DYNAMICS OF SPORT CLIMBING Yap Yaw Horng and FUSS F K School of Mechanical and Production Engineering Nanyang Technological University 50 Nanyang Avenue, Singapore 639798 INTRODUCTION Sport climbing is a form of roped climbing where bolts are used for protection. Bolts are positioned relatively close together, allowing the climber to climb safely. With the danger element removed, emphasis can be placed on technique and doing hard moves. Sport climbing requires different grip types, depending on the size and shape of the handholds available. Since the hands and feet are the main contact point between climber and the rock wall, the total weight of the body is distributed only through these contact points. As there are different shapes and sizes of artificial handholds, there will be different ways in which a climber can grip the handhold. There are basically 3 categories of finger position when gripping the handholds; they are the closed crimp, open crimp, and the extended crimp1. In the closed crimp, the first joint of the finger is fully open, sometimes, slightly beyond their moving range. The second joint is contracted and the thumb usually grabs over the index fingers. In the open crimp, again the first joint of the finger is fully open, and the angle between the second segment of the finger and the third segment, at the second joint, is ninety degree or even wider. The main difference between the closed crimp and the open crimp is the using of the thumb. In the extended grip position, the second joint is almost fully extended where as the first joint is flexed to its maximum. To date, no literature exists on the dynamics of sport climbing. Fuss et al.2 measured the handhold forces during the National Climbing Competition (men’s semifinal) and the Climbing World Cup (ladies’ quaterfinal). Both events took place in Singapore in August 2002, and the results are not available in printed form yet. A French research group3,4 measured the forces at hands and feet during hanging at a climbing wall. These projects, however, served the determination of posturographic principles, and were not destined at sports exercises, and completely ignoring the competitional effect. The aim of this research is to determine the forces between handhold and wall during climbing and to correlate the force with the grip type and climbing experience. The knowledge of this relationship is important for training and for preventing finger injuries. MATERIALS AND METHOD In this research, the climber has to complete a specific climbing route on top rope (climbing rope already set up). Within this specific route, two piezoelectric force transducers are attached to one of the handholds and the transducers are attached rigidly to the climbing wall. This small handhold and the fake wall are pre- manufactured. The handhold and a fake wall are directly attached to the wall using the available screw holes. When the climber grips the tile, the force time curve is recorded. Different grip types are being tested. The equipment used consisted of: 2 KISTLER piezoelectric force transducers, a Dewetron amplifier with 6 channels, an A/D- board, laptop computer with DASYlab 5.6 for data collection, and one handhold plus fake wall made of wood. The suggested climbing sequence for the handhold before the measured handhold should be big and the next handhold after the measured handhold should be another big one. The climbing wall is carefully studied before a suitable location of the handhold with the force transducer is mounted. Handhold and the fake wall are made using wooden beams and plywood respectively. Wood is used because it is easy to manufacture and relatively strong. The handhold is designed according to ergonomics of 4 fingers width; the height according to the dimensions of the sensors; the thickness as thin as possible so that we can assume the centre of pressure (COP) to be in the middle of the exposed surface. The total exposed top surface contact area is 1.7 x 6 cm. A simple rectangular block was chosen because the calculation could be simplify and for easy modelling of the handhold in AutoCAD2000. The sides and the bottom of the handhold are chamfered away to prevent the pinching of the handhold. A fake wall is used because it hides the redundant parts and exposes the necessary parts of the handhold. It is also used to eliminate the measuring of the unwanted forces when the fingers are in contact with the fake wall. The fake wall’s dimensions take the size of the handhold into consideration. There is a 2mm gap boundary between the handhold