Here are the basics:
The center of gravity (of the occupant + the chair) will be directly over where the rocker arc touches the floor when at rest. The distance from the floor to this center of gravity has to be shorter than the radius of the rocker arc. The closer these two values are together the farther the rocker will roll. The farther it rocks the longer the rocking period will be. Ideally you want to use a rocker radius that creates a rocking period equal to the occupant's at-rest breathing rate. You don't want the seat plane of the chair rocking forward past horizontal.
Rocking 5 degrees forward and back |
When M is less than R, or your center of mass is lower than the center of the rocker arc, the chair will return to center when rocked forward or back because the C.O.G. has been lifted up and gravity will pull it back down. In the diagram above the C.O.G lifts .0575" with 5 degrees of rocking forward or backwards.
Centered Position |
Having your feet flat on the floor will impede rocking motion. Ideally the occupant's feet should cycle from touching toes to touching down the heel as the chair rocks. This suggests the height of the front edge of the seat should be 16" to 18" or so. Less if the intended occupant is of small stature.
This all works because shifting weight moves the occupant forward or back from being centered. Since the center of gravity is straight down from the center of the rocker arc, moving forward or back lifts the occupant uphill. The incline gets steeper the farther one rolls. Shift your position on the rocker and you will "roll" to another centered position. Relax back to your rest position and the rocker slows to a stop.
Comments and questions are encouraged and welcome!