Jiulong instructor Barry Solway in Colorado offers a very impressive analysis of the physical properties of the Nine Dragon methods. This is a fascinating exploration which helps us understand the Jiulong movements from the perspective of physics and provides a clear explanation of what happens when we correctly apply the methods. There is no need to use confusing mystical language when explaining the way Jiulong works and Instructor Solway’s article is a testament to this fact. Take some time to read and re-read this. It is worth it. Enjoy!!
Matter in Motion: The Physics of Jiulong Baguazhang
© Barry Solway
Mr. Solway can be reached at info@spiralpatharts.com
What does the study of physics and Jiulong Baguazhang have in common? Both disciplines are a study of matter and motion, a look from different perspectives on how the world around us behaves. Taking a glimpse at the general principles of physics as applied to martial arts striking can more deeply inform our practice of Jiulong Baguazhang. The dynamics of the human body during movement and under stress are complex and varied and do not lend themselves to simple analysis. For the purposes of this article, many important considerations are put aside (such as the visco-elastic nature of the human organism, and the ways in which complex forces are dissipated and absorbed throughout the body). This limits the applicability of the models under discussion in the real world, but should provide a sufficient framework for useful discussion.. In particular, we shall attempt to derive some insights into our practice and reveal how Jiulong Baguazhang is rooted in natural principles.
Basic Physics
We start with a basic refresher in physics, the equation for generating force. This equation is F = ma (1), where m is the mass and a is acceleration. This equation indicates that a force is acting on a body only when it is accelerating. A body moving at a constant speed does not require a force to act upon it to maintain that speed. The body is said to have momentum, as expressed by Newton’s First Law of Motion. This occurs in the natural world in a vacuum, and is demonstrated by objects in space that move at high velocities for long periods without any external forces acting on them. For moving objects in our everyday experiences, we have various forces (such as wind resistance, internal and external friction, etc..) that act to slow objects down. In this case, there is a negative force acting on the body and we need to apply a counter-acting force in order to maintain a constant velocity.
When striking, a more useful way to express the forces involved are to look at the momentum of a body. Momentum is expressed as p = mv (2), where p is the momentum, m is the mass and v is the velocity. Momentum can be thought of as a measure of the difficulty of stopping an object in motion. We shall see in a moment why this equation is more useful than the equation for force above to our understanding of delivering power and force during striking. This gives us a second way to express force, as F = p/t (3), where p is momentum (kg*m/s) and t is time. One way to think of Eq. 3 is that it describes the amount of force necessary to bring an object of momentum p to rest.
Power is another useful concept in martial application. Power is work over time and is expressed as P = W/t (4), and given in units of Watts. Work occurs when we apply force over a distance, W = Fd (5). Power is proportional to the amount of work we do (i.e proportional to the force and the distance), and inversely proportional to how quickly the work is done. So the faster the work is done, the greater the power. Since work is force multiplied by distance, then (4) can be re-written as (6) P = Fd/t. The second part of this, d/t, is the equation for velocity. So P = Fv (7). To increase the power of a given movement we either have to move with more force or with more speed (or both). If we move with more speed, then the force will be transferred to the object we touch in a shorter period of time, resulting in a higher impact force, as we shall see below.
Collisions
Now, let’s look at the most basic of collisions. An object that weighs 1 kg is traveling at 10 m/s (meters/ second). This is about 21.6 mph (miles-per-hour). Since it is traveling at a constant velocity, there is no appreciable force acting on the body. A useful equation to express what is going on is the momentum equation (2), p = mv. This yields p = 1 kg * 10 m/s = 10 kg*m/s. Assuming an inelastic collision (the objects “stick” together), then when the objects collide, energy is transferred that may cause deformation to one or both objects. The force of impact is described by Eq. (3), F = p/t. In this case t is the duration of the collision.
