17 Bojan Jo{t, Milan ^oh, Janez Pustovrh, Maja Ulaga (1999). Analysis of selected kinematic variables…  KinSI, 5(1–2) : 17–25
ANALYSIS OF SELECTED KINEMATIC
VARIABLES OF THE TAKE-OFF IN SKI JUMPS
IN THE FINALS OF THE WORLD CUP ’99 AT
PLANICA
ANALIZA IZBRANIH KINEMATI^NIH
SPREMENLJIVK ODSKOKA SMU^ARJEV
SKAKALCEV V FINALU SVETOVNEGA
POKALA ’99 V PLANICI 
Bojan Jo{t
Milan ^oh
Janez Pustovrh
Maja Ulaga
ABSTRACT
The objective of the study was to establish, by means
of a 2-D kinematic analysis, the correlation between
the selected kinematic parameters of the take-off of
the jumpers and their performance from the aspect
of the jump length, on a sample of the best ski jum-
pers (first series n = 42; second series n = 30) parti-
cipating in the final competition of the World Cup in
Ski Flights at Planica in 1999 (K 180 m). 
By means of an analysis of correlation and single-fac-
tor analysis of variance, a smaller number of statisti-
cally significant correlations between the defined ki-
nematic variables and the jump length was obtained.
The differences in the vertical velocity of the take-
off on the edge of the take-off platform confirmed a
tendency towards positive correlation between this
variable and the jump length (the group of the best
ski jumpers attained the smallest vertical velocity in
both jumps; in the first jump, the differences bet-
ween the various quality groups of ski jumpers were
statistically significant. The best group of ski jumpers
showed tendencies towards a more pronounced
transfer of the hips and the common centre of gra-
vity in the forward direction (the take-off rotation
factor) relative to the axis of the ankle (the differen-
ces between the various quality groups of ski jum-
pers were statistically significant in the second jump). 
Key words: ski jumps, kinematics, take-off analysis,
World Cup Competition, Planica K 180 m, 1999
IZVLE^EK
Namen te {tudije je bil s pomo~jo 2D kinemati~ne
analize, na vzorcu najbolj{ih smu~arjev skakalcev
(prva serija n = 42; druga serija n = 30), nastopajo-
~ih na finalni tekmi svetovnega pokala v poletih v
Planici 1999 (K 180 m), ugotoviti povezanost med
izbranimi kinemati~nimi parametri odskoka smu~ar-
jev skakalcev in uspe{nostjo z vidika dol`ine skoka. 
S pomo~jo korelacijske analize in eno-faktorske ana-
lize variance je bilo ugotovljeno manj{e {tevilo stati-
sti~no pomembnih povezav definiranih kinemati~-
nih spremenljivk z dol`ino skoka. Razlike v vertikal-
ni hitrosti odskoka v to~ki na robu odsko~i{~a so po-
trdile tendenco pozitivne povezanosti te spremen-
ljivke z dol`ino skoka (skupina najbolj{ih skakalcev je
pri obeh skokih imela najmanj{o hitrost, pri prvem
skoku so bile razlike med razli~nimi kakovostnimi
skupinami skakalcev statisti~no pomembne). Naj-
bolj{a skupina skakalcev je kazala tendence bolj izra-
zitega prenosa bokov in skupnega te`i{~a telesa v
smeri naprej (faktor rotacije odskoka) glede na os
gle`nja (razlike pri drugem skoku so bile med razli~-
nimi kakovostnimi skupinami skakalcev statisti~no
zna~ilne). 
Klju~ne besede: smu~arski skoki, kinematika, anali-
za odskoka, tekmovanje za svetovni pokal, Planica K
180 m, 1999 
University of Ljubljana – Faculty of Sport, Gortanova 22, SI-1000 Ljub-
ljana, Slovenia
Tel: +386 61 140-10-77
Fax: +386 61 448-148
E-mail: bojan.jost@sp.uni-lj.si
Received: 30. 11. 1999 – Accepted: 20. 12. 1999

18 Bojan Jo{t, Milan ^oh, Janez Pustovrh, Maja Ulaga (1999). Analysis of selected kinematic variables…  KinSI, 5(1–2) : 17–25
INTRODUCTION
In the bio-mechanical layout studies of the techni-
que used in ski jumping, the problem lies in the ag-
gravated measurement environment. To properly
diagnose the characteristics of the ski-jumping tech-
nique, complete dynamic, kinetic and kinematic da-
ta is necessary. In the present research, however, the
subject of the study of the take-off technique is limi-
ted only to the kinematic aspect. By means of this as-
pect we could determine and hypothetically con-
firm or reject some theoretical assumptions concer-
ning the technique in ski jumping under real com-
petition conditions.