and the fake wall. This gap should not be too big or else the fingers can squeeze into the gap to get an additional grip, which in turn makes the reading inaccurate. Two force transducers are mounted horizontally next to each. The co-ordinate system used is: X-axis out of the wall, Y-axis upwards (climbing direction) and the Z-axis leftwards. The sensors are arranged next to each other because it is possible to calculate the COP along the Z-axis (which is along the top of the handhold), in the YZ plane. The distances between the centres of the two sensors are about the width of 4 fingers. The COP along the X-axis is assumed to be at the centre of the handhold, on the contacting surface (this is assumed because the relative thickness of the tile is small, compared to the width). A back plate is first mounted on the actual climbing wall using screws (identical to the normal mounting of the actual handholds). Next the fake wall and the two force transducers are mounted on the back plate using screws and nuts. After which, the front plate and the hand holes are mounted using screws. The handholds are made in such a way that the screw will be hidden inside the handholds. The connecting cables are then attached to the force transducers and the cables are carefully laid to the side of the walls and down to the amplifier and the amplifier is connected to the notebook. Three climbers are involved in this experiment. Each climber has to climb the specific route, on top rope, 8 times using all the handholds available on the wall. However, when the climber approaches the handhold with the force transducer, the climb must follow a fixed sequence of handholds, a big handhold to the handhold with the force transducer and to the next big handhold. When the climber comes to the handhold with force transducer, the climber must perform either the closed crimp or the open crimp (4 times for each crimp). Table 1 shows the biometric, performance, and experience data. A total of 24 readings were taken, 8 times for each climber. The data analysis was carried out as follows: 1) handhold contact time, 2) corrected impulse (area under the force-time graph; corrected to the body weight of the individual climbers), 3) maximum and mean coefficient of friction, µ (mean µ, is weighted according to the resultant force, as µ in small forces is insignificant), 4) smoothness of the curve (the smoothness factor of the force is the mean difference between the Y direction force-time graph and an ideal parabolic curve of the same impulse), 5) angle of the resultant forces in the XY plane and the YZ plane, 6) maximum and mean resultant forces, 7) position of the COP in YZ-plane according to the moment equilibrium about the X-axis, and 8) 4D-vector diagram (3D-vectors, colour-coded according to the time). The vector diagram was written in script-file format and imported into AutoCAD2000 subsequently, and combined with the 3D-model of handhold, transducers, and fake wall. Statistics calculation are done using ANOVA, one-way analysis of variance for independent or correlated samples. Table 1: Biometric, performance, and experience data (red point level is the hardest climb that the climber is capable of ascending; on-sight level is when the climber is given one preview and one attempt only) Body Weight No. of Experience in Red Point level On-Sight Level [N] Competitions Climbing [ yrs ] Climber A 596.82 5c 5b 2 2.5 Climber B 806.54 5b 5 1 2.5 Climber C 500.78 6c 6b 13 6.0 RESULTS AND DISCUSSION The results of the open crimp and closed crimp are compared between the 3 climbers. The training effect (improvement in climbing as the climbers get more familiarised with the climbing route) was also taken into account. From Table 2, the mean contact times, for the open crimp and the closed crimp, of all three climbers are different. Climber A, B, and C had a mean contact times of 6.06s, 8.45s, and 3.64s respectively. The results are significant for climber A and C (p<0.05), and for B and C (p<0.01). Another observation made was the mean coefficient of friction µ, for both the open crimp and the closed crimp, were different for all three climbers. Looking at Table 2, climber A has the lowest coefficient, 0.46 and climber B having a coefficient of 0.51 and climber C has the highest coefficient of friction of 0.54 (significant difference in all 3 climbers, p<0.01) The mean impulse, from Table 2, for both the open crimp and the closed crimp, for climbers A, B and C are 1.63, 1.62, and 1.04 respectively (significant difference between A and C, p<0.01).Another