(Adapted from "Unraisable body: The physics of martial arts", Sports Health, Autumn 2004. Reprinted with permission. (c))
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.
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. 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 practitioners (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 
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.
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.
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.
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).
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
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