Bowling ball

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Comparative sizes of bowling balls, portrayed on boards of a bowling alley.

A bowling ball is a hard, spherical ball used to hit bowling pins in the sport of bowling.

Balls used in ten-pin bowling typically have holes for two fingers and the thumb. The United States Bowling Congress (USBC) regulates bowling balls in the U.S. and maintains a list of bowling balls approved for competitive play.[1]

Balls used in five-pin bowling, candlepin bowling, and duckpin bowling are smaller, lighter, and without holes, and may be held in the palm of the hand.

Ten-pin balls[edit]

Two reactive resin bowling balls. Both are the same model, but one is pearlized (right) and one is not (left).

Specifications[edit]

The USBC and FIQ specifies that bowling balls may only be made from uniform, solid materials with a density less than or equal to 3.80 g/mL. The weight of the ball must not exceed 16.00 pounds (7.26 kg), with no lower bound for weight. The hardness of the ball must be at least 72, as measured by a Type D Shore durometer at room temperature (68-78 degrees Fahrenheit). A ball may have a circumference between 26.704 inches (67.83 cm) and 27.002 inches (68.59 cm), and a diameter in the range of 8.500 inches (21.59 cm) to 8.595 inches (21.83 cm).[2]

The surface of the ball is required to include markings to indicate the manufacturer's brand name, the name of the ball, the center of gravity (before drilling), the orientation of the core (the Pin), and the axes of the high and/or low radius of gyration (as applicable). Additionally, markings must include an individual serial number and the logo of the USBC.[2]

Holes are allowed to be drilled into a bowling ball for a variety of reasons, and bowlers must be able to demonstrate that such holes can be used as claimed. Up to five holes may be drilled for the bowler's fingers for one hand, and each finger hole may have a small additional hole that intersects for ventilation. A "balance hole" may be added to alter the mass distribution. The USBC recently changed their rules that affect no-thumb bowlers more than those using a conventional grip. Now any hole not used explicitly for gripping during the approach is to be considered a balance hole and only one balance hole is allowed. This means that no-thumb bowlers would have to take out their thumb hole or their balance hole if they have both. This is because it may give them the advantage of special weighting, which can help give the ball a higher spin rate.[3] A "mill hole" may also be used for inspection purposes.

Bowling balls are required to be balanced such that after drilling the difference in weight between the left and the right side (around a line bisecting the fingers and thumb) does not exceed 1 oz and the difference between the top and bottom of the ball does not exceed 3 oz. There are special scales designed to weigh/compare different halves of the ball.

The radius of gyration must fall between 2.460 inches (6.25 cm) and 2.800 inches (7.11 cm), and the differential radius of gyration must not exceed 0.060 inches (0.15 cm). The coefficient of friction must not exceed 0.320.[2]

Materials[edit]

Historically, bowling balls were often made from dense hardwoods such as Lignum Vitae, but starting in the early 20th century, hard rubber became the primary material for bowling balls. The first bowling balls to be made from polyester ("plastic") were produced in the late 1950s. This became the predominant material in the 1970s. In the early 1980s, polyurethane ("urethane") bowling balls were introduced. Urethane balls provided greater friction on the lane, which allowed for a greater angle of entry of the ball to the "pocket" (space between two of the front-most bowling pins, known for providing the greatest percentage of strikes), and as a better match to the increasing use of polyurethane varnish on wood lanes (replacing older lacquer varnishes), and with wood lane "overlays" and fully synthetic lanes using a polyurethane surface. This is desirable, as a greater entry angle tends to provide a higher striking percentage.[4][5][6]

In the early 1990s, a new material known as "reactive resin" was introduced. Reactive resin is still made from polyurethane, but has been treated with additives while in a liquid state that create pores in the coverstock that allow it to absorb oil. As oil is absorbed into the ball rather than sitting on the surface, there is greater friction between the ball and the lane.[4][5]

In the late 1990s, "particle" balls were introduced. By distributing small particles into the reactive polyurethane cover, manufacturers are able to create even higher friction. This is particularly noticeable on oily surfaces, where a particle ball is able to create considerably more friction than balls of other materials. The types of particles and their properties may vary between balls and manufacturers.[4][5]

Particle and reactive resin balls are common in modern play, particularly on lanes with relatively higher volumes and/or lengths of oil.[4][5]

Plastic balls are also commonly thrown when a bowler wants a ball that will move in a very straight line, particularly while trying to make spares. Urethane balls are less common, but may still be used for strike shots on less oily lanes.[4][5] Urethane balls have also made a comeback with some two-handed professional bowlers like Jesper Svensson and Kyle Troup, who often find reactive balls difficult to control given the high revolution rates they put on their shots.[7]

House balls lying on ball return.

