Faculty of Sport, University of Ljubljana, ISSN 1318-2269  7 Kinesiologia Slovenica, 16, 3, 7–13 (2010)
IZVLEČEK
Novo razvita eksperimentalno-numerično-analitič-
no metoda, zasnovana na analizi mehanskega odziva 
vrvi na obremenitev generirano s prostim padom uteži, 
omogoča določitev večih fizikalnih veličin, ki oprede-
ljujejo varnost plezalca: ujemno silo, spremembo pospe-
ška (pojemka), maksimalno deformacijo vrvi, ter spre-
membo togosti vrvi v enem ciklu obremenitve. Izračuni 
mehanskih lastnosti treh tipov vrvi so primerjani med 
seboj z uporabo novo razvite metode. Predstavljeni re-
zultati kažejo, da se časovno odvisne lastnosti vrvi, ki 
v skladu s standardom UIAA sodijo v isti kakovostno-
varnostni razred, dejansko med seboj močno razliku-
jejo. Pri eni izmed preizkušenih vrvi je sprememba po-
jemka presegla kritično vrednost 120g/s že pri drugi 
obremenitvi. To vrv, kljub temu, da izpolnjuje zahte-
ve standarda EN 892, ne moremo označiti kot varno. 
Predstavljeni rezultati potrjujejo potrebo po spremem-
bi obstoječih standardov za zagotavljanje varnosti ple-
za lcev.
Ključne besede: plezalne vrvi, ujemna sila, sprememba 
pospeška, viskoelastičnost
ABSTR ACT
A recently developed experimental-numerical-analyti-
cal methodology, based on a simple non-standard fall-
ing weight experiment, allows the calculation of several 
physical quantities that are important for the safety of 
a climber, such as: the maximum force acting on the 
rope; jolt, i.e., the derivative of the (de)acceleration; the 
maximum deformation of the rope; and modification of 
the stiffness of the rope within each loading cycle. This 
methodology was used in the mechanical characterisa-
tion of three commercial climbing ropes. The results in-
dicate that ropes which according to the existing UIAA 
standard belong to the same quality class actually ex-
hibit significantly different behaviour when exposed to 
the same loading conditions. One of the tested ropes ex-
ceeded the critical jolt value (120g/s) already during the 
second fall. Thus, although it satisfies the requirements 
of the EN 892 standard, this rope may not be considered 
safe. The results prove that the existing safety standards 
need to be reconsidered. 
Keywords: climbing ropes, maximum force, jolt, vis-
coelasticity 
1 
University of Ljubljana, Faculty of Mechanical 
Engineering, Ljubljana, Slovenia
2 
University of Ljubljana, Faculty of Sport, Ljubljana, 
Slovenia
*Corresponding author: 
University of Ljubljana, Faculty of Mechanical Engineering,
Aškerčeva 6 
SI-1000 Ljubljana, Slovenia 
Tel.: +386 1620 7100, Fax: +386 1 620 7100
E-mail: igor.emri@fs.uni-lj.si
EXAMINATION OF THE TIME-DEPENDENT 
BEHA VIOUR OF CLIMBING ROPES UNDER 
IMPACT LOADING
PREISKA V A ČASOVNO ODVISNEGA 
VEDENJA PLEZALNIH VRVI PRI 
IMPULZNIH OBREMENITV AH
Anatolij Nikonov
1
 
