3-d kinematics of the start in the downhill at the bormio

Pubblicato su SCIENCE AND SKIING II – Ed. Eric Müller et al., dr. V. Kovac - 2000
3-D KINEMATICS OF THE START IN THE DOWNHILL AT THE BORMIO
WORLD CUP IN 1995
R. POZZO12, A. CANCLINI1, C.COTELLI1, L.MARTINELLI1 , A. RÖCKMANN2
1) Lab. Alta Prestazione - Bormio (Fed. Italiana Sport Invernali - C.O.N.I.) 2)IFB-Köln
INTRODUCTION
In downhill the results obtained by elite athletes are very close to each other, so that a few
hundreds of second can make the difference towards winning a race. Therefore, every little
improvement of the total time can make the final difference. In past studies (Rauch 1975,
Mueller 1991, Cotelli 1994) the effects of different type of the leg movement before starting
and the force exerted on the ground were analysed in an experimental situation. There is no
relevant research on normal competition at high level.
In this study the starting phase was analysed with the following purpose: to evaluate the
individual characteristics in the kinematics of the movement sequence, to verify the
relationship between these parameters and the time performance, and to classify individual
and group specific technique.
METHODS
For the purpose of 3-D kinematics, two stationary camcorders (50Hz) were located 30 m from
the starting line on both sides of the track at 85° to each other (fig.1). The space volume of the
starting gate and the 8m in front of this was calibrated with a rigid frame (1x2x10m) in order
to apply DLT algorythms (Aziz-Karara 1971 ). The slope of the ground was 44%.
Another camcorder was placed perpendicular to the travel line in order to film the first 25 m
subsequent to the start and to obtain time and velocity of partial distance every 5m (Chow
1993). To obtain coordinates of motion the video sequences were digitised via video
converter (Screen machine Mod. 5011) connected to a 486 PC. 17 body landmarks were
defined (joint’s centre, foot edges and head centre), 2 points were used for the poles and 2
points for each ski. Centre of gravity of the body (CoG) was calculated with the algorythm of
Gubitz (1978). Row data were smoothed with 3th order cubic spline functions.
Numerical differentiation routine allowed the calculation of the first derivative of linear and
angular parameters. Maximal error was 30 mm for linear distance, 0,70 ms-1 for linear
velocity. Standard statistics procedure were applied to obtain mean values and standard
deviation. Furthermore, functional relationships between parameters were investigated by
regression analysis. 13 athletes of the 20 best world ranked in 1995 were taken into account
for the study. Duration of movement phases, distances between CoG and body markers and
starting gate, velocity of CoG and body segments, 3-D body angles, 2-D angles (poles and
trunk in sagittal plane, legs in the frontal plane) and angular velocity were defined. Three
critical positions were identified (fig.2): the maximal backwards location of the feet (MIN-F),
the moment of touching the gate (START) and the take off of the poles (T-OFF).
Subjects
The present analysis was performed on the following 13 athletes participating to the race. In
the brackets is reported the starting number.
(7) Alphand, Luc
(18) Runggaldier, Peter
(8) Ortlieb, Patrick
(22) Krauss, Stefan
(9) Mader, Guenther
(23) Assinger, Roland
(11) Vitalini, Pietro
(29) Mahrer, Daniel
(12) Kjus, Lasse
(31) Knaus, Hans
(14) Skaardal, Atle
(2) Trinkl, Hannes
(16) Giradelli, Marc
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Starting gate
Z
T1
2D-Cam
panning
T2
MIN-F
T3
30
m
T4
3D-Cam
10
m
START
Markers (5m)
T5
X
ng
ati
Sk
T-OFF
50 Hz Cameras
3D-Cam
Fig. 1 Experimental setup
Fig. 2 Definition of critical positions
Y' [mm]
RESULTS
Trajectory
Fig 3 shows the average trajectories of CoG, the ankles, the hips and the shoulders for all the
athletes. The highest position of the CoG is reached before the contact with the gate and in
this phase this curve is different from that of the hip. The ankles show a quite linear trajectory
in the positive part of the X axis.
3000
Shoulders reach their highest position at
Average Curves
the contact with the gate, followed by an
2000
inverse curvature with respect to the hips.
Y
Shoulders
Hips
The X and Y distances of the CoG with
respect to the origin of the coordinates
system were considered according to the
Co
0
0
critical positions mentioned above. At
G
Ankles
MIN-F and at START the X coordinate
-1000
mean values are –0,07m±0,07m and
X
0,26m±0,09m respectively. Mahrer shows
-2000
the minimun value with 0,13m while
-1000
0
1000
2000
3000
4000 X' [mm]
Assinger the maximum one with 0,41m.