Grips and finger holes[edit]

The way the finger holes are arranged on the ball surface changes how the bowling ball moves down the lane.[8] The drilling configuration is determined by the positions of the finger holes relative to the markings on the surface of the ball, and may also be positioned relative to the axis of rotation of a particular bowler. The axis is typically identified according to the Positive Axis Point (PAP), which marks the axis before axis migration has begun.[9]

In the United States, most bowlers only use holes intended for the middle and ring fingers of the dominant hand, as well as the thumb of the same hand. A "conventional" grip is one in which the bowler inserts the thumb fully, and the fingers up to the second knuckle from the tip. A "fingertip" grip is one in which the bowler inserts his fingers only to the first knuckle from the tip. Some variety of fingertip grip is favored among professionals and most amateurs, as this configuration allows most bowlers to impart greater rotational velocity on the ball. Some bowlers, notably Mike Fagan[10] and Robert Smith,[11] use the "Sarge Easter Grip," in which the middle finger is drilled to fingertip standards to the first knuckle, while the ring finger is drilled to conventional standards to the second knuckle.

Though fingertip grips traditionally include having the thumb fully inserted, some bowlers, notably Jason Belmonte[12] and Osku Palermaa,[13] hold the ball with two hands and do not insert the thumb. This style came into prominence in the 2000s.

It is common for bowlers, particularly those with fingertip style drillings, to place inserts into the holes rather than grip the holes directly. This can be done to vary the texture and shape of each hole to match a bowler's preferences.

Composition[edit]

The first bowling balls used in Hunan, China were made of wood. In about 1906 the first hard rubber balls were produced, such as the Brunswick "Mineralite" ball, and these remained the standard until the 1960s and 70s. These decades saw the emergence of plastic (polyester) balls.

In the early 1970s, they began experimenting with the hardness of the plastic balls. The reason for this is to allow the ball to "grab" the lane better. Plastic balls were difficult to hook on tough oil conditions. Until the 1970s, there were no rules regarding the hardness of the bowling ball's surface. PBA member Don McCune took advantage of the non-existence of such a rule. At the time, he worked for Chuck Hamilton, who invented the "soaker"—a plastic (usually polyester) ball he softened "in the garage" with chemical solvents such as MEK, which excrete a sticky substance, allowing the ball to hook more on oily conditions. At times, the balls were soaked to the point that the balls might even end up lopsided. Columbia—a more established manufacturer of bowling balls—came out with a series of "yellow dot" balls that were similar in function to the "soaker". The hardness of the ball's surface came under ABC scrutiny because of the increased scoring, particularly by McCune, who with his "soaker" won six PBA tournaments in 1973 and PBA Player of the Year honors. The ABC established a durometer hardness rule of 72, which barred even some of the out-of-the-factory softer balls. The PBA took the issue even further by applying a more strict 75 hardness rule. To effectively test the hardness, the PBA required each ball to bear a 0.25-inch deep hole, just above the finger holes. The durometer was inserted into the hole, allowing the meter to perform the test beneath the ball's surface.

Sanding of the bowling ball surface was another technique to soften the ball's surface. Once the track area was located on the ball, the bowler sanded it to make the surface more abrasive, allowing the ball to hook more. Bowlers also applied solvents to the surface during tournament play—rubbing the chemicals into the cover using a rag. More rules by the ABC had to be passed, including restrictions from doctoring the bowling ball's surface at any time once the ball has passed inspection by an official.

At some point in ball making and drilling, the ABC introduced ball balance regulations to prevent people from taking advantage of certain forms of "weighting". It was possible to drill the grip at a location relative to the weight block to achieve some effect, such as to help the bowler make it roll earlier or hook more. Guide holes were also used to stabilize the roll of the ball, by drilling the guide hole in perpendicular to the track area of the ball. This allowed the ball to avoid over-hooking or roll-out before hitting the pocket.

In 1981 Ebonite began manufacturing the very first urethane cover stock bowling balls and sold the rights to AMF. Ebonite produced AMF balls at that time. Ebonite did not believe that bowlers would pay the $80.00 price this new technology demanded. That ball became the AMF Angle and this one coverstock change allowed the ball to get a better grip on the urethane finishes used on natural wood lane surfaces, which changed the nature of the bowling game significantly. Then in 1991, Nu-Line Industries produced the X-Calibur, a reactive resin cover. Part-time professional Steve Cooper was the owner and president of the corporation. But production lagged in the early days, allowing firms like Storm, Brunswick and Columbia to enter the reactive market by the following summer. The race to create more and more dynamic balls was on.

