Sports Eng (2013) 16:255–264 DOI 10.1007/s12283-013-0139-6
ORIGINAL ARTICLE
Testing method for objective evaluation of cross-country ski poles Mikael Sware´n • Mikael Therell • Anders Eriksson Hans-Christer Holmberg
•
Published online: 26 September 2013 Ó International Sports Engineering Association 2013
Abstract The aim of the study was to develop an objective classification method for cross-country ski poles. A test device was designed to expose different pole models to maximal loading and impact tests. A load cell measured the axial forces in the pole shafts, and a laser distance meter measured shaft deflection when a load was applied via the wrist strap. In the loading tests, each shaft reached a plateau where no more force could be transferred. This maximal force transfer (MFT) value was a characteristic measure for flexural rigidity and thereby also strength. The developed test method enables a loading that is more similar to real-life skiing than a standard three-point bending test. Results show that the introduction of shaft indices for buckling strength is beneficial for comparison purposes. The MFT is a relevant parameter used in the characterization of poles. Keywords Impact
Bending Buckling Force transfer
1 Introduction Usage of the upper body and the importance of upper body strength in cross-country skiing have increased in recent
M. Sware´n (&) M. Therell A. Eriksson H.-C. Holmberg Department of Health Sciences, Swedish Winter Sports Research ¨ stersund, Sweden Centre, Mid Sweden University, 83125 O e-mail:
[email protected] M. Sware´n A. Eriksson Department of Mechanics, Royal Institute of Technology, Stockholm, Sweden H.-C. Holmberg Swedish Olympic Committee, Stockholm, Sweden
years due to the expansion of sprint events and new double poling techniques [1–3]. Numerous studies [1, 3–5], investigating the more explosive poling techniques used in today’s skiing, report an increased rate of force development and higher peak forces. The skier’s generated power, especially from the upper body, is transformed to a propulsive movement through the ski poles [6]. Cross-country ski poles consist of a shaft, a handle with a wrist strap and a ski-basket with a metallic tip. Modern racing shafts are constructed of carbon fibers in an epoxy resin, a design which generates high shaft strength with minimum weight, but also rather a high level of flexibility. The ski-basket generates support in the snow while the metallic tip creates grip on icy and hard ski-tracks or on roads when roller skiing. Cross-country skiers normally use pole lengths of 83–85 % of body height in classical skiing and 90 % of body height in the skating technique. Longer poles combined with higher peak forces due to the more explosive poling techniques generate higher bending moment and hence higher demands on the poles regarding shaft strength and power transfer. A lot of time and resources are invested in ski optimization through the use of different waxes and base structures. Also, numerous studies [7–10] have investigated different parameters that directly or indirectly affect the ski–snow friction to increase the understanding of optimizing the glide in cross-country skis. As regards the amount of time and resources invested in studying the ski– snow friction and ski testing, the lack of tests for ski poles is somewhat surprising. The current approach and method when testing/choosing poles are based upon the perception of the shaft during skiing, which is a very subjective way of choosing one of the most important pieces of equipment. In other sports, such as ice-hockey, pole vaulting and golf there are standard testing procedures and different
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characteristic indices that are well-established [11–15]. Bending characteristics for golf clubs are often tested by fixating the handle and attaching a weight at the club head whereas ice-hockey sticks as well as vaulting poles use a general stiffness index based on a standard three-point bending test [11, 12]. These test setups bend the equipment in similar ways to when it is used. However, in crosscountry skiing, a standard bending test or a three-point bending test loads the pole shaft in an unrealistic way as the ski poles mainly are loaded through the wrist strap, during skiing, which creates an axial force offset that needs to be considered when testing poles. The connection between the primary axial force, the bending strength and flexibility becomes an important issue, which is reflected in the buckling strength. Also, the tip of the ski pole can move in the snow, which allows the ski pole to bend and rotate in any direction when loaded. Hence, the use of a standard column buckling calculation as Euler’s buckling model [16] is difficult, as it demands correct assumptions of the fixation of the column. Also, Euler’s buckling model is not directly applicable to a cross-country ski pole due to the tapering shape of the ski pole’s shaft. To the authors’ knowledge, no relevant and objective test method exists to define and evaluate bending characteristics of cross-country ski poles. Hence, the purpose of this study was to develop an objective testing method and classification for cross-country ski pole shafts that can assist manufacturers, retailers and skiers when comparing and selecting pole shafts.
