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The Hecht vault performed at the 1995 World
Gymnastics Championships: Deterministic
model and judges' scores
Yoshiaki Takei a , Erik P. Blucker a , Hiroshi Nohara b & Noriyoshi Yamashita c
a Department of Kinesiology and Physical Education , Northern Illinois
University , DeKalb, IL, 60115-2854, USA
b Department of Physical Education , Kyoto University of Education , 1
Fukakusa, Fujinomori-cho, Fushimi-ku, Kyoto 612, Japan
c Research Center for Sports Science , Kyoto University , Yoshida Honmachi,
Sakyo-Ku, Kyoto 606, Japan
Published online: 09 Dec 2010.
To cite this article: Yoshiaki Takei , Erik P. Blucker , Hiroshi Nohara & Noriyoshi Yamashita (2000) The Hecht
vault performed at the 1995 World Gymnastics Championships: Deterministic model and judges' scores, Journal
of Sports Sciences, 18:11, 849-863, DOI: 10.1080/026404100750017788
To link to this article: http://dx.doi.org/10.1080/026404100750017788
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, 2000, , 849±863
18
Journal of Sports Sciences
The Hecht vault performed at the 1995 World
Gymnastics Championships: Deterministic model
and judges’ scores
YOSHIAKI TAKEI,1* ERIK P. BLUCKER,1 HIROSHI NOHARA2 and
NORIYOSHI YAMASHITA3
1Department of Kinesiology and Physical Education, Northern Illinois University, DeKalb, IL 60115-2854, USA,
2Department of Physical Education, Kyoto University of Education, 1 Fukakusa, Fujinomori-cho, Fushimi-ku,
Kyoto 612, Japan and 3Research Center for Sports Science, Kyoto University, Yoshida Honmachi, Sakyo-Ku,
Kyoto 606, Japan
Accepted 18 March 2000
The aim of this study was to determine the mechanical variables that govern success of the Hecht vault. The
participants were 122 male gymnasts from 30 countries performing the vault at the 1995 World Gymnastics
Championships. The vaults were ®lmed using a Photosonics 16-mm motion picture camera operating at 100 Hz.
Approximately 80 frames were digitized for each vault analysed. The method of Hay and Reid was used to
develop a theoretical model to identify the mechanical and physical variables that determine linear and angular
motions of the vault. Correlational analysis was used to establish the strength of the relationship between the
causal mechanical variables identi®ed in the model and the judges’ scores. Signi®cant correlations (P < 0.005)
indicated that the following were important determinants of success: large horizontal and vertical velocities at
take-oþfrom the board and the horse; large vertical and angular distances of pre-¯ ight; large vertical impulses
of high force and short duration exerted on the horse and the resulting large changes in vertical velocity on the
horse; and large horizontal and vertical distances and long times of post-¯ ight. Of the 18 signi®cant variables
identi®ed in the present study, the angular distance of pre- and post-¯ ights, the horizontal velocity and angular
momentum at take-oþfrom the horse, and the average moment of inertia and duration of post-¯ ight collectively
accounted for 57% of the variation in the judges’ scores.
Keywords: biomechanics, deterministic model, gymnastics, Hecht vault, judges’ scores.
de Gymnastique, 1993) required the body angle above
the horizontal at hand contact on the horse to be at
Introduction
°
least 30 . Subsequently, this angle was reduced to
Of the events in gymnastics, the fewest skills are
required in vaulting. All the vaults are categorized
into either the continuous rotation or counter-rotation
family of vaults. In the continuous rotation vaults, such
as the handspring vault, the direction of body rotation
about the somersaulting axis in the second ¯ ight phase
(post-¯ ight) is the same as that in the ®rst ¯ ight phase
(pre-¯ ight). In counter-rotation vaults, the direction
of body rotation in the post-¯ ight is in the opposite dir-
ection from that in the pre-¯ ight, as in the Hecht vault.
In the performanceof the Hecht vault, the original rules
of compulsory exercises (FŠdŠration Internationale
°
20 to promote more `dynamic performances’ (Fink
and Zschoke, 1994). The gymnast leaves the take-oþ
board with forward somersaulting rotation and con-
tinues to rotate forwards as the body travels forwards
and upwards over the horse during the pre-¯ ight and
early horse contact phases to attain the required body
°
angle of 20 above the horizontal (FŠdŠration Inter-
nationale de Gymnastique,1997). During the latter part
of the horse contact phase, the gymnast reverses the
direction of body rotation by blocking and pushing oþ
the horse with the upper limb and shouldermuscles and
¯ exing the trunk and hips slightly while on the horse
(Kaneko, 1974). However, many gymnasts ®nd it
* Author to whom all correspondence should be addressed.
Ó
Journal of Sports Sciences ISSN 0264-0414print/ISSN 1466-447X online 2000 Taylor & Francis Ltd
http://www.tandf.co.uk/journals

850
et al.
Takei
Fig. 1. The ®ve phases of the Hecht vault: approach (run-up approach followed by a hurdle step onto the take-oþboard), on-
board (foot contact on board to departure from the board), pre-¯ ight (the ®rst ¯ ight phase), on-horse (hand contact on horse to
departure from the horse) and post-¯ ight (the second ¯ ight). The vaults shown are the highest-scoring (upper, 9.65 points) and
=
the lowest-scoring (lower, 7.975 points) Hecht vaults from the 1995 World Gymnastics Championships. TD touchdown;
=
TO take-oþ.
diýcult to execute this `on-horse’ reversal of direction
with good form and technique, as shown by the lower
sequence in Fig. 1. After departing from the horse, the
gymnast must ful®l the post-¯ ight height and distance
requirements while continuing to travel forwards and
upwards as the body rotates backwards (a distinct rise of
the buttocks to at least 1 m above the horse and land at
least 2.5 m beyond the far end of the horse in a standing
position) (FŠdŠration Internationale de Gymnastique,
1997). Exceeding the post-¯ ight height and distance
requirements and maintaining the fully extended body
position throughout the post-¯ ight, as seen in the upper
sequence of Fig. 1, warrant possible bonus points, but
these features are diýcult to achieve when having to
elevation and forward body rotation in pre-¯ ight,
resulting in an `accidental body turnover’ while on the
horse (Kaneko, 1974). Therefore, it is a great challenge
for the gymnast to control this reversal action
by counteracting the undesirable `excessive’ forward
rotation eþect of today’s springy take-oþ board. Risk
of injury is great when the gymnast fails to reverse the
direction of body rotation, which results in disastrous
consequences such as landing upside down (Kaneko,
1974). Despite the seriousness of injuries, analysis of
techniques of blocking and pushing oþthe horse when
performing the counter-rotation vaults has been limited
(Takei
., 1998; King
et al
., 1999). The counter-
et al
rotation vaults are important in developing a foundation
not only for the vaults of the same family, but also for
the continuousrotation vaults (Kaneko, 1974).
