Pol. J. Sport Tourism 2018, 25, 3-9 Original research papers 3

BIOMECHANICS OF THE AXEL PAULSEN FIGURE SKATING JUMP

ANNA MAZURKIEWICZ, DAGMARA IWAŃSKA, CZESŁAW URBANIK Józef Piłsudski University of Physical Education in Warsaw, Faculty of Physical Education, Department of Anatomy and Biomechanics, Warsaw, Poland

Mailing address: Dagmara Iwańska, Józef Piłsudski University of Physical Education, Faculty of Physical Education, Department of Anatomy and Biomechanics, 34 Marymoncka Street, 00-968 Warsaw, tel.: +48 22 8342713, fax: +48 22 8651080, e-mail: [email protected]

Abstract Introduction. Figure skating is a sport discipline requiring a combination of artistic and athletic skills. The triple Axel Paulsen (Axel or A) jump is the most technically difficult jump of all figure skating jumps, which is why it is on the top of the Inter- national Skating Union (ISU) Judging System Code of Points (CoP). The purpose of this research was to explore the technical differences between the single Axel (1A), the double Axel (2A), and the triple Axel (3A) and to determine which parameters are the most important for performing the triple Axel successfully, using 3D kinematic analysis. Material and methods. In the study, one Polish elite male junior skater was tested. Following the usual warm-up, the skater performed a series of jumps on the ice, which were recorded. Six jumps of each type were recorded (6 x 1A, 6 x 2A, and 6 x 3A). Three jumps which were the best technically were chosen for further analysis. The APAS 2000 system automatically calculated the centre of gravity of the skater (CG) and generated the kinematic data of each jump. Results. The skater examined jumped higher when he was about to perform more rotations in the jump. The more rotations were to be made, the higher the jump was. Although the difference between the height of 2A and 3A was less than 10% and could not be considered significant, the height of 1A was significantly lower, by over 19%, that the height of the other two jumps. As also shown by previous research, the most substantial differences in the Axel jump technique were visible in the pre-take-off and take-off phases. Conclusions. We observed substantial differ- ences in the movement technique and kinematic parameters of the pre-take-off phase in the triple Axel performance compared to the performance of the other two Axels. It can be assumed that decreasing the ankle joint angle in the pre-take-off phase was most essential in achieving rotations in the Axel jump. This substantial change in ankle flexion caused greater stress on the blade before the take-off, which resulted in a reduction of vertical velocity and enabled an increase in the vertical take-off angle.

Key words: figure skating, Axel Paulsen, biomechanics, jump kinematics, 3D analysis

Introduction be performed from the forward outside edge and landed on the backward outside edge on the opposite leg to the one used for Since 1908, figure skating has been an Olympic sport disci- the take-off. Nowadays, skaters perform the single Axel (1A), the pline. It is regarded as requiring a combination of both artistic double Axel (2A), and the triple Axel (3A). The jumping tech- and athletic skills [1]. In single figure skating, skaters perform nique for 1A requires one and a half rotations in the air, the tech- specially choreographed programmes containing jumps, spins, nique for 2A requires two and a half rotations, and that for 3A steps, and spirals to music. They skate on the ice rink (30 x 60 m) requires three and a half rotations. wearing rigid leather boots with blades (about 4 mm in width). Furthermore, since jumps are generally completed in less Nowadays, the best figure skaters perform triple and even quad- than 0.65 s [2], coaches have difficulty discerning and defining ruple jumps, which means that they rotate on their own vertical parameters that are important in enabling the skater to success- axis in the air 3 or more times. One of the jumps where a skater fully land the most difficult revolutions. This is why research- is required to perform more than 3 revolutions is the triple Axel ers are constantly looking for the most effective and safest body Paulsen (3A). movement model for jumpimg technique. Being the most dif- The Axel Paulsen jump (Axel or A) is the most technically ficult jump, the Axel jump has also been studied the most often difficult jump of all figure skating jumps, which is why it is at the by researchers. Although Aleshinsky [3, 4, 5], Mishin [6], and top of the International Skating Union (ISU) Judging System Laak [7] have authored significant publications on this subject, Code of Points (CoP). It can be divided into three phases: the they have published most of their findings for coaching rather entrance phase, which ends with the take-off; the flight phase, than scientific reasons. Aleshinsky ascertained that the better when the skater is rotating in the air; and the landing phase, the skater, the greater the take-off velocities and jump lengths. which starts at the exact moment when the blade touches the Comparing double Axels to single Axels, he noticed that the ice and ends when skater is safely skating backwards on the full skaters exhibited greater pre-flight rotation, took off in more outside edge with one leg behind in the air. The entrance must closed positions, and attained greater rotational velocities in

Copyright © 2018 by the Józef Piłsudski University of Physical Education in Warsaw, Faculty of Physical Education and Sport in Biała Podlaska

