4
ROTATIONAL BALANCE ABOUT
THE CENTER OF MASS
IN THE BREASTSTROKE
J.M. CAPPAERT
U.S. Swimming, International Center for Aquatic Research
University of Colorado, Colorado Springs, USA
Abstract
The purpose of this study was to evaluate angular momentum about a breaststroker's
center of mass. Breaststrokers (n=8) were filmed using a four camera system at the
1992 Olympic Games during the men's 200m preliminary and final races. Two cameras
in underwater housings were placed on the floor of the pool underneath each laneline
defining lane four. Two cameras were placed Sm above the water (attached to the 50m
wall) on both sides oflane 4. These cameras were focused downward toward the center
of lane four at the 45m mark of the pool. All four cameras had the same view of the
swimmer during the competition. The videotapes were digitized to construct a threedimensional (DLT method) 14 segment rigid model. The center of mass was calculated
and displacement data were differentiated. Local angular momentum of the segments
and their remote angular momentum about the body's center of mass was calculated
(Dapena, 1978). Angular momentum data were not significantly correlated with
swimming velocity, but elite level breaststrokers were more symmetrical than less elite
athletes.
Keywords: Angular momentum, breaststroke, symmetry.
1 Introduction
The purpose of this study was to describe the center of mass and the segmental angular
momentum in the breaststroke. It was hypothesized that swimmers with better balance
30
Cappaert
of clockwise (CW) and counterclockwise (CCW) angular momentum about the three
cardinal axes would be more efficient and would be the fastest swimmers.
2 Methods
2.1 Subjects
The subjects included eight male breaststrokers participating in six preliminary heats, the
consolation final and the championship final of the 1992 Olympic Games. Subjects had a
range of swim velocities from 1.2 to 1.6 rnls (mean= 1.45 ± O.llm/s). Swimmers in the
first four preliminary heats were not elite level breaststrokers as compared to the
remaining four swimmers which included the world record holder for this event. Each
athlete's height and weight was gathered from the Olympic athlete database.
2.2 Video Recordings
During each preliminary heat and the two finals, the swimmer in lane 4 was recorded
using a four camera system. Two cameras in underwater housings were placed on the
floor of the pool underneath the lanelines defining lane 4. The optical axes of the
cameras were focused upward and toward the center of the lane. Swimmers were
videotaped as they swam toward the 50m wall at the 40-45m mark of the pool.
Two cameras were placed 5m above the water surface. The optical axes of these two
cameras were focused downward toward the center of lane 4. These two cameras also
videotaped the swimmers at the 40-45m mark. Therefore, all four cameras recorded the
same position in the pool and the same stroke cycle of the swimmers. The Direct Linear
Transformation method (Abdel-Aziz and Karara, 1971) was used for three-dimensional
analysis. This analysis was performed separately in the over and underwater camera sets.
2.3 Videotape Digitizing
Twenty-four body landmarks were digitized using the two underwater videotapes for
one complete stroke cycle to create a fourteen segment rigid model. During out of water
motions, the two over water videotapes were used for digitizing. Three-dimensional
under and over water coordinates were calculated separately. All coordinates were then
expressed in terms of a reference frame in which the X-axis defined the forward swim
direction, the Y -axis defined the sideways direction and the Z-axis was vertical.
2.4 Data Calculations
The center of mass was calculated (Dempster, 1955) and displacement data were
smoothed using a low-pass Butterworth filter (6Hz) and differentiated. Total angular
momentum about the body's center of mass was calculated using a method developed by
Dapena (1978). This method computes a local and remote angular momentum term for
each body segment. Segmental c.ontributions to the total body angular momentum were
evaluated.
Rotational balance about the center of mass in the breaststroke
31
3 Results
Angular momentum about the center of mass during a complete stroke cycle is
represented in Figure I. Average maximum clockwise and counterclockwise values
(Table I) were similar within the group of breaststrokers. Maximum and minimum
segmental contributions to the center of mass angular momentum are presented in (Table
2).
