As an engineering exercise, I was recently asked to give my analysis of a forward roll. Before I begin, however, full disclosure: I am an electrical engineering (EE) student, and make no claim to have any kind of expertise in human anatomy, mechanical systems, or thermodynamics. However, as part of my education as an EE I have a basic understanding of these subjects. This particular problem is fairly straightforward, though.
Rigid Bodies, Exchanging Energy
At the outset, please note that the projectile (in this case, your body) is made to be rigid. Since your body shape does not change, (at least during the roll itself, unless something has gone terribly amiss), and further, since no mass is lost, you possess, according to mechanical theory, a rigid body. In fact, the rigidity of your body is augmented by your muscles and joint cartilage, which take the brunt of stress during a fall, thereby relieving at least some structural strain. In mechanical terms, your joints and muscles act as a spring, which are compressed by the impact of falling.
Knowing this, the first step is to define the issue. In our case, the issue is the interplay between a rigid body and an exchange of energy, or more plainly stated, a forward throw.
Sensei teaches that rolls are meant to be taken close to the ground, to minimize injury. The principle behind her instruction is sound: the less distance an object travels from its original position, the less potential energy the object contains. The less energy the object contains, the less severe the jolt your body will receive at the moment of impact. (This is a good thing). Since energy can neither be created nor destroyed, the energy escapes from your body into the ground, partly in the form of heat, but also as stress on your legs, since you lowered yourself to take the fall.
The question, however, naturally arises: Why roll at all? Why not, in fact, fall straight down, if all we’re talking about is transferring energy from one system to another? Consider figure 1:
Here, the rigid circular body drops straight down. When force is applied in only one direction, or vector, there is only one point of impact, at the bottom of the circle. Assume the circle represents uke. Assume further that the point of impact represents, say, uke’s shoulder. In the situation described, therefore, the entirety of force represented by the arrow acts upon uke’s shoulder, causing maximum shear stress at that point. This is not a good thing, and may in fact cause injury.
We roll to transfer energy forward, so that the energy we receive is not just transferred downward, into the mat. Consider figure 2:
Here, we add a force, in the forward direction. This forward force creates a moment arm, which causes the body to rotate.
This rotation causes you to roll, which again is a good thing, since the energy now has a path that doesn’t lead straight down. (Ouch!) Essentially, the energy is defused into the forward roll.
This is why we roll. We use our rotation to transfer energy from an unwanted result, as described in figure 1, to one which allows us to practice another day. Both scenarios expend the same amount of energy. The difference is that in the latter, the structural integrity of uke is not tested, potentially to a breaking point.
We have one more wrinkle to discuss: Returning to our feet. Remember, a rigid body requires the same amount of energy to fall as it does to return to its former position. (That pesky law of conservation again.) The entire process, therefore, is balanced. Ideally, we as Aikidoka should use that energy, rather than oppose it, to maintain our own balance, on and off the mat.
Before I wrap up, I want to address a misconception I sometimes hear about forward rolls. It is a fallacy to state that the forward and downward motions described in figure 2 negate each other. In reality, the energy transferred into the roll is still very much present. If the vertical force was in fact negated by the horizontal force, then even a perfect sphere, (or the world’s roundest Aikidoka), would not roll. Rather, the startled fellow would merely slide, on his shoulder in our example. And yes, this would be a bad thing, since the unlucky Aikidoka could not make use of that rolling motion to transfer his energy into a graceful upright stance, ready to train again.