With the so-called V-technique that gained ground
in the 1991/92 season, the technique used in ski-
jumping changed significantly. These changes are
certainly most obvious under the most difficult iner-
tial conditions and in the competitions that place the
highest demands on the competitors. For this rea-
son, the competition in the finals of the World Cup in
Ski Flights in 1999 was selected to investigate the
characteristics of the technique used by ski jumpers.
Precisely in ski flights there shows the largest variabi-
lity of the ski-jumping technique that was the sub-
ject of many researches during its history. Some of
these researches (Janura, Vaverka and Elfmark,
1995; Arndt, Brugemann, Virmavirta and Komi,
1995; Komi and Virmavirta, 1997) were more focu-
sed on the study of the push-off and ascending pha-
se of early flight in ski jumpers, while others again fo-
cused more on the study of the flight technique (Hi-
roshi, Shunsuke, Tadaharu, Hirotoshi and Kazutoshi,
1995). A dividing line between the take-off and flight
is difficult to draw. However, between the two there
certainly exists the relationship of cause (take-off)
and effect (flight). The present research concentrates
on the study of the take-off in the support phase of
the push-off and the transition into flight, which we
could call the phase of ascent. According to the theo-
retical model of take-off (Vaverka, 1987; Vaverka,
Janura, Elfmark and Salinger, 1997), the ski jumper
must solve five independent motor tasks (factors of a
successfully performed take-off): vertical take-off ve-
locity,  rotation of the ski jumper, aerodynamic as-
pect, activity of the arms and accuracy of the take-
off.
Performance of a ski jumper from the aspect of the
aerodynamic factor depends on the optimisation of
the push-off factors in the support phase of the take-
off. Maximisation of the positive effect of an indivi-
dual factor shows only in the optimisation of the
common determinant of the take-off technique,
which contributes consequentially to the maximisa-
tion of positive aerodynamic effects in the flight pha-
se. This means that the factors (vertical push-off ac-
celeration, rotation, accuracy of the push-off and the
activity of the arms) are causal factors exerting inf-
luence on the aerodynamic factor of the take-off
whose true import does not reveal itself before the
ascent phase. 
The objective of the present research was to analyse
the selected kinematic variables of the ski-jumping
technique defined in the take-off phase, and to de-
termine their correlation with performance of ski
jumpers at the final competition of the World Cup
at Planica in 1999. The take-off phase represents a
constituent part of a ski jump which in the absolute
physical sense determines significantly the length, or
in other words, the successfulness of the jump. Of
course, the later phase of flight also decisively affects
the length of the jump in many respects. Some ex-
perts even attribute dominant importance to the
flight phase. Thus, we could formulate a hypothesis
that motor activity of the ski jumper in the take-off
and ascent phase is extremely important; however,
in general, the differences between the kinematic
motor variables do not differentiate statistically signi-
ficantly the quality groups of ski jumpers from the as-
pect of the jump length.
METHODS
In the research there were analysed the jumps of ski
jumpers (42 in the first series and 30 in the final se-
ries) who participated in the final competition of the
World Cup in Ski Flights at Planica (K 185 m) on 19
th
March 1999. The ski jumpers were divided into 4
quality groups according to the jump length (table
1).
The data on the length of the jumps were taken from
the official results of the competition for the world
cup.
The kinematic parameters of movement were mea-
sured by means of a 2-D video analysis (ARIEL PER-
FORMANCE). The recording was carried out with
two pairs of video cameras PANASONIC AG455,
with a frequency 25 frames per second. The first pair
of cameras recorded the last 10 m of the take-off
Name of the group Jump length (m) First jump (n) Second jump (n)
First (the best) group 200 and more 3 4
Second group 180-199.5 20 8
Third group 160-179.5 11 14
Fourth (the worst) group less than 160 8 4
Table 1: Number of the Ski jumpers divided into 4
quality groups according to the jump length 

19 Bojan Jo{t, Milan ^oh, Janez Pustovrh, Maja Ulaga (1999). Analysis of selected kinematic variables…  KinSI, 5(1–2) : 17–25
platform, and the second pair of cameras, the first
10 m of the flight.
