’

while treatment of both sheath and core results in a ‘‘super

dry’’ or ‘‘golden dry’’ rope. The water repellent treatment

of the sheath of both dry and super dry ropes is thought to

increase their abrasion resistance and decrease friction

when running over rock or through an aluminium belay

device.

2.2 Belay/abseil devices for mountaineering ropes

Belay/abseil devices are used as a force multiplier so that

the grip force of one hand can control rope tension–tension

which can be several times larger than body weight.

Manual belay/abseil devices are required to be secure, easy

to set-up and lightweight; preferably, they are free of any

moving parts and difficult to assemble incorrectly. At least

two distinct types of devices are commonly used to assist a

belayer in holding a fall. Both types are typically made

of Aluminium which is lightweight and a good heat

conductor.

Huit Figure 8 or 8-Ring As the name implies, these

devices are shaped like the numeral 8 with a large and a

small hole. A bight (loop) of rope is passed through the

large hole and looped back around the neck that joins the

holes, before a carabiner (snap-link) is used to attach

the small hole to the belayer’s harness or the belay station

(see Fig. 1). In Fig. 1, the loaded rope enters the photo from

the top while the belayer grips the lower, tail of the rope.

Huit 8-Rings can be used with a wide range of different

diameter ropes. They are easy to set-up and operate

Fig. 1 Huit 8-Ring threaded with rope. Hand force applied to tail of

rope on right of device while the belayer is clipped to the ring at the

bottom

W. J. Stronge, M. Thomas

smoothly when abseiling/rappelling but in many cases,

they produce insufficient force for application as a belay

device. The device also tends to cause residual twist in the

rope which then untwists during subsequent abseils. The

8-Ring is larger and heavier than conical devices.

Tubular devices A wide range of plate or cone devices

have a pair of slots in the bottom of a truncated cone (see

Fig. 2a–c). They are known by trade names such as Sticht

plate, Black Diamond ATC, Petzl Verso and Petzl Reverso.

These devices are set-up by passing a bight of rope through a

slot and then clipping the bight of rope with a carabiner

which is attached to either the belayer’s harness or the belay

anchor. In almost all cases, a 2nd slot is provided for a second

rope which is commonly used either while abseiling or when

leading while using double rope technique.

Tubular devices or cones are small, lightweight and

simple to use for climbing ropes from 8.1 to 10.4 mm

diameter. The devices with V-shaped grooves in the exit

slot (Verso and Reverso) tend to be more effective than

devices without exit grooves. The action of the grooves is

similar to that of a V-belt pulley, essentially increasing the

normal force acting on the rope that is passing through the

grooved section of the device [7].

3 Measuring effectiveness of belay/abseil devices

The effectiveness of a belay device in amplifying the hand

force acting on the rope is obtained from a load amplifi-

cation factor;

Amplification ¼ T1=T0; ð1Þ

where T1 is the rope tension on the live side and T0 is the

rope tension on the tail side of the device. This amplifi-

cation also has been termed a brake factor [2, 9]. The load

amplification is obtained from measurements of the force

required to draw the rope through the device when the tail

end of the rope is loaded by a specified weight (i.e. the

hand force). Measurements of the load amplification factor

were made with the block and tackle rig illustrated in

Fig. 3 which was mounted on a tensile test machine. At the

device, the tension T1 was obtained from the recorded

tensile force at the load sensor, while the hand force

T0 = Mg was the weight Mg of a mass hung on the tail of

the rope. The purpose of the pulley system is to increase

the speed at which the rope could be drawn through the

device; the present tests were performed with a rope speed

through the device of 0.075 m/s and hand force angle

a = p/9.1

The tension required to draw the rope through the device

was measured for hand forces varying from 50 to 207 N.

These hand forces compare with a range of 150–350 N

measured for recreational rock climbers (see ‘‘Appendix

2’’). Figure 4 shows a set of typical traces obtained for

Fig. 2 Tubular belay devices a Sticht plate, b ATC, c Verso. Hand force applied to tail of rope on left of device while the round bar is a

carabiner attached to the belayer

1 Rope speed through the device had little effect on the amplification.

For each device, an increase in rope speeds from 0.042 to 0.074 m/s

resulted in less than 3 % decrease in amplification. This is in

agreement with experiments by Fenz [8] on friction between woven

PTFE and stainless steel but it contradicts the viscous force

assumptions made in the analysis of Fuss and Niegl [9].