The maximal Y coordinate mean values is
Fig. 3 Average trajectories of body landmarks
1000
3000
CoG Trajectories
2000
Assinger
Y '[mm]
1000
Y=1,14m
0
Alphand
Y=0,81 m
-1000
-2000
-1000
0
1000
2000
3000
4000
X' [mm]
0,98m±0,08m Fig. 4 shows the two
extreme trajectories of CoG, where the
critical values were found in Assinger
(1,14m) and in Alphand (0,81m). This
parameter is also dependent by the body
height The variation of the Y CoG
coordinate corresponds to the elevation
and represent the work done in the
upwards direction. The mean values was
0,28m±0,08m; Assinger showed the third
value (0,35m) and Alfand the lowest one
(0,12m).
Fig. 4 Extreme trajectories of CoG
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V [m/s]
Velocity
Typical time history of CM travel velocity (Vxcg) and resultant velocity (Vrcg) is shown in
fig. 5. Time to reach Vxcg-max from start (∆Τ1) and from poles take-off (∆Τ2) is also
defined. In the first part of the curve there are some discontinuities due to the movements with
high acceleration content of the feet.
The horizontal velocity of CM
6.00
∆
(Vxcg) revealed following mean
5.00
values 1,54±0,25 ms-1 in MIN-F,
vxCG
2,27±0,37 ms-1 in START and 5,52
∆2
4.00
vrCG
±0,16 ms-1 as peak value after T3.00
OFF.
For the vertical movement three
2.00
typical values of CM velocity
(Vycg) were found according to the
1.00
sequence: bending-upwards jump0.00
falling: -0,62±0,20 ms-1, 1,00±0,31
0
500
1000
1500
2000
ms-1 and –0,88±0,26 ms-1. In
contrast to the horizontal velocity
t [ms]
there is more variability for the
vertical velocity during the upwards
Fig. 5. Time history of CoG velocity at the start
phase. Vitalini reaches a maximum
of 1,69 ms-1 while Alfand the
-1
minimum of 0,41 ms
Time structure
Time to reach Vxcg peak value lasted 0,65±0,04s after START (∆Τ1) and 0,34±0,15s after
poles T-OFF (∆Τ2). The difference between these two variables gives the duration of poles
push-off phase (∆Τ3) which was 0,31s±0,05s. In this case the maximum was found in
Assinger (0,42 s) and the minimum in Mader (0,20 s).Another interesting time variable is
represented by the duration elapsed from START to the maximal velocity of the feet, which
must “run ahead” of CoG to support the falling into the ground. The mean value was
0,31s±0,10s which corresponds to the value of the pole push-off phase and is shorter then the
time needed to reach peak Vxcg value after START.
Body Position
The horizontal distance (projection) of the shoulders and feet were considered at the critical
positions and are reported in Tab. 1. The maximum difference between right and left ankle
was 0,24m (Runggaldier ) while the greatest leaning backwards was -0,96m (Ortlieb)
Tab.1: Mean values standard deviation of X coordinate of ankle and shoulders at
critical positions. Negative values indicate the rear position to the gate.
XminAnk-ri XminAnk-le XShou-ri(Start) Xshou-le(Start)
M
[m]
-0,73
[m]
-0,77
[m]
0,65
[m]
0,64
SD
0,13
0,14
0,11
0, 10
Angles and angular velocity
The three dimensional angle of knee, hip and elbow joints and the two dimensional angle of
trunk and poles with respect to the horizontal line in the sagittal plane will be discussed.
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Knee angle shows a minimum during the leg flexion just before the backwards leaning of the
feet and the mean value is 132°±7°, with a maximum of 143° (Mader) and a minimum of
113° (Trinkel).
Hip angle shows a typical three phase structure :87°±9° before START, 157°±12° after
START and 62°±10° during the legs recovering.
For elbow joint it was found a minimum of 66°±3°before START while at START the value
was 80°±5°. Of course, the most significant variation occurred in the following push-off
phase .
The inclination angle of the trunk was progressively decreasing from 32°±5° at MIN-F to
19°±8° at T-OFF and finally to 10°±5° as minimum. The poles showed following values:
62°±5° at MIN-F, 58°±6° at START and 41°±4° at T-OFF.
On the frontal plane, an angle was defined between the line connecting the ankle joint with
the hip joint and the Z-axis, i.e. describing the abduction-adduction movements of the leg.
One leg behaves as support and the other is mostly used as propulsion. The mean values are
53°±5° for the pushing leg and 87°±4° for the supporting leg.
The angular velocity of knee, hip and elbow joints were investigated. For the knee and hip
joints three values were considered: max1 during the first extension (backwards leaning of the
feet), min, during the following recovering phase under the CoG and, finally, max2 during
the push-off after START. For the elbow joint two values occurred at the flexion (fle) and
extension (ext). Tab 2 gives an overview of the values
Tab. 2: Mean, standar deviation and maxima and minima of angular velocity of joint angular
variations.