Prior to about 1990, the ABC "static" ball balance regulations were adequate. The core was usually a uniform sphere centred inside the ball. Then competition among ball manufacturers motivated the production of balls designed to offer more than the "static balance" tricks. Materials and fabrication changes have since allowed the assembly of balls whose interior components have a much greater range of density, thereby offering a new ball choice that, in physics terms, involves the moment of inertia of a solid sphere. Eventually, "dynamic balance" regulations had to be adopted.

Ball motion[edit]

The ball initially skids after first contact with the oily part of the lane, but enters a roll phase as full traction is eventually obtained in the dry portion of the lane. Side rotation and hook are not illustrated.
Diagram (top view) shows progression of various quantities as the ball moves down the lane:
  • ball speed and direction (size and direction of brown arrows),
  • rev rate (size of blue arrows),
  • axis rotation (direction of blue arrows)
  • graph: convergence of the ball's forward (translational) speed and rev rate (rotational speed).

Ball motion is commonly broken down into sequential skid, hook, and roll phases.[14] As the ball travels down the lane in the skid and hook phases, frictional contact with the lane causes the ball's forward (translational) speed to continually decrease, but to continually increase its rev rate (rotational speed).[15] Especially as the ball encounters greater friction in the last ~20 feet (approximate) of the lane, the ball's axis rotation (side rotation) causes the ball to hook away from its original direction.[15] Concurrently, lane friction continually decreases the angle of axis rotation until it exactly matches the direction of the ball's forward motion, and rev rate (rotational speed) increases until it exactly matches the ball's forward speed: full traction is achieved and the ball enters the roll phase in which forward speed continues to decrease.[15]

Release ratio denotes the ratio of the ball's forward (translational) speed to its rev rate (rotational speed) at time of release.[16] This ratio continually decreases throughout the ball's travel until it reaches exactly 1.0 when full traction is achieved upon entering the roll phase.[16] The distance for the ball to enter the roll phase varies with release ratio: a too-high release ratio causes the ball to reach the pins before entering the roll phase, and a too-low release ratio causes the ball to enter the roll phase before reaching the pins—both scenarios sacrificing power delivered to the pins.[16] Ball speed and rev rate are said to be matched if the ball enters the roll phase immediately before impacting the pins, maximizing power imparted to the pins and minimizing ball deflection.[16]

Effect of delivery characteristics on ball motion[edit]

Axis rotation (top view) Blue arrows: direction of rotation. Brown arrows: ball's direction. Pink arrows: fingers' motion, inducing axis rotation.
Axis tilt (view from behind). Black rings show the smaller tracks characteristic of greater degrees of axis tilt.
Bowling ball motion is affected by various characteristics of delivery, as discussed by, for example, Freeman & Hatfield (2018).[17] Ball motion is determined by a complex interaction of a variety of factors.

Various characteristics of ball delivery affect a ball's motion throughout its skid, hook and roll phases.[17] The following discussion considers delivery characteristics separately, with the understanding that ball motion is determined by a complex interaction of a variety of factors.

Greater ball speeds give the ball less time to hook, thus reducing observed hook though imparting more kinetic energy to the pins; conversely, slower speeds allow more time for greater hook though reducing kinetic energy.[17]

Greater rev rates cause the ball to experience more frictional lane contact per revolution and thus (assuming non-zero axis rotation) greater and earlier hook (less "length"— which is the distance from the foul line to the breakpoint at which hooking begins); conversely, smaller rev rates cause less frictional engagement and allow the ball to hook less and later (more "length").[17]

Analysis of the influence of axis rotation (sometimes called side rotation) is more complex: There is a degree of axis rotation—generally 25° to 35° and varying with ball speed and rev rate—that may be considered optimal in that hook is maximized; however, this optimum axis rotation also causes minimal length.[17] Specifically, Freeman & Hatfield (2018) report optimal axis rotation to be arcsin (ωr/v) where ω is rev rate (radians/sec), r is ball radius (m), and v is ball speed (m/s).[17] Below and above optimal axis rotation, more length and less hook are encountered, with greater-than-optimal axis rotation causing a sharper hook.[17]