Pol. J. Sport Tourism 2018, 25, 3-9

Mazurkiewicz et al.: BIOMECHANICS OF THE AXEL ... 4their double Axels. Alexey Mishin, who is considered to be one Following the usual warm-up, the skater performed a series of the best figure skating coaches in the world, did extensive kin- of recorded jumps on the ice. EachSkating trajectory jump was performed in com- ematic research into each jump in figure skating [6]. He based plete physical andCamera mental 1 comfort. This allowed him to perform his research on video analysis and the shape left on the ice by the jumps of the best technicalTake-off quality possible. Six jumps of each blades of the skates. Unfortunately, the specific results of that type were recorded (6 xFlight 1A, 6 x 2A, and 6 x 3A). All of them were research have not been made available to the general public. fully rotated and successfullyLanding landed. Nevertheless, three jumps Another figure skating coach and researcher, Trevor Laak [7], which were the best technically were chosen for further analysis. used kinenamic 3D analysis in order to create a list of charac- The choice was made with help of top figure skating coaches. teristics that can be used as rules or guidelines for coaches. The Using the APAS 2000 Program,Camera 2 the recordings of each jump researcher who made the biggest contribution to the research from each camera were manually digitised and synchronised. concerning the Axel jump was Canadian scientist King [2, 8].Figure 1Seventeen. Camera set -checkup and movementpoints were trajectory manually of the skatermarked during on videoeach recording frame The results of 3D kinematic analyses of single, double, and tri - of the recordings. Based on the marked check points, the APAS ple Axels indicate that skaters increase their number of turns by 2000 program automatically generated a 12-segment 3D model increasing their rotational velocity, not by increasing their time of the figure skater’s movement (stick figure) (Fig. 3). in the air. King’s [2, 8] research led her to assume that achieving a high rotational velocity by generating angular momentum at take-off and minimising the moment of inertia about the spin axis was the key to completing 3A successfully. Based on this as- sumption, she suggested the best off-ice exercises helping skat- ers perform better in jumping, that is box jumps and medicine ball throws [8]. Despite the fact that King’s research was very detailed, there are still many uncertainties around the topicFigure 2. Images from the original recording of one of the double Axels showing the of the best and safest technique of performing the triple Axel. Figure 2. Images from the original recording of one of the double Axels Some parameters allowing for the proper analysis of body movecharacteristic- showing moments the of characteristic each jump phase moments (entrance of –each first jump two images phase from(entrance the left, moment – first two images from the left, moment of take-off – third image, ment, like joint angles, were taken into consideration only inof take-off – third image, rotational position during the flight phase – fourth image, and jump landing analysis during the testing of a new type of skat- rotational position during the flight phase – fourth image, and moment moment of landing and landing stabilised position – remaining two images) ing boots [9]. of landing and landing stabilised position – remaining two images) The primary purpose of this research was to study the tech - nical differences between 1A, 2A, and 3A and to find out which parameters are of the greatest importance in the successful per-

formance of 3A, using 3D kinematic analysis and comparing the parameters of 1A, 2A, and 3A.

Material and methods

The research involved one Polish elite male junior skater. He was the first one in Poland to have ever performed the tri- ple Axel (3A), the quadruple Toe Loop (4T), or the quadruple Salchow (4S). He was 170 cm tall and had a body mass of 68 kg. In order to obtain kinematic data, two Canon LEGRIA HV40 (frame rate 50 Hz) cameras were positioned on the ice rink at an

angle of approximately 90 degrees in relation to each other. The Figure 3. Stick figures showing the double Axel divided into jump phases created in the camera settings were carefully planned in order not to disturb Figure 3. Stick figures showing the double Axel divided into jump the usual skating trajectory of the skater (Fig. 1). Both cameras APAS 2000 programphases and created used in in the the APAS analysis 2000 program and used in the analysis recorded all the phases of each of the jumps (Fig. 2) in order to achieve a 3D effect. The video cameras were turned on to record the 1.5 x 1.5 x 2.0 m calibration frame box and were then re- The APAS 2000 program also automatically calculated the

moved from the ice rink. The cameras remained turned on for centre of gravity of the skater (CG) and generated the kinematic the duration of data collection. data of each jump. The parameters taken into consideration in further analysis were: both leg joint angles (α, β, δ, α’, β’, and δ’) Skating trajectory and the take-off angle (γ, °) (Fig. 4), height of flight max(h , m)

Camera 1 (defined as the highest position of the skater’s centre of gravity

Take-off above the ice rink surface), and the horizontal (υxz, m/s) and vertical velocity (υy, m/s) of the CG. Flight The skater performed all the jumps entering on the left and Landing landing on the right leg. That is why in the analysis, during the entrance phase (n), the left leg was the supporting leg, and the

joint angles which were analysed were α, β, and δ (or αn, βn, and Camera 2 α – angle betweenδn ).foot During and tibia the of thelanding left leg, phase β – angle (w), between the right tibia and leg femur became of the the left leg,sup δ- – angle between torso andporting thigh of one the leftso leg,angles α’ – angleα’, β’, between and δ’ footwere and analysed. tibia of the right leg, β’ – angle between tibia Besides the joint angles, the take-off angle (γ) (Fig. 4) was and femur of the right leg, δ’ – angle between torso and thigh of the right leg, γ (take-off angle) – angle between Figure 1. Camera set-up and movement trajectory of the skater during video recordinganalysed. The take-off angle can be defined as the angle between Figure 1. Camera set-up and movement trajectory of the skater duringice rink surface theand ticehe long rink axis surface of the skater and’ sthe body. vertical axis of the skater’s body at video recording the moment of take-off. Figure 4. Figures demonstrating the angles measured in the study