Digitalisation of the frames was carried out manually.
For kinematic analysis, a 7-segment 2-D model (up-
per arm, lower arm, trunk, hips, thigh, shin, skis), de-
fined by 9 points denoting the joints, the extreme li-
mit points of the limbs and the skis was used.
The calibration of the space on the push-off platform
was carried out by means of two cubes with a side 1
m long that were placed at the beginning and end of
the space measured. For the calibration of the space
during the phase of ascent, a specially-made cross
was used. This cross enabled the calibration of the
space at the level of the curve of the ski jumpers’ as-
cent.
In the support phase of the take-off, i.e. at the first
point (position - a) 4 m before the edge of the take-
off platform, at the second point (position - b) on the
edge of the take-off platform, and at the third point
(position - c) 4 m after leaving the edge of the take-off
platform, the following set of kinematic parameters
was defined (Figure 1). All angles given in Figure 1
were measured in the sagittal plane on the right side
of the body.
To establish statistical significance of the differences
between the groups, single-factor analysis of varian-
ce (ONEWAY) was used. The significance of the cor-
relation between the kinematic variables and the
length of the jump was established by Pearson’s coef-
ficient of correlation. The criterion of statistical signi-
ficance was in both statistical procedures accepted
with a 5 % two-sided alpha error.
RESULTS
The results of the single-factor analysis of variance
conducted on the variables of the jump length are
shown in Table 2.
The differences between the defined quality groups
of ski jumpers in the variables of the jump length
were statistically significant. The difference in the
average length of the jumps between the two extre-
me groups was 75.5 m in the first jump and 55 m in
the second jump.
Table 3 (first, second and third part) gives the results
of the single-factor analysis of variance and the cor-
relation between the criterion variable and defined
kinematic parameters defined in the support phase
of the take-off 4 m before the edge, on the edge of
the take-off platform, and in the phase without sup-
port 4 m after leaving the edge of the take-off plat-
form in the first and second jump.
The variable which indicates the angle between the
right foot and the shin (ANKLE) attained generally
the minimal value at the point 4 m before the edge of
the take-off platform in all groups of ski jumpers. The
group of the best ski jumpers had on the average the
smallest value in both ski jumps. In the second ski
jump, the difference between the best group (Mean
= 81.1°) and the worst group (Mean = 85.5°) was
statistically significant (F prob. = 0.00). After that,
the value of the mentioned angle increased in all
three groups of ski jumpers. The largest average va-
lue (Mean = 109.8°) was established in the first jump
and in the second quality group of ski jumpers. The
Figure 1. Graphical representation of the selected kinematic variables in the support phase of the take-off. 
Remark: 
The names of the variables are given in Table 3.

20 Bojan Jo{t, Milan ^oh, Janez Pustovrh, Maja Ulaga (1999). Analysis of selected kinematic variables…  KinSI, 5(1–2) : 17–25
Table 2: Results of the analysis of variance of the length of the jump, WC Planica, 1999, K180m 
First group Second group Third group Fourth group
Mean SD Mean SD Mean SD Mean SD F prob.
