The Dynamics of a Knuckle Ball
���The knuckle ball is probably the most interesting pitch in baseball.  It travels at only about 60 or 70 mph while a curve travels about 80 and a fastball approaching 95 mph.  So, a knuckle ball is much slower.  It is still an effective pitch, however, because it moves erratically.  To get this erratic movement, the pitcher grips the ball in such a way that when it is released, it travels through the air toward the batter with virtually no spin.  As previously discussed, it is the spin that makes curve balls drop and sliders curve.  But, for a knuckle ball, it is the absence of spin that makes the ball move.  As shown in the figure below, a knuckle ball has a drag force similar to the drag forces of other pitches as previously discussed.  However, because there is very little spin, an additional force is created.  Because there is a very small amount of spin, it is very susceptible to slight wind variations as it travels toward the plate.  Since the ball is not completely spherical (it has the protruding seams), as the ball slowly
Tim Wakefield (knuckle ball pitcher)
rotates, the movement of the seams causes the profile of the ball to continue to slightly change.  For this reason, the F(l) shown in the picture below changes as the ball slowly rotates.  This is how the ball 'flutters' or jumps around as it approaches the batter. 
    The maximum deflection of a slowly rotating ball, a knuckle ball, is given by the following formula:
where g is gravity, w is weight in pounds, and w is the rotation rate in radians per second.  It has been found through the use of this formula that an effective knuckle ball must experience between a quarter rotation and 2 full rotations on the way to home plate.
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