Fig. 3 Block and tackle rig used to increase rope speed through device. Notice that the hand force T0 acts on the rope which passes freely

through a hole in the lower test bar

Fig. 4 Regions 1–4 of tensile force at load sensor for hand forces of 9, 58, 107 and 156 N. Three tests at each hand force demonstrate

repeatability of measurement


hand forces of 9, 58, 107 and 156 N. This graph of force as

a function of time has an initial period (1) where the force

is being distributed through the various segments of rope,

period (2) where the rope is stretching, period (3) where

there is steady pulling of the rope through the device and

period (4) after the displacement of the cross-head on the

testing machine is stopped. The plateau region 3 of these

curves was taken as the steady state force required to pull

the rope through this system. The rope tension force T1 was

obtained from the measured force by a calibration which

took into account the measured friction in the pulleys as

well as the multiple strands of rope between the upper and

lower blocks.

3.1 Amplification factor of abseil/belay devices

For six new ropes with diameters ranging from 8.1 to

11 mm, Fig. 5 shows a comparison of the amplification

factor as a function of hand force for the Huit 8-Ring and

four different conical devices. For all ropes and devices,

Fig. 5 Amplification factor for various belay devices on 6 ropes; a 11 mm dia., b 9.7 mm dia.—Classic, no water repellent treatment, c 9.7 mm

dia.—Dry, d 9.7 mm dia.—Super Dry, e 8.1 mm dia.—Dry


the amplification decreases with increasing hand force. It

will be shown that this is because of decreasing friction

with increasing hand force—a result that is contrary to

Coulomb’s law of friction where the COF l is independent

of the normal force.

Comparison of Fig. 5a–f shows that for all devices, the

amplification decreases with rope size; i.e. for the hand force

of any particular belayer T0, the rope tension T1 generated on

the ‘‘live’’ side of the device for an 11 mm diameter Apollo

rope is 70 % larger than that generated by at 8.1 mm dia. Ice

Line rope. For all rope diameters, the Reverso has the largest

amplification while the Huit 8-Ring and Sticht plate have the

smallest amplification. For large diameter ropes, the Sticht

plate is more effective than the 8-Ring while for small

diameter ropes, this order is reversed; otherwise, the ampli-

fication factor of different devices is in the same order,

independent of rope diameter or hand force. The effect of

rope diameter on amplification factor is shown directly in

Fig. 6 where for 3 different devices and ropes with diameters

that range from 8.1 to 11 mm, the amplification factor is

plotted as a function of hand force.

In every case, the largest amplification occurred with the

Reverso device and the smallest amplification occurred with

either the Sticht plate or the Huit 8-Ring. The amplification

of the Reverso benefits from thin walls which force the rope

to pass around small radius of curvature corners and a

V-grooved exit channel which effectively increases the

normal force acting within the device. Among the devices

being tested, the Sticht plate and Huit 8-Ring force the rope

to have a relatively large minimum radius of curvature—a

minimum radius of curvature that is more than twice as large

as that in the conical devices. Previous measurements of

amplification (braking coefficient) obtained during drop

tests using various devices with a 9.7 mm Booster rope gave

somewhat smaller amplification than the results of the

present investigation; nevertheless, these results were con-

sistent with the present measurements in that the smallest

amplification occurred with the 8-Ring [2].

For the Booster 9.7 mm diam. rope, the effect of water

repellent treatment on the amplification factor was mea-

sured. Both Dry and Golden Dry versions of this rope were

compared with the untreated Booster Classic. There was no

significant difference in the amplification factor for new

ropes in a dry state as a function of whether or not they had

received the water repellent treatment. For conical devices,

the untreated rope had a slightly larger amplification

whereas for the 8-Ring, the Booster Golden Dry rope had

the largest amplification, but these differences were small.

