Friday, April 11, 2014

Physics of Yoga Asana (second write, more detail)

I have written previously on the physics of yoga and decided today to write again about this important topic. I feel that this work builds a powerful bridge between the understanding of physical forces and energetics that are utilized in yoga but not oftentimes understood. This work is powerful in that it involves direct sensory perception as immediate feedback which acts to create form out of feeling.

This article will start by defining a few terms from physics. Bear with me and hopefully it will all come together and make sense. I do think the definitions are important and at some point will elaborate further on them with diagrams.

The first definition I want to lay out is the concept of force as defined in physics.

Since I've long ago sold my physics texts, I will use Wikipedia to help out.
According to Wikipedia we have,

"In physics, a force is any influence that causes an object to undergo a certain change, either concerning its movement, direction, or geometrical construction. In other words, a force can cause an object with mass to change its velocity (which includes to begin moving from a state of rest), i.e., to accelerate, or a flexible object to deform, or both. Force can also be described by intuitive concepts such as a push or a pull. A force has both magnitude and direction, making it a vector quantity. It is measured in the SI unit of newtons and represented by the symbol F.
The original form of Newton's second law states that the net force acting upon an object is equal to the rate at which its momentum changes with time. If the mass of the object is constant, this law implies that the acceleration of an object is directly proportional to the net force acting on the object, is in the direction of the net force, and is inversely proportional to the mass of the object. As a formula, this is expressed as:
\vec{F} = m \vec{a}
where the arrows imply a vector quantity possessing both magnitude and direction."

Basically, since we are dealing with fixed masses in yoga (our bodies), what we are doing is influencing acceleration in a given direction. Lets stick with the definition above as including a change in velocity or speed as well as direction and leave aside the deformation of an object. We are considering force as it is communicated through bone, and bone for the most part can be considered stable for our purposes here.

Before defining the specific types of forces, lets take a look at the definition of Newton's third law.

(from Wikipedia)

" The third law states that all forces exist in pairs: if one object A exerts a force FA on a second object B, then B simultaneously exerts a force FB on A, and the two forces are equal and opposite: FA = −FB.[24] The third law means that all forces are interactions between different bodies,[25][26] and thus that there is no such thing as a unidirectional force or a force that acts on only one body. This law is sometimes referred to as the action-reaction law, with FA called the "action" and FB the "reaction". The action and the reaction are simultaneous, and it does not matter which is called the action and which is called reaction; both forces are part of a single interaction, and neither force exists without the other.[24]
The two forces in Newton's third law are of the same type (e.g., if the road exerts a forward frictional force on an accelerating car's tires, then it is also a frictional force that Newton's third law predicts for the tires pushing backward on the road).
From a conceptual standpoint, Newton's third law is seen when a person walks: they push against the floor, and the floor pushes against the person. Similarly, the tires of a car push against the road while the road pushes back on the tires—the tires and road simultaneously push against each other. In swimming, a person interacts with the water, pushing the water backward, while the water simultaneously pushes the person forward—both the person and the water push against each other. The reaction forces account for the motion in these examples. These forces depend on friction; a person or car on ice, for example, may be unable to exert the action force to produce the needed reaction force.[27]"

Understanding Newton's third law, we can then apply it directly to forces in a specific way with two more important definitions, the contact force and the normal force.

What is the contact force?

Again according to Wikipedia we have

"Contact force is the force in which an object comes in contact with another object. Contact forces are ubiquitous and are responsible for most visible interactions between macroscopic collections of matter. Pushing a car up a hill or kicking a ball or pushing a desk across a room are some of the everyday examples where contact forces are at work. In the first case the force is continuously applied by the person on the car, while in the second case the force is delivered in a short impulse. Certain contact forces describe specific phenomena and are important enough to have been given unique names. The most common instances of this include friction, normal force, and tension. According to forces, contact force may also be described as the push experienced when two objects are pressed together."

Normal force is (again, according to Wikipedia),

"In mechanics, the normal force  F_n\ is the component, perpendicular to the surface (surface being a plane) of contact, of the contact force exerted on an object by, for example, the surface of a floor or wall, preventing the object from penetrating the surface."


Ok, so we have all of these definitions. How do we manage to put all of these concepts together to form an understanding of how to work with asana?