°
meet the body angle requirement of 20 at touchdown
on the horse. In fact, `bonus points can only be awarded
for extremely high execution of the vault with a landing
far beyond the normal distance of 2.5 m’ (FŠdŠration
Internationale de Gymnastique, 1997).
The take-oþ board with a high coeýcient of restitu-
tion, adopted since 1956, often causes `excessive’ body
Yeadon
(1998) investigated the relationship of
et al.
pre-¯ ight characteristics to post-¯ ight performance
in 27 elite gymnasts performing the Hecht vault at the
1993 Canadian National Championships. They found
that the maximum height of post-¯ ight was positively

851
Mechanicalvariables in the Hecht vault
Fig. 2. Model showing ®ve factors that determine the linear and angular motions and aesthetic performance of the Hecht vault,
*
and zero-order correlations with the judges’ score ( denotes signi®cance). The number of lines linking variables indicates the
=
magnitude of the relationship (e.g. 5 lines indicate r 0.50).The dotted lines indicate a possible (untested) relationship involving
a non-quanti®able variable.
correlated with the vertical velocity and the body
angle at horse contact. The 1995 World Gymnastics
Championships provided an opportunity to study the
techniques of elite performances of this vault, 3 years
after its introduction into the compulsory competitions.
The World Championships include far more partici-
pating countries and gymnasts than the Olympic
Games, in which the participants are limited only to
those from the qualifying nations. Consequently, the
championships provided a good opportunity to study
the Hecht vault with a sample of gymnasts exhibiting a
Methods
Deterministic model
A deterministic model was developed to systematically
guide the analysis between the mechanical variables
and the judges’ score. The model consists of ®ve factors
(two pre-¯ ight factors,two post-¯ ight factors and form),
which are identi®ed in the second level and linked,from
below, to the `points awarded by judges’ shown in the
®rst level (Fig. 2). In developing a model to analyse the
pre-¯ ight, two factors must be considered:(1) the linear
motion re¯ ected in the path of the centre of mass and
(2) the angular motion re¯ ected in the angular distance
through which the gymnast rotates about the somer-
saulting axis. As shown in Fig. 3, the trajectory of the
centre of mass in pre-¯ ight is governed by the resultant
velocity at take-oþ from the board, the relative height
of take-oþ, the air resistance encountered in ¯ ight and
the acceleration due to gravity. The resultant velocity
at take-oþ from the board is the vector sum of the
horizontal and vertical velocities at take-oþ (4th level).
The somersaulting angular distance of the gymnast in
pre-¯ ight depends on the time of pre-¯ ight, the average
moment of inertia of the gymnast in pre-¯ ight and the
angular momentum of the gymnast at take-oþfrom the
board, as described by Hay and Reid (1988). The time
of pre-¯ ight is determined by the height of the centre of
mass and the vertical velocity at take-oþfrom the board,
the height of the centre of mass at touchdown on the
horse, the air resistance and the acceleration due to
gravity (4th level). With these variables identi®ed, the
®nal form of the model for the pre-¯ ight is shown in
Fig. 3.
relatively wide range of skill. Takei
(1998) investi-
et al.
gated the 25 highest- and 25 lowest-scoring vaults of
the 122 Hecht vaults ®lmed during the championships
to identify the kinematic and kinetic diþerences in the
techniques used by the two groups. The results of -tests
t
used to compare group means indicated that the vaults
receiving high scores demonstrated greater horizontal
velocity at take-oþ from the board, larger vertical
velocity at take-oþfrom the horse,and a longer duration
of post-¯ ight than those receiving low scores. Although
these diþerences are important for improving per-
formance, they do not indicate the strength of the
relationship between these variables and successful
performance of the Hecht vault as rated by the judges.
However, Takei
(1998) noted a trend towards a
et al.
signi®cant positive relationship between the judges’
score and the aforementioned mechanical variables,
in which larger mean values were found for the high-
scoring vaults. The present study was designed to
determine the strength of the relationship between the
causal mechanical variables of the vault and the judges’
scores. We wished to identify the mechanical variables
(through development of a deterministic model and
subsequent correlational analysis) that are crucial for
achieving successin the performanceof the Hecht vault.
As shown in Fig. 4, the mechanical variables that
govern the trajectory of the centre of mass and the

852
et al.
Takei
Fig. 3. Model showing mechanical variables that determine the linear and angular motions of the pre-¯ ight phase of the Hecht
vault, and zero-order correlations with the judges’ score. Numerical and graphic displays of correlation coeýcients are as
=
described in the legend to Fig. 2. CM centre of mass. Note: The correlation coeýcient shown at the top of each box enclosing
the quanti®able variable in the 3rd and 4th levels indicates its relationship with the judges’ score, rather than the relationship with
the variable linked immediately above.
somersaulting motion in the post-¯ ight phase are
similar to those identi®ed in the third and fourth levels
of the model for the pre-¯ ight (Fig. 3). The variables
that determine the performance of the blocking and
pushing oþ the horse and subsequent post-¯ ight are
identi®ed in the third to seventh levels of the model in
Fig. 4. More speci®cally, the vertical velocity at take-oþ
from the horse shown in the fourth level is the sum
of the vertical velocity at touchdown on the horse and
the change in the vertical velocity that occurs while on
the horse (5th level). The change in the vertical velocity
is determined by the gymnast’s mass and the vertical
impulse that the gymnast exerts (and that which the
horse, in reaction, exerts on the gymnast) (6th level).