Figure 2. Images from the original recording of one of the double Axels showing the characteristic moments of each jump phase (entrance – first two images from the left, moment of take-off – third image, rotational position during the flight phase – fourth image, and moment of landing and landing stabilised position – remaining two images)

Table 1. Maximal horizontal velocity value (υxz max), velocity of the take-off (υ3Dsc take-off), and the percentage difference between these velocities in the 1A, 2A, and 3A Difference Type of jump vxz max [m/s] v3Dsc take-off [m/s] Pol. J. Sport Tourism 2018, 25, 3-9[%] 1A 5.42 4.02 26 Mazurkiewicz et al.: BIOMECHANICS OF THE AXEL ... 5 The most significant moments during the entrance 2Aphase moment5.23 of take-off (40% difference).3.40 For 2A, the35 reduction was (n) are the transition zone, called also the pre-take-off phase, 35%, and it was 26% for 1A. and the take-off itself. The beginning of the transition zone3A was 4.83 2.89 40 operationally defined as the start of the skater’s upward motion Table 1. Maximal horizontal velocity value (υxz max), velocity of the take- signified by the beginning of the positive vertical velocity of the off (υ3Dsc take-off), and the percentage difference between these velocities skater’s centre of gravity (υy). The moment of take-off was de- in the 1A, 2A, and 3A

termined based on the velocity of the centre of gravity (υ3Dsc). Directly before the take-off, 3Dsc υ achieves its maximum. Type of jump vxz max [m/s] v3Dsc take-off [m/s] Difference [%] Therefore, the moment of take-off was designated as the mo- 1A 5.42 4.02 26 ment registered in the first recording frame after the skater reached the maximum υ3Dsc. Once the data had been generated, 2A 5.23 3.40 35

the relative error was counted for each parameter of each jump 3A 4.83 2.89 40 Figureattempt 3. Stick in order figure to scheck showing the repeatability the double of the A xelperformance divided into jump phases created in the of the jumps. The errors of all the parameters were lower than APAS 10%2000 taken program as the upperand used limit ofin normal,the analysis which showed that 3.8 there were no significant differences between the kinematic pa- rameters of jumps with the same number of rotations in the air. 3.6 12% 14% In view of these results of the relative error calculations, only 3.4

one jump of each type was taken into consideration in further [m/s] y 3.2 analysis. v 3.0 2.8 1A 2A 3A

Figure 5. Vertical velocity of the take-off moment (υy, m/s) in 1A, 2A, and 3A Figure 5. Vertical velocity of the take-off moment (υy, m/s) in 1A, 2A, and 3A

60 50

] o 40 21.4% 36.5% α – angle between foot and tibia of the left leg, β – angle between tibia and femur of the left leg, δ – angle between torso and thigh of the left leg, α’ – angle between foot and tibia of 30 α – anglethe between right leg, β’ –foot angle andbetween tibia tibia ofand thefemur left of the leg, right β leg, – δ’angle – angle betweenbetween torso tibia and femur[ angle of the left leg, δ – angle and thigh of the right leg, γ (take-off angle) – angle between ice rink surface and the long 20 betweenaxis torso of the andskater’s thigh body. of the left leg, α’ – angle between foot and tibia of the right10 leg, β’ – angle between tibia 1A 2A 3A and femur Figureof the 4. right Figures leg, demonstrating δ’ – angle betweenthe angles measuredtorso and in thigh the study of the right leg, γ (take-off angle) – angle between o ice rink surface and the long axis of the skater’s body. Figure 6. Take-offFigure angle 6. values Take-off ( ) forangle 1A, values 2A, ando( ) for 3A 1A, 2A, and 3A Results The skater gained the highest vertical velocity of the take- The data obtained in the study were analysed in each speci- off performing 3A (3.7 m/s), and he had the lowesty υ in 1A Figurefied 4. Figuresphase of thedemonstrating jump. The first the phase angles considered measured was the inen- the (3.19study m/s) (which means that there was a 14% difference). The