Greater degrees of initial (at-the-foul-line) axis tilt cause the ball to rotate on smaller-circumference "tracks" (rings on the ball at which it contacts the lane on each revolution), thus reducing the amount of frictional contact to provide greater length and less hook; conversely, smaller degrees of axis tilt involve larger-circumference tracks with more frictional contact per revolution, thus providing less length and more hook.[17]

Loft—the distance past the foul line at which the ball first contacts the lane—determines the effective length of the lane as experienced by the ball: greater loft distances effectively shorten the lane and provide greater length, while smaller loft distances engage the lane earlier and cause an earlier hook.[17]

Effect of coverstock and core on ball motion[edit]

Bowling ball motion is affected by ball design, as discussed by, for example, Freeman & Hatfield (2018).[15][18] See also the USBC ball motion study by Stremmel, Ridenour & Stervenz (published circa 2008).[19]

Various characteristics of ball core structure and coverstock composition affect a ball's motion throughout its skid, hook and roll phases.[14] Such motion is largely governed by the lane's frictional interaction with the ball, which exhibits both chemical friction characteristics and physical friction characteristics.[15] Also, the ball's internal structure—especially the density, shape and orientation of its core (also called "weight block")—substantially affect ball motion.[15]

A "dull" (rough) ball surface, having spikes and pores,[20] provides greater friction in the oil-covered front end of the lane but reduced frictional contact in the dry back end of the lane, and thus enables an earlier hook.[15] In contrast, a "gloss" (smooth) ball surface tends to glide atop oil on the front end but establishes greater frictional contact in the dry back end, thus promoting a sharper hook downlane.[15] Accordingly, because different lane conditions and bowler styles favor different hook profiles, there is no single "best" surface.[15]

According to Freeman and Hatfield (2018), in most circumstances it is chemical friction—controlled by the manufacturer's proprietary coverstock formulation governing the its "stickiness"—that primarily determines ball motion.[15] A ball's radius of gyration ("RG") characteristics, as determined by the core's shape and orientation, are also significant.[15] Further, surface finish—modifiable by sandpaper, polish and the like—is also a material factor.[15] A USBC ball motion study circa 2005-2008 determined that, in addition to surface roughness, a ball's oil absorption rate was a top contributor to ball motion, even more so than RG characteristics.[21]

Though manufacturer literature often specifies track flare—exhibited by successive tracks of oil in a "bowtie" pattern and caused by RG differential—the USBC ball motion study showed flare's influence to be small,[22] assuming that a minimal threshold of flare exists to present a "dry" surface for successive ball revolutions.[18] Similarly, though manufacturer literature often describes specific core shapes, differently-shaped cores can make exactly the same contribution to ball motion if they have the same overall RG characteristics.[18]

Commonly cited specifications, RG (radius of gyration) and Differential of RG (indicative of flare potential), plotted on orthogonal axes.[23] Freeman & Hatfield (2018) minimize the contribution of differential to ball motion.[18]
Bowling ball cores, sometimes called "weight blocks", are described by various technical specifications such as RG, differential of RG, intermediate differential, and symmetry/asymmetry.[24] This diagram illustrates general concepts, not actual cores.

Manufacturers commonly cite specifications relating to a bowling ball's core, include radius of gyration (RG), differential of RG (commonly abbreviated differential), and intermediate differential (also called mass bias).[23]

Analytically, the United States Bowling Congress defines RG as "the distance from the axis of rotation at which the total mass of a body might be concentrated without changing its moment of inertia".[25] In practice, a higher RG indicates that a ball's mass is distributed more toward its cover—making it "cover heavy"—which tends to make the ball enter the roll phase later (further down the lane).[23] Conversely, a lower RG indicates the ball's mass is distributed more towards its center—making it "center heavy"—which tends to make it enter the roll phase sooner.[23]

Differential of RG is the difference between maximum and minimum RGs measured with respect to different axes.[23] Differential indicates the ball's track flare potential, and contributes to how sharply a ball can hook.[23] A higher differential indicates greater track flare potential—more angular motion from the break point to the pocket—and a lower differential indicates lower flare potential and a smoother arc to the hook.[23]

The lesser-used intermediate differential rating (sometimes termed mass bias rating) quantifies the degree to which a bowling ball core is symmetrical or asymmetrical.[23] Analytically, ID is defined by the USBC as the "difference in radius of gyration between the Y (high RG) and Z (intermediate RG) axes".[25] In practice, a higher ID indicates greater asymmetry, which causes more area to be created at the break point to cause the ball to respond more quickly to friction than symmetrical balls.[23]

