Anatomical Analysis

Tae Kwon Do is a Korean, unarmed martial art and is best known for its kicks (Park, 2001). The roundhouse kick is a turning kick and happens to be the most commonly used kick during competition (Lee, 1996). For this reason, the roundhouse kick will be analyzed in reference to sparring competition.
The roundhouse kick, a multiplanar skill, starts with the kicking leg traveling in an arc towards the front with the knee in a chambered position (Pearson, 1997). The knee is extended in a snapping movement, striking the opponent with the top of the foot. One’s goal would be to make front torso contact with the kick, while avoiding leaving one’s self open to a counter strike.
The movements that comprise the roundhouse kick begin with a fighting stance: both feet on the ground, toes pointing straight ahead, back foot turned outside up to 22 degrees, front foot approximately 1.5 the distance of one step from the back foot, both feet approximately one length of one foot apart, extension of both legs, slight rotation of the torso in the direction of the back leg, fists held in front of the chest, flexion at the shoulders by about 45 degrees, flexion at the elbow by about 60 degrees, and flexion of the fingers.
One initiates the preparatory phase of the roundhouse kick from the fighting stance: rotation of the torso in the direction of the front leg, flexion and abduction at the hip, flexion at the knee of the back leg which brings the knee to the torso and maintains a minimal relative angle at the knee to the thigh, plantar flexion of the foot, and lateral flexion of the spine toward the ground away from the kicking leg (Table 1).
The fighter is then ready to initiate the movement phase: extension at the knee with a relative angle to the thigh of about 180 degrees, lateral rotation of the grounded foot between 90 and 120 degrees, and additional lateral flexion of the spine.
After attempting to make contact with the opponent, the fighter immediately follows up with the recovery phase: flexion at the knee, lateral flexion of the spine opposite the aforementioned direction, during a slight rotation of the torso, extension of the hip, and dorsiflexion of the foot. This brings the fighter back into the fighting stance with the opposite leg in the front and is now ready to perform the next strike or counterstrike.

Mechanical Analysis

One must obtain optimum speed and accuracy in order to fulfill the purpose of making front torso contact without allowing for a counterstrike to one’s own front torso (Hamilton, 2002). In a sparring competition, a competitor must also avoid falling to the ground, thus balance is also included among the mechanical objectives.
The roundhouse kick is an angular movement, so when taking optimum speed into consideration as an objective, it is understood that angular velocity, denoted as z, is equal to the angular displacement, denoted h, divided by the change in time, denoted Dt (Hall, 1999).
z= h
Dt