DSK 1(m) 208.50 9.12 186.90 3.97 171.31 6.89 133.00 25.71 0.00*
DSK 2(m) 207.12 5.40 188.00 7.26 174.21 4.91 150.75 6.50 0.00*
First group Second group Third group Fourth group
r Mean SD Mean SD Mean SD Mean SD F prob
1. Angle between right foot and right shin in XY-plane - ANKLE (angular degrees)
1a -.29 82.47 2.59 84.72 4.04 86.08 3.30 86.77 4.16 0.30
1b -.02 95.61 4.51 95.50 6.52 97.75 6.25 96.11 4.15 0.79
1c .06 105.46 5.54 109.84 4.20 107.49 4.92 107.60 5.23 0.31
2a -.38* 81.11 4.54 82.37 2.09 86.94 3.63 85.57 2.94 0.00*
2b .08 95.89 1.93 92.45 4.28 94.27 4.41 93.42 4.13 0.56
2c -.26 104.42 4.32 104.47 3.56 108.89 5.79 107.79 4.22 0.17
2. Angle between velocity vector TT (body’s centre of gravity) and X-axis in XY-plane - ALE (angular degrees)
1a -.22 8.18 0.40 7.96 0.51 7.80 0.51 8.20 0.66 0.40
1b -.28 5.19 0.21 5.88 0.49 5.94 0.38 6.06 0.34 0.03*
1c .19 7.35 0.86 7.08 0.96 7.04 0.79 6.69 0.21 0.61
2a .09 8.25 0.28 7.94 0.57 8.12 0.69 8.04 0.67 0.86
2b -.06 5.51 0.20 5.96 0.73 5.96 0.52 5.86 0.44 0.54
2c .11 6.37 0.56 6.84 0.78 6.68 0.43 6.16 0.72 0.25
3. Angle between right shin and X-axis in XY-plane - LEGX (angular degrees)
1a .16 133.94 2.88 132.79 5.00 130.98 4.99 131.01 1.70 0.55
1b -.06 119.12 2.82 120.03 7.64 117.59 6.25 120.36 6.92 0.78
1c .00 108.56 3.52 105.72 4.55 106.72 4.20 106.35 4.29 0.74
2a .05 133.83 3.96 136.11 3.60 132.77 3.79 133.59 5.63 0.33
2b -.01 117.42 4.06 122.81 6.01 120.37 4.94 118.89 4.91 0.35
2c .16 105.80 2.33 108.59 3.06 105.47 3.78 104.86 2.94 0.17
4. Angle between ankle-shoulder and X-axis in XY-plane - LSAH (angular degrees)
1a .06 123.37 0.98 123.77 3.33 121.37 3.72 123.42 3.44 0.31
1b .18 121.53 1.22 121.31 3.83 119.12 4.01 119.72 4.94 0.46
1c .18 120.55 2.54 118.69 3.70 118.55 3.75 117.94 4.74 0.80
1a .14 122.48 2.61 123.89 1.52 122.35 2.98 122.13 2.98 0.41
1b .31 121.14 2.56 122.82 2.67 119.61 2.78 119.16 2.86 0.06
2c .32 120.49 3.46 121.53 2.22 118.04 3.07 117.80 2.58 0.04*
5. Angle between ankle-TT and X-axis in XY-plane - LTTAH (angular degrees)
1a .13 110.81 1.45 109.38 3.65 107.74 3.69 108.93 2.75 0.47
1b .17 111.36 2.11 109.97 4.41 108.44 4.15 108.71 4.67 0.63
1c .20 111.10 3.26 107.98 3.68 108.24 4.16 107.31 4.60 0.56
2a .18 110. 55 2.85 111.86 2.15 108.76 2.94 109.49 4.61 0.15
2b .27 110.92 2.87 112.42 3.07 109.28 3.23 107.97 3.74 0.09
2c .33 110.15 3.16 111.06 2.30 107.61 3.37 106.72 2.40 0.04*
Legend: 
DSK1 - length of the 1st jump; DSK2 - length of the 2nd jump; ‘ Mean - arithmetic mean of the group; SD - standard deviation within the group; F
prob. - significance of the F-test, where the asterisk (*) denotes statistically significant differences between the quality groups of the ski jumpers.