Fig. 6 Effect of rope diameter on amplification factor for a Reverso, b ATC and c Huit 8-Ring


3.2 Comparing amplification factor of used and new

ropes

Figure 7 shows the amplification factors as a function of

hand force for three different ropes which had experienced

usage as described in Table 1. These curves can be com-

pared with similar curves for new ropes (Fig. 7). The only

obvious signs of wear on these well-used ropes were some

broken threads protruding from the mantel and slight

darkening of the mantel colour. Despite wear being minor

in terms of the surface appearance, the amplification fac-

tors for used ropes were 10–20 % larger than those for new

ropes. Subsequently, we will show that the COF for these

used ropes also was larger than the COF for new ropes.

3.3 Comparing amplification factor of dry and wet

ropes

Figure 8 shows the amplification factors for the various

belay/abseil devices as a function of hand force for wet

and dry states of the untreated Booster Classic and the

water repellent Booster Golden Dry ropes. The wet state

was obtained by immersing the rope in water for 12 h

immediately prior to testing. Absorbed water acts as a

plasticizer that reduces the elastic modulus of yarn and

reduces the number of falls to failure; this occurs because

absorbed water molecules decrease the strength of

molecular hydrogen bonds within the polyamide fibres

[10, 11]. At the same time, water within the rope

Fig. 7 Amplification factor of devices on used ropes; a 10.2 mm dia. new, b 10.2 mm dia. used (1), c 10.2 mm dia. used (2), d 8.1 mm dia. new,

e 8.1 mm dia. used


increases inter-yarn abrasion and causes some damage to

filament surfaces [12, 13].

As noted previously, in the dry state the Reverso device

on the untreated rope had a somewhat larger amplification

than the same device on the water repellent rope. For dry

rope, all other devices gave roughly the same amplification

for the treated and the untreated ropes.

The effect of water on the untreated rope was to

decrease the amplification factor for almost all devices on

the order of 15 %; i.e. the devices were less effective if the

rope was wet. The Huit 8-Ring was the only exception; on

the untreated rope, it showed a small increase in amplifi-

cation when the rope was wet rather than dry. For the water

repellent rope however, there was little difference in

effectiveness between dry and wet ropes. This decrease in

amplification was measured despite the COF of wet rope

being somewhat larger than that for dry rope (see

‘‘Appendix 2’’). In fact, both the Verso and Huit 8-Ring

devices were slightly more effective on wet rather than dry

rope. For both wet and dry ropes, the Verso and Reverso

provided the largest amplification while the Huit 8-Ring

and Sticht plate gave the smallest amplification.

4 Causes of the amplification factor

There seem to be two sources of retarding force acting in

belay/abseil devices, (a) friction of the tensioned rope

Table 1 Mountaineering rope characteristics

Rope

name

Diameter

(mm)

Treatment Notes

Apollo II 11 Dry Heaviest rope on test

Edlinger 10.2 Untreated New rope

Edlinger

(Used 1) 10.2 Untreated Used 35 days lead

rope ? 3 months top rope at

indoor wall

(Used 2) Used for 6 months as ‘in situ’

rope at indoor wall

Booster

Classic

9.7 Untreated New rope

Booster

Dry

9.7 Dry New rope

Booster

Golden

Dry

9.7 Super Dry New rope

Stinger

(used)

9.4 Dry 100 day’s use, both as a winter

and alpine rope. Later used

for 5 years to practice knots

Ice Line 8.1 Dry New rope

The Ice Line is designed for

use as a ‘half rope’; this rope

is at the lower limit of the

recommended range of rope

diameters for belay devices

Ice Line

(used)

8.1 Dry 9 seasons use for alpine, winter

and traditional rock climbing

Fig. 8 a Booster Classic (untreated) rope in both wet and dry states with each belay device, b booster Golden Dry rope in both wet and dry states

with each belay device


around corners and (b) inter-cord slippage due to bending

of the fibrous rope within the device.

(a) As the rope slides through the rounded corners in a

belay/abseil device, friction resists sliding of the rope. The

sliding friction is represented by the capstan equation for

slender ropes;

T1=T0 ¼ elh; ð2Þ

where h is the sum of the angles through which the rope is

bent within the device. The COF l in this equation is a

property of both the sheath of the rope and the Aluminium

surface over which it slides. This equation assumes sliding

throughout the entire contact area between the rope and a

cylindrical surface. It is noteworthy that the capstan

equation is independent of the radius of curvature of the

rope around the cylindrical surface—it is applicable also if

the radius of curvature is not constant. This source of

amplification, including the effect of the V-grooved exit

slots, has been described by Belofsky [7].