The vertical impulse exerted on the gymnast is, in turn,
determined by the average vertical force exerted and
the time during which the force acts ± that is, the time
of support on the horse (7th level) (Hay and Reid,
1988). The horizontal motion variables were similarly
identi®ed (see Fig. 4). Form, the aesthetic characteristic
of performance referred to as `segmentation’ by George
(1980), includes the position of body parts and the
manner in which they move from one position to
another during the vault. However, Hay and Reid
(1988) stated that, while form is important in deter-
mining the overall success of the vault, the eþort
required to identify all of its elements, de®ne them
mechanically and analyse them in a meaningful manner
is much greater than any bene®t that might be gained
from doing so. Concurring with Hay and Reid, we
believed the mechanical analysis of aesthetics or form
to be beyond the scope of the present study, and thus
the model was not developed in this direction.
Data collection
=
Male gymnasts (
122) from 30 countries were ®lmed
n
using a Photosonics 16-mm motion picture camera
operating at 100 Hz as they performed the Hecht vault
at the 1995 World Gymnastics Championships. The
camera was positioned 67.86 m from the long axis
°
of the horse with its optical axis 90 to the gymnast’s
horizontal direction of motion (direction of runway)
°
and 85 to his vertical direction of motion to record

854
et al.
Takei
the vault from the designated ®lming area. Angle
board and the horse as well as touchdown on the mat
were identi®ed. From these critical instants, the on-
board, pre-¯ ight, on-horse and post-¯ ight phases were
de®ned (Fig. 1). The horizontal velocity at take-oþfrom
the board was determinedby dividing (a) the horizontal
displacement of the centre of mass from the ®rst frame
showing the gymnast oþ the take-oþ board to the last
frame showing the gymnast in the air before contact
with the horse,approximately 20 frames later, by (b) the
elapsed time between these two instants. The vertical
°
veri®cation of downward camera tilt of 5 below the
horizontal was performed by determining the inverse
sine of the horse height computed from its ®lm image,
divided by the actual height of the oýcial horse used
during the competition (1.35 m). Subsequently, using
the method described by Takei (1991), the vertical
coordinates of all the digitized body points were
corrected for camera tilt before computing the whole-
body centre of mass. The measured dimensions of the
oýcial vault apparatus included in each frame were
used to establish a linear scale and horizontal reference.
Internal timing lights pulsing at a frequency of 100 Hz
were used to mark the sides of the ®lm to provide a basis
for determiningappropriate temporal scales.
velocity at take-oþfrom the board (
) was computed
nVTO
using the vertical displacement of centre of mass (D )
y
from the ®rst frame showing the gymnast oþthe board
to the last frame before contact with the horse, and the
elapsed time (D ) between these two frames:
t
2
=
[D + 4.905(D ) ]/D
y
t
t
nVTO
Data reduction
The vertical velocity at touchdown on the horse (
was computed using the following equation of uni-
formly accelerated motion:
)
nVTD
For each vault analysed, approximately 80 frames of
®lm were digitized. These included every frame from
four frames before take-oþ from the board to four
frames after take-oþ from the horse, then every third
frame until touchdown on the mat and four additional
consecutive frames. An M-16C Vanguard projection
head and HIPAD Plus 9200 digitizer linked on-line to
a microcomputer were used for digitizing. The hori-
zontal and vertical coordinates of 21 points de®ning a
14-segment model of the human body described by
=
nVTD nVTO
- 9.81(D )
t
The velocities at take-oþfrom the horse and touchdown
on the landing mat were computed in a similar fashion.
The height and mass of 79 of the 122 gymnasts had to
be estimated, as this information was not available. The
missingheight data were estimated usinga method simi-
lar to that used by Hay and Nohara (1990), which was
based on the segment lengths obtained from digitized
data. The missing mass data were estimated using the
following regression equation derived from the known
masses and heights of the 67 male gymnasts competing
in the 1992 Olympic Games (Takei, 1998):
Clauser
(1969) were recorded for each frame
et al.
analysed. When using the cubic spline technique for
data smoothing, a minimum of three additional data
points are required for padding at the beginning and
end of the sample to ensure there is no distortion of
the data to be analysed. Therefore, we digitized the
four consecutive frames before take-oþfrom the board
and those after touchdown on the mat. These data were
then used as input to a computer program designed
to display the curves of the digitized body points (Hay
and Nohara, 1990). Any gross outliers identi®ed
were aligned manually to the curves or redigitized,
after which the cubic spline smoothing procedure
(Hutchinson, 1986) was applied to these position data.
Subsequently,the location of the centre of mass in each
digitized frame was computed using the segmental mass
proportion and segmental centre of mass location
2
=
=
=
0.73)
mass height (86.73) - 82.45
(
0.86,
r
r
The angular distance the gymnast rotated during the
¯ ight phase was de®ned as:
ÅÅÅ-
1
=
(
)
t
h
HI
ÅÅ
H
Å
=
=
where
the somersaulting angular momentum,
I
the average moment of inertia of the gymnast about the
=
same axis and
time (Takei, 1992; Takei and Dunn,
t
data of Clauser
procedure described by Hay (1993).
(1969) and the basic segmental
1997). The angular momentum of the gymnast about
the transverse axis through the mass centre during
the pre-¯ ight and post-¯ ight were calculated using the
et al.
The time of contact was de®ned as the time from the
®rst frame when the gymnast contacted the board or
horse to the ®rst frame when he lost contact with the
board or horse. The time of ¯ ight was de®ned as the
time from the ®rst frame when the gymnast lost contact
with the board or horse to the ®rst frame when he con-
tacted the horse or landing mat. The frames depicting
the instants of touchdown on and take-oþ from the
method described by Hay
(1977) and the segment
et al.