Table 3: Correlation analysis between the length of the jump and the kinematic parameters and results of the
analysis of variance 

21 Bojan Jo{t, Milan ^oh, Janez Pustovrh, Maja Ulaga (1999). Analysis of selected kinematic variables…  KinSI, 5(1–2) : 17–25
First group Second group Third group Fourth group
r Mean SD Mean SD Mean SD Mean SD F prob
6. Angle between ankle-hip axis and X-axis in XY-plane - AOZ (angular degrees)
1a .15 93.45 2.15 89.31 3.67 89.55 3.43 89.93 3.90 0.33
1b .24 101.10 3.40 98.09 4.65 97.87 3.92 96.77 5.22 0.57
1c .24 104.64 4.03 100.29 3.92 100.89 4.38 99.49 5.13 0.35
2a .17 92.52 3.44 94.33 3.25 90.17 3.43 91.73 5.70 0.11
2b .27 100.68 3.31 101.94 3.75 98.34 4.09 96.34 4.37 0.09
2c .30 102.75 2.66 103.89 2.91 100.12 4.00 98.89 2.21 0.04*
7. Angle between right shin and right thigh in XY-plane - KNEE (angular degrees)
1a .06 95.04 4.91 90.03 5.71 92.31 6.14 92.34 5.40 0.43
1b .31* 143.50 4.38 136.72 9.28 141.18 7.62 133.28 10.96 0.18
1c .46* 172.00 3.89 169.11 4.40 168.16 3.09 166.09 6.30 0.22
2a .21 92.32 4.58 92.32 2.41 91.16 5.56 90.10 2.75 0.83
2b .33 146.65 8.79 138.93 6.72 136.52 6.83 135.22 5.53 0.07
2c .28 173.61 3.14 170.58 4.42 169.04 3.93 168.08 1.77 0.15
8. Angle between right thigh and right trunk side in XY-plane - HIP (angular   degrees)
1a .04 50.59 3.11 47.99 7.15 47.82 4.59 49.63 8.94 0.87
1b .19 98.37 7.37 92.75 12.46 95.32 5.76 91.29 12.94 0.72
1c .25 126.11 8.83 119.03 9.45 118.37 4.96 117.60 11.22 0.54
2a .03 51.32 6.16 54.08 8.40 49.68 9.35 50.40 10.46 0.73
2b .11 101.34 5.74 98.69 11.49 96.08 13.80 91.77 10.07 0.68
2c .07 122.25 4.75 122.23 9.55 120.80 11.97 117.00 4.84 0.84
9. Angle between right trunk side and X-axis in XY-plane - TRUNKX (angular degrees)
1a .15 178.40 0.65 174.83 4.87 175.47 5.19 173.72 6.46 0.60
1b .06 164.24 2.21 163.99 7.90 163.45 5.46 162.35 7.83 0.95
1c -.01 154.46 4.09 155.81 7.49 156.50 3.11 154.84 6.81 0.93
2a .16 174.83 4.98 174.36 5.48 174.25 4.93 173.28 5.46 0.97
2b .13 162.72 2.93 163.05 8.25 160.80 9.97 162.35 4.39 0.93
2c .13 157.16 4.36 156.94 6.91 153.71 8.99 155.95 3.58 0.73
10. Angle between right upper arm and Y-axis in XY-plane - ARMX (angular degrees)
1a -.09 95.91 7.91 96.30 8.05 96.77 8.82 98.43 7.88 0.93
1b -.18 93.22 7.54 96.67 8.92 100.65 15.05 100.93 6.23 0.53
1c .05 93.46 5.57 104.78 39.77 99.85 15.10 99.43 5.27 0.90
2a -.05 84.74 6.02 92.31 9.74 93.16 8.72 90.42 7.85 0.39
2b -.32 82.54 6.93 95.95 9.17 98.43 10.37 98.80 6.50 0.04*
2c -.35* 87.99 12.58 94.42 6.36 97.25 8.59 103.84 10.75 0.10
11. Angle between frontal part of skis and X-axis in XY-plane - SKIX (angular degrees)
1a .06 11.43 0.41 11.35 0.57 10.96 0.91 10.93 0.94 0.38
1b -.09 11.37 0.77 12.33 0.81 12.59 0.66 12.13 1.05 0.16
1c -.04 12.71 2.55 13.05 1.94 13.13 1.25 12.58 2.52 0.92
2a -.33 10.51 0.81 11.05 0.47 11.01 0.47 11.35 0.48 0.18
2b .27 12.34 0.66 11.80 0.65 11.80 0.95 10.89 1.11 0.15
2c -.02 12.96 3.29 14.57 1.65 13.58 1.73 13.24 1.60 0.49
12. Velocity TT (body’s centre of gravity) in x-direction by time - Vx(t) (m/s)
1a .08 27.78 0.30 27.92 0.36 27.67 0.48 27.66 0.58 0.37
1b .25 27.61 0.27 27.70 0.45 27.50 0.39 27.41 0.21 0.29
1c .17 26.01 0.23 26.05 0.46 25.98 0.26 25.90 0.34 0.83

22 Bojan Jo{t, Milan ^oh, Janez Pustovrh, Maja Ulaga (1999). Analysis of selected kinematic variables…  KinSI, 5(1–2) : 17–25
minimisation of the value of this angle at all three
points confirms the basic assumption on the optimi-
sation of successfulness of the ski- jumping techni-
que from the aspect of rotation of the ski jumper at
simultaneous optimisation of the aerodynamic as-
pect of the course of the take-off and ascent.