Stojan Burnik
2
 
Igor Emri
1
*

8 Time-dependent behaviour of climbing ropes Kinesiologia Slovenica, 16, 3, 7–13 (2010) 
INTRODUCTION
Climbing ropes are designed to secure a climber. They are designed to stretch under a high load 
so as to absorb the shock force. This protects a climber by reducing the fall forces. Ropes should 
have good mechanical properties such as high breaking strength, large elongation at rupture and 
good elastic recovery (Jenkins, 2003; McLaren, 2006; Soles, 1995).
The UIAA (Union Internationale des Associations d’Alpinisme) has established standard testing 
procedures to measure, among other things, how a rope reacts to serious falls (Burnik, Simonič, 
& Jereb, 2004; Simonič, 2003). Ropes are drop tested with a standardised weight and procedure 
simulating a climber’s fall (EN 892:2004). This reveals how many of these hypothetical falls the 
rope can withstand before it ruptures. Currently all ropes on the market fulfil the requirements 
of the standard to withstand the required minimal number of falls, and some are even rated to 
a much higher number. The standard also prescribes the maximum force which is transmitted 
to a climber during a fall. 
The standard says little about the durability of ropes, which is more difficult to define and 
assess with simple procedures. Ropes are commonly produced from polyamide fibres that exhibit 
viscoelastic behaviour. Thus, in this case durability does not just mean the failure of a rope, but 
rather the deterioration of its time-dependent response when exposed to an impact force. The 
experiments prescribed by the UIAA standard are not geared to analyse the time-dependent 
deformation process of ropes, which causes material structural changes and consequently af-
fects the durability of ropes. The time-dependency of ropes also governs the evolution of all 
physical quantities that are responsible for climbers’ safety, e.g., the first derivative of climber 
(de)acceleration.
In this paper we utilise a recently developed experimental-numerical-analytical methodol-
ogy based on a simple non-standard falling weight experiment (Emri, Nikonov, Zupančič, & 
Florjančič, 2008) to analyse the viscoelastic properties and safety of three commercial climbing 
ropes. 
MATERIALS AND METHODS
Theoretical treatment
The time-dependent response of a rope under the dynamic loading generated by a falling mass 
(deadweight) may be identified from an analysis of force measured at the upper fixture of the 
rope (Emri, Nikonov, Zupančič, & Florjančič, 2008). This force is transmitted through the rope 
and acts on the falling weight (mass), as schematically shown in Figure 1(a). In such experiments 
a mass, m, is dropped from an arbitrary height, h ≤ 2l
0
, where l
0
 is the length of the tested rope.
Force measured as a function of time, F(t), may be expressed as a set of N discrete data pairs, 
F(t) = {F
i
,t
i
; i = 1,2,3, 
…
, N}. An example of such measured force is schematically shown in Figure 
1(b). The diagram is subdivided into three distinct phases A, B and C.
In phase A, the weight (mass) is dropped at t = 0, and falls freely until t = t
0
 = √2h/g where the 
rope becomes straight, which is indicated in Figure 1(a) as point T
0
, and represents the end of 
the free-falling phase of the mass, and the beginning of phase B. At point T
0
 in phase B, where 
τ = t – t
0
 = 0, the falling mass starts to deform the rope. Neglecting the air resistance, and the wave 
propagation in the rope, the equation of the motion of the moving mass between points T
0
 and 
T
7
 may be written as mx ¨(τ) = mg – F (τ). Here m is the mass of the weight, g is the gravitational 

Time-dependent behaviour of climbing ropes 9 Kinesiologia Slovenica, 16, 3, 7–13 (2010)
acceleration, x¨ ( τ ) denotes the second derivative of the weight displacement, x(τ), measured from 
point T
0
. Thus, x(τ) represents the time-dependent deformation of the rope. Taking the initial 
conditions at point T
0
 into account, i.e. x(τ = 0) = 0, and x ˙(τ = 0) =v
0
 = √2 gh, the solution of the 
equation of motion gives the displacement of the weight as a function of time, which represents 
the elastoviscoplastic deformation of the rope as a function of time (Emri, Nikonov, Zupančič, 
& Florjančič, 2008)
 
0
2
1
( ) ( )
2
0 0
g
x F d d v
m
τ λ
τ
τ υ υ λ τ = − +
∫ ∫
 
 
 
. (1)
At point T
1
, where τ = τ
1
, the force acting on the rope becomes equal to the weight of the mass. 
At T
2
, jolt (a derivative of de-acceleration) will reach its negative extreme value. The force acting 
on the rope and on the weight has its maximum at T3. If the rope’s properties were elastic, the 
location of the maximum force should coincide with the location of the maximal deformation; 
however, because of the viscoelastic nature of the rope, its maximal deformation will be delayed 
and take place at τ = τ
4
, that is, at point T
4
, where the velocity of deadweight is equal to zero. At 
τ = τ
5 
, indicated as point T
5
, the jolt will reach its positive extreme value. At T
6
, where τ = τ
6
, the 
force acting on the rope again becomes equal to the weight of deadweight. Finally, at point T
7
, 
where the force acting on the rope becomes equal to zero, the weight will start its free fly in an 
upward (vertical) direction.
Considering two characteristic times, τ
4
 and τ
7
, one may derive equations for the maximal 
deformation, s
max
 = x(τ
4
), elastic component, s
el
 = x(τ
4
) – x(τ
7
), and viscoplastic component, s
vp
 = 
x(τ
7
), of the rope deformation.
In addition, we may want to know the stiffness of the rope, k(F = mg), and maximal change of 
(de-)acceleration, M, commonly called jolt. The governing equations for these physical quantities 
are (Emri, Nikonov, Zupančič, & Florjančič, 2008):
 { } N i t F F
i i
, , 3 , 2 , 1 ; , MAX
max
 = = (2)
(a) (b)
 
l
0
mg
m
m
F(t)
F(t)
F(t)
F(t)
m
h
t = t
0
l
0
mg
m
m
F(t)
F(t)
F(t)
F(t)
m m
h
t = t
0
 
