Pirouette: “An act of spinning on
one foot, typically with the raised foot touching the knee of the supporting
leg.” (Free Dictionary, 2013)
Pirouettes, otherwise known as turns form a fundamental
component of the global ballet syllabus. This particular ballet skill can be
initially challenging and requires constant repetition and technical control of
the body. (Dodge, 1997) There
are three prominent characteristic that are highly important when executing the
movement which include body form, balance and rate of turn. (Laws, 1979) The atheistic body,
required to achieve dance excellence in all technical components of ballet,
including the pirouette, can only be properly achieved under the instruction of
a ballet teacher. In a purely aesthetic sense, turn out of both the supporting
leg and working leg, a deep plié or ‘bending
of the knee’ before retiré, ‘raising
the working leg up the knee’ are important properties of a technically
executed pirouette. (Laws & Swope, 2002) A biomechanical analysis however can give both dancers and
dance instructors a better understanding of the rotational mechanics required
to turn and generate further knowledge applicable to other areas of ballet
syllabus and modern dance. Some important considerations addressed from a
biomechanical viewpoint include the importance of the distribution of body
weight surrounding the rotational axis, the manner in which the torque is
exerted and angular momentum generated for the turn and lastly the way in which
the dancer maintains balance over the supporting foot. (Laws, 1979)
Figure 1 (Ballerina by day, 2010)
The Answer
In order to comprehend the
mechanics which permit ballet dancers to perform pirouettes there are several
biomechanical principles which must initially be understood.
Firstly, velocity is used to describe how fast an object is moving and in
what direction. Its scientific formula is distance divided by time plus
direction. Secondly, momentum is the
mass of an object multiplied by its velocity. Lastly force, “is a product of mass
and acceleration” (Blazevich, 2010). It induces a change in the current object and
therefore in order to change the objects momentum, force must be applied over a
period of time. Force
additionally encompasses both magnitude and direction, making it a vector
quantity. This demonstrates why arrows graphically represent forces. (Keznetsova, 2003) There are multiple
forces that act upon ballet dancers. Gravity, acts as a downward force, the support
from the floor is an upward force and friction from the floor aids as a sideways
force. (Keznetsova, 2003) The surface
of the floor when performing pirouettes in fact can have a huge impact on
dancer’s success. The floor should be smooth enough to proficiently turn, not
to slippery to fall and lastly not produce excessive amounts of grip. If
the floor produces too much grip the kinetic energy provided by the dancer will
transfer
down to where the ball of the foot hits the surface. This turns the energy into
heat which will cause the dancer to decelerate. (First Post, 2012) This
is called friction “force opposing motion
at the interface of two surfaces.” (Blazevich, 2010)
How is the initial torque generated?
A single pirouette is a 360◦ turn of
the body on one foot. Angular velocity
describes how fast the object or dancer spins. Angular velocity is also a
vector quantity as it is characterized not only by the direction of the
rotational axis but also its magnitude. Rotational
Inertia can be perceived as the inertia of a rotating object. Inertia is
the tendency for an object to remain in its current state of motion. Similarly Angular momentum is rotational inertia multiplied
by angular velocity and consequently if an object has a large angular momentum
it is harder to stop it spinning. A pirouette however can have both a
‘repetitive’ and ‘non repetitive’ nature meaning it has a definite beginning
and end as demonstrated in the case of a singular turn. It can additionally be
‘non repetitive’ as pirouettes can have a continuous nature or cycle, solely
dependent on the expertise of the dancer. (First Post, 2012) Torque measures how much force acting upon an
object causes it to rotate. Torques formula equals distance multiplied by
force. Change in angular momentum is additionally equal to the exerted torque
on an object multiplied by the time the torque was acting. (Blazevich, 2010)
|
Motion
|
Motion
with spin
|
|
Velocity
|
Angular Velocity
|
|
Mass
|
Rotational Inertia
|
|
Momentum
|
Angular momentum
|
|
Force
|
Torque
|
(Figure
2) (Blazevich, 2010)
The
table above can aid in overall understanding when comprehending the differences
in biomechanical terminology.
A dancer can ultimately be
considered as an object moving as a result of influential physical forces. The
motion of the body is determined by forces operating outside of the body. Factors
such as distribution of body mass and body configuration can only be controlled
by the bodily system itself.(Laws & Swope, 2002) The turns examined in this paper have no linear acceleration
and because of gravity the vertical forces of the body and floor are balanced,
with the total horizontal force equaling zero. (Laws, 1979) As
demonstrated above no change in bodily angular motion can occur without a
torque. When initiating a turn the ballet
dancer spins around a vertical axis, giving rise to the torque. This is biomechanically
given by the force and the vertical distance from the line of action of the
force to the rotational axis. (Laws, 1979) Here
the total horizontal force on the body equals zero and a torque can be formed
by a force, consisting of equal and opposite forces with certain distance
between the lines of the forces.
When a ballet dancer applies a
horizontal force to the floor, Newton’s third Law demonstrates that the floor
then exerts an equal and opposite force back against the dancer’s foot. This
aids as an external force acting upon the dancers body and produces a
rotational motion, commonly known as a pirouette. The torque used to initiate a
turn can be applied with one or two feet with little or more distance between
them. For example a turn from fifth position, with a small distance between the
feet requires a greater force to produce the same torque than a turn in which
the distance is larger.
Where does angular moment reside when performing pirouettes?
