Martial arts, like any sport, can be resolved into physics. The principles of Tae-Kwon-Do, the ancient Korean art of “kicking and punching”, is a clear example of the ways in which physics is applicable to biomechanics. The beauty of Tae Kwon Do lies in the fact that every motion can be explained in physics terms. The principles of conservation of energy, torque, center of mass, and power are directly applicable to Tae Kwon Do. Understanding these physics derivations and reasons can create stronger fighting and more applicably, self defense for the layman. Techniques in Tae Kwon Do are often performed incorrectly due to laziness or sloppiness which results in a lack of appropriate force and power. Physics can explain why the way we are taught by our teachers truly is the best way to perform a technique, reinforcing the realization that when Tae Kwon Do was first born in the jungles of Korea, the masters understood the supreme importance of physics.

Firstly, there are some assumptions that must be made. The mass of an individual is constant. We will also assume perfect conservation of energy, with little or no energy transferring into heat. Air resistance is negligible for any techniques involving jumping and spinning. Nextly, it is important to note that it is the energy of the kick or technique, rather than the force that causes significant impact.

In the Axe kick, the martial artist lifts his leg up, extends it high in the air, and then brings it back down, snapping the leg at the point of impact. In this case, it is very clear to see that the higher that the artist can extend his leg, the more energy he will have on impact, as
Potential Energy = Mass X Acceleration due to gravity X Height.
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COM.jpgIn the case of any kick, center of mass is of prime importance. Center of mass is the concept that determines the balance of a martial artist. When on one foot, and especially while spinning, the artist must maintain his balance to not only ensure a strong kick, but also be impervious to an attacker’s attack. When kicking, one part of the body must compensate for another part of the body, so fluid motion occurs and the kick is strong. The center of gravity is where the main gravitational force is concentrated, and is at the same spot as the center of mass as there is a uniform gravitational field.

In this case, the center of mass/gravity is above the supporting leg.
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Picture1.pngWhile tripping of flipping an individual, force must be applied in two different directions, and a force “couple” is created. By sweeping an opponent’s leg towards him and pushing an opponent’s arms away from him, rotation is caused twice as easily. This rotation is commonly experienced as a “take down”. The torque created in the “take down” is the magnitude of the two forces times the perpendicular distance between the two. Hence, the most effective take down would occur with a leg sweep and a shoulder push.

Illustration of a force couple in two different directions.
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In the 360 spinning hook kick, the artist stores up energy by rotating and then releases the energy in a high powered, high kick. In order to have a powerful kick, the kick must be fast, and rotational velocity must be high. However, rotational momentum is the moment of inertia X rotational velocity, or turns per second. Rotational momentum is conserved, so decreasing the moment of inertia, or increasing the easiness of the artist to spin, will give the artist more speed, and a stronger kick.
Tutorial on how to kick a back hook kick.
The damage that a well-placed back hook kick can do...

Kicking a target in a roundhouse kick is almost like an elastic collision. The foot of the artist and the kicking target are the two masses in question. If 1 = foot and 2= target:
m1v1i + m2v2i = m1v1f + m2v2f
This equation may be simplified into:
m1v1i = m1v1f + pt, with pt as the momentum the target experiences.

Since the foot always travels back the same way it came (snap back) it can be assumed that the velocity of the foot after impact is negative, making the equation:
m1v1i + m1v1f = pt or
m1(v1i + v1f) = pt
This formula shows how the momentum of the target is completely dependent on the speed at which the target is kicked.
Thie concept of pt is important because the higher this is, the higher impulse is generated. Impulse is defined as:
Impulse = Δp, or in this case, pf - pi
Substituting in would yield Impulse = pt – 0 = pt
Since Impulse = ForceΔtime as well, FΔt = Δp, which means that
F = Δp/Δt
F = pt/Δt
To maximize Force, the pt must be high and the Δt short, and when the artist has a high speed, Δt is short due to the equation d = vt, considering that distance is always constant and Δt is time measured from t=0 to time of impact.
Thus, the faster an artist kicks, the higher his ultimate force will be.

Physics very clearly has many applications in Martial Arts. There are still more concepts that can be explained by physics: Why are people with longer legs prone to a stronger kick and impact on a target? Why is the torque involved in a joint lock proportional to pain? These questions and many more await further research in the physics of Tae Kwon Do.


Sam Edwards - Is there any physics behind Tae-Kwon-Do's punches? - Yes, there is. I don't know why exactly, but punches should be spiraled in because then the fist will contact the body (mostly water) in such a way that the force will be concentrated so to speak on one area instead of the force dispersing radialy had the punch been simply straight on.

Brandon Siegenfeld- Which kick would have more power according to physics a spinning/round kick or a front/strait kick? - Keeping in mind that "power" is really energy. A spinning kick would have more energy behind it because before kicking a spinning kick, the artist "winds up" by twisting the trunk and then kicks. There is rotational potential energy stored up in the "wind up" and that potential energy is much more than the potential energy that would have been stored up in a front kick.

Robert Lopez - Is there a way to calculate the force exerted on the object being kicked? how about the amount of pain one can recieve? - One can kick a force meter or use an accelerometer to measure acceleration of the kicking foot/arm and find force from that. Pain is generally subjective to a person’s innate ability to resist pain.

James Song- What are the different effects of kicking into a person and kicking in a swinging motion? - Kicking into a person means that the force is stopped and thus, there is an impulse. Kicking in a “swinging motion” or without a target would indicate that the force does not stop unless the artist himself stops.

Greg Sturm - With Newton's third law and all with opposite reactions for every action, what are the measures taken when punching/kicking so that the force exerted on your foot/hand does not hurt you? - We tend to kick with the flat, top part of our feet because it leads to minimal "pain" and when punching, we punch with the knuckles of the first two fingers and have the thumb behind them as support. (Fold the thumb into the palm and fold fingers straight down.)

Kevin Norris - What kinds of defensive techniques are there and how can physics explain them? - Most defensive techniques involve moving back and out of range of the opponent, and there isn't much physics involved in that. The main kicking defense technique is a "cut kick" and that is essentially when one artist blocks a kick with his foot.

Will Chan - Which kicking technique would produce the most force? - A spinning jump kick (360, 540 etc, depending on how good the artist is) because it has the most potential energy.

Sohini Sheth - this is just a comment not a question. You said earlier that: "
There are still more concepts that can be explained by physics: Why are people with longer legs prone to a stronger kick and impact on a target?" This could be because of the torque of a kick since the force = rsintheta. If the "r" or the length of the leg is longer, more force will be provided.(?) --just a thought !

Ari Horowitz - While preforming martial arts most people don't wear shoes; is there a reason for this? -kicking something barefoot doesn't seem like a good idea. We would rather suffer a little sting in our feet than have less mobility and trip and fall. :) And well, martial artists can wear shoes, but it really doesn't make much of a difference. Again, the "pain" of kicking someone is not really an issue unless the artist has particularly bad aim and kicks the elbow (very, very painful for the attacker) and in that case, even shoes can't ease that pain.

Douglas Chin - What about a drop kick? Would a flying straight
kick with both feet and with the whole body compressed as a lateral spring, still not be as powerful as a spinning jump kick?

naveen Shetty - How dpes sparring gear make a difference?...also i can still beat u up - Sparring gear doesn't change much regarding the normal force of an artist- the gear is surprisingly light. But it does decrease some mobility. This is offset by the fact that the artist will be less beat up after the round. And if we look at physics, I'm pretty sure I could flip you.