trance. observed differences between the υy values of 2A and 3A were As already mentioned, in the entrance phase, the beginning very small. Moreover, the value of the take-off angle (Fig. 6) for of the transition zone was operationally defined as the start of 3A was the highest (52°), which means that the skater took off the skater’s upward motion signified by the beginning of the more vertically in the triple Axel than in the other Axels. The positive vertical velocity of the skater’s CG (vy). It began an aver- difference between the values of the take-off angle for 1A and 2A age of 0.24 s before the last contact with the ice (take-off) for 1A was over 21%, and it was over 36% for 1A and 3A, both of which and 0.22 s before this moment for 2A and 3A. Although there were significant differences. These differences were also notice- 1A 2A 3A were differences in the time of the pre-take-off phase between able on the stick figures generated in the APAS program. The the single Axel and the multiple rotation Axels (2A and 3A), skater took off much more vertically in multiple rotation jumps they cannot be considered significant. (2A and 3A) (Fig. 7). The more rotations the skater was supposed to perform,Figure 7.the Stick figures of the skater in the take-off position entering 1A, 2A, and 3A lower the vertical velocity he gained was. The skatergenerated achieved in the APAS 2000 program the highest horizontal velocity, of 5.42 m/s, entering the 1A; the υxz max for 2A was over 3% lower (5.23 m/s), and that for 3A was almost 11% lower (4.83 m/s). Nevertheless, the biggest differ-

ence between maximal and take-off velocity (υxz difference) was observed in 3A (Tab. 1). During the 3A entrance, the skater re- duced his horizontal velocity from 4.83 m/s to 2.89 m/s at the 180 160 140 ] o [ 120 α 100 80 60 40 0.34 0.36 0.38 0.40 0.42 0.44 0.46 0.48 0.50 0.52 0.54 0.56 0.58 0.60 0.62 0.64 0.66 t [s] α 1A α 2A α 3A

Figure 8. Changes in the ankle joint angle (α) value of the left (supporting) leg during the pre- take-off phase in 1A (light grey line), 2A (grey line), and 3A (dark grey line). Horizontal grey

60 50 ] o 40 21.4% 36.5%

30

angle [ angle line shows the beginning of the pre take-off phase. Black dots show the lowest value of the

20 60 angle during the pre-take-off phase 10 1A 502A 3A ]

o 40 21.4% 36.5% Figure 6. Take-off angle values (o) for 1A, 2A, and 3A 30 [ angle 140 20 120 10 ] o 1A 2A [ 100 3A 25.4%

α o Figure 6. Take-off angle values ( ) for 1A, 2A, and 3A 80

60 1A 2A 3A Pol. J. Sport Tourism 2018, 25, 3-9

1A 2A 3A Figure 9. Lowest values of theMazurkiewicz ankle joint etangle al.: BIOMECHANICS (α) during the OF pre THE-take AXEL-off ... phase in 1A, 2A, 6 cal grey line on Figure 11), hip angle increased by about 25° in the and 3A time of 0.16 s, whereas 0.06 s before the take-off, the values of δ Figure 7. Stick figures of the skater in the take-off position entering 1A, 2A, andchanged 3A from about 140° up to 160° (2A and 3A) or 170° (1A). The knee angle changed very similarly. During the first 0.18 s after the generated in the APAS 2000 program pre-take-off phase started, β values grew by 20°, while during the last 0.06 s before take-off, they increased by 35°. 1A 2A 3A 180 160 Figure 7. Stick figures of the skater in the take-off position entering 1A, 140

Figure 7. Stick figures of the skater in the take-off position] entering 1A, 2A, and 3A 2A, and 3A generated in the APAS 2000 program o 120

[

β 100 180generated in the APAS 2000 program 80 160 60 140 ] o [ 120 40

α

100 0.34 0.36 0.38 0.40 0.42 0.44 0.46 0.48 0.50 0.52 0.54 0.56 0.58 0.60 0.62 0.64 0.66 80 60 β 1A β 2A β 3A 180 40 180 160 Figure 10. Changes inFigure theB 160knee 10. Changes angle in (β) the kneevalue angle of (β)the value left of (supporting) the left (supporting) leg during the entrance

0.34 0.36 0.38 0.40 0.42 0.44 0.46 0.48 1400.50 0.52 0.54 0.56 0.58 0.60 0.62 0.64 0.66

] leg during the entrance pre-take-off phase in 1A, 2A, and 3A. Horizontal

o 140 [ 120 pre-take-offt [s] phase in 1A, 2A,grey and line 3A.shows Horizontal the beginning greyof the pre-take-offline shows phase the beginning of the pre- α α 1A α 2A α 3A ] 120 o 100 [ δ 100 line shows the beginning of the pre take-off phase. Black80 dotstake show-off the phase lowest value of the 180 Figure 8. Changes in the ankle joint angle (α) value of the left B Figure 8. Changes in the ankle joint angle (α) value60 of the left (supporting) leg during16080 the pre- angle during the pre(supporting)-take-off phaseleg during the pre-take-off phase in 1A (light grey line), 60 2A (grey line), and 3A (dark grey line). Horizontal40 grey line shows the 140 take-off phase in 1A (light grey line), 2A (grey line), and 3A (dark grey line). Horizontal40 grey ] 120 beginning of the pre take-off phase. Black dots show the lowest value of o 0.34 0.36 0.38 0.40 0.42 0.44 0.46 0.48 0.50 0.52 0.54 0.56 0.58 0.60 0.62 0.64 0.66 [ δ

