Daniel James
("Unraisable body: The physics of martial arts", Sports Health, Autumn 2004,reprinted with permission (c))
See Also Unbendable arm
Abstract
Experienced practitioners of the martial arts can demonstrate impressive feats of coordination and skill. Often their skills are shrouded in mysticism and eastern spirituality and these feats are sometimes attributed to the development of Ki or Chi energy. In particular the 'internal arts', which are those that use primarily soft blending movements, focus on the development of Ki and Chi. This paper focuses on these internal aspects as applied the physical test or feat called unraisbale body and its development in the art of aikido, but is somewhat generalisable to other martial arts. Some historical background to the concept of Ki is presented as well as suggesting why it is used as a teaching paradigm. Unraisable body, a teaching curriculum example of Ki development is presented and an equivalent physical paradigm is suggested. The test is performed under laboratory conditions with a tri axial force plate to validate the physical paradigm.
Keywords: Biomechanics, aikido, Ki, Chi, Tai Chi, Kung Fu, Pa Kua, Xsing Xi
Introduction
When a new student begins training in martial arts they are confronted with aspects of eastern culture, much of which is incorporated into the basic ethos of the class. This usually includes lots of bowing and various phrases of an asian language. And while initially this is all quite strange it turns out there are very good reasons for this ritual behaviour. Bowing for instance is not some strange religious act but a method of encouraging respect for the art, its founder, the teacher and fellow students. Ritual also forms an integral part of Asian culture. Central to the techniques of aikido are the concepts of Ki and liberal use of the word is made in a typical class in both a martial and philosophical /spiritual sense. This discussion will centre on comparing the Ki paradigm with the paradigms of physics for performing the various techniques of aikido. The philosophical, spiritual aspects of Ki are not dealt with in this discussion, although the development of these aspects is considered an important and integral part of the art.
The culture of Ki
One of the first things students have to deal with is the concept of Ki and its application to aikido as well as perhaps their way of life. Explanations here range from a religious experience to explanations as mundane as the momentum of an opponent. Today there are many different styles of aikido some placing more emphasis on Ki and Ki development than others, this seems in some way to be a reflection of different interpretations of Ki. Tohei defines Ki as "cosmic power" and states that "Ki is a very complex word... and even more difficult to translate to westerners"[1]. Westbrook and Ratti [2] speak of the difficulty of defining Ki in a purely physical or mental sense.
The concept of Ki is a Japanese concept (Chi originates in China). and is more easily interpreted in the context of the roots of Japanese society. However to a westerner Ki is sometimes something of a struggle to grasp conceptually (though it appears that many Japanese find this difficult as well), this is compounded by having not usually internalised many of the precepts of Japanese society. Ideally then one would study all facets of Japanese society including some of the various religions and philosophies (such as Shinto, Zen etc.) to fully interpret Ki in its cultural context, unfortunately though this is a serious undertaking and would require a significant investment in time. The translation can, however be assisted if we look at some words that include the Ki character as it appears in the calligraphy for aikido. There are a number of different characters that represent Ki, alluding to it having a wider use within the Japanese society [3]. While there are many Japanese words that include this character for Ki which have deeply philosophical meanings there are also many that have purely physical meaning. Some examples that have a more physical meaning (together with their accompanying English translation) include denki (electricity), sekiyu (petrol/gasoline) and kiryoku (force). While this method of translation is at best a superficial one it demonstrates the generalised use of Ki in Japanese language and society. This is perhaps in line with Tohei 's teachings of Ki pervading all things. Perhaps using the physical sciences to examine Ki we need to be mindful of the development of science in eastern culture.