Knee
Hip
[°s-1]
ωright ωleft ω support ω push ωrigth ωleft
ωright ωleft ωrigth
ω left
ωrigth ωleft
max1 max1 min min max2 max2 max1 max1 min min
max2 max2
M
236
215 -254 -203 188
224
396
372 -303 -309 240
234
SD
59
37
58
67
93
85
46
52
70
70
77
55
Min
166
160 -154 -114
87
115
257
262 -250 -177 111
127
Max
402
312 -379 -362 397
346
437
437 -475 -424 352
296
Elbow
[°s-1]
ωleft
ωright
ωleft
ωrigth
fle
fle
ext
ext
M
-236
-290
347
370
SD
88
167
65
55
Min
-143
-165
189
234
Max
-441
-486
414
420
Partial velocity in the run up
According to the methods, velocity values were calculated referring to the partial distances(5
m) in the 25 m subsequent the start. Fig. 6 gives an overview of the singular values taken at
the corresponding markers (T2, T3, T4, T5). It is easy to note that those athletes who achieve
the best score at the 30m have not necessarily equivalent best values in the early part of the
30m run up. Differences in the gliding properties of the materials, in the body mass and the
possibility to perform efficient pushing movements seem to be the reason to account for.
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V T2
V T3
V T4
V T5
1 2 .0 0
V [m/s]
1 1 .0 0
1 0 .0 0
Trinkl
Krauss
Knaus
Assinger
Mahrer
Viatalini
Skaardal
Rungald.
Ortlieb
Mader
Kjus
Alphand
8 .0 0
Giradelli
9 .0 0
Fig. 6. Individual velocity profile for the partial distance covered 30 m after the start
Correlation analysis
The first issue to be respond is whether relations exist between the velocity achieved by the
start on the gate and the velocity gained during the 30m run-up after the start.
TheVxcg max shows correlation with the: velocity of 1st partial distance VT2 at 15m beyond
the gate (r=0,70) but not with that of the subsequent partial distances. The correlation
coefficients indeed decrease with the progressive values of the partial velocity.
y = -2.3417x + 7.4367
R2 = 0.4653
Vxmax CG [ms-1 s]
5.70
5.80
y = 0.37x + 5.7521
R2 = 0.2204
5.70
5.60
5.60
5.50
5.50
5.40
5.40
Vxmax CoG [ms-1 ]
5.80
5.30
5.30
5.20
0.70
0.80
vertical coordinate of CoG [m]
0.90
-1.00
-0.80
-0.60
-0.40
-0.20
0.00
Lowering velocity CoG [ms-1 ]
Fig. 7. Relationship between start velocity and vertical position (left) and vertical velocity of
CoG (right)
It is also interesting to know which kind of relation exist between the Vxcg and the other
parameters of the whole movement analysed.
The Vxcg correlates with the vertical movement of CoG. Fig. 7 shows the relationship
between the Vxcg and the vertical coordinate of CoG (r=-0,61) as well the lowering velocity
(r=-0,52), so those athletes who jumped less vertically and moved their CoG slowly down to
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the ground obtained as well the highest values of Vxcg. There is also a significant correlation
with the distance of the feet in the backwards leaning during the preparation phase (r=0,68).
Another relationship exist between Vxcg and some angular parameters (fig.8): with the
leaning angle of the trunk with respect to the ground (r=-0,55) and with the angular velocity
of elbow flexion (r=-0,77).
5.70
5.80
y = 0.0013x + 5.8296
R2 = 0.5395
y = -0.0136x + 5.6597
R2 = 0.2573
5.70
5.60
5.60
5.50
5.50
5.40
5.40
5.30
5.30
5.20
0
5
10
15
20
trunk inclination[°]
25
-500
-400
-300
-200
-100
Vxmax CoG [ms-1 ]
Vxmax CoG [ms-1 ]
5.80
0
Elbow angular velocity [Grad -1]
Fig. 8. Relationship between start velocity and inclination of the trunk (left) and angular velocity of
elbow flexion (right)
Thus, keeping the trunk flat to the ground and slowly flexion of the elbow joints induce an
increase in the maximal Vxcg.
On the other hand, time to reach Vxcg maximum(∆Τ1) contributes to a total performance
time. There is a significant correlation (r=0,64) between ∆Τ1 and the poles push-off time
(∆Τ2). This last parameter is correlated with inclination of the trunk (r=0,68) and of the poles
(r=0,60) at the MIN-F.
Discussion
Although the number of subjects is not optimal to ensure statistical significance, the results
identify parameters and mean values which describe objectively this movement pattern. The
negative correlation of Vxcg with time to push-off may relate to the capacity to create great
force impulse in short time. The other correlations of Vxcog suggest that the CoG should
move slowly downwards (to the ground) and reduces the maximal height; that the trunk
should keep as parallel as possible to the ground and that the elbow joint should be flexed
slowly.
On the other hand, to reach peak Vxcg early the push-off time should be short and to achieve
this, at MIN-F, the body and the poles should have a small inclination angle with respect to
the ground. Elite athletes seem to be able to create great force impulse with the upper limbs
supporting on the poles and to execute this action in a short time, whereas body and poles
inclination play an important role. The question arise if this finding is also true for other
slopes of the ground
Acknowledgement
This study was supported by the Ufficio Studi e Ricerca Metodologica of the Italian Olympic Comitee.
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