the angle during the pre-take-off phase 0.34 0.36 0.38 0.40 0.42 0.44 0.46 0.48 0.50 0.52 0.54 0.56 0.58 0.60 0.62 0.64 0.66 100 t [s] α 1A α 2A α 3A 80 δ 1A δ 2A δ 3A 140 60 Figure 8. Changes in the ankle joint angle (α) value of the left (supporting) leg during the pre- 120 Figure 11. Changes in the40 hip angle (δ) value of the left (supporting) leg during the entrance ] 0.34 0.36 0.38 0.40 0.42 0.44 0.46 0.48 0.50 0.52 0.54 0.56 0.58 0.60 0.62 0.64 0.66 o take-off phase in 1A (light grey line), 2A (grey line), and 3A (dark grey line). Horizontal grey [ 100 25.4% pre-take-off phase in 1A, 2A, and 3A. Horizontal grey line shows the beginning of the pre- α δ 1A δ 2A δ 3A 80 take-off phase

60 Figure 11. ChangesFigure in the 11. hip Changes angle in the(δ) hip value angle of(δ) thevalue left of the (supporting) left (supporting) leg leg during the entrance

1A 2A 3A during the entrance pre-take-off phase in 1A, 2A, and 3A. Horizontal pre-take-off phase in 1A, 2A,grey lineand shows 3A. the Horizontal beginning of grey the pre-take-off line shows phase the beginning of the pre- Figure 9. Lowest values of the ankle joint angle (α) during the pre-take-off phase in 1A, 2A, Figure 9. Lowest values of the ankle joint angle (α) duringtake- theoff pre-take- phase 2 and 3A off phase in 1A, 2A, and 3A 1.5 The changes in the ankle joint angle in time during the en- [m] 1 ysc

trance phase in 2A and 3A were very similar. During the whole D phase, there were no significant differences between the values 0.5 of the α angle180 in 2A and 3A (Fig. 8). On the other hand, the 20 skater demonstrated160 significantly different joint flexion during

entering 1401A than in multiple rotation (2A and 3A) jumps. The 1.5 0.02 0.10 0.18 0.26 0.34 0.42 0.50 0.58 0.66 0.74 0.82 0.90 0.98 1.06 1.14 1.22 1.30 1.38 1.46 1.54 [m] values of] the α angle were higher in 1A than 2A and 3A dur-

o 120 [ 1 Dy sc 1A Dy sc 2A Dy sc 3A ysc ing the entireβ 100 time of the entrance phase (Fig. 8). The lowest D recorded value80 of this angle in 2A and 3A was exactly the same 0.5 Figure 12. Centre ofFigure gravity 12. Centre vertical of gravity displacement vertical displacement (Dy sc) during (Dy sc) during1A, 2A, 1A, 2A,and 3A (91°), while60 in 1A, it was over 25% greater (122°) (Fig. 9). As shown in the chart below (Fig. 10), there were no sig- 0 and 3A 40 nificant differences in the β angle values during the pre-take-off 0.02 0.10 0.18 0.26 0.34 0.42 0.50 0.58 0.66 0.74 0.82 0.90 0.98 1.06 1.14 1.22 1.30 1.38 1.46 1.54 phases of 1A, 2A,0.34 and0.36 0.38 3A.0.40 0.42 The0.44 curves0.46 0.48 0.50 illustrating0.52 0.54 0.56 0.58 0.60 the0.62 changes0.64 0.66 in The parameters analysed in the flight phase were based on the values wereβ 1A very similar.β 2A Whatβ 3A is more, the differences ob- centre ofDy gravity sc 1A verticalDy scdisplacement 2A Dy sc(D 3Ay sc) (Fig. 12). As already served in hip flexion values were also insignificant (Fig. 11). Both mentioned, the moment of take-off was determined based on β and δ angle values were the lowest at the beginning of the pre- the velocity of the centre of gravity (υ3Dsc) and knowing this, the Figure 10. Changes in the knee angle (β) value of the left (supporting)Figure leg12. during Centre the of entrance gravity vertical displacement (Dy sc) during 1A, 2A, and 3A take-off phase and grew continuously during the whole phase moment of landing was verified on the Dy sc chart. The centre of pre-take-off phase(Fig. in 101A, and 2A, Fig. and 11). 3A. The Horizontal value growth grey increased line shows rapidly the just beginning before of thegravity pre- of the skater was on the same height in the moment of the take-off. From the beginning of the pre-take-off 0.7phase (verti- take-off and at the moment when the1.80 skater’s blade touched the take-off phase 0.68 A [m] B [s]t 1.75

0.66 max

h 1.70 0.64 0.62 1.65 0.6 1.60 0.58 1.55 0.56 1.50 0.7 1A 2A 3A 1.80 1A 2A 3A

0.68 A [m] B

t [s]t 1.75

Figure0.66 13. Time of the flight phase (A). Values of themax maximal height of the centre of gravity

h 1.70 0.64 placement0.62 for 1A, 2A, and 3A (B) 1.65 0.6 1.60 0.58 1.55

0.56 1.50 1A 2A 3A 1A 2A 3A Figure 13. Time of the flight phase (A). Values of the maximal height of the centre of gravity placement for 1A, 2A, and 3A (B)