Lets make sense of it...
We have an active component (muscle) that engages a change in momentum and acceleration, interacting with a solid object (usually the floor), which in turn triggers a contact force (because the floor resists the foot with its friction, assuming it is not too slippery) and simultaneously increases the normal force, which is felt through the bone, equal and opposite in direction to the direction of the contact points.  In other words, if we press into the floor with the leg, the floor will push back into the bone with equal and opposite strength. This "return" force can be directly felt through the bones and carried all the way through the body. The extent that we can carry this feeling of the contact force all the way through the bone pathways of the body gives rise to our sense of connection and the engagement of the body as a whole.

Lets break it down further. Try this exercise. 

Stand with our feet apart several feet distance, with our feet turned out 45 degrees and our legs held straight at the knee.

Push the feet both down and out with a bit of effort. The feeling will that of "ripping the floor in half with the feet". What muscles are being utilized? The plantar flexors of the lower leg, or in other words, the muscles in the deep posterior (back) of the calf. We can consider these the "shin" muscles. This is what is meant by "engage the shins". We push the feet and lower leg strongly into the floor and separate the feet from one another. Do NOT attempt to raise the thighs here (I'll explain why in a moment).

Notice that as we create the force (our mass plus the change in velocity of the leg in a given direction parallel to the leg and downwards both out and down simultaneously), that there is a return force coming back into our leg, equal and opposite to the force which is pushing down. This is a direct experience of both contact force (leg coming into contact with floor) and also normal force (the floor prevents the leg from going into it and gives rise to a contact force). This direct experience leads to the experience of Newton's third law, in which we feel the equal force pushing back into our leg as that which is generated by the leg downwards into the floor. How high up can we carry this feeling? It will depend on if we can keep the force of the legs in the downward and outward direction constant and how strongly we can do it.

In yogic terminology, there are two things that have to be observed here. According to Patanjali, in the Yoga Sutras 2.46, we have "sthiram sukham asanam" or "the asana has both firm components and components which are at ease". Do we understand the difference?  The firm or sthiram component is the engagement of the shin which pushes the foot downwards and outwards.  

The firm or sthiram component sets up the contact force

We may be tempted to engage all of the muscles of the legs which include the quadriceps of the thighs and more. Our hips may want to engage. We may think that the more muscle we engage the better. However, every muscle above the knee that comes into the picture is actually going to interfere with the ease or sukham component of the asana.  

In other words, we have to relax everything above the knee, including the hips, in order to actually feel the contact force coming up through the bones. This is sukham or ease, which allows us to receive the contact force.

You may notice that at some point along the "return journey" of the contact force through your bones that there is a jamming feeling. This is where we actually are resisting the contact force. Good for muscle building as this sets up a standing wave of felt energy in the leg, but bad for the deeper feeling of connection that we want to establish in terms of connecting the feeling all the way through the body. 

One of the most difficult parts of the body to get the contact force through is the hips. If we consider the legs as beginning with the coxal bones of the hip rather than at the femur head (or another way of thinking is that the legs start at the navel), we have the capacity to relax the upper sections of the leg and hip much more greatly. Another way of thinking about it is that the navel is sending an intention out to the shin and foot. Information comes back through the leg to the navel. Out from the navel, and back from the earth to the navel. It is really just our shin that is working on the physical level, but the feeling is that the whole leg is being pushed out from the navel. The more we push out from the navel, the more that we feel coming back through the bones of the leg to the navel, as long as we can relax everything above the knee. 

What then? The twin vectors of force (force with magnitude and direction) which are returning from the floor from both legs (which are working in opposition to each other) add up to drive the contact force directly up the legs and into the spine. From here, we relax the periphery of the spine, including the ribs, the obliques, abdominals, organs and everything around the spine, to allow the spine itself to feel the fullness of the contact force surging through the central column. We keep pushing into the feet until we feel that contact force rise to the crown.  

It may seem a little bit strange at first, but we can also wire the hands and arms to this contact force by connecting to it at one of the lower centers. The texts usually recommend the navel center but it can also be done lower down. If we consider the arms as starting at the navel rather than the shoulder, we attempt to "separate" the arms and the spine at the navel. We then distribute the felt contact force upwards into three sections, the spine and the two arms. It will then feel almost as if the arms are "floating" on the contact force as they lift, with very little muscular effort. This can be done with the arms at either the sides or in the upward direction. It can be done until the feeling of the contact force drives right into the fingers. 

All of this work is driven by the legs. My teacher used to say, "the legs generate the power, the arms manifest it". If you understand the contact force, this will make sense. 