2 Method Seven different pole models that were commonly used in the cross-country ski World Cup 2011/2012, were analyzed using a specially designed testing device (TD) (Fig. 1).
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Tested poles were: Rex Wizard (Oy Redox Ab, Hartola, Finland), Komperdell National Team Carbon (Komperdell Sportartikel GesmbH, Mondsee, Austria), Swix CT1 Star (Swix Sports AS, Lillehammer, Norway), Swix Triac (Swix Sports AS, Lillehammer, Norway), OneWay Storm Max 10 (OneWay Sport OY, Vantaa, Finland), OneWay Storm Premio 10 (OneWay Sport OY, Vantaa, Finland) and Skigo Racing (Christer Majba¨ck AB, Kiruna, Sweden). Three poles for each length (145, 155, 165 and 170 cm) and model were tested. Lengths were measured from the bottom of the ski-basket to the entry of the strap in the handle. The method was used to measure shaft length generated lengths shorter than the values specified by the manufacturers. Thus, only one model was available in 175 cm, whereas all but one model were available in 170 cm, hence the irregular increments in shaft lengths to increase the numbers of pole models to test in a length longer than 165 cm. The TD consisted of a frame made from four horizontally positioned aluminium beams. A linearly moving sled, sliding on the two lower beams, was connected to a threaded rod, allowing the sled to move backwards and forwards. Each shaft was placed between the two lower and the two upper horizontal beams with the ‘‘front’’ of the shaft facing upwards. The handle strap was attached to the sliding sled, allowing the sled to load the shaft. The ski-basket at the end of the shaft was mounted to a load cell (One K Toyo 333A, KTOYO co. Ltd, Korea) with the tip in a ‘‘cup’’ of an inelastic attachment that allowed for unrestricted rotation within the required range of motion. Only brand-specific skibaskets with a centrally placed tip were used. The load cell was calibrated using 25 kg competition weights (Eleiko Sport AB, Halmstad, Sweden). The sled could be connected to a wire that was led through a system of pulleys, where a 10 kg weight could be dropped to create a rapid eccentric axial impact load on the shafts (Fig. 1).
Fig. 1 a The test device with an attached pole that is exposed to a compressing force. The attachment point for the drill is on the far left side of the test device. Data collection box is visible in the low right corner. b Schematic picture of the test device
Cross-country ski poles
Shaft bending was measured using a laser distance meter (SICK DT20-P214P, SICK AG, Waldkirch, Germany), mounted on a sled attached to the two upper aluminium beams. The sled with the laser distance meter could be moved along the entire length of the test device and a linear encoder (SICK BCG08-K1KM03PP, SICK AG, Waldkirch, Germany) was attached to the laser to position the laser along the shaft. Two guide pins were positioned on each side of the shaft to direct the bending direction of the shaft upwards, directly underneath the laser distance meter (Fig. 2). The total cost for the TD was 3,000 EUR, not including the labor. 2.1 Test protocol The maximal loading test for each shaft was performed by increasing the load until no more force could be transferred by the shaft and only buckling-like bending occurred. In this case, the load was applied via a nut on the threaded rod (M10 9 1.5) and was operated by a handheld drilling machine (Robert Bosch GmbH, Leinfelden-Echterdingen, Germany) at a constant speed of 800 rpm. The pitch of the threaded rod was 1.5 mm per thread which results in a linear velocity of 1.2 ms-1 at 800 rpm. The force was monitored live via a laptop computer connected to the load cell. The speed of the drilling machine was reduced when no more force could be transferred via the pole to avoid uncontrolled rupture of the pole shaft.