Measurements of the COF l shown in the Appendix,

Table 2, were made with the rope draped over a large

radius Aluminium cylinder; the ratio of cylinder radius Rcyl

to radius of a standard oval carabiner Rcrab was on the order

of Rcyl/Rcrab = 16. The aim of this large cylinder radius is

to make negligible any effect of bending on the amplifi-

cation factor.

In addition to measurements of the COF for dry ropes

shown in Table 2, similar measurements were made on

ropes that had been soaked in water for 12 h, Table 3. A

summary comparing the COF for wet and dry ropes, as

well as for new and used ropes is shown in Fig. 9. The

worn surface of used rope results in a small increase in the

COF; the wet rope resulted in a larger increase on the order

of 10–20 %. Notice that the rope used to obtain Fig. 9 was

an Edlinger with no water repellent treatment. However, a

similar increase in COF was obtained after the dry treated

Ice Line rope was soaked in water.

It is important to recognise that Fig. 9 indicates that for

both dry and wet ropes, the COF is decreasing with

increasing rope tension. This decrease contributes to the

decrease in amplification which occurs with increasing

hand force.

(b) But friction does not account wholly for the ampli-

fication of rope tension in a belay/abseil device. As shown

in Fig. 10, the amplification increases with decreasing

radius of edges in the device; i.e. with edge sharpness.

These measurements were made with the rope draped over

cylindrical bars so that h = p. For an edge radius similar in

size to the cross-sectional radius of a lightweight carabiner

(4.25 mm), friction can account for only 55 % of the

amplification. Conical belay devices incorporate even

smaller edge radii (on the order of 1.5–2 mm) that result in

a smaller part of the total amplification being due to fric-

tion. In Fig. 10, the best fit line for the effect of edge radius

on amplification is represented by

T1

T0

¼ 1:7þ 0:8Rrope

Redge

: ð3Þ

This amplification factor was obtained for large hand

forces, between 0.254 and 0.354 kN. In this range, the rope

tension caused by hand force has only an insignificant

effect on the dissipation due to bending.

Titt [1] has suggested that the additional, non-frictional

energy dissipation is related to bending the rope through

tight radius bends. Distortion of the cross-section results

from slippage between cords in the core of the rope

because of the difference in fibre length between the inside

0.0 0.2 0.4 0.60.14

0.16

0.18

0.20

0.22

0.24

0.26

0.28

0.30co

effic

ient

of f

rictio

n, µ

hand force (kN)

New Dry EdlingerUsed (2) Dry EdlingerNew Wet EdlingerUsed (2) Wet Edlinger

Fig. 9 Comparison of friction coefficients for wet and dry, new and

used ropes (10.2 mm dia. Edlinger)

0.0 0.5 1.0 1.5 2.0 2.5 3.01.5

2.0

2.5

3.0

3.5

4.0

4.5 Ice Line 8.1mm 0.254kN Edlinger 10.2mm 0.254kNApollo 11mm 0.254kNIce Line 8.1mm 0.354kNEdlinger 10.2mm 0.354kNApollo 11mm 0.354kN

ampl

ifica

tion,

T1/

T0

edge sharpness, Rrope/Redge

Fig. 10 Amplification variation with edge sharpness ratio for hand

forces of 0.254 and 0.354 kN on new Ice Line, Edlinger and Apollo

ropes


and the outside fibres in the core as it passes around a bend.

Part of this difference in length comes from a difference in

stretch of the fibres and the associated variation in fibre

tension across the core, but this difference also results in

shear stress and slip between the cords in the core. After a

tensioned rope has passed around a tight bend, it is

noticeable that the cross-section has changed from circular

to oval as a result of internal slippage between the cords,

although after a distance of perhaps five rope diameters

beyond the bend, the cross-section of the tensioned rope

has returned to circular.