180 B 160 140

] 120 o [

δ 100 80 60 40 0.34 0.36 0.38 0.40 0.42 0.44 0.46 0.48 0.50 0.52 0.54 0.56 0.58 0.60 0.62 0.64 0.66

δ 1A δ 2A δ 3A

Figure 11. Changes in the hip angle (δ) value of the left (supporting) leg during the entrance pre-take-off phase in 1A, 2A, and 3A. Horizontal grey line shows the beginning of the pre- take-off phase

2

1.5

[m] 1 ysc D 0.5

0

0.02 0.10 0.18 0.26 0.34 0.42 0.50 0.58 0.66 0.74 0.82 0.90 0.98 1.06 1.14 1.22 1.30 1.38 1.46 1.54 Dy sc 1A Dy sc 2A Dy sc 3A

Figure 12. Centre of gravity vertical displacement (Dy sc) during 1A, 2A, and 3A 200 150 ] O

' [ ' 100 α Pol. J. Sport Tourism 2018, 25, 3-9 50

Mazurkiewicz et al.: BIOMECHANICS OF THE AXEL ... 0 7 0.7 1.80 1.26 1.28 1.30 1.34 1.36 1.38 1.40 1.42 1.44 1.46 1.48 1.50 1.52 1.54 1.32 0.68 A [m] B

t [s]t 1.75

0.66 max α' 1A α' 2A α' 3A h 1.70 0.64 0.62 1.65 0.6 Figure 14. Changes in1.60 the ankle joint angle (α’) value of the supporting leg during the landing 1.55 0.58 phase in 1A, 2A, and 3A. Vertical lines show the moment of landing in each jump 0.56 1.50 1A 2A 3A 1A 2A 3A Figure 13. 13. Time Time of the flightof the phase flight (A). phase Values of(A) the . Valuesmaximal height of the of the maximal centre of gravityheight placement of the centrefor 1A, 2A, of and gravity 3A (B) placement for 1A, 2A, and 3A (B) ice for the first time after the flight phase. The skater took off for 200 1A and 3A at 0.66 s and for 2A at 0.64 s counting from the be- 150 ginning of the entrance phase. Although the time of the take-off ] for each jump was very similar, as shown on the chart above, the O ' [ ' 100 time of landing was different for each jump. That means that the β flight phase of each jump was different. The more rotations were 50 made, the longer the flight phase was. In 1A, the flight phase lasted 0.6 s; in 2A, it lasted 0.64 s; whereas in 3A, it was 0.68 s 0 long (Fig. 13A). The biggest difference for the time of the flight 1.24 1.26 1.28 1.30 1.32 1.34 1.36 1.38 1.40 1.42 1.44 1.46 1.48 1.50 1.52 1.54 phase was observed between 1A and 3A (12%). What is more, the maximal height of the skater’s centre of β' 1A β' 2A β' 3A gravity was also different for each type of jump. The lowest hmax was observed in 1A (1.59 m), and the highest valueFigure of this 15.param Changes- Figure in the 15. knee Changes joint in theangle knee (β’) joint value angle (β’) of value the supportingof the supporting leg during the landing eter was found in 3A (1.77 m) (Fig. 14B). After subtracting the leg during the landing phase in 1A, 2A, and 3A. Vertical lines show the height of the skater’s normal standing position from the cen- moment of landing in each jump phase in 1A, 2A, and 3A. Vertical lines show the moment of landing in each jump tre of gravity (1.1 m), the height of the jump was counted. The height of 1A was 0.49 m, that of 2A was 0.61 m, and the height 200 of 3A was 0.67 m. The difference between the two multiple rota- 150 ]

tion jumps (2A and 3A) and 1A amounted to over 19%. o ' [

During the landing phase, the ankle (α’), knee (β’), and hip δ 100 (δ’) angles of the supporting (right) leg were analysed. The val- ues of the α’ (Fig. 14), β’ (Fig. 15), and δ’ (Fig. 16) angles in each 50 jump decreased just after the moment of landing and stabilised 0 as the skater stabilised the landing position (the positions are

shown in Figure 2). The time of achieving a stabilised position 1.24 1.26 1.28 1.30 1.32 1.34 1.36 1.38 1.40 1.42 1.44 1.46 1.48 1.50 1.52 1.54 was different for each Axel jump. The time of that phase was t [s] 0.04 s in 1A, 0.08 s in 2A, and 0.1 s 3A. Thus in 1A, the stabilisa- δ' 1A δ' 2A δ' 3A tion phase was the shortest; the differences in the values of the angle were minimal, and it decreased from 153° to around 140°. Figure 16. Changes in the knee joint angle (δ’) value of the supporting During this phase, in 2A, the α angle changedFigure from 130° 16. to Changes 89°, inleg the during knee the jointlanding angle phase in(δ’) 1A, 2A,value and of3A. theVertical supporting lines show theleg during the landing and in the triple Axel, it changed from 145° to 95°. The α angle moment of landing in each jump in the landing position was similar in 2A andphase 3A, but in in 1A, 1A, the2A, and 3A. Vertical lines show the moment of landing in each jump value of the angle was about 40° (about 30%) higher. The stabilisation of the knee flexion during the landing