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For the deflection tests, each shaft was pre-loaded with 10 N as a baseline. The load was thereafter increased to 100 N and then with an increment of 100 N until the next level could not be reached due to breakage. Maximal shaft deflection was identified by moving the laser distance meter along the entire length of the shaft at each load. The deflection data was collected with a sampling rate of 100 Hz and the time to move the laser distance meter along each shaft varied between 2.5 and 3 s. The impact test was performed by dropping the 10 kg weight, attached to the movable sled by an UHMWPErope, from a height of 25 cm. Each pole was tested three times. The dropped weight landed on an oil damper which lengthened the impact and reduced the force. The same measuring setup was used as that for the load test with the exception of the laser distance meter which was placed in the middle of the poles. The mean and standard deviation of the impact forces were calculated for each pole model and length. Peak force from the falling weight on a rigid interface was 955 ± 10 N (n = 20), which is 4–6 times higher than reported peak pole force during cross-country skiing [1, 4, 17]. 2.2 Signal processing Load cell signal data were processed using a strain gauge input module (SCM5B38-01, Dataforth Corp., Tucson, AZ, USA). Matched-pair servo/motor controller modules (SCM5B392-12, Dataforth Corp., Tucson, AZ, USA) were used for the laser- and wire-distance meter signals. The modules were mounted to a backplane (SCMPB05-1, Dataforth Corp., Tucson, AZ, USA), and a signal processor (USB-1608FS, Measurement Computing Corp., Norton, MA, USA) was connected between the backplane and a computer. All data collection was performed at 100 Hz using TracerDAQ (Measurement Computing Corp., Norton, MA, USA). A MuscleLab 4010 unit (Ergotest Innovation A.S., Porsgrunn, Norway) was used to display applied force when performing the stiffness test. Matlab R2010b (MathWorks, Inc., Natick, MA, USA) and Microsoft Excel 2007 (Microsoft Corp., Redmond, WA, USA) were used for data analyses. 2.3 Data processing
Fig. 2 A close-up on the short distance laser meter and the movable target-plate that rests on the shaft to ensure a correct reflection of the laser beam. The target-plate moves along the two pins that ensure an upwards bending motion of the pole shafts during loading
A mean pole B value (flexural rigidity) was calculated as a theoretical reference, where B represents the effective bending stiffness of a beam section. In isotropic, ideally elastic beam sections of homogeneous material, this would be the product of the material stiffness E and the second moment of inertia I, but here, due to the inhomogeneity of the cylinder walls, it can only be seen as an aggregate value for the current composition. It is possible to calculate the
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B value regarding the attached pole to be pinned at both ends by inserting Euler’s expression (Eq. 1) for the critical force FC in Eq. 3 where I (Eq. 2) is the second moment of inertia for a homogeneous hollow circular section and EI is replaced by B. L in Eq. 1 represents the length of the pole, d0 and di in Eq. 2 are the outer and inner diameter of the shaft, respectively. EI L2
ð1Þ
pðd04 di4 Þ 64
ð2Þ
FC ¼ p2 I¼
dmid ¼
0:0625FeL2 B 1 FFc
ð3Þ
Equation 3 gives the midpoint deflection dmid from an end moment Fe on a simply supported bent beam of constant sectional properties. After inserting Eq. 1 and extracting B in Eq. 3 the following expression was achieved for B, also refining Eq. 3 using the maximal displacement of the shaft in the same loading situation, which gives a slightly different coefficient: B¼