moment of inertia data of Whitsett (1963). The angular
momentum of pre-¯ ight was the arithmetic mean of
approximately 20 angular momentums from all the
frames analysed for the pre-¯ ight phase. The angular
momentum of post-¯ ight was similarly obtained by
computing the mean of approximately 45 post-¯ ight

855
Mechanicalvariables in the Hecht vault
=
angular momentums. To facilitate comparisons among
gymnasts, the angular momentums and moments of
inertia of the whole body about the somersaulting
axis were normalized using the method described by
Hinrichs (1987):
vertical velocity at touchdown on the horse. This
nVTD
equation, when rearranged, yields an expression for
ÅÅ
FV
for each gymnast:
ÅÅ
FV
=
[ (
-
)/ ] +
t W
nVTO nVTD
m
-
2
1
=
normalized value (absolute value)[(mass)(height )]
Data analysis
To identify the mechanical variables that are crucial for
success, Pearson product±moment correlations were
computed between (a) each quanti®able variable in the
second level of the model and the judges’ score, and
(b) the judges’ score and the variables in the next lower
(3rd) level that were linked to the signi®cant variable
immediately above. Step (b) was then repeated to
advance the analysis to progressively lower levels of the
model. Correlational analysis was chosen to establish
the strength of the relationship between the known
causal mechanical variables identi®ed in the model and
The error estimates (mean ± ) of normalized angular
s
momentums for the pre-¯ ight and post-¯ ight phases
in the 122 gymnasts were 0.017 ± 0.0055 and 0.013 ±
0.0027, respectively. Body angles were determined by a
horizontal reference line extending backwards through
the gymnast’s lateral malleolus, and a line connecting
the lateral malleolus and the base of the mid-neck
(the midpoint between the manubrium and the seventh
cervical vertebra). They were measured from the hori-
zontal reference line in a clockwise direction (Fig. 5).
The impulses and average forces exerted during
the on-horse phase were determined by the impulse±
momentum relationship (Hay and Reid, 1988; Takei,
1998). For example:
the score awarded by the judges. A value of < 0.005
P
was chosen to indicate signi®cance and to control the
potential increase in Type I error rate (where variables
indicate a signi®cant relationship merely by random
chance) as a result of performing multiple correlations.
ÅÅ
FV W t
=
(
-
)
( -
nVTO nVTD
)
m
To evaluate the practical signi®cance of the variables,
2
ÅÅ
FV
t
=
=
=
where
weight,
average vertical force exerted,
body
=
body mass,
the coeýcient of determination ( ) was computed
W
r
time of horse support,
for each variable that was found to be signi®cantly
correlated with the judges’ score.
m
=
vertical velocity at take-oþ from the horse and
nVTO
h
Fig. 5. The body angle ( B), velocities and angular momentum (H) at touchdown (TD) and take-oþ(TO) from the horse. The
signi®cant variables (*P < 0.005;** P < 0.001)are indicated by asterisks. During the course of blocking and pushing oþthe horse,
ÅÅ
the vertical reaction force (F ) exerted by the horse tends to increase the gymnast’s vertical velocity ( ) while simultaneously
nV
V
decreasing forward angular momentum, enabling a reversal of direction of body rotation while on the horse. On the other hand,
ÅÅ
the horizontal reaction force (F ) tends to decrease horizontal velocity ( ) while simultaneously increasing forward angular
nH
H
momentum and the chance of accidental `body turnover’ while on the horse.

856
et al.
Takei
Table 2) yielded a signi®cant correlation coeýcient of
similar magnitude in each case with the judges’ score.
This meant that they were almost equally important,
as they accounted for similar variances with the judges’
score. The signi®cant correlation for the resultant
velocity at take-oþ meant that the greater the resul-
tant velocity at take-oþ from the board, the higher the
judges’ score. Subsequentanalysis of the horizontal and
vertical velocities at take-oþfrom the board (4th level of
the model in Fig. 3) yielded a signi®cant correlation
coeýcient with the judges’ score in each case (vertical,
Results
In this section, we present the model, signi®cant corre-
lations and our interpretationof the results.The analysis
and interpretation of the results begins with the vari-
ables in the second level of the model and advances to
those in the lower levels, one phase or branch at a time.
Pre-¯ ight mechanical variables and judges’ score
Two variables were identi®ed in the second level of
the model (Fig. 3), of which only the somersaulting
angular distance was quanti®ed because it was
impossible to describe the `trajectory of body centre of
mass’ with a single number for the purpose of analysis.
The signi®cant correlation between somersaulting
angular distance and the judges’ score indicated that
the greater the forward body rotation in pre-¯ ight, the
higher the score awarded by the judges. However, none
of the three variables that determine the somersaulting
angular distance of pre-¯ ight was signi®cantly corre-
lated with the judges’ score (Tables 1 and 2).
The four variables that determine the trajectory of
the body’s centre of mass in pre-¯ ight were identi®ed in
the third and fourth levels of the model (Fig. 3). The
resultant velocity at take-oþ from the board ( 0.31;
Table 3) and the relative height of take-oþ ( 0.37;
=
=
0.25; Table 3). These corre-
0.36; horizontal,
r
r
lations indicated that the greater the horizontal and
vertical velocities at take-oþfrom the board, the higher
the score awarded by the judges. However, the vertical
velocity at take-oþfrom the board was more important
than the horizontal velocity at take-oþ in achieving
success because it accounted for twice the variance with
the judges’ score.
Finally, the signi®cant correlation reported above for
the relative height of take-oþindicated that the greater
the vertical distance travelled by the body centre of mass
in pre-¯ ight, the higher the judges’ score. However,
neither the height of centre of mass at take-oþfrom the
board nor the height of centre of mass at touchdown
on the horse yielded a signi®cant correlation coeýcient
with the judges’ score (Table 2). The diþerences in the
=
=
r
r
Table 1. Descriptive statistics and correlations (r) with the judges’ score for somersaulting angular
motion variables in the Hecht vault
±
Variables
Mean
s
Min
0.28
Max
0.42
r
Normalized angular momentum (s-1)
pre-¯ ight
±
0.34 0.03
0.08
-
-
±
-
-
-
-
-
-
change on horse
post-¯ ight
0.43 0.03
0.51
0.14
0.33
0.03
0.31**
0.40**
±
0.09 0.02
Normalized average moment
of inertia
±
pre-¯ ight
post-¯ ight
0.076 0.003
0.060
0.044
0.084
0.062
0.05
0.36**
±
0.054 0.003
°
Body angle at critical instants ( )
±
±
±
horse touchdown
change on horse
horse take-oþ
178
9
4
8
157
-
20
154
206
4
203
0.32**
0.40**
0.11
-
7
-
-
-
172
°
Angular distance ( )
±
pre-¯ ight
post-¯ ight
54
8
33
85
-
25
0.28*
0.52**
-
±
-
67 13
93
Average angular velocity
(degrees per second)
pre-¯ ight
±
258 21
216
138
318
-
32
0.06
0.38**
-
±
-
post-¯ ight
91 18
* P < 0.005; ** P < 0.001.