The development of science in the east and west
The development of the physical sciences in Japan as we know it today was in conjunction with its contact with the west (though this is perhaps an ethnocentric observation), however development of the internal mind and philosophies was widely prevalent and advanced in East well before this Western influence [4]. Prior to this contact the development of the physical sciences in the East focused primarily on observation [5], for example the observations of the early Chinese astronomers was highly regarded. Discovery of the relationship between cause and effect was seen as less important [5], hence a theory such as Ki could satisfy observable data without discovering causality. The effects of the Ki paradigm then would be well documented but an understanding of how it works would not. Hence a physical science approach is not required or sought after for describing the physical world when a more philosophical description fits the observable. This would explain the tendencies of historical eastern culture to favour these sorts of explanations when describing complex observed events as this was more easily understood. However for today's scientific mind, assimilation of information in this way is difficult to accept. As scientists we can then try to understand the techniques of aikido and other eastern martial arts using paradigms that we are more familiar with. This paper suggest physics as a suitable alternative paradigm for some of the physical concepts and meaning of Ki a provide an example analysis. Clearly though this is a non-trivial task given the complexity of modern physics when used for even simple interactions. To apply modern physics to a physical interaction, a thorough understanding of Newtonian mechanics, mathematics to calculus level and biomechanics is an essential requirement. This paper describes how this might be achieved and provides a simple but popular Ki test called unraisable body as an example. In this example a 'conversational' level of physics is presented as an alternative to the traditional Ki concept.
A physical look at the techniques of aikido
A conversational level of ability in physics allows us to describe physical interactions, though to pursue a more rigorous solution is considerably more demanding. Newtonian mechanics allows us to calculate the interaction of simple particles and shapes for elastic and non-elastic collisions [6]. Here the position of any point in arbitrary space can be described using only 3 numbers in orthogonal space (x,y,z). To describe this point's movement in space another 3 numbers for three velocity components are necessary. To model the interaction of 2 people we would need to describe their position and velocity in space over a period of time and so this becomes a considerably more complex task. In this case a mechanics equation is required to describe the motion of each independent part of the body for a given movement. For example to represent the motion of a person by describing only the major interconnecting bones, we are dealing with approximately 20 equations using one for each joint of the body. The approach itself is still simplistic in that we are ignoring the complexity of muscle action and reaction on each of the interconnecting bones. Each of these equations would then contain descriptions for position (3 variables), velocity (3 variables) and acceleration (3 variables) say. If we try to describe the interaction of them over even a short period of time, say a three second aikido technique, and we analyse the motion every 0.01s we end up dealing with about 2x20x9x300 = 100,000 unknown variables to compute. Clearly this becomes a considerable task even on today's computers, assuming the expertise was available to code this.
Static analysis of human joints is a complex but straightforward task. The analysis of how a variety of joint control and pinning techniques such as nikyo[7] and sankyo[8] as performed in aikido and other martial arts has been described previously. These works present the anatomical basis of these controls but do not describe the interaction of the attacker and defender prior to or during application of the control. Thus far this complex interaction has not been analysed technically in the available literature or adequately explained otherwise. This too would seem also to be beyond the scope of this paper. Instead this paper will examine a simpler interaction between attacker and defender that is often used to develop Ki power or extension in an aikido student. This analysis will use basic physics to explain the physical forces developed during this Ki test and how an aikidoka (practitioner of aikido) manipulates these to demonstrate Ki development. The analysis is then validated using experimental results.
Unraisable body
Unraisable body is an exercise performed to aid in the development of Ki in an aikido student; and it is an essential skill for performing many of the techniques of aikido[2]. Similarly this test is also used in other martial arts for the development of internal energy. In this test the student is asked to calm their mind and then two other people will try to lift him/her off the ground by lifting through the forearms. Figure 1 shows the student (C) with two other practioners (A) and (B) trying to raise him off the ground by lifting through the forearms. For the purposes of this study Cartesian co-ordinates will be used and are labelled in the figure. Testing of higher-level students is accomplished by varying the severity and suddenness of the lifting force applied. The test is usually repeated a number of times and the student is encouraged to experiment with a variety approaches to try and pass the test. Initially the student is encouraged to resist the application of the force by using strength, then to completely collapse the body, finally the student is encouraged to calm their mind and extend Ki. This Ki extension is often taught using a number of visual or kinaesthetic cues. Physical observation of the test shows slight variations in posture when performing the test by resistance and when using Ki. These variations will be explored in this paper.
Figure 1: Unraisable Body[2]
The physics of unraisable body
The physical interaction of the student with those trying to perform the lifting as described previously can be simplified somewhat for the purposes of analysis using physics. In this example we will look at the person to be raised as having completely rigid arms with only movement available originating at the shoulder joints. Later on we will look at how this can be extended to include elbow and wrist joint mobility. This simplification enables the applied forces to be resolved into horizontal and vertical components.
