The Physics of Tai Chi Punches
Randal Templeton's article presentation at the 2nd Autumn Moon Symposium of The Canadian Taijiquan Federation.
September 29, 2018
Understanding the physics of delivering a powerful punch can greatly enhance your Tai Chi practice, even if your main interest in Tai Chi is health and mindfulness.
In the 19th century China, Tai Chi practitioners were known for their ability to deliver devastating punches, even though they advocated slow, seemingly gentle practice of their forms. This apparent contradiction is described in the classics. The power of Tai Chi's punches can be readily explained by Newtonian physics, and the cultivation of natural movement within Tai Chi forms is a very effective way to acquire this power. As a bonus, learning how to generate this power also enhances all the health benefits we have come to associate with Tai Chi practice such as balance, joint opening, and mindfulness.
Let's begin with a quick review of Newton's laws:
Newton's first law states that every object will remain at rest or in uniform motion in a straight line unless compelled to change its state by the action of an external force. If that velocity is zero, then the object remains at rest. If an external force is applied, the velocity will change because of the force.
The second law explains how the velocity of an object changes when it is subjected to an external force. The law defines a force to be equal to change in momentum (mass times velocity) per change in time.
For an external applied force, the change in velocity depends on the mass of the object. A force will cause a change in velocity; and likewise, a change in velocity will generate a force. The equation works both ways.
The third law states that for every action (force) in nature there is an equal and opposite reaction. In other words, if object A exerts a force on object B, then object B also exerts an equal force on object A. Notice that the forces are exerted on different objects.
Source pages found on the NASA website.
In terms of martial effectiveness, if a person cannot respond to the impact fast enough, the energy of impact must be absorbed by deformation of the body itself. A few practical examples can demonstrate these principles:
1) if we simply extend our fist as our adversary approaches us, their forward velocity and their weight creates a force of impact. The punch need have no force, but must form a structure that can absorb the impact.
2) if we extend our fist and move forward into our adversary, faster than they retreat, our punch will have force from our weight and movement. The punch itself does not require force, but must form a structure that can absorb the impact.
These first two examples demonstrate the principle of kinetic energy; energy that a body possesses by virtue of being in motion. To understand how an object (such as a fist) comes to be in motion, we must also consider potential energy: energy possessed by a body by virtue of it's position.
3) if we can create a situation where we can allow our body to drop and fall into our adversary we use the force of gravity to create velocity. Before we start falling we have "potential energy", which we convert to "kinetic energy".
4) "Potential energy" can be sourced from gravity, but also by stretching or compressing springs. The quadraceps, in our legs are able to act like springs, so that if we can "spring up" into our adversary, this will also generate velocity and force. Our muscles act very much like the spring in picture A.
Picture A: spring
The fifth way of generating force uses angular momentum. With angular momentum, the velocity is not linear, but instead travels in a circular manner, always at right angles to the radius of a circle. To understand this force, consider the playground merry-go-round in picture B.
Picture B: merry-go-round
Most of us have experienced what happens if we try to grab one of the hand-holds while the merry-go-round is in motion; or worse, what happens if someone riding the merry-go-round sticks their hand out while passing us. In creating angular momentum, the body acts like a spring, but instead of a linear spring as in Picture A, it is acts more like a clock spring as in Picture C.
Picture C: Clock Spring
In the T’ai Chi Classics power is described as, “rooted in the feet, developed in the legs, directed by the waist, and manifest in the hands.” Although there are several interpretations of this, one way of interpreting this is that our bodies resemble three merry-go-rounds stacked vertically and sharing the same centre axle. Our feet are on the lowest circle, our hips on the next, and our shoulders on the upper-most circle. Proper body alignment allows us to generate angular momentum in our hips and transfer it to our shoulders and hands. Surprisingly, our bodies can generate more power with angular momentum than any other way. Perhaps even more surprisingly, the way to increase this power is not to force it, but rather to reduce our own internal resistance to the movement.
Most Tai chi principles such as "sinking" and maintaining good spinal alignment serve to reduce internal resistance to the hip rotation that generates angular momentum. The body is not a man-made machine, so the effect of sinking and turning often results in a spiral motion. Also, because the movement is rotational, a large change in velocity of the hands can be generated by a very short movement in the hips. Often Tai Chi movement is described as carried motion, which means that hand motion is being driven by angular rotation of the hips, rather than by relative movement of the arms themselves.