0:0642FeL2 FL2 þ 2 dmax p
ð4Þ
where F is the load on the shaft, e is the offset distance for the load from the centre of the shaft and dmax is the maximum measured deflection for the shaft along its length for a given axial load F. The constants of 0.0625 and 0.0642 can be derived from the standard equation for calculation of the deflection of a beam, simply supported at the ends, with an acting moment at one end, Eq. 5a–5b [16] dmid ¼
ML2 16EI
ML2 dmax ¼ pffiffiffi : 9 3EI
ð5aÞ ð5bÞ
In the flexural rigidity calculations was F = 200 N with corresponding deflections values (d) used, measured in the deflection test, and e = 0.017 m. Very high deflections occurred for F [ 200 which decreases the accuracy for calculations based on buckling instability and F = 200 N was the load where minimum deflection occurred, but still with deflection differences between the 145 and 170 cm shafts. The Southwell plot [18] was used to validate the maximal loading test with an established method to calculate the critical buckling load. The mean deflection value for every load for each shaft model and length was plotted in a Southwell plot where deflections w at various loads P were plotted as the value of w/P on the vertical axis vs. w on the horizontal axis. This plot approaches to a straight line
whose inverse slope gives the buckling failure load (PC ) for this eccentrically compressed shaft as the load when deflections go towards infinity. Hence, PC is comparable to Euler’s FC but established by calculations based on experimental load and deflection data lower than FC . To verify the calculated theoretical buckling loads from the Southwell plots and the measured maximal static force, one FEM analysis was performed for one shaft, OneWay Storm Max 10 155 cm. The outer diameter was 15.8 mm at the top of the shaft, with a tapered shape at the tip; the final outer diameter of the thickness of the material was 0.8 mm. The shaft was modeled in SolidWorks 2010 (Dassault Syste`mes, Waltham, MA, USA) using aluminium 1060 with an E-modulus of 69 GPa as material due to the unavailable information regarding the representative E-modulus of the material in the carbon-fiber shaft. As a reference model, another shaft was modeled, also in aluminium 1060, with constant outer- and inner-diameters of 15.8 and 14.2 mm, respectively. The FEM analyses for both shafts were performed using the SolidWorks Simulation software (Dassault Syste`mes, Waltham, MA, USA) and its buckling situation scenario. The shockwave propagation velocity for a general shaft model was used for investigating if the impact test could be analyzed in a quasi-static manner or if the impact could cause a dynamic buckling scenario. Calculation of the shockwave propagation velocity was done by: pffiffiffiffiffiffiffiffiffiffiffiffiffiffi cp ¼ ðEq1 Þ ð6Þ where E is the estimated E-modulus for the CFRP used in the shaft and q is the density of the shaft, 1,638 kg m-3. The correct E-modulus for a carbon fiber reinforced polymer (CFRP) shaft is difficult to obtain due to company secretes regarding material and fiber orientation. However, according to the literature is the E-modulus in longitudinal direction for CFRP materials somewhere between 145 and 220 GPa [19]. Hence, the E-modulus used for calculating cp was set to 200 GPa, to not overestimate the elastic properties which would result in an overestimation of the shockwave propagation velocity. The shockwave propagation time to move along the length of a pole was calculated by: t ¼ lc1 p