This way of working can be applied to literally all of the standing postures. This way of working has released deep seated injury and emotional blockages for me and given rise to a much deeper understanding of connectivity throughout the body. I had to unlearn many years of "raising the thighs", squeezing the pelvic floor, and many other unnecessary and actually obstructive muscular actions. 

Ok, so fine for the standing postures, what about the rest of the postures? The important point to remember with this work is to set up the contact points with the floor. In other words, we have to know, what (muscularly) is driving something into the floor and what is getting out of the way in order to receive the return contact force upwards? 

Lets take downward facing dog pose (adho mukha svanasana). Come into down dog. Relax the hands and feet and step the feet close enough in that the heels contact the floor (this may be difficult for first timers so if so ignore this one for now, I don't really consider this a beginner pose). Don't worry about hip tilt or anything like that. Begin to push the hands at the base of the wrist down and forward while simultaneously pushing the shins and feet down and backwards. Two different contact forces are established here, one in the arm and the other in the leg. Is it possible to relax the upper torso and arms and also the thighs to allow the contact force to rise through to the hip and navel? Can we equalize the twin contact forces so that there is a feeling of connection of the twin forces joining at the center? It will feel like the building of a bridge. Separate the spine from the arms at the navel so the feeling is that the arms and legs are what is building the contact force bridge. Then, utilize the feeling coming back up the leg and separate it into the spine and extend the crown from that feeling, separate from the arms. If you do the posture in this way it will feel almost effortless and simultaneously very energizing.

Lets look at some more poses.
Take dhanurasana or bow pose. We lie on the belly. We lift the legs behind us and grab the ankles. By pulling the hands against the ankles we are pulling the arms and legs apart. But the hold of the hand resists that pulling apart so there is a force which is driven down through the arms and legs directly into the navel spine which is in contact with the floor. From this downward contact point, we set up a contact force which then travels back upwards into the body. The key here is to separate the arms and spine at the navel. The spine can then carry the contact force in the upward direction. It helps if we can relax the "horizontal muscles" of the gluts (butt muscles) and the rhomboids (muscles between shoulder blades and spine) as these muscles actually inhibit spinal extension (backward bending). To do this, inwardly rotate the arms and legs just a little bit. The spine is then freed to rise upward on the feeling of the contact force, assisted by the erector spinae (spinal muscles). There are other factors as well, such as the turning up of the eyes (which engages the suboccipitals, which further drive the spinal extension deeper). 

The seated posture. Try sitting up straight with legs crossed and knees lifted and shins crossed in front of you. Wrap the arms around the outer legs and hold one wrist or clasp the fingers. Pull with the arms the legs in as you simultaneously push and resist the legs out against the arms. This sets up a force which drives the sit bones down into the floor, setting up a contact force which then surges back up through the spine. The more we drive the sit bones into the floor, the more the spine can receive the contact force in the upward direction, given we can relax enough of the peripheral muscles around the spine to allow it to receive the feeling that derives from that force. Then the trick is to slowly let go of the legs with the arms and allow the action of the sit bones and spine start to take over on their own. In other words, can the sit bones and spine become like an isolated system? Can we get the sit bones to drop without the peripheral muscles? Can we relax enough in our peripheral body to allow the central column to rise on its own? It is very important not to sit on cushions or height here, but rather to allow the spine to learn to support itself.

Inversions are also engaged in this way. Many systems of yoga teach utilizing the shoulders for sarvangasana. Lifting the c7 vertebrae of the neck while driving the shoulders down, especially on height actually does not create a contact force established by the spine but rather by the arms. And it weakens the spine. More powerful is to drive the cervical spine into the floor, setting up a contact force in the spine, relaxing the arm lines in the manner of niralambha sarvangasana (without arm support) to allow the spine to bear the full weight and allow the normal force to rise through the central column and carry it up through to the legs. In the beginning this will look more like "banana pose" but over time, it will really get through. It takes time and a lot of concentration and perseverance but the end pose will be vastly different than the "ram rod straight" pushing that many have been taught.   

There is so much more to say. 

Working with the physics of contact and normal forces are a very powerful way to enter what Patanjali calls the "instrumental body". This is the body of feeling. Forces are felt. The body of feeling is connected to what the ancients called prana. Prana is felt. Physical forces are felt. Deep in the bone. This is very direct work. If you follow the feeling of this work and learn to get out of the way of the contact forces, a deep sense of connection will arise throughout the body and a deeper learning will take place.  

Have fun with it and let me know what you discover.