Assuming that the result in Fig. 10 for negligible edge

sharpness represents solely the effect of friction between

the mantel and a smooth Aluminium device, and that the

effects of bending and friction are independent, an estimate

for amplification due both to mantel friction and rope

bending can be obtained as

T1

T0

¼ 1þ 0:47Rrope

Redge

� �elh: ð4Þ

While the experiments in Fig. 10 were performed with a

wrap angle of h = p, experiments by Titt [1] have shown

that for small wrap angles h\p/2 the tensile force

required to distort the cross-section of the rope increases

with increasing h. Titt estimated that for a 10 mm diameter

rope running through a Sticht plate with 4 mm radius bends

of 80�, 185� and 42�, that 61 % of the amplification factor

is from bending while the remaining 39 % is from friction.

Equation (4), which does not take into account any

variation of amplification due to bending with angle h,

provides an estimate that 38 % of the Sticht plate

amplification is due to bending and 62 % is from friction.

5 Conclusion

The amplification factor is a measure of effectiveness of

belay/abseil devices. Rope tension on the ‘‘live’’ side of the

device leading to the falling climber is the product of the

hand grip force on the rope and the amplification factor.

Amplification depends on both (1) friction between the

belay device and the nylon rope and (2) dissipation of

energy within the rope due to slip of cords and fibres as the

tensioned rope slides around small radius corners. In the

range of hand force 100–200 N, all ropes and devices show

a decrease in amplification with increasing hand force as

noted previously by Fuss et al. [8]; nevertheless, tension T1

in the ‘‘live’’ end of the rope continually increases with

increasing hand force. The decrease in amplification has

been related to the coefficient of sliding friction between

the mantel of the nylon rope and the aluminium device—a

friction coefficient which decreases with increasing normal

pressure (see ‘‘Appendix 1’’).

Tubular belay devices with ‘V-shaped’ exit grooves and

small radius edges provide amplification on the order of

50 % larger than that of the Huit 8-Ring or Sticht plate. For

a moderate hand force of 200 N on a dry 10.2 mm

climbing rope, the tubular devices (Verso, Reverso) have

amplification *8 while the Sticht plate and 8-Ring have

amplification *5. The ATC has a little larger amplification

than the Sticht plate or 8-Ring. Transverse V-shaped

grooves in the exit channel are the probable reason for the

superior performance of the Verso and Reverso; these

grooves increase the normal force in this segment of the

belay device. All belay devices have larger amplification

with larger diameter ropes and they are more effective with

worn rather than new ropes. For dry treated ropes in a dry

state, water repellent treatment has a negligibly small effect

on both the COF and the amplification factor.

After soaking in water for 12 h, climbing ropes without

water repellent treatment suffer a 15 % reduction in

amplification, whereas dry-treated ropes show little effect

of water. The reduction in amplification for wet classic

ropes is due to a combination of water increasing the COF

between the rope surface (mantel) and the Aluminium

belay device while at the same time, water reduces the

distortion energy related to slippage between cords within

the core of the rope. Dry treated, water repellent ropes

show almost no difference in amplification whether wet or

dry.

Appendix 1

Measurements of COF for various ropes

The kinetic COF between the mantel of the rope and pol-

ished Aluminium was measured for rope sliding over a

large radius Aluminium cylindrical bar. The ends of the

rope on either side of the bar were loaded by weights

representing (1) hand force and (2) tension in the rope

connected to the falling climber. For the minimum differ-

ence in weights where the rope slipped freely over the

cylinder, these measurements were used in Eq. (2) to obtain

an estimate of the Coulomb friction coefficient.

Note that the COF between the nylon rope and aluminium

is decreasing with increasing hand force; a result previously

noticed by Titt [1]. For rubber sliding on aluminium, Persson

[14] showed a similar decreasing kinetic COF with

increasing normal pressure; he attributed this to vibrational

energy dissipation excited by the relatively soft polymer

sliding over hard asperities on the aluminium surface. Fenz

[8] measured friction between woven PTFE and stainless

steel which again exhibited a decrease in friction coefficient

with increasing pressure, possibly due to lubrication by

surface melting of the high points on the polymer.


Appendix 2

Measurement of ‘‘hand force’’

Table 4 lists the mass in kilogram of the maximum weight

lifted by a recreational rock climber using either the left or

right hand gripping a 9.4 mm diameter climbing rope.