ð7Þ
where l is the pole length.
3 Results All shafts were tested in each length, except for Skigo Racing where no 170 cm shafts were available at the time of the study. The results are presented as mean values
Cross-country ski poles
±standard deviation (±SD). However, as only three poles were tested for each length and model, it not possible to calculate any reliable statistics or levels of significance between the different pole models and lengths. 3.1 Load and deflection test In the maximal load tests, each shaft reached a plateau where no more force could be transferred by the shaft, (Fig. 3). This plateau, here named maximal force transfer (MFT), was individual for each pole, but clear differences in MFT were observed between the different models and shaft lengths. The mean MFT for all shafts and lengths was 577 ± 89 N. All poles were deemed to be moving towards a buckling-type failure, with increasing transversal deflection, but without primary material failure. In general, MFT decreased with increasing pole length within each brand, with the exception of the SWIX Triac pole where MFT increased at 165 cm compared to the
Fig. 3 Example of transferred force curves for different shaft lengths for OneWay Storm Max 10 poles. The plateau for each pole where no more force can be transferred via the shafts and only buckling occurs is clearly visible and is named maximal force transfer (MFT)
Fig. 4 Mean maximal force transfer (MFT) ±SD for each pole model and length
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155 cm length, due to the differently designed shafts in lengths above 165 cm. The overall mean MFT for all shafts decreased by 19 % between the 145 and 170 cm shafts, whereas the corresponding value for critical load, using Euler’s buckling model, was calculated to a 28 % decrease for the 170 cm shafts compared to the 145 cm shafts. All MFT data are presented in Fig. 4. Shaft deflection increased with increasing pole length and applied load, Table 1. Rex Wizard showed the highest deflection for all lengths and loads whereas Komperdell National Team Carbon had the lowest deflection in 14 out of the 16 different situations. 3.2 Impact test The mean shockwave propagation time for lengths of 1.45–1.7 m was calculated to be 0.14 ms which is shorter than the average time to peak pole force which was 18.0 ± 1.5 ms for all tests. The resulting value for cp and
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260 Table 1 Mean peak shaft deflection in mm for the static loads 100, 200, 300 and 400 N for each pole model and length Load (N)
100
200
300
400
Shaft length (cm)
Shaft deflection (mm) Rex Wizard
Komperdell National Team Carbon
Swix CT1 Star
Swix Triac
OneWay Storm Max 10
OneWay Storm Premio 10
Skigo Racing
145
2.6 ± 0.1
0.7 ± 0.6
1.2 ± 0.1
1.2 ± 0.1
1.5 ± 0.2
1.4 ± 0.1
1.8 ± 0.0
155
3.0 ± 0.1
1.3 ± 0.2
1.3 ± 0.0
1.4 ± 0.1
1.8 ± 0.1
1.6 ± 0.1
2.3 ± 0.6
165 170
3.3 ± 0.5 3.1 ± 0.4
1.5 ± 0.2 1.8 ± 0.2
1.6 ± 0.1 1.6 ± 0.1
1.7 ± 0.2 1.5 ± 0.3
2.0 ± 0.5 1.8 ± 0.0
2.0 ± 0.2 2.2 ± 0.9
2.1 ± 0.1
145
5.7 ± 0.6
1.9 ± 0.4
2.7 ± 0.1
2.7 ± 0.2
3.2 ± 0.3
3.4 ± 0.1
4.1 ± 0.0
155
6.8 ± 0.1
3.3 ± 0.1
3.3 ± 0.1
3.0 ± 0.3
4.0 ± 0.5
3.6 ± 0.5
5.6 ± 1.9
165
8.1 ± 1.1
3.4 ± 0.0
3.7 ± 0.3
4.6 ± 0.3
4.6 ± 0.8
4.9 ± 0.2
5.3 ± 0.0
170
8.6 ± 0.3
3.9 ± 0.3
4.6 ± 0.2
3.8 ± 0.3
4.4 ± 0.9
4.7 ± 0.9
145
11.7 ± 1.3
3.2 ± 0.3
5.3 ± 0.4
5.3 ± 0.5
5.3 ± 0.2
6.3 ± 0.5
7.7 ± 0.0
155
13.7 ± 0.4
4.5 ± 0.4
6.7 ± 0.5
6.5 ± 1.2
7.7 ± 0.7
6.9 ± 0.1
10.8 ± 4.0
165
18.4 ± 2.7
6.5 ± 0.2
7.7 ± 0.2
9.1 ± 0.4
8.7 ± 1.6
9.9 ± 1.2
10.4 ± 0.1
170
18.4 ± 1.0
6.8 ± 0.5
10.3 ± 0.4
7.4 ± 0.6