857
Mechanicalvariables in the Hecht vault
Table 2. Descriptive statistics and correlations (r) with the judges’ score for temporal and linear
motion variables in the Hecht vault
±
Variables
Mean
s
Min
Max
r
Time (s)
pre-¯ ight
on-horse
post-¯ ight
±
0.21 0.04
0.11
0.12
0.59
0.33
0.22
0.90
0.21
0.44**
0.37**
±
-
-
0.16 0.02
±
0.74 0.05
Horizontal displacement of CM (m)
pre-¯ ight
post-¯ ight
±
1.30 0.22
0.76
2.16
2.09
1.86
4.28
4.37
0.37**
0.44**
0.49**
±
3.44 0.42
±
3.39 0.48
oýcial distance of post-¯ ight
Height of CM at critical instants (m)
board take-oþ
horse touchdown
horse take-oþ
peak of post-¯ ight
mat touchdown
±
1.28 0.04
1.18
1.51
1.88
2.07
0.84
1.37
1.93
2.21
2.70
1.19
0.22
0.22
0.17
0.36**
0.17
±
1.75 0.07
±
2.08 0.06
±
2.33 0.11
±
1.03 0.07
Relative height of take-oþ(m)
board TO to horse TD
horse TO to mat TD
±
0.47 0.07
0.27
1.35
0.65
-
0.82
0.37**
0.01
-
±
-
1.05 0.08
=
=
=
** P < 0.001. CM centre of mass; TO take-oþ; TD touchdown.
Note: The height of CM at peak of post-¯ ight was calculated using the vertical velocity at take-oþfrom the horse.
The heights of CM were measured from the ¯ oor.
Table 3. Descriptive statistics and correlations (r) with the judges’ score for the velocity variables in
the Hecht vault
±
Variables
Mean
s
Min
Max
r
Resultant velocity (m´s-1)
board take-oþ
±
7.07 0.53
5.71
3.59
8.44
6.09
0.31**
0.38**
±
5.15 0.45
horse take-oþ
Horizontal velocity (m´s-1)
board take-oþ(pre-¯ ight)
change on horse
±
6.25 0.58
4.44
2.99
3.23
7.68
0.25*
0.06
0.28*
-
±
-
-
0.90
5.70
-
-
1.60 0.37
±
horse take-oþ(post-¯ ight)
4.65 0.45
Vertical velocity (m´s-1)
board take-oþ
horse touchdown
change on horse
horse take-oþ
±
3.28 0.19
2.73
0.29
0.23
0.93
3.65
2.65
1.78
3.13
0.36**
0.02
0.46**
0.38**
±
1.32 0.36
±
-
0.87 0.30
±
2.20 0.35
* P < 0.005; ** P < 0.001.
gymnasts’ physiques may have been a confounding fac-
tor in the above relationship. Therefore, partial correla-
tions were computed with the eþect of the gymnast’s
standing height removed. The results of the relative
were nearly identical to the zero-order correlation,
although the last variable approached signi®cance.
On-horse and post-¯ ight mechanical variables and judges’
score
=
height of take-oþ ( 0.36, < 0.001), the height of
r
P
=
centre of mass at take-oþ from the board ( -0.21,
r
=
0.02) and the height of centre of mass at touchdown
Two variables were identi®ed in the second level of the
model (Fig. 4). Of these, only the somersaultingangular
P
=
=
0.008) with the judges’ score
on the horse ( 0.24,
r
P

858
et al.
Takei
distance could be quanti®ed, as stated earlier. The
somersaulting angular distance correlated signi®cantly
signi®cant correlation coeýcient with the judges’ score
in both cases (Table 3). These correlations indicated
that the greater the horizontal and vertical velocities at
take-oþfrom the horse, the higher the score awarded by
the judges. Of these two variables, however, the vertical
velocity at take-oþfrom the horse was more important
than the horizontal velocity at take-oþ in achieving
success because it accounted for a greater variance with
the judges’ score. Analysis of the variables that deter-
mine the horizontal and vertical velocities at take-oþ
from the horse, identi®ed in the ®fth level of the model
in Fig. 4, yielded signi®cant correlation coeýcients with
the judges’ score for the horizontal velocity at touch-
=
with the judges’ score ( -0.52; Table 1). This corre-
r
lation indicated that the greater the backward body
rotation in post-¯ ight, the higher the score awarded by
=
the judges. Subsequent analysis of the time of ¯ ight (
r
0.37), the average moment of inertia of the gymnast
=
in post-¯ ight ( 0.36) and the gymnast’s angular
r
=
momentum at take-oþ from the horse ( -0.40)
r
yielded a signi®cant correlation coeýcient with the
judges’ score in all three cases (Tables 1 and 2). These
correlations indicated that the higher the score awarded
by the judges, the longer the duration of post-¯ ight, the
greater the average somersaulting moment of inertia in
post-¯ ight and the greater the backward somersaulting
angular momentum at take-oþ from the horse. They
also indicated that these three variables were equally
important in achieving success because they accounted
for similar variances with the judges’ score.The analysis
of the angular momentum at touchdown on the horse
=
down on the horse ( 0.25) and the change in vertical
r
=
velocity on the horse ( 0.46), but not for the other two
r
variables (Table 3). These correlations indicated that
the higher the score of the Hecht vault, the greater
the horizontal velocity at touchdown on the horse
and the greater the change in the vertical velocity while
on the horse. Of these variables, however, the change in
the vertical velocity on the horse was far more important
than the horizontal velocity at touchdown on the horse
in achieving success because it accounted for more than
three times as much variance with the judges’ score.
As for the variables that determine the change in the
vertical velocity on the horse,the vertical impulse on the
horse, identi®ed in the sixth level of the model in Fig. 4,
=
(
0.08) and the change in angular momentum
r
=
while on the horse ( -0.31) (4th level of the model
r
in Fig. 4), which together determine the angular
momentum at take-oþfrom the horse, yielded a signi®-
cant correlation coeýcient with the judges’ score only
for the latter variable. This correlation indicated that the
greater the change in the angular momentum while on
the horse, the higher the score awarded by the judges.
The ®ve variables that determine the time of post-
¯ ight were identi®ed in the fourth level of the model.
Similarly, the four variables that determine the trajec-
tory of body centre of mass in post-¯ ight were identi®ed
in the third and fourth levels of the model in Fig. 4.