Now the first important lesson is revealed. When a collision occurs, an major consideration is the velocity of the object right before impact. The method of achieving that velocity isn’t as important as the velocity achieved. At high velocity, the body has high momentum, resulting in a great impact force when the object collides with another object. In addition, we are interested in t, the amount of time it takes to stop the object. This translates into a negative acceleration,. From equation (3) above, we can see that if the object stops. a force must be acting on it. The quicker the object stops, the more force is acting on it. In our example, if the object stopped in 1 second, it would have a force of F = p/t = 10 kg*m/s / 1 s = 10 N acting on. If the object stops in 1/100th of a second (10 ms), then the force acting on it is F = p/t = 10 kg*m/s / 0.01 s = 1000 N (about 224 pounds). Another way to think of this is that the faster the object stops, the quicker it is de-accelarting, and the higher the force is, as given by Eq. (1).
Back to the Real World
How does this theory apply to our common understanding of martial arts?
We have already seen that the important element in striking is velocity. This is an intuitive observation. Since velocity is related to momentum, we can see how Jiulong Baguazhang uses the principles of physics to achieve high impact by maintaining a high momentum through constant movement. [3] gives values on the order of 3 seconds for sprinters to achieve 98% of maximum velocity. In martial application, we have only fractions of a second to execute a movement, and would like to maximize velocity prior to the strike. Constant movement is important, because it takes time to break our inertia from standstill. It is therefore possible to achieve a higher velocity in the same amount of time if you are already moving then if you are standing still.
Secondly, we see that if we are moving at speed x, then if we can add a sudden burst of acceleration directly before impact, we can increase the final velocity of our bodies before striking, and increase the force of the strike. This is the essence of how fa jing can add a tremendous amount of speed to our strikes, creating maximum energy for deformation on impact or throwing. As an example, [1] shows that karate practitioners can accelerate a standing forward punch from standstill to maximum velocity of 6 to 9 m/s in 200 ms.
Additional insights are revealed by research on the breaking of objects such as boards and blocks by martial artists. A summary of results are presented here without elaboration, please see the references for details.
The first interesting observation is establishing a baseline reference when talking about impact force. [2] gives a table that compares the force necessary to break wood, concrete and living (wet) bone. It takes a force of 670 N to break a wood board, dry white pine of dimensions 28 cm x 15 cm x 1.9 cm. It takes 3100 N to break a concrete block of dimensions 40 cm x 19 cm x 4 cm. Interestingly, living human bone is stronger than either wood or concrete, requiring up to 5400 N to break a wet long bone of 2 cm diameter and 30 cm in length. These numbers assume the ends of the object are held firmly in place, such as during a board break. This insures that the collision is inelastic, collision times are minimal (< 10 ms) and all the force will go towards deformation, not pushing the object away.
And how much impact force can we generate in Jiulong Baguazhang? Derivations by [1] and [2] reveal that karate experts could be expected to generate in the realm of 5000 N of force for a standing forward punch. Velocities of 7 to 9 m/s are common for this type of strike, with instances of 14 m/s being observed. Since only the arm is involved in the strike, the mass is considered to be the hand and arm, estimated at 10% of total body weight or ~7 kg for a 70 kg fighter. Impact times of less than 10 ms are recorded in [1] (with observed times of 5 ms in [2], with de-acceleration in excess of 3500 m/s2). Assuming the 10 ms impact time, yields a total force of F = 7 kg * 7 m/s / 0.01 s = 4900 N. This is sufficient to break a long bone of diameter less than 2 cm. However, placement is important. It was observed that when subjects failed to achieve proper breakage, a frequent reason wasn’t that the force was too low, but that the placement was not correct. The power levels described here assume the object was hit in the center. Hitting slightly off-center changes how the forces are applied to the object being struck and can reduce the effectiveness of the strike considerably. The area of the strike is important also. The force per square centimeter is higher if we focus the strike on the heel of the palm, as opposed to the entire palm. So choosing the striking area is important to the overall effect of the strike.
However, this is not the way we apply techniques in Jiulong Baguazhang. This example is of a standing fighter drawing an arm back to the hip and throwing it out in a forward punch. In Jiulong Baguazhang, we are constantly moving and the force comes from our legs and waist, not from the arm. This more resembles the speeds and forces generated from sprinting. From [3], we have typical maximum sprint speeds in the range of 11 m/s. Typical walking speeds are in the range of 1.5 m/s (about 3 mph). In Jiulong Baguazhang, we normally walk at fast walking speeds, in the range of 3 to 5 m/s. Using fa jing directly before a strike could theoretically lead to velocities upon impact greater than 10 m/s, likely exceeding the values given for a standing forward punch.