These tests were conducted with either a bare hand or the

hand covered by a pigskin belay glove and without wrap-

ping the rope around the hand.

The tests indicate a wide range of hand force (grip

strength) varying from 0.074 to 0.368 kN. With a belay

glove, the hand force is slightly smaller. Generally, these

forces are larger than the 0.16 kN quoted by Manin et al.

[2]. For Table 4 the duration of gripping the rope is\10 s,

similar to the time occurring while holding the initial jolt

Table 2 Kinetic friction measurement for climbing rope sliding over large radius aluminium cylinders (dry state)

Hand

force

(N)

Al. cylinder

radius (mm)

l Edlinger

(new,

10.2 mm)

l Edlinger (used

(1), 10.2 mm)

l Edlinger (used

(2), 10.2 mm)

l Booster Classic

(new, 9.7 mm)

l Booster gold dry

(new, 9.7 mm)

l Ice Line-dry

(new, 8.1 mm)

56 83 0.20, 0.19 0.23, 0.23 0.21, 0.25 0.18 0.19 0.19, 0.20

58 38

96 83 0.19

105 83 0.20, 0.18 0.20, 0.19 0.21, 0.21 0.17, 0.15 0.17, 0.16 0.17, 0.19

154 83 0.17 0.17 0.20, 0.21 0.16 0.17

157 76 0.25

204 83 0.17, 0.16

207 38 0.21

207 76 0.21

207 83 0.20 0.17 0.19, 0.21 0.15 0.16 0.18

253 83 0.19, 0.16 0.17, 0.21 0.15 0.15 0.15, 0.17

351 83 0.18 0.17 0.20 0.15 0.17

401 83 0.17 0.17

499 83 0.17 0.16 0.17, 0.18 0.15 0.14 0.15, 0.15

597 83 0.15 0.16 0.16

794 83 0.15

Table 3 Kinetic friction measurement for climbing rope sliding over

large radius aluminium cylinders (wet state)

Hand

force

(N)

Al.

cylinder

radius

(mm)

lEdlinger

(new,

10.2 mm)

l Edlinger

(used (1),

10.2 mm)

l Edlinger

(used (2),

10.2 mm)

l Ice

Line-dry

(new,

8.1 mm)

56 83 0.23, 0.30 0.27, 0.36 0.23, 0.36 0.23

105 83 0.20, 0.27 0.38 0.22, 0.34 0.20, 0.22

154 83

207 83 0.19, 0.21 0.35 0.18, 0.30 0.19, 0.22

253 83 0.20, 0.21 0.25, 0.26 0.19, 0.26 0.22, 0.22

351 83 0.17, 0.20 0.24, 0.27 0.21, 0.26 0.20, 0.18

499 83 0.17, 0.22 0.25, 0.24 0.24 0.20, 0.21

Table 4 Maximum mass (kg) of weight lifted with one hand using

9.4 mm diameter climbing rope

Bare hand With gloves Max Min

Right Left Right Left

Alan 35.00 35.00 30.00 30.00 35.00 30.00

Margaret 12.50 8.75 12.50 8.75 12.50 8.75

Mary W 18.75 18.75 15.00 12.50 18.75 12.50

Charles 15.00 15.00 15.00 15.00 15.00 15.00

Jim 17.50 22.50 17.50 17.50 22.50 17.50

Mary S 18.75 17.50 15.00 12.50 18.75 12.50

Clare 30.00 25.00 25.00 17.50 30.00 17.50

Dave 37.50 37.50 27.50 27.50 37.50 27.50

Rich 30.00 25.00 30.00 25.00 30.00 25.00

Carrie 22.50 22.50 22.50 20.00 22.50 20.00

Oliver 25.00 25.00 15.00 17.50 25.00 15.00

Rob 17.50 17.50 17.50 17.50 17.50 17.50

Dan 15.00 15.00 15.00 15.00 15.00 15.00

Bill 7.50 12.50 7.50 15.00 15.00 7.50

Virgil 25.00 25.00 25.00 25.00 25.00 25.00

Mass (kg) Weight (kN)

Max. 37.50 0.368

Min. 7.50 0.074

Average 20.27 0.199


during a climbers fall [11]. The grip strength decreases

with increasing time after this initial period [15].

