3-d kinematics and kinetic analysis of g-slalom in elite

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Pubblicato su SCIENCE AND SKIING III – Ed. Eric Müller et al., Meyer & Meyer Sport 2004
3-D KINEMATICS AND KINETIC ANALYSIS OF G-SLALOM IN
ELITE SKIERS AT VALBADIA WORLD CUP RACE IN 2002
R. Pozzo1,3, A. Canclini1, C. Cotelli1, G. Baroni2
1) Lab. Alta Prestazione – S.Caterina Valfurva (Fed. Italiana Sport Invernali - C.O.N.I.), Italy
2) Dipartimento di Bioingegneria, Politecnico di Milano, Milan, Italy.
Dipartimento Scienze Motorie, Università di Medicina di Udine., Italy
Introduction
In competitive skiing one of the most important factors influencing the performance is to keep a
high level of average velocity while maintaining an optimal trajectory. In each turn around the
gates, the skiers has to change his instantaneous trajectory an this produce a very high centripetal
force acting on the centre of mass of the body (CG).A great amount of eccentric and concentric
muscular activity is needed to counteract this kind of load (BERG 1995). Provided the limited
amount of studies reporting movement kinematics during ski competition (POZZO 2001), we
focused our work on colletting three-dimensional kinematics data on athletes during a world cup
giant slalom race. The data reported in this work are related to the World Cup men’s slalom, which
took place in December 2002 in Val Badia (Italy).
Methods
Four digital camcorders (Canon XM2- 50 Hz) were
located along the slope and acquired the skier’s
motion throughout three gates in the middle part of
the race. A dedicated software for video analysis,
allowing the operators to freely pan, tilt and zoom
the TV cameras, was used in order to ensure the
largest possible working volume (Baroni et al.,
1998). The system calibration was performed by
means of the DLT method. The 3-D localization of
the control points (gate poles, nets supports, etc.)
was obtained by means of a geodetic theodolite
immediately before the start of the race. The
biomechanical model of the skier consisted of 17
body landmarks in correspondence of joint centres,
foot edges, head centre, as well as skis and poles
extremities. The total body centre of mass (CG) was
calculated according to Gubitz. The joints ranges of
motion were calculated on average slope plane (xz Fig. 1. Images sequences of the turns
horizontal plane), uphill 23°, and on the orthogonal considered in the analysis
direction to this plane, namely vertical direction (y).
The instantaneous radius of the turn was calculated
for the path of the CoG in the critical phase of turning the gates. This allows evaluating the
centripetal acceleration which, in turn, is an indirect indicator of the centripetal force acting on the
CoG of the skiers.
.
Proceedings ICSS 2004 – Aspen, CO – pag. 125-135
1/6
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Results
The results are presented referring to four athletes who are representative for the first 10 skiers of
the race. Following parameter are discussed:
• CG trajectories on the slope
• instantaneous radius of the turn and ed centripetal acceleration
• CG velocity on the slope
• CG vertical movement with respect to the slope plane and angles of body inclination
• Body angles
CG trajectories on the slope
displacememt Z (m)
Fig 2 shows the trajectories of CG on the slope plane. The gates were located at a distance of 27-29
m from each other. From a macroscopic overview, trajectories seem to be very close to each other,
especially during the gate clearance.
Mayer
Miller
Blardone
Simoncelli
A deep analysis however, shows that Val Badia 2002 - CoG's trajectories
some differences appear mostly during
-25.000
the changing of the edge.
direction of motion
This means that the centripetal
-15.000
acceleration is influenced by both
factors, the trajectory and the
-5.000
instantaneous velocity.
Instantaneous radius of the
turn and ed centripetal
5.000
-110.000
-100.000
-90.000
-80.000
-70.000
The characteristics of turning are
-60.000
-50.000
-40.000
15.000
-30.000
displacememt X (m)
summarised in tab.1. There different
combination between and within the Fig. 2 Trajetories of CG for four skiers. The arrow indicates
the falling line.
subjects. The maximum and minimum
of trajectory radius were founded for
Bode-Miller (24,9m) and for Simoncelli (11,3m). Some skies tend to maintain the minima or the
maxima. Centripetal accelerations are calculated via instantaneous values of CG velocity and of
corresponding trajectory radius. Calculated values are in the range of di16,6 ms-2 to 32,3 ms-2 . If
this values are multiplied by the subjects mass an estimation of the centrifugal force acting on the
CG is obtained. The calculated force are well in agreement with those values collected by direct
measurements via force plate mounted between boots and skies.
Tab. 1 instantaneous radius of the turns and centripetal acceleration acting on CG.