More importantly, however, is that fact that the Baguazhang player will attempt to strike with the full weight of the body. The hand and arm contains 10% of the mass of the body. By using the full mass of the body behind the strike we increase the effective mass up to 9 times the values calculated above. In practice, this will be hard to achieve, and possibly undesirable. It may not be prudent to commit all of one’s mass into one strike, possibly off-balancing oneself. However, the increase seen in the force generated is intriguing. The theoretical force of impact of a 70 kg sprinter hitting a brick wall at full speed is in excess of 40,000 N, see [5]. This would give us an upper theoretical limit. A force in excess of 10,000 N (~2400 pounds) would seem realistic for a Baguazhang player of similar mass, where the velocity on impact is 7 m/s (2/3 of a sprinters), only 1/2 of the mass was involved in the technique, and the impact distance is equivalent to trials as described in [2] (in the range of 8 cm). Note that the impact velocity of 7 m/s is conservative as empirical evaluation in [2] shows speeds of various martial arts strikes up to 14 m/s, thereby doubling our estimate above. Our estimate of the total mass involved is also conservative. However, there is no direct empirical research to validate the higher claim, and it remains unresolved as to whether such forces are attainable in practice. The closest analogy is [4], suggesting impact forces of 9000 N or more in collisions involving football players at similar speeds (6 m/s). In this case, the stopping distance is likely longer due to the properties of the padding the players wear, implying targeted combat strikes could have more impact force. Obviously, the application of the technique would heavily influence the maximum force attainable. For example, more force would be generated if the opponent was moving towards the strike as opposed to moving away from the strike.
Jiulong Baguazhang training adheres to natural principles to achieve tremendous forces for striking and throwing. Continuous movement establishes a high baseline momentum. Fa jing allows us to generate power to increase velocity over short distances directly prior to a strike or throw. Together, these methods allows the trainee to achieve maximum velocity. Using “whole body power” puts more mass into play. Proper structure is necessary to direct the force into the opponent at the moment of collision and insure that the force is not absorbed by the joints of the body. Greater velocity and mass leads to maximum momentum and higher impact forces.
Theory can help inform and clarify the purpose of training methods, but cannot replace the need for constant practice. Subtle increases in velocity, mass and form can lead to dramatic differences in the effectiveness of a technique. This requires patience and hard work, but the player is rewarded with an intuitive understanding of the underlying physics of movement in the natural world.
Mr. Solway can be reached at info@spiralpatharts.com
Bibliography
[1] Karate Strikes, Jarel D. Walker, Physics Department, Cleveland State University, March 24, 1975 from The Physics of Sports, 2nd Edition, 1993
[2] The Physics of Karate, S.R. Wilk, R.E. McNair, & M.S. Field, Department of Physics and Spectroscopy Laboratory, Massachusetts Institute of Technology, September 28, 1982 from The Physics of Sports, 2nd Edition, 1993
[3] Physics of Sprinting, Igor Alexandrov and Phllip Lucht, Department of Physics, University of Utah, Salt Lake City, Utah; American Journal of Physics 49, 2t4-247(1981); © American Association of Physics Teachers
[4] Tackling Physics By Rhfonda Hillbery, Caltech News, California Institute of Technology, from Tim Gay’s The Physics of Football.
[5] Visit http://hyperphysics.phy-astr.gsu.edu/hbase/carcr.html#cc3 for a simulation of a car colliding into a tree allowing the user to change parameters. Example in article uses mass = 70 kg, velocity = 11 m/s and collision distance = 0.1 m (about 4 inches)
Hi Barry,
Very good analysis! I hope you continue this series. Two ares of particular interest to me are : 1. Kinesiology of breaking. 2. Angular momentum and acceleration in Baguazhang movements.
Thank you,
Charlie Pasquariello