The angle of the vector of the velocity of the com-
mon centre of gravity of the body and the skis to the
x-axis (ALE) changed in general in all groups of ski
jumpers at all three defined space points. The mini-
mal value of this angle was attained on the edge of
the take-off platform. The difference between the
average value of the best group (Mean = 5.19°) and
the worst group (Mean = 6.06°) was statistically sig-
nificant (F prob. = 0.03). The mentioned realisation
confirms the tendency towards the development of
a high vertical take-off velocity on the edge of the
take-off platform as a result of a high level of the ge-
neration of the push-off force impulse.
The angle between the thigh and shin (KNEE) shows
that 4 m before the edge of the take-off platform, the
ski jumpers were still closer to the so-called ap-
proach squat position. Then followed a fast exten-
sion of the legs at the knee joint. In the first jump it
reached an average value of 143.5 angular degrees
on the edge of the take-off platform in the best
group, and 133.2 angular degrees in the worst
group. Similar tendencies were also observed in the
second jump. The mentioned variable showed a sta-
tistically significant correlation with the length of the
jump on the edge of the take-off platform (r = 0.31)
and 4 m after leaving the edge of the take-off plat-
form (r = 0.46).
The angle between the chord connecting the ankle
with the hip axis and X-axis (AOZ) increased from
the point defined 4 m before the edge of the take-
off platform up to the point defined 4 m after leaving
the edge of the take-off platform in all groups. At the
last point, the difference between the average value
of the best group (Mean = 102.7°) and the worst
group (Mean = 98.8°) was statistically significant (F
prob. = 0.04).
A statistically significant difference (F prob. = 0.04)
was established in the second jump in the angle bet-
ween the right upper arm and Y-axis in the XY-plane
(ARMX). The average of the best group on the edge
of the take-off platform (Mean = 82.5°) was signifi-
cantly lower than the average of the qualitatively
worst ski jumpers group (Mean = 98.8°).
First group Second group Third group Fourth group
r Mean SD Mean SD Mean SD Mean SD F prob
2a .20 27.68 0.71 27.74 0.38 27.53 0.62 27.56 0.47 0.85
2b .10 27.55 0.35 27.28 0.36 27.60 0.33 27.36 0.22 0.17
2c .23 25.90 0.21 25.87 0.44 25.97 0.27 25.63 0.39 0.40
13. Velocity TT (body’s centre of gravity) in y-direction by time - Vy(t) (m/s)
1a .22 -4.03 0.14 -3.94 0.30 -3.83 0.26 -4.05 0.40 0.46
1b .23 -2.51 0.11 -2.86 0.24 -2.89 0.18 -2.93 0.19 0.04*
1c -.20 -3.20 0.34 -3.17 0.39 -3.12 0.36 -2.97 0.13 0.58
2a -.16 -4.08 0.27 -3.92 0.25 -3.94 0.33 -3.95 0.35 0.84
2b .02 -2.70 0.10 -2.85 0.35 -2.90 0.23 -2.81 0.21 0.56
2c -.10 -2.81 0.23 -3.05 0.32 -2.97 0.19 -2.76 0.26 0.20
14. Velocity TT (body’s centre of gravity) in xy-plane by time - Vxy(t) (m/s)
1a .06 28.07 0.28 28.20 0.38 27.94 0.48 27.96 0.61 0.41
1b .24 27.73 0.28 27.85 0.46 27.65 0.40 27.57 0.23 0.33
1c .19 26.21 0.25 26.24 0.46 26.17 0.27 26.07 0.35 0.76
2a .22 27.98 0.73 28.02 0.37 27.81 0.60 27.84 0.44 0.84
2b .09 27.68 0.35 27.43 0.36 27.76 0.33 27.50 0.23 0.16
2c .24 26.05 0.21 26.05 0.43 26.14 0.27 25.78 0.40 0.34
Legend: 
1 - first jump
2 - second jump
- position 4 m before the edge of the take off table, 
- position on the edge of the take-off table, 
- position 4 m after leaving the edge of the take-off table 
* - means statistically significant differences between the quality groups of ski jumpers or statistically significant correlation, p < 0.05

23 Bojan Jo{t, Milan ^oh, Janez Pustovrh, Maja Ulaga (1999). Analysis of selected kinematic variables…  KinSI, 5(1–2) : 17–25
DISCUSSION
Any motor activity of a ski jumper reflects signifi-
cantly in the velocity of movement of the common
centre of gravity, which shows in the direction of the
trajectory of the flight curve of the common centre of
gravity of the jumper-skis system and also in its hori-
zontal and vertical component. The velocity in the
direction of the trajectory of the curve of the move-
ment of the common centre of gravity (Vxy) did not
show statistically significant differences between the
individual qualitatively different groups of ski jum-
pers. In both jumps, a slight tendency towards the
reduction of this velocity was noticed in the course of
the push-off and ascent, considering the total deve-
lopment of the take-off and ascent. A more noti-