Informally, a low-differential ball has been likened to one whose core is a spherical object (whose height and width are the same); a high-differential ball has been likened to a tall drinking glass (whose height and width are different); and a high-mass-bias ball has been likened to a tall drinking mug with a handle on the side (which has different widths in different directions).[24]

Higher-friction surfaces (lower grit numbers) cause balls to hook earlier, and lower-friction surfaces (higher grit numbers) cause balls to skid longer before reacting (hooking).[26]

Reactive cover stocks finishes include matte (aggressive reaction), shiny (longer skid distance than matte finish), pearl (greatest skid distance among reactive cover stocks), and hybrid (combination of skid distance and back end reaction).[26]

Effect of lane characteristics on ball motion[edit]

The phenomenon of lane transition occurs when balls absorb oil from the lane as they pass, a process which, over time, creates paths of relatively dry lane surface.[27] As balls subsequently encounter the dry paths, they experience increased friction and hook more strongly than they would otherwise.[27] Conversely, carry down occurs when balls deposit oil onto areas that had been dry, which subsequently causes balls to experience less friction and reduced hook.[27] Lane transition and carry down are influenced by the oil absorption characteristics and rev rates of the balls that were previously rolled.[27]

Lane materials with softer surfaces such as wood engage the ball with more friction and thus provide more hook potential, while harder surfaces like synthetic compositions provide less friction and thus provide less hook potential.[27]

The lanes' physical topography—hills and valleys that diverge from an ideal planar surface—can substantially and unpredictably affect ball motion, even if the lane is within permissible tolerances.[27]

Higher-viscosity lane oils (those with thicker consistency) engage balls with more friction and thus cause slower speeds and shorter length but provide more hook potential and reduced lane transition; conversely, lane oils of lower viscosity (thinner consistency) are more slippery and thus support greater speeds and length but offer less hook potential and allow faster lane transition.[27] Various factors influence an oil's native viscosity, including temperature (with higher temperatures causing the oil to be thinner) and humidity (variations of which can cause crowning and cupping of the lane surface).[27]

Manufacturers[edit]

Duckpin bowling balls[edit]

Duckpin balls weigh 2–4 pounds (0.91–1.81 kilograms) each, with up to three balls delivered per round (or "frame") of bowling for one bowler. The duckpin ball has a maximum diameter of 5 inches (13 cm), slightly larger than a candlepin ball but, like a candlepin ball, contains no finger holes. Duckpins are correspondingly shorter and lighter than their ten-pin equivalents and it is more difficult to knock them all down with a single roll.

Five-pin bowling balls[edit]

Five-pin bowling balls have no finger holes and are between 4.75 to 5 inches (12.1 to 12.7 centimetres) in diameter. They weigh between 3.50 and 3.625 pounds (1.588 and 1.644 kilograms). The smaller size and lighter weight of the balls allows bowlers to hold the ball in the palm of their hand when bowling.

Candlepin bowling balls[edit]

The ball used in candlepins has a maximum weight of 2 lb 7 oz (1.1 kg), and has a maximum diameter of 4.5 in (11 cm), making it the smallest bowling ball of any North American bowling sport.[28] The nearly identical weight of the ball, when compared to that of just one candlepin, tends to cause rapidly delivered balls to sometimes bounce at random when impacting a full rack of pins on the first delivery of a frame, and sometimes when hitting downed "dead wood" pins on subsequent deliveries—the candlepin bowling sport is the only major one that allows fallen pins, provided no part of any fallen pin extends more than 24 inches (61 cm) forward of the head-pin spot, to remain on the lane's pindeck to be used in knocking down more pins with the next ball delivery in the same round—up to three balls are delivered, much as in duckpins, in each round of candlepins for one bowler.

Publications[edit]

  • Benner, Donald; Mours, Nicole; Ridenour, Paul; USBC, Equipment Specifications and Certifications Division (2009). "Pin Carry Study: Bowl Expo 2009" (Slide show presentation). bowl.com. Archived (PDF) from the original on December 7, 2010.
  • Freeman, James; Hatfield, Ron (July 15, 2018). Bowling Beyond the Basics: What's Really Happening on the Lanes, and What You Can Do about It. BowlSmart. ISBN 978-1 73 241000 8.
  • Stremmel, Neil; Ridenour, Paul; Stervenz, Scott (2008). "Identifying the Critical Factors That Contribute to Bowling Ball Motion on a Bowling Lane" (PDF). United States Bowling Congress. Archived (PDF) from the original on June 3, 2012. Study began in 2005. Publication date is estimated based on article content.
  • United State Bowling Congress (USBC) (February 2012). "USBC Equipment Specifications and Certifications Manual" (PDF). bowl.com. pp. 26–29. Archived from the original on December 28, 2018.
  • United States Bowling Congress (USBC) (February 2018). "Bowling Technology Study: An Examination and Discussion on Technology's Impact in the Sport of Bowling" (PDF). bowl.com. Archived (PDF) from the original on December 31, 2018.
  • United State Bowling Congress (USBC) (2018). "2018-2019 Playing Rules and Commonly Asked Questions" (PDF). bowl.com. Archived from the original on December 27, 2018.