Additional tests on just 2 recreational climbers measured

the influence on hand force (grip strength) of rope diameter

and whether the rope was wet or dry. The tests were con-

ducted on an Apollo 11 mm, Booster Dry 9.7 mm and Ice

Line Dry 8.1 mm ropes; either dry or after soaking in water

for 12 h. The results indicated that there was no significant

influence resulting from whether the rope was dry or wet.

There was however, a significant reduction in hand force

for the smaller diameter ropes. For the 8.1 mm Ice Line the

hand force was 70 % of that for the 9.7 mm Booster rope.

No significant difference in grip strength occurred between

the 11 mm Apollo and the 9.7 mm Booster ropes

(Table 5).

References

1. Titt J (2009) Belay device theory, testing and practice. http://

www.bolt-products.com/Glue-inBoltDesign.html

2. Manin L, Richard M, Brabant J-D, Bissuel M (2006) Rock

climbing belay device analysis, experiments and modelling. In:

Moritz EF, Haake S (eds) Engineering of sport 6. Springer,

Berlin, pp 69–74

3. Beverly M, Attaway S (2005) Hang em’ high: how far can you

trust your belay device. Int’l Technical Rescue Symposium

4. Pavier M (1998) Experimental and theoretical simulations of

climbing falls. Sports Eng 1:79–91

5. Attaway S (1996) Rope system analysis. http://lamountaineers.

org/xRopes.pdf

6. Jung JH, Pan N, Kang TJ (2008) Generalized capstan problem:

bending rigidity, nonlinear friction and extensibility effect. Tribol

Int 41:524–534

7. Belofsky H (1976) On the theory of power transmission by

V-belts. Wear 39:263–275

8. Fenz D (2002) Frictional properties of non-metallic materials for

use in sliding bearings: experiments. http://mceer.buffalo.edu/

publications/reesaccom/02-SP09/pdfs_screen/19_Fenz.pdf

9. Fuss FK, Niegl G (2010) Understanding the mechanics of

dynamic rope brakes. Procedia Eng 2:3323–3328

10. Nikonov A, Saprunov B, Zupancic B, Emri I (2011) Influence of

moisture on functional properties of climbing ropes. Int J Impact

Eng 38:900–909

11. Spierings AB, Henkel O, Schmid M (2007) Water absorption and

the effect of moisture on the dynamic properties of synthetic

mountaineering ropes. Int J Impact Eng 34(2):205–215

12. Song J, Ehrenstein GW (1990) Effect of water uptake on the

properties of polyamides. Kunstst Ger Plast 80(6):722–726

13. Cotugno S, Mensitueru G, Musto P, Nicholais L (2010) Water

sorption and transport in polymers. In: Nylon and ropes for

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Committee, 8 March 2002; CCMT Centro Studi Materiali e

Tecniche

14. Persson BNJ (2001) Theory of rubber friction and contact

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15. Nakada M, Demura S, Yamaji S, Nagasawa Y (2005) Exami-

nation of reproducibility of grip force and muscle oxygenation

kinetics on maximal repeated rhythmic grip exertion. J Physiol

Anthropol Appl Human Sci 24(1):1–6

Table 5 Weight (kN) lifted with one hand using dry and wet ropes

without glove

Rope (diameter) Dry Wet

Bill (kN) Mat (kN) Bill (kN) Mat (kN)

Apollo (11 mm) 0.157 0.206 0.186 0.226

Booster (9.7 mm) 0.157 0.206 0.157 0.177

Ice Line (8.1 mm) 0.108 0.157 0.108 0.157


http://www.bolt-products.com/Glue-inBoltDesign.html

http://www.bolt-products.com/Glue-inBoltDesign.html

http://lamountaineers.org/xRopes.pdf

http://lamountaineers.org/xRopes.pdf

http://mceer.buffalo.edu/publications/reesaccom/02-SP09/pdfs_screen/19_Fenz.pdf

http://mceer.buffalo.edu/publications/reesaccom/02-SP09/pdfs_screen/19_Fenz.pdf

effectiveness of mountaineering manual belay/abseil devices

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