Describing Pitch Movement with Right-Hand Rules
A. Terry Bahill
Dave Baldwin
Systems and Industrial Engineering
http://www.sie.arizona.edu/sysengr/slides/rightHandRules.ppt
© 1998-2006, Bahill
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a major league baseball pitcher is asked to describe the flight of one of his pitches; he usually illustrates the trajectory using his pitching hand, much like a kid or a jet pilot demonstrating the yaw, pitch and roll of an airplane. The hand used as an analog in this way is a gestural example of a somatic metaphor. We develop a sense of space and of the potential of action from the feel of the body as it interacts with the environment. Like other kinds of analogies, the somatic metaphor helps a modeler form a conceptual system to deal with the external world.
The right-hand rules form a pair of gestural metaphors that has been widely used for centuries as mnemonic or heuristic devices in science, mathematics and engineering. Unlike the somatic metaphor used by the baseball pitcher to describe the trajectory of his pitch, these rules have been formalized to increase accuracy and repeatability. This pair comprises an angular right-hand rule and a coordinate right-hand rule. The angular rule describes angular relationships of entities relative to a given axis and the coordinate rule establishes a local coordinate system, often based on the axis derived from the angular rule.
The spin axis of a pitch can be found by using the angular right-hand rule. If you curl the fingers of your right hand in the direction of spin, your extended thumb will point in the positive direction of the spin axis.
The direction of the spin-induced deflection force can be described
using the coordinate right-hand rule. Point the thumb of your right hand in the
direction of the spin axis, and point your index finger in the direction of
forward motion of the pitch. Bend your middle finger so that it is
perpendicular to your index finger. Your middle finger will be pointing in the
direction of the spin-induced deflection. The spin-induced deflection force
will be in a direction represented by the cross product of the angular velocity
vector and the linear velocity vector of the ball: Angular velocity x Linear velocity = Spin-induced deflection
force. Or mnemonically, Spin axis x Direction = Spin induced
deflection (SaD Sid). This acronym only gives the direction of
deflection.
The right-hand rules show the direction of the spin-induced deflection of baseball pitches. Thus, they explain the movement of the fastball, curveball, slider and screwball. Our new model for the magnitude of the lateral spin-induced deflection of the ball considers the orientation of the axis of rotation of the ball relative to the direction in which the ball is moving. This paper also describes how models based on somatic metaphors might provide variability in a pitcher’s repertoire.
This lecture is suitable for engineers and the general public. It requires a computer projector, PowerPoint and a video player such as Windows Media Player. This talk takes about a half-hour.