Time -t
Force -F(t)
T
4
T
6
t
9
0 t
0
t
4
t
1
T
1
mg
First loading cycle Second loading cycle
C A B
t
6
T
0
T
4
T
7
F
max
T
3
T
9
t
2
t
7
T
2
T
5
T
8
0
t
3
t
5
t
8
1
t
2
t
3
t
4
t
5
t
6
t
7
t
8
t
9
t
Figure 1: Schematics of a rope exposed to a falling weight (a) and force measured during the 
falling weight experiment (b)

10 Time-dependent behaviour of climbing ropes Kinesiologia Slovenica, 16, 3, 7–13 (2010) 
 
4 2
4
max 4 0  4
0 0
1
( ) ( )
2
g  
s x F d d v
m
τ λ
τ
τ υ υ λ τ
 
= = − +
 
 
∫ ∫
, (3)
 
7
4
2 2
7 4
4 7 0 7 4
0
( ) 1
( ) ( ) ( ) ( )
2
el
g
s x x F d d v
m
τ λ
τ
τ τ
τ τ υ υ λ τ τ
 
−
= − = − − −
 
 
∫ ∫
 (4)
 
7 0
0 0
2
7
7
7
) (
1
2
) ( τ λ υ υ
τ
τ
τ λ
v d d F
m
g
x s
vp
+






− = =
∫ ∫
 (5)
 
max
1 ( )
MAX
dF t
M
m dt
 
=
 
 
, and (6)
 
( )
F mg
dF s
k
ds
=
=
, where (7)
 










= ≤ ≤ +








− = = = =
∫ ∫
N i t t t v d d F
m
gt
t s s t F F s F
i i
t
i
i i i i
i
, , 3 , 2 , 1 , 0 ; ) (
1
2
) ( ), ( ) (
7 0
0 0
2
 θ τ τ
θ
. (8)
These parameters are summarised in Table 1.
Table 1: Physical quantities used to analyse the safety of climbers and durability of ropes
Physical quantity Symbol Unit
Maximum force F
max
N
Maximum deformation s
max
m
Elastic part of rope deformation s
el
m
Viscoplastic part of rope deformation s
vp
m
Maximum jolt M
max
m/s
3
Stiffness of the rope at F = mg k N/m
Experimental setup
The experimental setup is schematically presented in Figure 2. A force sensor is fixed to the 
console around 6 m above the floor. The rope being tested is connected to the force sensor at 
one end and to the weight at the other in such a way that both ends of the rope are on the same 
level. The weight is then dropped so as to expose the rope to an impact force, which is measured 
with the force sensor. The measured signal is amplified, converted into digital form (using at 
least a 12 bit A/D converter) and processed with a specially developed LabView program. In all 
experiments the mass of the weight was 43.85±0.02 kg. 
Free fall tests were conducted on three different commercial ropes. The diameter of each rope 
was roughly the same, i.e., 9.8 mm. The ropes were first cut into four pieces of equal length, 
i.e., 3.38±0.04 m. Both ends of each specimen were then sewn to form a noose, as schematically 
shown in Figure 3. The length of each specimen was measured and recorded before and after 
the testing.

Time-dependent behaviour of climbing ropes 11 Kinesiologia Slovenica, 16, 3, 7–13 (2010)
All experiments were performed with the same room temperature (26±2oC) and moisture 
conditions.
Figure 3: Specimen with nooses
Each specimen was exposed to 10 consequent falls, with 5 minutes’ waiting time between two 
falls. The measured signals were stored and later analysed with self-developed software named 
DAR. We performed four such series of experiments for each rope. 
R ESULTS
From the measured force, F(t), we calculated the following physical quantities: maximum force, 
F
max
, maximum deformation of the rope, S
max
, maximum derivative of (de)acceleration, M
max
, 
and stiffness of the rope, k. By using these physical quantities we compared the performance of 
three commercial ropes, identified as R1, R2 and R3. According to the existing UIAA standard, 
these ropes belong to the same quality class.
Two examples of the force response measured on rope R1 during the first and tenth impact 
loadings are shown in Figure 4.
 
