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Excerpt from Aikido Exercises for Teaching and Training

The Physics of Ukemi

by Dr. Wendy Gunther

"Falling down" is equivalent to being hit, slugged, punched, or shot at by the ground moving at the acceleration of gravity. Whether you are hit by ground or by bullet, the wounding energy is proportional to:

mass (m) multiplied by velocity (v) squared
divided by the time (t) it takes for the wounding surface to contact you,
and also divided by the area (a) of the wounding surface.

In symbols, this is expressed as:

Wounding energy = mv2 / ta

Hence wounding energy decreases if we can increase time and area.

Increasing Time. If I take a bullet and touch it slowly to your skin, you aren't wounded because the marked reduction in velocity means a marked increase in t. During falls, you slow down the contact by rolling into it or slapping the mat with your arm like a spring. Even fractions of seconds of increase in t significantly reduce wounding energy.

Increasing Area. Suppose I take the same bullet and hammer it into a huge flat sheet of lead and fire it at you (in a vacuum where there's no air friction) with the same velocity (v) as a bullet leaving the muzzle of a gun.

The bullet will wrap itself as a flattened surface over your skin (with an area of say 720 square inches). You are extremely unlikely to be wounded simply because of the increase in area (a). Wounding energy is extremely low.

In contrast, if the area through which the kinetic energy is being transferred is reduced to the size of your chin, say 2 square inches, wounding energy is high.

To recap, the larger the mass and the higher the velocity of the oncoming object, the more dangerous the situation.

The larger the area and time of contact, the safer the situation.

We usually can't change our mass or velocity, but we can increase time and the surface area of contact with the oncoming mass, mat, sidewalk, or planet.

The means of doing so are the skills of ukemi.