David Skaggs wrote:
When taking a step forward is the step an extension in the direction that the sway (chaotic figure eight) is already moving?
In other words there already is momentum in the direction of the step.
Yes. That is why walking the way we do is so efficient. By overdriving the balance sway slightly, which is almost free,we fall into our next step.
But this goes to your question about the possible vertical dimensions of the pattern in quiet stance, some analogs of which are probably seen in typical gross motion. And there is a gross difference in motion between in two important forms of that movement for aikido 1) walking 2) the sliding irimi step.
In walking the premium is on energy conservation. In irimi the premium is on stability conservation.
A gait is a regime that optimizes a certain performance feature of motion. Running optimizes maximum applied accleration (to obtain maximal dynamic inertia). Jogging optimizes for maximum total work (constant acceleration over distance). Walking optimizes conservation of total energy. and Irimi optimizes conservation of stability (obtaining greater static inertia -- the inverse of running) (Ah, stillness in motion).
In walking you loft the moving hip up and forward, this clears the foot from the ground and inputs an eccentric forward moment hat casue the leg to fall under gravity swinging freely forward. Once it passes center its momentum is stolen by the hips and that momenutm is used to carry the center over the swinging foot as it plants, with its hip still cocked up. The rocking momentum bringing the center over up over the planted foot is also used to create the forward eccentricity that gives the other leg potential forward swing and the lateral hip eccentricity to loft the other hip up and over to free the foot to swing, etc.
Walking requires mainly just the energy to lift and rock the leg forward with the hip slightly and keep the leg from collapsing under weight in a fall of about 1 cm. There really is no "push-off" in the most efficient form of gait -- although it can be added to accelerate the swing of the leg, this adds driving energy in the pendulum that is not necessary to the basic dynamic which is driven by gravity and manipulation of pivoting falls.
Irimi is a differnt gait, like walking, jogging and running are different gaits. Irimi is not not just a "driven" walking gait, as mentioned above.
Irimi is the inverse of walking, with emphasis on the horizontal rotaiton of the hips with the leg as a grounded pivot for horizontal swing , rather than the leg as rod pivoting vertically from the ground and hip, alternately. The advancing hip is in the direction of travel, like walking, but carrying the weight immediately onto the forward planted leg. This unloads the rear leg.
The moving leg is allowed to basically hang freely from the hip in a relaxed, non-rigid way. It is not free to rotate like a pendulum, i. e. - it is left propped loosely against the ground. The twist of that hip basically pulls it forward into the front position, and as the wieght shifts over that leg, it freeing the hips to rotate horizontally the other way, etc.
Irimi makes the unloaded hip hang lower than the loaded hip, (opposite to walking) making the gait a rotary horizontal hip-driven motion, rather than a hip-modulated vertical swing and fall under self-weight with the hip lofted in walking.
The stability benefit comes from the unloaded and dropped hip. Any upsetting moment in the body can be countered not only by the normal hip rotation and balance system with access to a freely swinging inertial moment arm. Extending the unloaded leg and hip outward creates magnified inertial dampening effect compared ot what both hips, rigidily connected to the ground, can do alone. The increased static inertial moment is positional -- relying on mass, orientation and radius, not timing or force. By dropping weight vertically 1 -2 cm over the weighted leg, the other leg now engages the ground firmly and thus becomes a brace as well.
The mechanics of irimi motion is more relaxed and fluid for stability efficiency. It is less rigid in its mechanics than walking, which relies on fairly straight-limb pendulum effects for energy efficiency.
In proper tai sabaki (especially in randori) I shift from one gait to the other, approaching an opponent by walking and then dropping into an irimi gait for contact, in the same manner as dropping gait from a a run to a jog, because the ground seems more diffcult going -- or from a jog to a walk, because I see something ahead that I need to navigate more carefully. Irimi is just the next step in that gait progression of care about positional stability.