ceable and in the first jump even statistically signifi-
cant difference (F prob. = 0.04) was established in
the vertical velocity of the movement of the com-
mon centre of gravity (Vy) at the point on the edge
of the take-off platform. In the best ski jumpers, the
average value of the vertical velocity was the lowest
in both jumps. The horizontal velocity of the lifting of
the centre of gravity of the jumper-skis system did
not show statistically significant differences between
the groups of ski jumpers classified with respect to
the jump length. The horizontal velocity (Vx) decrea-
sed also in both jumps, at the defined distance of 8
m, during the course of the take-off and ascent.
The results showing the velocity of the movement of
the common centre of gravity thus in some way con-
firm the hypothesis that during the time of the ski-
jumper’s take-off and in the first ascending phase of
his flight there occur no statistically significant diffe-
rences associated with the jump length. The diffe-
rence shows only in the vertical velocity of the move-
ment of the common centre of gravity reached im-
mediately before the edge of the take-off platform.
This hypothetically means that during the take-off,
the jumper must develop an adequate level of force
impulse which will enable him to develop suitable
(optimal) vertical velocity of the take-off. However,
due to the fact that the ski jumpers have just begun
the flight phase, the parameters of the movement of
the common centre of gravity show consequentially
in the continuation of the flight as a reflection of the
geometry of the position of the jumper-skis system
in the air. In accordance with the theory of the tech-
nique of the movement of a ski jumper in the flight
phase, the jumper must, at each point of the flight,
assume such a position which will maximise the ho-
rizontal velocity at simultaneous minimisation of the
vertical velocity of the movement of the common
centre of gravity.
The jumper-skis system represents several appa-
rently mutually separated body segments and the
skies, which, however, in a real situation act in a clo-
se interdependence and interrelation. At each point
of the push-off and ascent, the ski jumper should
place his body segments and the skis so as to maximi-
se the positive tendencies of the aerodynamic effects
during the whole time of the take-off and flight, and
at the same time minimise the angle of elevation of
the movement of the common centre of gravity. It is
exactly at this angle (ALE) that in the first jump, a sta-
tistically significant difference was established bet-
ween the groups of the best and worst ski jumpers (F
prob. = 0.03). The angle of elevation while ascen-
ding depends above all on the magnitude of the time
and space of the production of the push-off force.
The studies by Virmavirta and Komi (1993a, 1993b
and 1994) showed a tendency towards a high level
of the push-off force developed in short time at the
point as close as possible to the edge of the take-off
platform. As a consequence, this contributes to the
raising of the angle of ascent of the common centre
of gravity of the jumper-ski system towards the edge
of the take-off platform. The raising of the trajectory
of the flight curve of the common centre of gravity
of the jumper-skis system is possible only if a favou-
rable shin position is assumed in the support phase
of the push-off of the ski jumpers. This angle (AN-
KLE) was statistically significant and the most impor-
tant factor for distinguishing between the best and
the worst group of ski jumpers (F prob. = 0.00), es-
pecially in the second jump.
An important element of the ski-jumper’s push-off
technique represent the angles that indicate the abi-
lity of transferring the common centre of gravity, abo-
ve all the hips, in the forward direction (LSAH, LT-
TAH, AOZ). This tendency, as a statistically signifi-
cant factor for differentiating between the group of
the best and the group of the worst ski jumpers, sho-
wed at the point 4 m after leaving the edge of the
take-off platform. The transfer of the common cen-
tre of gravity and the hips of the body in the forward
direction is of course possible only by fast extension
of the legs at the knee joint (HIP), which fact was al-
so confirmed within the scope of this study: in the
first jump, the mentioned angle was statistically sig-
nificantly correlated with the length of the jump (r =
.46; p <.05).