took longer in each jump than in the ankle joint. It took the skater 0.06 s in 1A and exactly 50% more in 2A and 3A. The dif- 200 ferences in angle values were minimal between 2A and 3A, but the values for 1A were significantly different from those recorded 150 for the two multiple rotation jumps. During the stabilisation, ] O the β’ angle decreased by 42° in 1A, by 62° in 2A, and by 66° 3A,

' [ ' 100 α which means there was a 30% difference between 1A and multi- 50 ple rotation jumps. Nevertheless, the differences in the β’ angles of the stabilised landing positions between the three types of 0 the Axel jump were insignificant. The last angle analysed was the last one in which the skater achieved stabilisation during 1.26 1.28 1.30 1.32 1.34 1.36 1.38 1.40 1.42 1.44 1.46 1.48 1.50 1.52 1.54 the landing phase. This moment was also considered as the mo- ment of achieving a fully stabilised landing position. In 1A, this α' 1A α' 2A α' 3A moment was observed after 0.08 s from the beginning of the landing; in 2A, this took the skater 0.16 s; and in 3A, this took Figure 14. Changes Figurein the 14. ankle Changes joint in the angle ankle (α’)joint anglevalue (α’) of value the of supporting the supporting leg duringthem the twice landing as long as in 2A and four times longer than in 1A leg during the landing phase in 1A, 2A, and 3A. Vertical lines show the (0.32 s). During the stabilisation of the landing, the hip angle phase in 1A, 2A, and 3A. Vertical momentlines show of landing the inmoment each jump of landing in each jumpin 3A changed by 113°, which was above 60% more than during

200

150 ] O

' [ ' 100 β 50

0 1.24 1.26 1.28 1.30 1.32 1.34 1.36 1.38 1.40 1.42 1.44 1.46 1.48 1.50 1.52 1.54

β' 1A β' 2A β' 3A

Figure 15. Changes in the knee joint angle (β’) value of the supporting leg during the landing phase in 1A, 2A, and 3A. Vertical lines show the moment of landing in each jump