For a fixed body of mass the moment
of inertia will only increase if the body mass moves further from the
rotational axis. If there is an external torque acting upon the body the total
angular momentum can change. When the dancer rises up onto the supporting foot,
the initial torque has been exerted in which the angular momentum remains
constant, and decreases slowly due to the friction force of the floor. (Laws, 1979)
Ultimately the torque is equal to
the rate of change of angular momentum which suggests that the same angular
momentum can be produced by exerting a smaller torque for a longer time or a
larger torque for a shorter time. (Laws,
1979) The angular momentum remains constant when the torque ceases allowing
the dancer to control the angular velocity or rate of turn via controlling the
way in which the mass of the body is distributed across the rotational axis.
This suggests that the moment of inertia is decreased by bringing the arms into
to the rotational axis. The angular velocity will increase correspondingly,
allowing the angular momentum to remain constant.
When dancers execute a pirouette,
their angular momentum resides predominantly in the arms, gesture leg and
torso. When the torso completes a turn the dancers head whips around, commonly
known as spotting and thus absorbs some angular momentum, slowing both the body
and angular velocity. (Laws & Swope, 2002) To minimize the effects of the absorption of angular
momentum the head should be kept on the axis of rotation where its moment of
inertia is smaller. When the pirouette comes to an end the foot should return
back to the floor, allowing the friction to increase, the arms should
additionally be extended, slowing the angular velocity for the remaining angular
momentum. The coordination of the two slowing actions permits the dancer to technically
execute pirouettes in the desired orientation. (Laws, 1979)
What key principle will allow ballet dancers to maintain or lose
balance whilst turning?
Balance requires no total force and no total torque. To
maintain balance no total force is needed to ensure that momentum does not
change. No total torque is additionally required to ensure the angular momentum
stays the same. (Keznetsova, 2003) When
performing pirouettes the dancer’s center of gravity should ultimately be spread
between the base of your support, “a
point at which the mass and weight of the object are balanced in all directions”
(First
Post, 2012)
The
magnitude of the spinning angular momentum of a dancer will determine the
analysis when predicting balance. If the
angular momentum is not very large the rotational effects can be ignored and
the balance can be analyzed as if the dancer was not rotating but rather poised
above a supporting point. If the angular momentum is large the dancer has to be
treated like a spinning top. (Laws & Swope, 2002)
An
average female ballet dancer with a mass of 50kg will have a moment of inertia
of roughly 0.5kg-m whilst in pirouette position. She will be spinning at
approximately two revolutions per second or 126 radian per second, making the
angular momentum 6kgm² /S². If the ballet dancer is
displaced vertically off balance by an angle of 10◦, the tumbling torque will
equal approximately 100 Newton meters. (Laws, 1979) This torque would produce a tumbling angular momentum eight times
larger than the magnitude of the spinning angular momentum in the time of one
revolution. This confirms that the spinning angular momentum is not large compared
to the tumbling angular momentum. (Biringen, 2010).
Ballet
dancers generally instinctively realize that it is not possible to regain balance
whilst on one foot. What they generally do not recognize however is that
balance is not acquired by the manipulation of the body directly but more so
the horizontal force exerted to the floor. This achieves the shift in position
of the center of mass which ultimately restores balance, proving that the movements
of the body which maximize the horizontal force of the supporting foot on the
floor will be most effective in either destroying or restoring balance. (Laws, 1979)
Figure 3 (Pirouettes, 2010)
How else can
we use this information?
The information utilized in this
essay can easily be transferable to all areas of modern dance where turns are
applicable. Areas such as modern jazz, tap, contemporary and even hip hop all incorporate
a variety of turns within their individual syllabuses. (Dodge, 1997)
In addition angular momentum,
balance and angular velocity are all important movements in gymnastics. (Top end sports, 2012) Rhythmic gymnastics in particular
possesses many of the qualities of traditional ballet and many rhythmic
gymnasts seek ballet training prior to and throughout their careers.
In conclusion, biomechanical analysis can help give dancers,
both elite and professional, a greater understanding of the underlying
principles of biomechanics and can help dance teachers alike give students
constructive and correct advice regarding technique, body placement and
physics.
References
Biringen,
E. (2010). Analysis of
Pirouette Execution for Improved Performance. Medical Problems of Performing Artists. 25, 136.
Blazevich, A. (2010). Sports Biomechanics the Basics,
Optimizing Human Performance. A&C Black Publishers. London.
Dodge S.
(1997.) The Physics of ballet dancing. From http://www.scribd.com/doc/2452927/Fisika-Physics-of-Ballet-Dancing
First Post. (2012).
Biomechanical Analysis of a Pirouette. From http://www.firstpost.com/topic/organization/texas-am-university-corpus-christi-biomechanical-analysis-of-a-pirouette-by-erica-andrade-video-xP7jt9dr1a8-90934-8.htm
Keznetsova,
F (2003) Physics of Dance. From http://ed.fnal.gov/trc_new/demos/present/physofballet.pdf
Laws, K.
(1979). An Analysis of turn in Dance. Dance
Research Journal, 11, 12-19.
The Free
Dictionary. (2013). From http://www.thefreedictionary.com/pirouette
Pirouettes. (2010).Pictures of pirouette sequence.
From http://www.artofballet.com/exer2.htm
Top end
sports. (2012). The sports + science resource.
The physics of gymnastics. From
http://www.topendsports.com/sport/gymnastics/physics.htm