Figure 2 depicts Figure 1 showing student (C) lifted by (A) and (B) in two ways. Figure 2(a) represents (A) and (B) lifting (C) diagrammatically where the arrows show the direction of the lifting force applied to (C). Figure 2(b) depicts the resultant force diagram. Here (C) is represented as 700N (70kg) and (A), (B) apply the tension force T at an angle of ? to the horizontal x-axis.
Figure 2: Force diagram of an unraisable body (C) lifted by (A) and (B)
Using basic mechanics the force diagram is resolved into horizontal (x) and vertical components (y). Thus T, the force required to the student can be calculated.
Table 1 shows the calculated force(T) that needs to be applied by (A) and (B) to lift our student (C), this is calculated for various angle of ?. The lifting force here is represented both in Newtons required to lift and as an apparent mass of the student. Notice the dramatic change in forces required as the angle is shifted away from a straight vertical (90o) lift to a more lateral lift. At angles approaching for example 00 the force required lifting a person approaches infinity. In fact even at a 10o angle the lifters (A) and (B) would need to exert a force equivalent to the mass of nearly 6 people each, if they were to succeed in raising the student.
Angle(deg) Force(N) Apparent Mass(kg)
90 700 70
80 710 71
70 740 74
60 810 81
50 910 91
40 1090 109
30 1400 140
20 2050 205
10 4030 403
0 Infinity Infinity
Table 1: Force required by (A) and (B) to lift an unraisable body (C) at an angle ?
It's clear, that if student (C) can vary the angle of interaction with lifters (A) and (B) to approach 00 degrees they can become almost impossible to lift. However in this position the arms would appear to be almost horizontal and the test would look somewhat different to that shown in Figure 1. Nevertheless, this is the fundamental technique for success, and so we need to improve the realism by adding elbow and wrist joints. As such the illustrated figure only demonstrates forces generated from an angle of variation occurring at the shoulder joint. It does not show elbow and wrist mobility. One can see though, that the angle of lift can be varied not only at the shoulders, but also at the elbow and wrist joints to help perform unraisable body.
Performing unraisable body
Using the physical explanation described above as a model for describing this relatively simple aikido exercise, one can successfully perform the unraisable body Ki test and pass. This is a gradual process best explained in three steps as depicted in Figure 3(a), (b) and (c). In each of these cases the direction of lift is shown and the angles of the joints are described using (?1-3). Figure 3(a) represents manipulating only the shoulder joint (?1) to pass the test. This results in limited success though it is possible to pass the test. However using nearly horizontal arms are generally not regarded as mastery of the test. Figure 3(b) involves manipulating the angle of the shoulder joint (?1) and elbow joint (?2). Notice that the arms are now beginning to resemble a more natural posture and the direction of lift is more horizontal than in figure 3(a).
Figure 3(c) demonstrates utilisation of the wrist joint to aid in the redirection of the applied lift to an almost horizontal angle. Even though the applied lifting force is around the wrist joint movement of the joint enables the direction to be shifted. In many cases the angle of the wrist serves to effect this change by reducing mobility in the lift, hence the wrist can sometimes be pointing downward or even inward depending on the exact nature of the grip used to apply the force. When all steps in Figure 3 are implemented the angular manipulations have become quite subtle and resemble that of a skilled aikido student.
Figure 3: (a)Shoulder, (b)elbow and (c)wrist angular manipulations for the unraisable body test
The analysis previously described will enable a student to pass the unraisable body test without difficulty. It is however by no means complete as it does not describe the dynamic interaction of the three parties during the actual moment of the attempted lift. This is more difficult to describe because a lift is rarely applied instantaneously, nor is it a steady set level of force. A number of factors here can add complexity to the lift such as firstly the subtle weight transfer of the lifters both as they prepare to and perform the lift.
Secondly, the reactions of the lifters as they meet the unraisable body play an important role in the interaction. For example the horizontal component of the applied force is transmitted to the other person attempting the lift. To avoid unbalancing, the other lifter must exert additional force in the horizontal direction, thus aiding the person performing the unraisable body test.
