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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

Ball properties

The ball is 8.59” in diameter and between 6 and 16 pounds, with most professionals using 14-16 pounds. The core shape and density are manipulated by the manufacturer to adjust the ball’s principle moments of inertia. All radii of gyration are required to be between 2.43 and 2.80” by the USBC, and to have the biggest difference between radii less than 0.080 in. Note that an 8.59” diameter uniform sphere would have radii all equal to 2.780”. Some balls have 2 distinct moments of inertia, and are referred to as symmetric by bowlers. Asymmetric balls have 3 distinct moments of inertia. Additionally, the mass center of the ball is not necessarily at the geometric center. The USBC requires that right and left halves of the ball be the same weight ± 1 ounce. The top/bottom and finger/thumb differences can be ± 3 ounces. The surface of the ball has a major role in creating the friction needed to make the ball hook. The cover can be made of various materials: rubber, polyester, urethane, resin, or resin doped with other particles. The later materials have come into the market in more recent decades and generally have more friction. The cover can be made rougher or smoother by sanding or polishing the surface, which can be done by the manufacturer or by the user.

Lane properties

Lanes have evolved over the decades from wood surfaces coated with lacquer to synthetic surfaces coated with oils. The oil is not uniformly applied across the lane. The depth of oil is varied transversely (from the middle of the lane to the gutters) and longitudinally (from the foul line to the pins). Usually the first 40 feet or so of the lane are oiled, and the remaining 20 feet are stripped dry.  Applying more oil in the middle of the lane and less oil near the gutters makes the game much easier. Missing toward the center of the lane will make the ball encounter more oil and hook less, possibly still hitting the headpin or pocket. Missing toward the gutter will make the ball encounter less oil and hook more, again hitting the headpin or pocket. This can make the game more flattering for the recreational bowler, but the Professional Bowler’s Association has adopted its own set of 5 oil patterns that are considerably more challenging.

Pin properties

The diameter of a bowling pin is specified at several different heights by the United States Bowling Congress (USBC):
Bowling pin dimensions
As specified in the USBC 2010 Equipment specifications and certification manual

Bowling terminology

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. 

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