References[edit]

  1. ^ "BOWL.com - Home". Retrieved 25 October 2014.
  2. ^ a b c "Archived copy" (PDF). Archived from the original (PDF) on 2012-10-16. Retrieved 2013-07-25.
  3. ^ "BOWL.com - USBC modifies rule on bowling ball gripping holes". Retrieved 25 October 2014.
  4. ^ a b c d e "Bowling Ball Evolution". bowlingball.com. Retrieved 25 October 2014.
  5. ^ a b c d e "Understanding the relationship between core and cover stock By Nick Siefers, USBC Research Engineer". Retrieved 25 October 2014.
  6. ^ http://www.bowl.com/uploadedFiles/Equipment_Specs/Information/pinCarryStudy(1).pdf
  7. ^ "PBA Profile, Jesper Svensson". PBA.com. Retrieved August 24, 2016.
  8. ^ Ball Dynamics and Hook Potential at bowlingball.com
  9. ^ "Your Bowling Ball Positive Axis Point". bowlingball.com. Retrieved 25 October 2014.
  10. ^ Mike Fagan. "Fagan on Tour". Retrieved 25 October 2014.
  11. ^ "PBA TECH TALK - Robert Smith". Archived from the original on 25 October 2014. Retrieved 25 October 2014.
  12. ^ "Archived copy". Archived from the original on 2009-11-23. Retrieved 2013-07-25.
  13. ^ "Osku Palermaa". Retrieved 25 October 2014.
  14. ^ a b Stremmel, Ridenour & Stervenz 2008, p. 3.
  15. ^ a b c d e f g h i j k l Freeman & Hatfield 2018, Chapter 8 ("Why Does My Ball Hook?").
  16. ^ a b c d O'Keefe, Bryan (2015). "Bowling Release Ratio". USBC Bowling Academy. Archived from the original on April 2, 2016. (date is approximate)
    "Adjusting Entry Angle". USBC Bowling Academy. 2015. Archived from the original on April 17, 2017. (date is approximate)
  17. ^ a b c d e f g h i Freeman & Hatfield 2018, Chapter 13 ("Create a Bowler's Tool Kit").
  18. ^ a b c d Freeman & Hatfield 2018, Chapter 9 ("Track Flare, or Much Ado About Nothing?").
  19. ^ Stremmel, Ridenour & Stervenz 2008.
  20. ^ Stremmel, Ridenour & Stervenz 2008, p. 8.
  21. ^ Stremmel, Ridenour & Stervenz 2008, pp. 7, 9, 11.
  22. ^ Stremmel, Neil; Ridenour, Paul; Stervenz, Scott (2008). "Identifying the Critical Factors That Contribute to Bowling Ball Motion on a Bowling Lane" (PDF). United States Bowling Congress. Archived (PDF) from the original on June 3, 2012.
  23. ^ a b c d e f g h i "Bowling Ball RG And Differential Range Ratings". BowlingBall.com (Bowlversity educational section). 2014. Archived from the original on December 26, 2014. Retrieved 25 September 2018.
  24. ^ a b "Ball Dynamics and Hook Potential". BowlingBall.com (Bowlversity educational section). 2005. Archived from the original on November 24, 2005. Retrieved 25 September 2018.
  25. ^ a b "Technical Terms" (PDF). bowl.com. United States Bowling Congress. Archived (PDF) from the original on September 20, 2018. Retrieved 25 September 2018.
  26. ^ a b "Understand Your Bowling Ball Reaction". BowlingBall.com (Bowlversity educational section). May 22, 2016. Archived from the original on December 2, 2018.
  27. ^ a b c d e f g h Freeman & Hatfield 2018, Chapter 14 ("Applying Your Tools").
  28. ^ New Hampshire Candlepin Bowling Association. "Candlepin Bowling Rules". Archived from the original on 26 January 2016. Retrieved 22 January 2016.

External links[edit]