2 g a te
M a ye r
B o d e M ille r
S im o n c e lli
B la rd o n e
RC
17
22
21
14
(m )
,1
,0
,5
,9
a -c e n t
24
19
17
24
3 g a te
(m / s* s)
,9
,3
,1
,2
R C (m ) a -c e n t (m / s* s)
2 3 ,1
1 6 ,6
2 4 ,9
1 7 ,4
1 1 ,3
3 2 ,3
1 8 ,5
2 1 ,4
CG velocity on the slope
Fig. 3 shows the time history of the instantaneous CG velocity on the slope plane for two
representative athletes. Obviously, CG deceleration and acceleration occurs during the gate
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clearance (vertical dashed line on the graph). Different patterns with respect to the peak values, are
easy to be recognised. This means, that different amounts of CG acceleration are influencing the
mean velocity of CG. So, for same trajectories, a high mean CG velocity is the goal of the skiers’
technique.
2 2
C G
v e lo c it y
o n
th e
s lo p e
B o d e - M ille r
V C G -X Z
2 1 ,5
2 1
V [m/s]
2 0 ,5
2 0
G a te s
1 9 ,5
1 9
1 8 ,5
1 8
t[s ]
1 7 ,5
0
V [m/s]
C G
2
2
2
2
2
2
1
1
1
1
1
0 ,5
V e lo c it y
2
2
1
1
0
0
9
9
8
8
7
1
o n
th e
1 ,5
s lo p e
2
2 ,5
3
3 ,5
B la r d o n e
4
4 ,5
V C G -x z
t[s ]
0
0 ,5
1
1 ,5
2
2 ,5
3
3 ,5
4
Fig. 3 Time history of CG velocity on the slope plane. Vertical dahed lines decribe the time of
clearence the gate.
In fig4 mean peak values and the mean value of CG velocity are presented. Maximum mean
velocity value of 20 ms-1 was obtained by Bode-Miller, while peak values are similar for BodeMiller, Mayer and Simoncelli. The most significant difference between the skiers is the minimum
peak value. Simoncelli shows the greatest difference between maximum and minimum peak value,
i.e. the highest acceleration and deceleration on CG. Blardone conversely, has the lowest peak
values variations. According to these data, it is possible to introduce a overall criterion of
mechanical effectiveness of the skiers’ technique. By constant mean CG velocity, small variations
of CG acceleration represent a better distribution of loading forces on the CG.
v e lo c ità d e l C G s u l p ia n o
V R m e d ia
V R m ax
V R m in
25
V [m/s]
20
15
10
5
0
Bla .
Bo d e .
M ay.
S im o .
Fig. 4 Mean value (VRmedia) and peak values (VRmax, VRmin) and standard deviations of CG
velocità for four skiers..
On the other hand, if the peculiarities of the neuromuscular mechanisms of leg actions (e.g. strechshortening cycle) are taken in to account, a certain amount of deceleration-acceleration onto the CG
is necessary to obtain the optimal response from the muscular system (power, force).
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CG vertical movement with respect to the slope plane and angles of body
inclination
The vertical CG motion with respect to the slope plane can be divided in two parts: the loweringlifting of the legs by flexion-extension of the ankle- knee- and hip joints, and the body tilting on the
frontal plane, i.e. the inverse pendulum-like inclination of the body with respect to centre of the
curve during the turns.
In the fig. 5 the time history of the vertical CG motion (red line) and his corresponding vertical
velocity (blue line) are demonstrated for two representative athletes. Same amount of vertical
displacement are associated to a different pattern of vertical velocity, and vice versa. In the first
turn, for example, the peak velocity value is 1,2 ms-1 for both skiers, while the amount of the
vertical displacement is quite different.
C G v e r t . d is p la c e m e n t a n d v e lo c ity - B la r d o n e
V C G ve r t
C G ve r t
1 ,5
0 ,5
1
0 ,4
0 ,3
0
- 0 ,5
0 ,5
1
1 ,5
2
2 ,5
3
3 ,5
4
t [ s ] 4 ,5 0 ,1
0
-1
- 0 ,1
- 1 ,5
- 0 ,2
-2
- 0 ,3
V C G ve r t
C G v e r t ic a l d is p la c e m e n t a n d v e lo c it y - B o d e .
C G ve r t
1 ,5
0 ,5
1
0 ,4
0 ,3
0 ,5
V [m/s]
Y [m]
0 ,2
0
0 ,2
0
- 0 ,5
0
0 ,5
1
1 ,5
2
2 ,5
3
3 ,5
4
t[s ]
4 ,5 0 ,1
Y [m]
V [m/s]
0 ,5
0
-1
-0 ,1
- 1 ,5
-0 ,2
-2
-0 ,3
Fig. 5 time history of vertical CG motion (red line) and velocità (blue line) for
two representative skiers.
The mean values and standard deviations of vertical CG lowering, lifting and total displacement are
illustrated in fig. 6. For all the skiers, the mean value of total displacement is 50±30 cm and 1,3±0,5
ms-1 for the corresponding velocity. Simoncelli has the same values of total displacement as Mayer
and Bode-Miller, whereas the values of the CG velocity are significant higher. .
m o to v e r tic a le d e l C G
V -in n a lz .
V -a b b a s s a .