So, one would obtain an optimum velocity by increasing the distance over which the position changes of the kicking foot over a minimal amount of time. A kick can be performed at a high velocity when the aforementioned technique is used, creating an ideal circumstance for angular displacement, where the radius of a given point, the foot, on a rotating body, the lower leg, and the axis of rotation, the knee, is minimal, thereby reducing the linear distance covered which can in turn be performed in a minimum period of time (Hall, 1999).
Another factor worth consideration is the moment of inertia, denoted as I, or the tendency of a rotating body to resist change in its state of motion which is based on both mass, m and the distance over which the mass is distributed from the axis of rotation, denoted as r (Hall, 1999).
I=mr2
This concept is key in the technique of the kick as the low relative angle of the knee to the thigh in the preparation phase reduces the radius of gyration, denoted as k, in reference to the lower leg and foot (Hall 1999).
I=mk2
These factors, the angular velocity of the lower leg, distribution of the mass of the leg and foot, with respect to the axis of rotation, the knee, and the mass of the leg and foot itself, all build to form the angular momentum, denoted as H (Hall, 1999).
H=mk2z
However, because the primary goal is to achieve optimum velocity, optimum momentum is obtained through angular impulse. The series of movements before contact with the target attempts a kinetic chain with an efficient sequence of movements previously noted in the description of the preparatory phase (Champion, 2002). The internal muscles move first, such as the serape and spinal flexors and rotators, out to the Gluteus maximus, to the Rectus femoris, transferring the large body movements from the trunk to the smaller body segments of the foot. If the movements are timed correctly, one will have maximum speed upon reaching the next movement, until the point of application (Champion, 2002).
Another valuable aspect to consider is drag, which is a resistance force slowing down the motion of the leg and foot through the fluid medium, air (Hall, 1999). The most relevant form of drag here is surface drag, where the size of one’s leg and the increased surface area created by the traditional uniform, in addition to its texture play prominent roles in decreasing the velocity of the kick.
Once the kick has been executed, impact must be taken into account. The result of the impact of one’s foot with the opponent’s front torso largely depends upon the velocity of the kick, the velocity of the opponent if in motion at the point of contact, the size and shape of one’s leg and opponent’s front torso, the environmental temperature, and elasticity of protective gear. It is difficult for a fighter to judge impact if his or her opponent is in motion. If one or the opponent is hot and is sweating through the protective gear, it will become more plastic, reducing the rebound and influencing the velocity of the movement in the recovery phase.
The other mechanical objective, balance, is in other words the ability to control equilibrium (Hall, 1999). A fighter maintains balance when offsetting his or her center of gravity while flexing at the hip and knee by countering this redistribution of mass by lowering the head and torso. Stability is related to this concept of equilibrium and is defined as the resistance to disruption of equilibrium (Hall, 1999). During the starting and ending position of the roundhouse kick, optimum stability achieved with the footing noted previously in the discussion of the movement phases, which maximizes the base of support. Whether or not a fighter can stay on his or her feet weighs heavily upon the component of friction too. If there is minimal friction existing between the supporting foot when performing the kick and the ground surface, a fighter will have a tendency to fall frequently. If there is too much friction present, the fighter may be restricted in his or her chain of movements.

Error Detection and Prescription

Those new to the practice of Tae Kwon Do may tend to shy away from removing socks during a lesson. A teacher will insist upon removal of socks or the student will soon learn first-hand about the effects of little friction between the foot and the ground surface. A simple correct here is to practice barefoot or to invest in appropriate sparring footgear.
Beginners also tend to skip flexion at the hip and knee before extending at the knee, instead going from the fighting stance to the flexion of the hip with the knee fully extended right to the target. This, of course, slows down the kick considerably because of a number of reasons. This performance error results in a greater linear distance covered by the foot with the rotating body, the fully extended leg. There is a greater moment of inertia with the increase in mass of the segment in this one motion. Surface drag is also increased in this one motion as the surface area has increased. This can be corrected simply by instructing the beginner of the correct technique in flexing the knee in addition to the hip before extending at the knee.
One other common error that occurs with beginners is an extension at the elbows as one kicks. This is a natural action one takes in order to maintain balance. However, a fighter must not leave the front torso open to a strike, so this reaction must be corrected by lowering the torso and head.


Figure 1, Free Body Diagram

References
Champion, L., Introduction to Biomechanics, Lecture, Fitchburg State College, Fitchburg, MA, March 28, 2002.

Hall, S.J., Basic Biomechanics, McGraw-Hill Comp., New York, NY, 1999.

Hamilton, N., K. Luttgens, Kinesiology, Scientific Basis of Human Motion, McGraw-Hill Comp., New York, NY, 2002.

Lee, K.M., Tae Kwon Do, Techniques and Training, Sterling Publishing Comp., New York, NY, 1996.

Park, Y.H., Tae Kwon Do, Lesson, Master Park’s Tae Kwon Do College, Lunenburg, MA, 2001.

Pearson, J.N., Kinematics and Kinetics of the Taekwon-Do Turning Kick, A dissertation submitted in partial fulfillment of the requirements for the degree of Bachelor of Physical Education with Honours at the University of Otago, Dunedin New Zealand, 1997.