Of these, only the resultant velocity at take-oþ from
=
yielded a signi®cant correlation coeýcient ( 0.43)
r
with the judges’ score (Table 4). This correlation
indicated that the greater the vertical impulse exerted
while on the horse, the higher the score awarded by the
=
judges. Finally, the time of horse support ( -0.44)
r
=
and the average vertical force on the horse ( 0.51)
r
(7th level of the model in Fig. 4), which together deter-
mine the vertical impulse on the horse (Hay and Reid,
1988), yielded a signi®cant correlation coeýcient in
each case with the judges’ score (Tables 2 and 4). These
correlations indicated that the higher the score of the
Hecht vault, the shorter the time of hand supporton the
horse and the greater the normalized average vertical
force exerted while on the horse. The result also indi-
cated that these two variables were equally important in
achieving success of the vault because they accounted
for similar variances with the judges’ score.
In short, the higher judges’ scores were negatively
related to the time of contact on the horse and positively
related to: (1) the horizontal and vertical velocities at
take-oþfrom the board; (2) the vertical displacement of
body centre of mass and the angular distance of forward
body rotation in pre-¯ ight; (3) the vertical impulse
exerted on the horse and the change in vertical velocity
and angular momentum while on the horse; (4) the
horizontal and vertical velocities and the backward
somersaulting angular momentum at take-oþ from the
horse; and (5) the angular distance of backward body
=
the horse ( 0.38) yielded a signi®cant correlation
r
coeýcient with the judges’ score (Table 3). This corre-
lation indicated that the greater the resultant velocity at
take-oþ from the horse, the higher the score awarded
by the judges. Since the diþerences in the gymnasts’
physiques may have been a confounding factor in the
analysis of the relative height of take-oþ ± that is, the
height of the centre of mass at take-oþ from the horse
relative to its height at touchdown on the landing mat ±
partial correlations were computed with the eþect of
the gymnast’s standing height removed. However, the
=
results of the relative height of take-oþ ( -0.01,
r
=
0.97), the height of centre of mass at take-oþ from
P
=
=
0.01) and the height of centre of
the horse ( 0.22,
r
P
=
=
0.03) with
mass at touchdown on the mat ( 0.20,
r
P
the judges’ score were nearly identical to the zero-order
correlation (Table 2).
=
Subsequent analysis of the horizontal ( 0.28)
r
=
and vertical ( 0.38) velocities at take-oþ from the
r
horse (4th level of the model in Fig. 4), which together
determine the resultant velocity at take-oþ, yielded a

859
Mechanicalvariables in the Hecht vault
Table 4. Descriptive statistics and correlations (r) with the judges’ score for forces and impulses
during the on-horse phase of the Hecht vault
±
Variables
Mean
s
Min
Max
r
-
±
±
±
±
±
±
-
-
-
-
-
Horizontal impulse (N´s)
Vertical impulse (N´s)
Average horizontal force (FH) (N)
10 126
198
-
14
51
0.02
0.43**
0.18
0.42**
0.20
0.51**
55 19
640 181
967 152
1.04 0.29
112
296
ÅÅ
-
-
-
1347
493
ÅÅ
Average vertical force (FV) (N)
1361
0.44
2.21
ÅÅ
-
-
-
Normalized FH
2.17
0.82
ÅÅ
Normalized FV
1.57 0.22
** P < 0.001.
rotation,the average momentof inertia and the duration
of post-¯ ight.
The above summary is re¯ ected in the results of
a comparison of the technical characteristics of the
25 highest- and 25 lowest-scoring vaults in the present
sample. The 25 highest-scoring vaults had signi®cantly:
travelled by mass centre, and the height of body mass
centre and the body angle at touchdown on the horse.
In the handspring with full turn (or twist) vault (Takei,
1998), the higher judges’ scores were negatively related
not only to the ®rst three variables mentioned above for
the handspring vault, but also the degree of forward
body rotation in pre-¯ ight. However, for the Hecht
vault, the higher judges’ scores were positively related
to the vertical distance travelled by the mass centre and
forward body rotation in pre-¯ ight. In the presentstudy,
re¯ ecting the above results, the 25 highest-scoring
larger horizontal and vertical velocities at take-oþ
from the board;
·
greater horizontal and vertical distances travelled by
mass centre and greater forward body rotation in
pre-¯ ight;
·
°
Hecht vaults had a signi®cantly higher body angle (181
°
or 1 above horizontal)than the 25 lowest-scoringvaults
higher body angle at touchdown on the horse,shorter
·
°
°
time of contact on the horse and yet greater average
vertical force and greater vertical impulse exerted
while on the horse, and greater change in both the
vertical velocity and angular momentum while on the
horse;
larger horizontal and vertical velocities and greater
backward somersaulting angular momentum at take-
oþfrom the horse (Table 5).
(173 or 7 below horizontal). These diþerences may
be due, in part, to the diþerence in the blocking and
pushing-oþ technique required to achieve the desired
changes in the horizontal and vertical velocities and
angular momentum while on the horse and, subse-
quently, to depart from the horse with appropriate
body position and orientation to enable the required
somersaulting or twisting rotation in a timely manner
to achieve successful performance.These diþerences in
technique may also be attributed to the fact that a body
·
°
°
angle of 200 or 20 above the horizontal at touchdown
on the horse is required for the Hecht vault. In fact,
failure to achieve the required body angle results in a
loss of a performance point, while exceeding this angle
warrants a bonus point. However, there is no such
requirementnor bonuspoint assigned to the continuous
rotation vaults of any variation.
Discussion
Board take-oþtechniques and pre-¯ ight performance
The results of the present study are similar to those
reported for the continuous rotation vaults, such as the
handspring (Takei, 1989), handspringand salto forward
tucked (Takei, 1988; Takei and Kim, 1990) and hand-
spring with full turn (or twist) (Takei, 1998), in which a
large horizontal velocity at take-oþfrom the board is an
important determinant of success. However, it was not
only the large horizontal velocity at take-oþbut also the
large vertical velocity at take-oþ from the board that
determined success of the Hecht vault. The diþerences
in techniques between the continuous rotation vaults
and the Hecht vault became more distinct in the per-
formance of the pre-¯ ight. In the handspring vault
(Takei, 1989), the higher judges’ scores were negatively
related to the duration of pre-¯ ight, the vertical distance
Blocking/pushing-oþtechnique and post-¯ ight performance
In the present study, the large vertical force and large
vertical impulse exerted while on the horse, the large
change in the vertical velocity and angular momentum
while on the horse, and the short time of contact on the
horse were important determinants of success (Fig. 5).