Breaststroke
Center of Mass
15
10
5
EJHCMx
0
+HCMy
eHCMz
-5
-10
-15
0.0
Elite
1.20
T(s)
Figure 1:
Angular Momentum Values of the Center ofMass about the X-axis (front
view), Y-axis (side view), and Z-axis (overhead view).
Table 1:
Angular Momentum Data of the Center of Mass about the X-axis, Y-axis,
and Z-axis.
Variable
Mean (Std)
Maximum CW about Y-axis (kgm2/s)
-13.3
% of stroke cycle that max CW occurs
about Y -axis (%)
Maximum CCW about Y-axis (kgm%)
38.3 ( 2.6)
12.8 { 3.0)
( 3.3)
32
Cappaert
% of stroke cycle that max CCW occurs
about Y -axis (%)
Average about X-axis (kgm2/s)
Average about Z-axis (kgm%)
Table2:
80.6 (10.4)
0.3 ( 0.3)
-0.6 ( 0.4)
Maximum Counterclockwise (CCW, positive values) and Clockwise
(CW, negative values) Angular Momentum Data of the Body Segments
about the X-axis, Y-axis, and Z-axis.
Variable
Right Arm
2
About X-axis (kgm /s)
2
About Y-axis (kgm /s)
2
About Z-axis (kgm /s)
Left Arm
2
About X-axis (kgm /s)
2
About Y-axis (kgm /s)
2
About Z-axis (kgm /s)
Right Leg
CW About Y-axis (kgm2/s)
CCW About Y-axis (kgm2/s)
2
About Z-axis (kgm /s)
Left Leg
CW About Y-axis (kgm2/s)
2
CCW About Y-axis (kgm /s}
About Z-axis (kgm%)
Head CW about Y-axis (kgm2/s)
Head CCW about Y-axis (kgm2/s)
Trunk CW about Y-axis (kgm2/s)
Trunk CCW about Y-axis (kgm2/s)
Mean (std)
1.3
1.2
-3.3
(0.3)
(0.4)
(0.8}
-1.3
1.5
3.3
(0.2)
(0.3)
(0.7)
-4.0
4.7
-7.2
(1.1)
(1.5)
-4.0
4.2
6.8
-3.2
2.7
-2.5
2.0
(1.0)
(1.2}
(1.1)
(0.8)
(0.7)
(0.6)
(0.4)
(1.1)
4 Discussion
The center of mass data about theY-axis (the angular momentum values about the Xand Z-axes were very close to zero, Table I) showed a larger CW (motion upward to
Rotational balance about the center of mass in the breaststroke
33
breathe) than CCW. The head and trunk about theY-axis mimicked the center of mass
data. Together these data may suggest that breaststrokers emphasize the upward motion
to breathe rather than the downward diving motion to begin the pull.
The group of eight breaststrokers were very symmetrical in their segmental
contributions to the total angular momentum about the center of mass (Table 2). In
general, the right and left arms had almost equal and opposite angular momentum values
about the three axes. The legs showed slight asymmetries about the Y- and Z-axes
suggesting that the kick may be less efficient than the arm pull. This inefficiency in the
legs may be due to the lack of visual cues as to the positioning of the legs during the
kick.
Although none of the calculated variables were significantly correlated to swimming
performance, elite level breaststrokers were more symmetrical than non-elite
breaststrokers especially in the legs during the kick. The slowest swimmer of the group
had large maximum angular momentum differences about the Z-axis during the kick (9.7 vs. 5.3 kgm2/s, right and left legs respectively), whereas the fastest four swimmers
had similar and opposite amounts.
5 References
1.
2.
3.
Abdei-Aziz, Y.I. and Karara, H.M. (1971) Direct linear transformation: From
comparator coordinates into object coordinates in close-range photogrammetry.
Proceedings ASPUI Symposium on Close-Range Photogrammetry. American
SocietyofPhotogrammetry, Church Falls, VA, pp. l-19.
Dapena, J. (1978). A method to determine the angular momentum of a human
body about three orthogonal axes passing through its center of gravity. Journal
ofBiomechanics, 11:251-256.
Dempster, W.T. (1955). Space requirements of the seated operator, WADC
Technical report, Wright-Patterson Air Force Base, Ohio.