2 ,0
2
1 ,5
1 ,5
1 ,0
1
0 ,5
0 ,5
0 ,0
-0 , 5
0
B la .
B od e .
M a y.
S im o .
-0 , 5
-1 , 0
-1
-1 , 5
-1 , 5
-2 , 0
-2
Y spostamento [m]
Velocità [m/s]
s p o s ta m e n to
Fig. 6 Mean values and standard deviation of CG vertical displacement (wihte bar) and of the
corresponding lowering (blue bar) and lifting velocity (yellow bar).
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Thus, it is relevant to obtain a separate evaluation of the two components of the vertical CG
motion. As shown in fig 7, two parameters can define these two elements. One is the inclination
angle of the legs with respect to vertical axes on to the frontal plane and the other is the virtual
segment linking the ankle joint with
Y
the hip joint (∆L-leg). The inclination
angle was calculated separately, for
Y
the virtual leg segment and for the
tibia anatomical segment.
Fig 8 describe the time history of the
vertical CG movement (black line) and
of the legs-segment variations (left
panel) for two skiers. Mayer shows a
∆
tendency to lower the CG with a great
amount of flexion-extension of the
legs, whereas this is not the case for
Bode-Miller. This means, that for Fig. 7 Sketch simplification of the motion components accounting for
similar vertical CG displacement, the the vertical displacement of CG with respect to the plane
tilting mechanism is more pronounced in Bode Miller. In fig 8 (right panel) the mean values and
standard deviations of the tilting angle for all athletes are shown. Simoncelli tends to assume a more
pronounced inclination for all the considered angles.
M o v im e n to v e r tic a le C G e p ie g a m e n ti- B o d e .
a rt o -d x
a rt o -s x
C G ve rt
Angoli di inclinazione sul piano frontale
1
90
0 ,4
80
0 ,2
- 0 ,2
0
1
2
3
4
t [s ]
- 0 ,4
Movimento verticale C G e piegamenti-Mayer
arto-dx
arto-sx
CGvert
1
spostamento [m]
0,8
60
tibia-sx
50
arto-dx
40
arto-sx
30
0,6
20
0,4
10
0,2
0
-0,2
tibai-dx
70
0
[Gradi]
spostamento [m]
0 ,8
0 ,6
0
1
2
3
-0,4
0
4
t[s]
Bla.
Bode.
May.
Simo.
Fig. 8 Left panel) time history of the CG vertical motion (black line) and of the legs flexion-extension movements for
two skiers. Right panel). Mean values and standard deviation of inclination angles (shank and total leg).
Body joint angles
The variation of the virtual leg segment is due primarily by the knee joint variation. In tab 2 the
peak values of maximal knee flexion and extension and the corresponding angular velocity are
documented. Mean values are 150±16 deg and 60±6 deg for extension and flexion respectively, and
165±35 deg s-1 and -140±30 deg s-1 for the corresponding angular velocities.
Simoncelli is the skier with the extreme joint minimum values, whereas Blardone shows the highest
maximum values. The highest values of angular velocity for both the flexion and extension are
presented in Simoncelli.
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Tab. 2 Peak values of knee flexion and extension(degrees) and of corresponding angular
velocity(degrees/s) for all the skiers.
Skier knee r knee r knee l knee l V_knee-r V_knee-r V_Knee-l V_Knee-l
max min max min
max
min
max
min
170
70
170
55
180
-150
160
-150
Bla.
65
135
60
170
-130
110
-100
Bode. 150
130
70
140
55
150
-100
140
-130
May.
55
153
60
193
-184
220
-170
Simo. 150
Based on this data a partial analysis of correlation between relevant parameters was carried out.
Significant linear correlation were found between CG velocity on the plane and the knee joint
angular maximum as well as the flexion and extension angular velocity of the same joint. Due to the
very small number of subjects of the sample, this statistical results are to be taken very carefull.
Summary and conclusions
The main findings of this work support the possibility to obtain relevant data (radius of turns,
centripetal acceleration, peak values of CG velocity) to be used for determine the actual loading
conditions in competitive situation and for evaluate specific constrains which are to be matched by
the biomechanical system. Nonetheless, it is possible to make some distinctions in the individual
patterns of joint motion, which could be of great relevance for training purposes.
REFERENCES
BARONI, G. FERRIGNO,G., RODANO,R., CANCLINI,A., COTELLI,C.,POZZO,R. (1998) 3D
sport movement analysis by means of free floating TV cameras with variable optics. Proc. of ISBS
1998 (D)
POZZO, R. CANCLINI, A. BARONI, COTELLI, C.(2001) 3D kinematic analysis of slalom in elite
skiers at the Bormio ski final world cup in 2000 , Proc. of ECSS 2001 (D)
RASCHNER, C., MÜLLER, E., SCHWAMEDER, H. (1997). Kinematics and kinetics analysis of
slalom turns as a basis for the development of specific training methods to improve strength and
endurance. Proceedings of ICSS 1996 (A)
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3-d kinematics and kinetic analysis of g-slalom in elite

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