8.6 ± 1.5
10.3 ± 1.5
145
23.5 ± 2.9
4.7 ± 0.5
9.9 ± 0.7
9.5 ± 0.7
7.8 ± 0.1
10.1 ± 1.2
12.9 ± 0.5
155
30.9 ± 0.2
8.2 ± 0.5
12.8 ± 0.4
13.2 ± 2.2
12.7 ± 1.7
12.3 ± 0.2
22.2 ± 11.3 21.0 ± 3.8
165
59.2 ± 21.3
11.9 ± 0.3
17.0 ± 1.3
19.1 ± 0.6
15.2 ± 2.3
16.9 ± 0.8
170
68.8 ± 7.0
13.2 ± 0.3
24.9 ± 0.6
14.7 ± 0.3
15.9 ± 1.4
17.6 ± 3.6
Table 2 Mean maximal impact force ±SD and mean time to peak force ±SD for each pole model and pole length Pole model
Shaft length 145 cm Peak force (N)
155 cm Time to peak force (ms)
Peak force (N)
165 cm Time to peak force (ms)
Peak force (N)
170 cm Time to peak force (ms)
Peak force (N)
Time to peak force (ms)
Rex Wizard
732 ± 2
17.8 ± 0.6
733 ± 5
17.7 ± 0.8
738 ± 12
17.8 ± 0.5
738 ± 4
17.7 ± 0.4
Komperdell National Team Carbon
796 ± 23
18.9 ± 1.3
801 ± 6
19.3 ± 0.4
799 ± 1
20.4 ± 1.3
801 ± 4
19.4 ± 1.2
Swix CT1 Star
734 ± 8
17.1 ± 1.1
750 ± 5
17.3 ± 0.8
771 ± 5
17.8 ± 1.0
712 ± 6
18.0 ± 0.5
Swix Triac
772 ± 13
15.8 ± 0.6
714 ± 71
18.6 ± 2.4
752 ± 5
17.0 ± 0.5
765 ± 26
17.6 ± 1.6
OneWay Storm Max 10
792 ± 5
17.4 ± 0.5
781 ± 13
16.9 ± 0.7
781 ± 5
17.3 ± 0.8
771 ± 4
16.6 ± 0.4
OneWay Storm Premio 10
781 ± 4
17.2 ± 0.9
786 ± 5
17.0 ± 0.3
733 ± 16
17.7 ± 0.7
745 ± 22
18.9 ± 1.8
Skigo Racing
791 ± 8
16.5 ± 0.9
799 ± 10
16.9 ± 1.0
800 ± 1
17.7 ± 0.9
the short shockwave propagation time suggests that a quasi-static view on the loading situation is appropriate, and that the dynamic effects are limited, even in an impact situation. Results from the impact tests showed up to a 25 % reduction of force transfer caused by the poles, 712 N compared to 955 N on a stiff interface. All impact results are presented in Table 2. Swix CT1 Star and Swix Triac showed the highest damping differences with 8 % between different lengths, whereas both Komperdell National Team Carbon and Rex Wizard only had 1 %
difference between the highest and lowest values. Impact forces were on average 24 % higher than the MFT value. 3.3 Theoretical calculations On average, the MFT values were 14 % lower than the calculated critical loads based on the Southwell plots, (Fig. 5). Critical load from the FEM simulation for the modeled OneWay Storm Max 10 155 cm shaft was 290 N compared to the critical load result for the shaft with
Cross-country ski poles
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Fig. 5 A Southwell plot for the OneWay Storm Max 10 170 cm pole. Deflection, w (m) along the x-axis and the ratio between deflection and load, P(N) on the y-axis. Critical load, PC, is defined as PC = m-1, where m is from the equation for a straight line, y = mx ? c, fit to the measurements. PC for the displayed shaft is 648 N
Table 3 Generalized EI values at 200 N of load for each pole model in 145 and 170 cm lengths Shaft length (cm)
Generalized EI value (GN m2) Rex Wizard
Komperdell National Team Carbon
Swix CT1 Star
Swix Triac
OneWay Storm Max 10
OneWay Storm Premio 10
Skigo Racing
145
123
284
213
213
186
189
155
170
132
220
196
225
202
193
167a
a
The Skigo Racing pole was not available in 170 cm and was therefore tested with a 165 cm shaft
constant diameter which was 2.4 % higher (297 N). Calculated critical load, using Euler’s buckling model (Eq. 1), for the shaft with constant outer and inner diameter of 15.8 and 14.2 mm, respectively, was 301 N. Generalized B values were only calculated for F = 200 N as it was the load where minimum deflection occurred, but with deflection differences between the 145 and 170 cm shafts. The generalized B values are presented in Table 3 and where 5 out of 7 show an increased flexural rigidity of the 170 cm shafts compared to the 145 cm shafts.