Similar results have been reported for the handspring
vault (Takei, 1989) and the handspring and salto for-
ward tucked vault (Takei, 1988; Takei and Kim, 1990).

860
et al.
Takei
Table 5. Comparisons of mechanical variables between the highest-scoring and
lowest-scoring Hecht vaults (mean)
Highest-scoring Lowest-scoring
vaults
vaults
=
=
Variable
(n 25)
(n 25)
t
Horizontal velocity (m´s-1)
board take-oþ
change on horse
horse take-oþ
6.64
1.70
4.93
6.02
1.56
4.46
4.06**
1.36
3.80**
-
-
-
Vertical velocity (m´s-1)
board take-oþ
change on horse
horse take-oþ
3.44
1.02
2.48
3.18
0.61
2.00
5.75**
5.40**
4.97**
Normalized angular momentum (s-1)
board take-oþ
change on horse
horse take-oþ
0.35
0.44
0.09
0.34
0.41
0.07
1.69
-
-
-
-
-
-
3.58**
3.04*
Displacements of CM in pre-¯ ight (m)
horizontal
vertical
1.40
0.50
1.14
0.42
4.24**
4.45**
Body angle at touchdown on
181
173
3.10*
°
horse ( )
°
Angular displacement ( )
pre-¯ ight
56
49
2.94*
-
-
-
post-¯ ight
71
55
4.40**
-
91
-
2.50
Angular velocity of post-¯ ight
(degrees per second)
78
Time (s)
-
horse contact
post-¯ ight
0.15
0.79
0.17
0.71
4.93**
5.73**
Force and impulse on horse
normalized vertical force
vertical impulse (N´s)
1.72
63
1.36
39
6.49**
4.81**
=
* P < 0.005; ** P < 0.001. CM centre of mass.
For coaches and gymnasts, the present ®ndings suggest
that the blocking and pushing oþ the horse should be
done `forcefully and rapidly’ to bring about the desired
large changes in the vertical velocity and angular
momentum while on the horse.
momentum at take-oþ from the horse determined
success of the Hecht vault.
All gymnasts in the present study contacted the horse
°
with a body angle of less than 26 above the horizontal
°
and departed from it with a body angle of less than 23
The large vertical velocity at take-oþ from the horse
was an important determinant of success in the per-
formance of both the handspring (Takei, 1989) and the
handspringwith full turn (or twist) (Takei, 1998) vaults.
On the other hand,both the large horizontal and vertical
velocities at take-oþfrom the horse were the important
variables in achieving success of the handspring and
salto forward tucked vault (Takei and Kim, 1990). In the
present study, not only the large horizontal and vertical
velocities at take-oþbut also the large backward angular
above the horizontal. This caused the body mass centre
to remain posterior and superior to the point of hand
contact throughout the course of blocking and pushing
oþthe horse (Fig. 5). The large upward vertical impulse
exerted on the gymnast by the horse caused a large
change in the vertical velocity on the horse. This
enabled the gymnast to depart from the horse with a
large vertical velocity even though the time of contact
was very short. The vertical force simultaneously tends
to reduce the gymnast’s forward angular momentum

861
Mechanicalvariables in the Hecht vault
while on the horse (Fig. 5). In the present sample, the
eþect of the vertical reaction force ± that is, exerting a
counter-clockwise moment on the gymnast ± was far
greater than that of the horizontal reaction force
exerting a clockwise moment (Fig. 5). Consequently,
all gymnasts not only decreased the forward angular
momentum to zero by means of `blocking’, but
also generated the backward angular momentum by
`pushing-oþ’ the horse to reverse the direction of body
rotation while on the horse. In fact, the 25 highest-
scoring vaults of the 122 Hecht vaults analysed had
similar normalized forward angular momentum at
touchdown on the horse, a signi®cantly greater change
of this variable while on the horse, and signi®cantly
greater backward angular momentum at take-oþ from
the horse compared with the 25 lowest-scoring vaults
(Table 5).
performance is largely in¯ uenced by what took place
during the preceding on-horse phase, which in turn is
dependentuponthepre-¯ ightperformance,whichinturn
is governed by what took place during the preceding
on-board phase. Therefore, on-board mechanical vari-
ables are likely to have an important `causal in¯ uence’
on the subsequent three sequential phases of the vault
and overall outcome of performance. In this regard,
the vertical velocity at take-oþ from the board yielded
signi®cant correlation coeýcients with the body angle
=
at horse contact ( 0.49, < 0.001), the time of horse
r
P
=
support ( -0.40, < 0.001), the vertical velocity at
r
P
=
horse take-oþ ( 0.35, < 0.001) and the maximum
r
P
=
height of post-¯ ight ( 0.46, < 0.001). These corre-
r
P
lations meant that the greater the vertical velocity at
take-oþ from the board, the higher the body angle
at touchdown on the horse, the shorter the time spent
on the horse, the greater the vertical velocity at take-oþ
from the horse and the greater the maximum height
of the body centre of mass attained in post-¯ ight.
Mechanically speaking, if everything else is equal, the
greater the vertical velocity at take-oþ from the horse,
the greater the maximum height of post-¯ ight, the larger
the horizontal distance travelled in post-¯ ight and the
longer the duration of post-¯ ight and, thus, the easier
it is to control the body for display of `form’ for bonus
points and simultaneously prepare for landing on the
mat.