Lastly, not only does Tai Chi practice inform us on how to generate force, but according to some transmissions, allows us to take advantage of the Newton's Third Law. Consider the game of croquet: If we hit one ball and it strikes another ball, one ball moves in the direction of the strike and the other rebounds; but if the balls are touching and we put our foot on the first to prevent rebound as shown in picture C; all the energy is transferred to the second ball.
Picture C: Newton's Third Law in Croquet
Similarly, when we strike an opponent we must absorb the equal and opposite reaction of the collision. In other martial arts styles this is often managed by assuming a rigid posture, essentially by bracing the back leg, as in picture D.
Picture D: Punch with Rear Leg Braced
This tactic works, but it requires physical and mental commitment. Also the line of resistance is fairly narrow, so precision in the movement is essential. In Tai Chi we manage the rebound energy with a soft well-rooted structure, so that the energy of the rebound is also transferred to the adversary as in Picture E.
Picture E: Yang Cheng Fu soft structure punch
Notice that Yang Cheng Fu's posture in Picture E is subtly different. His rear leg is not fully extended, nor is his punching arm. Also his waist is only slightly, not forced into an extreme twist. All of these factors provide a softer stance, with more room for error. In this case the entire body structure is shaped to absorb the recoil and channel it into the feet.
Understanding how the body generates angular momentum is complicated. Some authors have proposed that the hips act like a large flat gear or mill wheel that is turned by smaller gears in the hips. In some respects this is a good analogy, but it implies that the central axis of rotation is always in the centre of the hips. In fact the central axis about which the body turns is usually off-centre. The axis of rotation is often situated over the weight bearing foot. Power for the rotation may come from the leg that bears less weight, and/or it can be generated by a spiralling action in the weight bearing leg. Usually in Tai Chi we turn the shoulders in alignment with the hips, but there is always a subtle twisting in the torso that adds some angular momentum. To make things even more complicated, movement in the form usually combines rising or falling effects, as well as some flexing of the back or chest. The notion that Tai Chi deploys all the body's strength at once is not an idle one.
In the example of Yang Cheng Fu's punch above, the power is generated mostly in the legs pushing against the ground. Power from the hips is then transmitted by the waist into the shoulders. Rotation of the shoulders drives the straightening arm forward. Although there is some speed and power added by extension of the arm, the main source of power is the shoulder moving in a slight rotational movement. At the moment of impact, the entire body rests into a supporting structure, so that the energy of the rebound can be absorbed and then redirected back into the target. If executed perfectly, the punch will consist of a short series of pulses until all the energy is dissipated. I suspect this level of skill is rare, and generally would happen at speeds difficult to detect; however the more broadly experienced effect of sinking into a punching bag and feeling your weight behind it, so that there is no visible rebound can be quantified by modern technology. Devices that measure punching power can demonstrate that a punch performed with good weight transfer can add 30% more power to the punch even thought the speed of the two punches is about the same. This theory has been transmitted to Cold Mountain from Dr. Shen Zaiwen.
Another interesting aspect of Tai Chi included in some lineages is the "short jing". Although not the same as Bruce Lee's famous 1 inch punch, the objective of delivering a powerful strike without any visible wind-up is the same. At first the Tai Chi "short jing" strike seems impossible, because our common experience is that power in a punch requires a long travelling distance to build up speed.
This is not the case. As with other Tai Chi and boxing strikes, most of the power comes from the angular momentum driving shoulder rotation. This rotation is driven by a complex network of organic springs all working together to push against the ground, to create a spiralling energy. The travel distance of the shoulder in both a longer range punch and the "short jing" strike is almost the same; a distance of one to four inches. Power added by extending the arm is a fraction of the total power applied. What creates the power is the ability to accelerate the shoulder quickly, and maintain the structure to absorb and redirect the rebound.
The value of good Tai Chi practice is highlighted by understanding the source of Tai Chi striking power:
slow practice allows the mind to understand timing and forward motion
posture transitions allow us to study how to harness gravity, and how to apply the large over-capacity we have to work against gravity
the postures provide excellent ways to form structures that can withstand the force of impact with an adversary.
by practicing the Tai Chi principles of good alignment we can learn how to eliminate sources of internal resistance, especially the value of sinking which allows the hips to turn freely.
while moving through the postures of the form we can learn how to harness combinations of the sources of power
by understanding the power of natural movement we can avoid injury from relying on isolated muscle movements and straining of joints.
When Tai chi is practiced in this way we learn to appreciate that quick or jerky movement detracts from the power of natural movement, and that real power does not originate from muscular upper body strength, but from allowing our bodies to move as they are designed to do.