Timescales, averaging, and baseball

Please pardon the summer blogging slowdown - it's been a surprisingly busy couple of weeks, between an instructor search, working on papers, proposal stuff, and trying to write more on my big long-term project. 

Thanks to an old friend for pointing me to this link, which does a great job looking at why a knuckleball is so erratic in its flight from pitcher to batter.  For non-Americans:  In baseball, a pitcher throws a ball to a catcher, while a batter attempts to hit the ball.  There are several types of pitches, depending on the pitcher's grip on the ball (which has seams due to the stitching that holds the leather cover on), the throwing motion, and the release.  A fastball can reach speeds in excess of 100 mph (161 kph) and typically spins more than 1000 rpm.  In contrast, a knuckleball can drift by the batter at a leisurely 70 mph yet be nearly unhittable because of its erratic motion.   A knuckleball barely spins, so that it may complete only 1-2 revolutions from leaving the pitcher's hand to reaching the batter.  This means that the positioning of the seams is absolutely critical to determing the aerodynamics of the motion, and no two knuckleballs move the same way.  In physics lingo, a knuckleball has almost none of the orientational averaging that happens in basically every other pitch.  I propose the definition of a new dimensionless parameter, the Wakefield number, \(W\), that is the ratio of the ball's period of revolution to its time-of-flight from pitcher to batter.   A knuckleball is a pitch with \(W \sim 1\).