The trajectory of the ball is a rather complicated interaction of the inertial and surface properties of the ball and the surface of the lane. The resulting pinfall involves many collisions and is highly dependent on the kinematics of the ball. In short the complexities of bowling dynamics are the following:
- Mass center oﬀset of ball
- Unequal principle moments of inertia of ball
- Principle axes of ball not aligned with lane
- Nonuniform distribution of oil on the lane
- Many collisions of many bodies
A lot of bowling jargon is used in this project. Definitions of commonly used terms are presented below.
Asymmetric refers to a ball with three distinct principal moments of inertia. A hanger pin and mass bias indicator on the surface of the ball indicate the orientation of the core inside.
Axis rotation \(\theta\) is the orientation of the initial angular velocity vector of the ball in a horizontal plane. \(\theta = 0^\circ\) corresponds to an angular velocity vector pointing to the left and \(\theta = 90^\circ\) points backward.
Axis tilt \(\beta\) is the angle between the angular velocity vector and a horizontal plane. \(\beta = 0^\circ\) indicates the angular velocity vector is somewhere in the horizontal plane and \(\beta = 90^\circ\) means the angular velocity is vertical (upward).
Core is the dense center of a bowling ball.
Differential is the difference between the minimum and maximum radii of gyration of a bowling ball.
Drill angle is the angle between the hanger pin and positive axis point. It is a common metric in describing how a ball is drilled.
Entry angle is the heading angle of the ball immediately before first pinstrike.
Flush refers to a shot that sends the 1-pin directly toward the 7-pin and the 3-pin directly toward the 10-pin. See also "light" and "high".
Full oil refers to a lane with oil applied along its entire length, in contrast to partial oil.
Hanger pin is the rod on which the ball is hung during manufacturing. It is cut to be flush with the surface of the ball and is typically a different color from the rest of the ball. It is often referred to simply as the "pin", not to be confused with the 10 pins at the end of the lane.
High refers to a shot that is left of flush, but still hits the right side of the 1-pin. See also "flush" and "light".
Hook is the ratio (as a percent) of leftward to forward travel of the ball from the foul line to first pinstrike.
Light is a shot that is right of flush, but still hits the 1-pin. See also "flush" and "high".
Mass bias indicator or simply mass bias, is a marking on the surface of an asymmetric ball identifying the location of the intermediate principal axis.
Partial oil refers to a lane with oil applied to only its first 40' or so (2/3 the length of the lane) with the remaining 20' stripped dry, in contrast to full oil.
Pocket is the area between the 1 and 3 pins (the middle pin and the one to its immediate right) that right-handed bowlers attempt to hit to get a strike. Left-handed bowlers aim between the 1 and 2 pins (the 2 pin is immediately left of the 1 pin).
Positive axis point (PAP) is the point on the ball's surface that an initial angular velocity vector starting at the ball's center would pierce. In other words, it is the point on the ball's surface about which the ball spins initially.
Slide is the distance the ball travels along the lane before rolling without slip ensues.
Strike is a shot that knocks down all 10 pins.
Symmetric is a ball with only two distinct principal moments of inertia. A hanger pin flush with the surface of the ball indicates the orientation of the core inside.