4 Discussion The bending test in this investigation was performed in a static situation with a slow and constant increase in force, something that is not the situation when skiing. However, the developed test method enables a more skiing realistic way of applying a load to bend the pole compared to a standard three-point bending test. The incrementally increased load was applied via the handle strap in a realistic way and enabled a controlled and objective method of investigating pole shaft behavior. It is likely that some flexion occurred in the handles during the tests as the loads were applied via the handle straps and hence with an offset to the handles and the shafts. It is important to include the handle when evaluating cross-country ski poles as the load is applied via the handle and the handle strap when skiing
and the rigidity of the handles will hence affect the amount of force that the pole can transfer from the handle strap to the ground. However, no bended or damaged handles were observed during or after the tests so it is likely that the rigidity of the handles are higher than of the shafts and therefore not affect the force transfer capacities or bending characteristics of the poles. Depending on skiing velocity, reported peak pole force among elite skiers varies in the range 145–250 N while skiing on a treadmill [1, 4]. Mean MFT in the current study is more than two times higher than what the poles are exposed to while skiing in these studies. However, Sto¨ggl and Holmberg [5] demonstrated resulting peak pole forces [450 N for the fastest skier during a maximal skiing velocity test on a treadmill, which is in the range of, and even higher, than the measured MFT for some of the tested poles. In addition, there are most likely situations in which the poles are exposed to higher forces than those recorded in scientific studies. For example, losses of balance or falls are common among cross-country skiers and the poles are then used for extra support which results in high pole forces and even pole failure. Also, skiers apply most of their body weight to the poles during the first push-off in the sprint start and mass start, causing the poles to deflect excessively. Future studies are needed to investigate the loads on the poles during these situations. The differences in bending behavior between different shafts all followed a similar trend where MFT decreased and deflection increased with increased shaft length. Clear
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differences in MFT were also seen between different pole models, e.g. Rex Wizard had 38 % lower MFT compared to OneWay Storm Max 10 for the 145 cm poles. Still, as seen in Fig. 4, all pole models had similar SD in the maximal loading test throughout each individual test series. However, Skigo Racing 155 cm had a SD of ±171 N and retests were therefore performed to exclude any error in measurement. However, no difference between measurements was noticed and the high variation in MFT might depend on varying pole quality due to production problems. It is noteworthy that the pole with the highest MFT also had the lowest displacement and vice versa for the three 155 cm Skigo Racing poles. This confirms that the cross-sectional area varies for these poles due to e.g. varying thickness of material. Hence, MFT tests where the load is applied via the handle strap, as in the developed method, are useful for comparing different cross-country ski poles. It could be beneficial for comparison purposes to combine MFT and deflection results to indices which can describe parameters as MFT, bending behavior and maximal deflection in an objective and understandable way for skiers, consumers, retailers and manufacturers who want to compare different pole models or check the quality of the production process. The deflection characteristics of the shaft during the dynamic load application when skiing is considered to be the major aspect of ‘‘the feel’’ of the pole and the equipment works the best is an individual choice for every skier; the testing method developed in our study does not say anything about how well different poles perform during cross-country skiing. However, the method used in this study provides objective information about pole shaft behavior, which should be considered when comparing different shaft models and lengths. The maximal load test and the calculations of B were performed statically, assuming a quasi-static situation for the theoretical calculations. The short shockwave propagation time shows that the critical condition for dynamic buckling are not reached as the shockwave created by the impact moves slower through the shaft, 0.1 vs. 18 ms. The use of static testing for CFRP shafts is also supported by Betzler et al. [11] who investigated the static and dynamic stiffness behavior in golf shafts. They found during dynamic testing of CFRP golf shafts at strain rates within and beyond the range caused by a golfer during the swing that the limits of linear stress–strain behavior will not be surpassed during the golf swing [11]. In addition, it is important to note that the behavior of the shaft is described by a stiffness measure which describes the deformation of the shaft when applying a force, and also a strength value which is a measure of the force capacity of the shaft. The bending stiffness, which in itself describes the degree to which the shaft is bent when applying a transversal force, is also an important