Thirdly if the student (C) exerts a slight horizontal force, then the horizontal component of force will have an additional non-zero term introduced into it. While this term is small it is sufficient to change the angles ?(1-3) increasing the force required to lift (C) to approach infinity. A slight horizontal force exerted by (A) is consistent with the Ki principles of extension.
The analysis is not completely rigorous (given the complexity of the dynamic interaction) and yet it demonstrates how the paradigms of physics can be applied to some of the interactions in aikido training. In this case the scientific method of physics demonstrates an alternative understanding of the unraisable body test and a way to pass this test. While a physical understanding of the test is sufficient to enable one to pass, to master the test the development of associated aikido type motor skills would also be required. Using a similar analysis it is possible to demonstrate the principles of unraisable body for when only one person performs the lift (performed by lifting the student under the arms) as well as for other tests, though this is beyond the scope of this investigation.
Experimental Results
An experimental investigation into unraisable body was undertaken. In this test a force plate was placed under person (B) from Figure 1 when performing the test. The force plate allows us to measure the ground reaction forces exerted by the lifter, these forces are equal and opposite to those applied to the unraisable body of student (C). A tri-axial Kistler force plate allows the forces to be measured in the vertical direction (y), the in plane (x) and out of plane (z) horizontal forces at 1000samples/second. Figure 4 shows the measured forces during a typical lift. Note that the vertical component will measure both the mass of the lifter as well as the applied lifting force. A lifter stepping onto the force plate triggered the recording to begin the experiment. At time=1s the lift begins and there is no appreciable horizontal component to the force. At time=1.5s, the aikido student is redirecting the applied force, the vertical force has reached a plateau and there is an appreciable horizontal component force.
Figure 4: Tri axial force plate measurements during an unraisable body lift
Results from several trials were compiled and averaged over the period of time that the lift attempt was made. Both the attempted (unraisable) and successful (normal) lifts were so measured. Figure 5 shows the results of a lift on a senior aikido student during a standard lift (Normal) and an unraisable body lift (Ki). Clearly when the student is standing normally when lifted, the lifters are exerting force primarily in the vertical direction (y). The average force here is approximately 1100N which is the mass of a lifter plus half that of the student. When the attempted lift of the student is made whilst practicing Ki extension there are significant horizontal forces generated in the (x) direction and the component force in the vertical direction (y) is reduced to less than that necessary to lift them. This interaction confirms the physical theory derived earlier.
Figure 5: Forces exerted by a lifter during a standard lift(Normal) and an unraisable body lift(Ki).
Conclusion
This paper has introduced the concept of Ki as practiced in the traditional martial art of aikido. It presents a cultural basis for its development as a dominant paradigm. Unraisable body, a specific example of Ki development as practised in aikido was described and an alternative paradigm that uses basic physics was presented. The physics paradigm was applied to the unraisable body example in a theoretical and experimental investigation. The results were analysed and demonstrated the validity of the physical model. While the analysis cannot be generalised across all aikido practice it nonetheless has demonstrated that some aspects of Ki can be explained using physics for examples that are sufficiently simple
References
[1] Tohei, Koichi , "Aikido :The co-ordination of mind and body for self-defence", Souvenir Press , London first edition 1966
[2] Westbrook, A. and Ratti, O. "aikido and the dynamic sphere: an illustrated introduction", Charles E. Tuttle company Rutland, Vermont and Tokyo First Edition 1970
[3] Kenkyusha,"Kenkyusha's FURIGANA english-japanese distionary", 1990 Kenkyusha limited, Tokyo Japan
[4] Capra, Fritjof "The tao of physics" Shambala Press, Boulder 1975
[5] Nakayama, Shigeru "Academic and scientific traditions in China, Japan, and the west", University of Tokyo Press, Tokyo 1984
[6] Ohanian, Hans "Physics", Norton and Co. New York, 1985
[7] Eckert,J.W and Lee, Ta-Kwong "The anatomy of nikyo (aikido's second teaching)", Perceptual and motor skills v77 pp707-715 1993
[8] Olson, G.D.,Seitz,F.C, Guldbrandsen, F. "An anatomical analysis of aikido's third teaching: an investigation of sankyo", Perceptual and motor skills, V78, pp1347-1352, 1994
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