The transition of the ski jumper from the approach
position into an optimal position for flight is a com-
plex and difficult motor task, which, from the aspect
of the terminology of motor behaviour, requires a
high level of strength, co-ordination, accuracy, ba-
lance, orientation in space, visualisation, boldness,
courage etc. Thus, in the flight phase, the differen-
ces between the best and worst ski jumpers show as
a consequence (Jo{t, Kugovnik, Strojnik and Colja,
1997) in the kinematics of flight, which fact was es-

24 Bojan Jo{t, Milan ^oh, Janez Pustovrh, Maja Ulaga (1999). Analysis of selected kinematic variables…  KinSI, 5(1–2) : 17–25
tablished on the dynamic level (Mahnke and Hoch-
muth, 1990; Tavernier and Cosserat, 1993; Wata-
nabe K. and Watanabe I., 1993; Hiroshi, Shunsuke,
Tadaharu, Hirotoshi and Kazutoshi, 1995) in the ex-
perimental study in the wind tunnel. 
On the basis of the results obtained by research, the
following conclusions can be drawn:
– The variability of the defined quality groups of ski
jumpers from the aspect of the jump length was
large and statistically significant (F prob. = 0.00);
– The velocity of movement of the common centre
of gravity of the jumper-ski system in the horizon-
tal direction and in the direction of the trajectory
of the curve of the movement of the common
centre of gravity during the course of the take off
and in the first part of the flight (ascent) decreased
constantly;
– The velocity of movement of the common centre
of gravity of the jumper-skis system in the vertical
direction reduced towards the point at the edge
of the take-off platform, while at a distance 4 m
after leaving the platform, it began to increase
again. This tendency reflected in the angle formed
between the vector of the trajectory of the move-
ment of the common centre of gravity of the jum-
per-skis system and the horizontal (in the first
jump the difference between the various quality
groups of ski jumpers was statistically significant, F
prob. = 0.03);
– The differences in the vertical velocity of the take-
off at the point located on the edge of the take-off
platform confirmed the tendency of a positive sig-
nificance of this variable (the group of the best ski
jumpers had the smallest velocity in both jumps;
in the first jump, the differences between the va-
rious quality groups of ski jumpers were statisti-
cally significant, F prob. = 0.04);
– At the point 4 m before the edge of the take-off
platform, the best group of ski jumpers had a smal-
ler average angle between the shin and the foot
(in the second jump, the difference between the
groups of ski jumpers was statistically significant, F
prob. = 0.00); on the edge of the take-off plat-
form, the differences were smaller and began to
increase again up to the point 4 m after leaving the
edge of the take-off platform. The mentioned ten-
dencies are a reflection of the dynamics of the
specific take-off technique used by the ski jum-
pers: this dynamics was larger in the best group of
ski jumpers;
– The best group of ski jumpers showed tendencies
towards a more pronounced transfer of the hips
and the common body’s centre of gravity in the
forward direction (the factor of the take-off rota-
tion) with respect to the ankle axis (in the second
jump, the differences between the various quality
groups of ski jumpers were statistically significant
(F prob. = 0.04);
– The best ski jumpers were more extended at the
knee joint on the edge and four metres after lea-
ving the take-off platform. The correlation bet-
ween the HIP variable and the jump length was
statistically significant (r = 46; P .05) in the first
jump. Therefore, we could make an inverse conc-
lusion about a larger push-off dynamics in the
take-off of the best ski jumpers;
– The active work of the arms was less pronounced
in the best ski jumpers than in the groups of poo-
rer ski jumpers (in the second jump, the differen-
ces between individual quality groups of ski jum-
pers at the point on the edge of the take-off plat-
form were statistically significant (F prob. = 0.04);
– Every change in an individual variable has a mul-
ti-factor effect on all other variables. These effects
are hypothetically independent when inter-va-
riable observation (various subjects and a compa-
rison between them) is concerned, and they are
hypothetically interdependent and inter-influen-
tial when intra-variable observation (the same
subjects) is concerned. This means that despite
the acting of the general tendencies there occur
completely individual tendencies and the effects
associated with them.
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