M. Sware´n et al.
factor in the vibration of the shaft and in the failure load when buckling is the decisive failure aspect. The buckling force in this situation is a more important aspect of failure than the material strength. The impact forces produced an average 24 % higher forces than measured MFT values, but also higher than the previously reported pole forces in scientific studies. The poles can withstand the higher impact forces, compared to the static MFT forces, due to the dynamic buckling scenario, where the creation of shockwaves that travel up and down the shafts and where maximum buckling occurs at a wave length much shorter than the length of the shaft. Mean time to peak pole force, from initial contact, was 18.0 ms in the impact test, which is faster than in the results presented by Holmberg et al. [1]. They found that the skiers had time to peak pole force of at least 70.0 ms when double poling on a treadmill [1]. Sto¨ggl et al. [20] presented time to peak pole force as low as 51 ms during diagonal stride and 53 ms during double poling on roller skis at maximal velocity. Still, the rate of force development in our study is higher than in a normal skiing situation and can be explained by a more elastic impact compared to a real skiing situation. In our study, the tip of the pole is directly placed inside the cup of the load cell without any damping material between the two contact points. In crosscountry skiing the snow is normally too soft for the tip, thus the tip sinks down and the force is transferred by the skibasket. Still, roller skiing on paved,rolled involve more elastic type impacts, similar to the setup in the used TD. It can be argued that the force transfer should be via the skibasket and not via the tip. However, this will create a posteriorly placed contact point which will decrease the bending stiffness of the shaft along the longitudinal pole axis. Also, the interface between the ski-basket and the load cell will not have similar damping effect as snow as the damping effect of snow always changes due to e.g. temperature, snow crystals, the age of the snow, humidity or by how the tracks have been groomed and by how many skier that have skied in the tracks. Hence, the used test setup provides a repetitive method to measure impact and time to peak pole force without a posteriorly/anteriorly placed contact point and still is relevant for e.g. roller skiing or for very hard/icy conditions where the ski-basket does not sink down in the snow. However, future projects should develop a test setup where the rate of force development is similar to the one occurring when cross-country skiing on snow. This would require measurements of pole forces and time to peak pole force while skiing on different types of snow. Adjustments of the damping to enable different time to peak pole force could be achieved using softer and/or adjustable softer oil dampers or by placing different damping materials between the tip and the cup of the load cell. Yet, the short time to peak pole force
Cross-country ski poles
produces a higher peak force which could be of interest when measuring shaft strength as it put higher demands on the pole for not breaking. Mean MFT values were 14 % lower than the theoretical values predicted by the Southwell plots. The overestimation from the Southwell plots is most likely due to the decreasing cross-section area at the tip and the eccentrically applied load. In addition, as with vaulting poles, the flexible CFRP ski poles are not in a state of buckling instability due to their elastic properties which can explain the overestimation of the Southwell plots. It is also likely that the materials in the shafts are non-linear when exposed to high loads and deflections, due to the decreasing crosssectional area of the shafts and the eccentrically applied load via the strap. Hence, the buckling shape of the shafts is not a one-wave sinus curve, which is necessary for high accuracy when using Southwell plots to calculate critical loads. It is noteworthy that in the theoretical B value calculation, most poles showed an increased B value for the 170 cm shafts compared to the 145 cm shafts, Table 3. This behavior can explain the overestimations from the Southwell plots. The narrowing tips on the shafts always have the same absolute length for each shaft model and the total shaft length is adjusted by increasing/decreasing the length of the part with a constant cross-sectional area. This affects the generalized B value more for shorter shafts due to a higher percentage of decreasing cross-sectional area in the shaft. It can also explain why the mean measured MFT decrease was 19 % compared to a theoretical FC decrease of 27 % between lengths 145 and 170 cm. The issue with a tapering shape of the shaft is also present in golf clubs. Huntley et al. [21] compared static and dynamic behavior of carbon-fiber composite golf club shafts and determined a correction factor of 62.4 % to adjust the dynamic stiffness values of the golf club shafts. The difference between measured and theoretical values shows the difficulty in using theoretical calculations to estimate the flexural rigidity in CFRP shafts. A test method which provides repetitive and objective data without damaging the shafts should therefore be used to measure and compare the flexural rigidity in cross-country ski poles instead of using theoretical calculations as the correction factor will vary according to e.g. carbon-fiber orientation and shape of the shaft. However, the MFT value and deflection measurements offer accurate and reliable data for establishing the flexural rigidity in CFRP cross-country ski poles.
5 Conclusion The findings imply that the introduction of shaft indices for strength and deflection could be beneficial when comparing
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different pole shaft models and brands. The direct benefits of a strong shaft might be minor when using a short shaft (\145 cm), but the need for strength increases with increased shaft length where buckling becomes a dominant failure mode. The shaft’s MFT could be a fair parameter to use as a comparison standard. For all tested poles, buckling was the primary failure mode. The MFT also gives an indirect measure of bending flexibility, i.e. the ‘‘feel’’ of the pole. Also, small variations in MFT were noticeable between different poles of the same length and model, which makes the developed method a possible means for manufacturers to check the quality of the manufacturing process. Conflict of interest of interest.
The authors declare that they have no conflict
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