0
1000
2000
3000
4000
5000
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6
t (s)
F(t) (N)
1
st
 fall
10
th
 fall
Figure 4: Force response of rope R1 during the first and tenth impact loadings
Figure 2: Schematic apparatus layout

12 Time-dependent behaviour of climbing ropes Kinesiologia Slovenica, 16, 3, 7–13 (2010) 
A comparison of the time-dependent behaviour of the three different ropes exposed to impact 
loading is presented in Figures 5 and 6. In diagrams the calculated characteristics of the ropes 
are presented as functions of the number of falls. Figure 5 shows the average values of maximum 
force, F
max
, and the maximum deformation of the rope, S
max
. The average values of maximum 
jolt, M
max
, and the stiffness of the rope at the beginning of rope deformation, k, are presented in 
Figure 6. The maximum absolute deviations from the average values for each physical quantity 
are presented in Table 2.
(a)  (b)
3500
4000
4500
5000
5500
1 2 3 4 5 6 7 8 9 10
Number of falls [/]
Fmax [N]
 
 
0.9
0.95
1
1.05
1.1
Number of falls [/]
smax [m]
Legend: ◊ - rope R1, □ - rope R2, △ - rope R3
Figure 5: The maximum force (a) and the maximum deformation of the rope (b) as functions 
of the number of falls
(a)  (b)
800
1000
1200
1400
1600
Number of falls [/]
Mmax [m/s
3
]
 
3500
4000
4500
5000
Number of falls [/]
k [N/m]
Legend: ◊ - rope R1, □ - rope R2, △ - rope R3
Figure 6: The maximum jolt (a) and the stiffness of the rope at the beginning of rope deformation 
(b) as functions of the number of falls
Table 2: Maximum absolute deviations of physical quantities 
Physical quantity Max. deviation
Maximum force 66 N
Maximum deformation 0.03 m
Maximum jolt 252 m/s3
Stiffness of the rope at F = mg 63 N/m

Time-dependent behaviour of climbing ropes 13 Kinesiologia Slovenica, 16, 3, 7–13 (2010)
DISCUSSION AND CONCLUSIONS
From the diagrams presented above we may recognise that ropes designated equal according 
to the existing standard exhibit significantly different behaviour when they are exposed to the 
same impact loading conditions.
After the tenth fall rope R2 generated 15% bigger maximum force, 10% smaller maximum 
deformation and 35% bigger maximum jolt than ropes R1 and R3. Therefore, rope R2 may be 
considered more dangerous for climbers than the other two ropes. The stiffness at the beginning 
of the rope deformation is a little bigger for rope R2 in comparison to that of ropes R1 and R3.
Jolt, i.e., a derivative of climber acceleration or de-acceleration, is a very important parameter 
for the safety of climbers and may be used to evaluate the quality of climbing ropes. From 
experience of human space explorations and from car crash experiments we know that a change 
in acceleration or de-acceleration, i.e., the magnitude of jolt, is more dangerous for human beings 
than the magnitude of acceleration (inertial force) to which a body is exposed. According to 
these investigations, the maximal jolt should not exceed M
max
 = 120 g/s, which approximately 
corresponds to the value M
max
 = 1200 m/s
3
.
The obtained results clearly demonstrate that ropes R1 and R3 reach this critical value only after 
ten consecutive loadings. However, for rope R2 this critical value is already exceeded after the 
second fall, which could be fatal for a climber. This is particularly important for inexperienced 
beginners who are learning climbing techniques and are likely to fall more often.
The results indicate that ropes which according to the existing UIAA standard belong to the same 
quality class and are declared to have the same UIAA standard characteristics actually exhibit 
significantly different behaviour when they are compared according to the new 
experimental-analytical methodology which takes new physical quantities such as jolt into ac-
count. 
We may therefore conclude that the testing of ropes according to the UIAA standard is not 
sufficient to guarantee climber safety! 
REFERENCES
Burnik S., Simonič E., & Jereb B. (2004). Odpornost plašča plezalnih vrvi [Resistance of climbing rope’s 
sheath]. Šport, 52(2), 62-66.
Emri I., Nikonov A., Zupančič B., & Florjančič U. (2008). Time-dependent behaviour of ropes under impact 
loading: a dynamic analysis. Sports Technology, 1(4-5), 208-219.
EN 892:2004 (E): Mountaineering equipment. Dynamic mountaineering ropes. Safety requirements and 
test methods. The European Committee for Standardization, November 2004.
Jenkins, M. (2003). (ed.), Materials in Sports Equipment, Woodhead Publ. Ltd., Cambridge.
McLaren A.J. (2006). Design and performance of ropes for climbing and sailing, Proceedings of the Institu-
tion of Mechanical Engineers, Part L: Journal of Materials: Design and Applications, 220(1), 1-12.
Simonič, E. (2003). Standardi in obraba vrvi [Standards and wear of ropes]. Unpublished bachelor’s thesis, 
Ljubljana: Univerza v Ljubljani, Fakulteta za šport.
Soles C. (1995). Single-rope buyer’s guide. Rock & Ice, 68, 117-134.