Pol. J. Sport Tourism 2018, 25, 3-9

Mazurkiewicz et al.: BIOMECHANICS OF THE AXEL ... 81A and more than 40% than in 2A. Moreover, the angle of the cant parameter was the time of achieving a fully stabilised land- stabilised landing position in 3A was 50% lower than in 2A and ing position. The more rotations were made by the skater, the 1A, which was a significant difference. longer it took him to achieve stabilisation. It took the longest for the skater to stabilise the hip flexion in all the jumps. It took Discussion him twice as long to stabilise in 2A and four times longer in 3A compared to 1A. This large differences was probably caused by As already mentioned, the primary purpose of this research the increasing impact forces in multiple rotation jumps, which was to study the technical differences between 1A, 2A, and 3A was found by Lockwood in his research on landing forces in and to determine which parameters are the most important in figure skating [11]. Landing forces can be decreased by using performing the triple Axel successfully. Although some of the articulated boots, as demonstrated by Bruening and Rich- parameters considered in this study were analysed in previous ards [9]. Using this type of boots could improve work of the research, some new parameters were examined as well. What is muscle-tendon complex during the amortisation of a jump. more, not all the data confirmed the results of previous studies. An appropriate stretch-shortening cycle decreases ground re- King suggested that a figure skater must increase their time action forces [12] and injury risk during landing [9], although in the air and/or rotate faster in order to increase the number the exact kinematic mechanism of the movement technique of of revolutions completed in a jump [2, 8, 10]. While the current jumping is still unclear. For that reason, striving to achieve the research confirmed King’s hypothesis in that the skater spent optimal technique of jumping seems to be a crucial element of more time in the air when he was performing jumps with more the training process, especially that in order to be competitive rotations, we reached the opposite conclusions concerning today, elite skaters should perform more than 50 jumps per day. jump height. King’s data showed that skaters jumped no high- er in their triple Axels than in their double or single Axels and Conclusions thus spent a similar amount of time in the air in each jump. The skater examined in this study, however, jumped higher when he The research showed some differences in the movement was about to perform more rotations in the jump. The more ro- technique and kinematic parameters of the pre-take-off phase tations were to be made, the higher the jump was. Although the that are important for performing the triple Axel. According to difference between the height of 2A and 3A was less than 10% the data, the biggest differences were observed between multi- and could not be considered significant, in the single Axel, the ple rotation Axels and the single one. It can be assumed that de- skater jumped significantly lower, by over 19%, than in the other creasing the ankle joint angle in the pre-take-off phase was the two jumps. As was found in previous research, this study also most essential for achieving more rotations in the Axel jump. showed that the most substantial differences for the Axel jump This substantial change in ankle flexion caused greater stress technique were visible in pre-take-off and take-off. on the blade before the take-off, which caused a reduction in According to the data collected during the research, the vertical velocity and made the take-off angle more vertical. This skater slightly changed his pre-take-off technique in order to caused the jump to become longer and higher, and, in the end, perform more rotations in the air in the Axel jump. Though the helped the skater to perform more rotations in the air. Differ- time of the pre-take-off phases were very similar in each jump, ences in the landing phase were assumed to have been due to an differences were observed in horizontal and vertical velocities increase of impact forces during landing. and joint and take-off angles. The biggest difference between maximal horizontal and take-off velocity was observed in 3A. Literature When entering 3A, the skater reduced his vertical velocity by 40%; in 2A, the reduction amounted to 35%; and in 1A, it was 1. Hines J.R. (2006). Figure skating. A history. Champaign, IL: 26%. Reducing the horizontal velocity enabled the skater to University of Illinois Press. achieve greater vertical velocity, which was significantly high- 2. King D.L., Arnold A.S., Smith S.L. (1994). A kinematic com- er in 2A and 3A than in 1A. What is more, the figure skater’s parison of single, double and triple Axels. Journal of Applied take-off angle was also greater in the double and triple Axels. Biomechanics 10, 51-60. DOI: 10.1123/jab.10.1.51. The skater took off more vertically, the more rotations he was 3. Aleshinsky S.Y. (1986). What biomechanics can do for fi- to make. Taking into consideration the joint angles of the sup- gure skating. Part two. Skating 63(10), 11-15. follow by porting leg, the only significant difference was observed in ankle Sharp C.M.P. (1999). A biomechanical analysis of the single joint flexion. During the whole pre-take-off phase, the values of toe loop and the single loop jump of novice figure skaters. the α angle in 1A were nearly approximately 25% higher than in file:///C:/Users/User/Downloads/31762104283245%20 2A and 3A. This means that the skater pushed the blade harder (1).pdf before multiple rotation jumps, which was visible in the ankle 4. Aleshinsky S.Y. (1987). A biomechanical report of USFSA/ joint flexion and the vertical velocity reduction. Considering USOC/PSGA junior elite camp participants. The Profes- insignificant differences in the other joints analysed, it can be sional Skater. 18(1), 24-28. follow by Sharp C.M.P. (1999). assumed that the skater pushed harder on the blade (decreas- A biomechanical analysis of the single toe loop and the ing the value of the ankle joint angle), not by leaning forward, single loop jump of novice figure skaters. file:///C:/Users/ which would have caused a more vertical rather than horizontal User/Downloads/31762104283245%20(1).pdf take-off, but by turning the blade perpendicularly to the skating 5. Aleshinsky S.Y. (1990). Biomechanics explores differences direction; this also led to greater υxz reduction and increased the in Boitano’s axels. American Skating World 21, 12-13. υy at the same time. This blade turning additionally caused pre- 6. Mishin A. (1981). Figure skating jumps. Moscow: Fitzkultu- take-off rotation on the ice, which helped the skater perform ra i Sport. [in Russian] multiple rotation jumps. 7. Laak T. (2008). Jump manual. Madison: Skating Jump The analysis of the joint angles of the supporting leg in the Secrets and the TAL Group, LLC. Retrieved from https:// landing phase showed some differences in the performance of pl.scribd.com/document/29509583/Figure-Skating-Jump- this part of the Axel jump. Besides joint angle values, a signifi- ing-Coaches-Jump-Manual. Pol. J. Sport Tourism 2018, 25, 3-9

Mazurkiewicz et al.: BIOMECHANICS OF THE AXEL ... 8. King D.L. (2005). Performing triple and quadruple figure 11. Lockwood K.L., Gervais P.L., Mccreary D.R. (2006). Lan9- skating jumps: Implications for training. Canadian Journal ding for success: A biomechanical and perceptual analysis of Applied Physiology 30(6), 743-753. DOI: 10.1139/h05-153. of on-ice jumps in figure skating. Sport Biomechanics 5(2), 9. Bruening D.A., Richards J.G. (2006). The effects of articula- 222-237. DOI: 10.1080/14763140608522876. ted figure skates on jump landing forces. Journal of Applied 12. Sands W.A., Kimmel W.L., McNeal J.R., Murray S.R., Biomechanics 22, 285-295. DOI: 10.1123/jab.22.4.285. Stone M.H. (2012). A comparison of pairs figure skaters in 10. King D.L., Smith S.L., Brown M.R., Mccreary J.L., repeated jumps. Journal of Sports Science and Medicine 11, Munkasy B.A., Scheirman G.I. (2008). Comparison 102-108. Retrieved from https://www.ncbi.nlm.nih.gov/ of split double and triple twists in pair figure pmc/articles/PMC3737852. skating. Sport Biomechanics 7(2), 222-237. DOI: 10.1080/14763140701841662. Submitted: September 8, 2017 Accepted: October 22, 2017