In the present study, the average angular speed of
post-¯ ight correlated signi®cantly with the judges’
score (Table 1), indicating that the faster the backward
rotation of the body in post-¯ ight, the higher the score
awarded by the judges. This contrasts with previous
®ndings for the handspring and salto forward tucked
vault (Takei, 1992) and the handspring with full turn
(or twist) vault (Takei, 1998), which indicated that the
slower the somersaulting rotation of the body in post-
¯ ight, the higher the judges’ score. As odd as it may
seem, these contrasting diþerences are in accord with
the performance guidelines of the respective vaults. As
A large gain of vertical velocity on the horse is almost
always accompanied by large reductions in both
horizontal velocity and angular momentum (Takei,
1992; Takei
, 1996). Therefore,maximizing vertical
et al.
velocity at take-oþ results in a high trajectory of the
mass centre and helps the gymnast to ful®l the post-
¯ ight height requirement. If everything else is equal,
the larger the vertical velocity at take-oþfrom the horse,
the greater the maximum height of mass centre and the
longer the duration of post-¯ ight. Furthermore, in
the continuous rotation vaults, maximizing the vertical
velocity at take-oþtends to decreasethe forward angular
momentum and forward somersaulting potential in
post-¯ ight (Takei, 1992; Takei
., 1996) and thus
et al
increase the danger of stalling in mid-air. On the other
hand, a large gain in vertical velocity and a simultaneous
decrease in forward angular momentum, large enough
to cause a reversal of body rotation while on the horse,
positively in¯ uence the post-¯ ight performance of the
counter-rotation vaults. A large vertical impulse, which
causes a large change in the vertical velocity and angular
momentum while on the horse, is therefore an impor-
tant determinant of success (Fig. 5). In coaching terms,
it aids the gymnast not only to prevent `accidental
body turnover’ and to perform an `impressive’ on-horse
reversal of body rotation from the body angle well
°
stated earlier, a body angle of 20 above the horizontal
at horse contact is required for the Hecht vault, and
exceeding this body angle warrants a bonus point. On
the other hand, there is no such requirementnor bonus
points in the handspring category vaults. High-scoring
handspring and salto forward tucked vaults (Takei,
1991) and high-scoring handspring with full turn (or
°
in excess of the required 20 above the horizontal at
touchdown, but also to achieve large backward body
rotation, great maximum height of mass centre and
long duration of post-¯ ight which the judges seek in
awarding bonus points.
twist) vaults (Takei
, 1996) displayed similar
et al.
angular distance of somersaulting rotation in post-¯ ight
and signi®cantly longer time of post-¯ ight compared
with their respective low-scoring vaults. A combination
of comparable angular distance of somersaulting body
rotation and the longer duration of post-¯ ight in the
high-scoring vaults resulted in signi®cantly smaller
average angular speed of forward somersaultingrotation
Additional factors of signi®cance
According to Hay and Reid (1988), errors or faults in
performance revealed during the latter phase of a skill
are likely to be caused by the performance of the earlier
phases. This means that the outcome of post-¯ ight

862
et al.
Takei
compared with the low-scoring vaults. The present
®ndings on the Hecht vault are consistent with its per-
formance guidelines;that is, the higher the body angle at
touchdown on the horse, the greater the backward body
rotation required during the subsequent on-horse and
post-¯ ight phases to bring the gymnast’s body back to
an upright position for a controlled landing on the mat.
In fact, as seen in Table 5, the 25 highest-scoring Hecht
vaults in the present sample had signi®cantly greater
angular distance of post-¯ ight and longer duration of
post-¯ ight than the 25 lowest-scoring vaults. A com-
bination of the greater backward body rotation required
for successful landing and the longer time of post-¯ ight
in the 25 highest-scoring vaults resulted in a greater
average angular speed (non-signi®cant) than that of
the 25 lowest-scoring vaults (Table 5). In short, for the
Hecht vault, the better vaulters rotate through a greater
angular distance and, therefore, must rotate faster than
the low-scoring vaulters. In the handspring category
vaults, most gymnasts rotate through a similar angular
distance, with the better vaulters rotating more slowly
than low-scoring vaulters as they have more time in
the air.
to the heel of the gymnast at touchdown on the mat
(OFFDPST), the body angle at touchdown on the horse
(ANTDHRS) and the time of post-¯ ight (TIMEPST) ±
were identi®ed as important in predicting the judges’
score. These three predictor variables in the equation
collectively account for 39% of variation in the judges’
score and are relatively easily measured by the coaches
during daily training sessions on the ®eld or in the
gymnasium. The equation useful to coaches is:
=
judges’ score 5.580 + 0.266 (OFFDPST) +
0.012 (ANTDHRS) + 0.893 (TIMEPST)
2
=
=
(
0.63,
0.39)
r
r
Conclusions
Based on the results of the present study, success of
the Hecht vault is most likely when the emphasis is on
achieving:
Large horizontal velocity at touchdown on the board
by sprinting the approach and departing from it with
large horizontal and vertical velocities.
·
The angular distance of post-¯ ight (ANGDPST)
was the best single predictor of the judges’ score and
accounted for 27% of variation in the judges’ score.The
equation was:
Large vertical distance travelled by mass centre and
·
large forward body rotation in pre-¯ ight by reaching
as far forward as possible towards the far end of
the horse with the hands and arms (¯ exion of the
humerus)upon leaving the take-oþboard.
=
judges’ score 8.445 - (ANGDPST)
2
Large change in the vertical velocity and angular
=
=
0.27)
(
0.52,
r
r
·
momentum while on the horse, and resulting large
vertical velocity and large backward somersaulting
angular momentum at take-oþ from the horse,
by exerting large vertical impulse of high force and
short duration via blocking and pushing oþthe horse
`forcefully and rapidly’ using the muscles of the
shoulders and shoulder girdle.
The results of the stepwise regression analysis of the
18 signi®cant variables in the present study indicated
that six variables are important in predicting successful
performanceas rated by the judges: the angular distance
of post-¯ ight, the time of post-¯ ight (TIMEPST), the
horizontal velocity at take-oþ from the horse (VHTO-
HRS), the angular distance of pre-¯ ight (ANGDPRE),
the normalized average moment of inertia of post-¯ ight
(NAVIPST) and the normalized angular momentum
at take-oþ from the horse (NHTOHRS). These six
predictor variables collectively account for 57% of the
variation in the judges’ score.The equation is:
Large average moment of inertia by extending the
·
body fully to display Hecht or ®sh-like body position
throughout the post-¯ ight, while simultaneously
preparing for a controlled landing on the mat.
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=
judges’ score 4.909 - 0.045 (ANGDPST) -
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1.48 (TIMEPST) + 0.179 (VHTOHRS) +
0.012 (ANGDPRE) + 65.85 (NAVIPST) +
30.55 (NHTOHRS)
2
=
=
(
0.75,
0.57)
r
r
Finally, we tried to develop a multiple regression
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score by entering the additional variables that are
typically used by the judges in evaluating the vault.
Three variables ± the oýcial horizontal distance of
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