point observed, from Table 2, was the mean smoothness factor for both the open crimps and the closed crimp for climbers A, B and C are 52.25N, 47.40N and 26.00N respectively. Climber C’s Y-direction force time graph is most closely related to the ideal parabolic curve and climber A’s Y-direction force time graph does not really follow an ideal parabolic curve. Table 2: Differences between the 3 climbers (open and closed crimp combined; the corrected impulse is negative, as the normal force Fy is negative with respect to the co-ordinate system). Climber A Climber B Climber C Mean Contact Time [s] 6.06 8.45 3.64 Mean Coefficient Of Friction µ 0.46 0.51 0.54 Mean Corrected Impulse [Ns/BW] -1.63 -1.62 -1.04 Mean Smoothness [N] 52.24 47.40 26.00 Mean angle of force in YZ plane [o] 267.50 266.98 273.53 Table 3: Differences between climbers and grip types. All 3 Climber A Climber B Climber C Climbers Closed Mean Angle Of Forces in YZ Crimp 266.33 269.27 276.67 270.75 plane [o] Open Crimp 268.68 264.70 269.40 266.33 Contact Time [s] vs. Climbing Sequence 20.0 18.0 16.0 14.0 12.0 10.0 8.0 6.0 4.0 2.0 0.0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 Climber A Climber B Climber C Linear Fit (Climber A) Linear Fit (Climber B) Linear Fit (Climber C) Figure 1: Reduction of the contact time with increasing number of trials. From the tabulated results in Table 2 and Table 3, the mean angle of the YZ-resultant, for both the open and close crimp, for the 3 climbers A, B and C are 267.50°, 266.98° and 273.53° respectively (significant difference between A and C, and B and C, p<0.01). Another observation made was a difference between the mean angles for the YZ-resultant for the two different grip types. The mean angle of the closed crimp and open crimp (combined mean of all 3 climbers) are 270.8° and 266.3° respectively (significant difference between the two grip types, p<0.05). From the above Figure 1, we can also observe the training effect. This can be shown when the climbing sequence for each climber is plotted against the contact time. From the negative sloping linear fit for all 3 climbers, we can clearly see that there is a decrease in contact time. When comparing the first 4 trials of all climbers to the last 4 ones, a significant training effect becomes apparent for the decreasing contact time (p<0.05), the decrease in impulse (p<0.005), and increase in the mean coefficient of friction µ (p<0.001). 100 blue=A, green=B, red=C mean smoothness (N) 80 60 40 20 0 2 3 4 5 6 7 8 9 10 contact time (s) Figure 2: Mean smoothness vs. contact time; the black line separates climber C from the two other ones. CONCLUSION In conclusion, the results show a greater difference between the 3 climbers than between the open crimp and closed crimp. There was a significant difference in the contact time, coefficient of friction µ, impulse and smoothness factor between all three climbers. Climber C, with the most experience, has a shorter contact time, higher mean coefficient of friction µ, lower corrected impulse and a smaller smoothness factor when compared with climber A and B (Fig. 2). When comparing the open crimp and closed crimp, a significant difference is seen from the resultant angle in the YZ plane. Training effect can also be seen in the results. When the climber makes more ascents on the same route, there is a significant decrease in contact time; decrease in impulse; increase in mean coefficient of friction µ and standard deviation of the resultant angle in both the XY plane and YZ plane. These results are important for Singaporean climbers, who do not have the possibility of obtaining a high mountaineering experience. This disadvantage can be overcome by repetitive training of standard cruxes (i.e., the most difficult part of a climbing route). ACKNOWLEDGEMENTS We would like to thank Mr. Mohd Amir B Moostafa, trainer and supervisor of the National Climbing Centre of Singapore, and Mr. D. Tung, Projects & Events Executive, for allowing us to use the SARFA Yishun climbing wall, and to Mrs. Lim Lang Hiang, Christina, MOM-lab, MPE, for all the lab support she has given. REFERENCES 1. Goddard D & Neumann U (1993). Performance Rock Climbing. Stackpole Books, Mechanicsburg, PA 2. Fuss FK, Boey LW, Niegl G & Xiang L (2002). Unpublished data. 3. Quaine F & Martin L (1999). A Biomechanical Study of Equilibrium in sport rock climbing. Gait and Posture, 10:233-239. 4. Testa M, Martin L & Debû B (1999). Effects of the type of holds and movement amplitude on postural control associated with a climbing task. Gait and Posture, 9:57-64.