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M = Center of (the occupant's) mass above the floor plane.

R = Radius of the rocker arc.

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. The center position is when M is directly below the center point of the rocker arc.

From a side view, M is normally located at a Human's belly button when he/she is in a sitting position. For women it may be slightly forward of the belly button. A value for M can be found by positioning the human above the floor in a comfortable at-rest sitting position. Measure from the belly button to the floor to find M.

R > M, and a good dimension for R is 39" or so. Increasing R reduces the period of a rocking cycle. Reducing R increases the period of a rocking cycle. By changing R slightly the rocking period can be "tuned" to match the breathing rate of the occupant. The simple act of breathing, then, will shift the occupant's mass, causing the chair to rock back with each inhale and forward on exhale.

Feet on the floor will impede rocking motion. Ideally the occupant's feet will cycle from touching at toes to touching down the heel as the chair rocks.

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Q: What is the physics theory about rocking chairs?
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