Abstract
Tracing its historical roots from European monarchs to modern-day pool halls, pool is a common pastime across the globe. But behind the various versions are the same engineer designs and physical laws that rule the game. The essential equipment—tables, balls, cues, and chalk—all have been carefully engineered. Additionally, the physics behind collision, deflection, and rotation dynamics are crucial for mastering the game. With the appropriate physics, all can gain the knowledge to engineer the perfect pool shot.
Introduction
Throughout history, notable figures from William Shakespeare to Abraham Lincoln to Elvis Presley have wielded a cue stick in desire for mastery. From the halls of monarchs to the modern-day pool halls of bustling cities, the game of pool has become an ideal pastime across the globe. The allure of the game has even made its way into contemporary popular culture. Hollywood adopted the thrilling nature of the game into movies such as The Hustler and The Color of Money with stars like Tom Cruise. These cinematic portrayals have only added to the game’s allure, captivating audiences with struggles of skill, strategy, and competition. But beyond the Hollywood portrayals, pool is a sport filled with physics that, matched with dedication and skill, can lead to mastery.
In this article, you will learn the engineering behind the essential equipment of the game. As well as the physics behind collision, deflection, and rotation dynamics which are critical to engineering the perfect pool shot.
A Brief History
The origins of the game can be traced back to 15th century France where a variation of croquet was moved indoors. The word billiard, as it was first called, is believed to be derived from either the French word ‘billart’ meaning one of the wooden sticks or ‘billie’ meaning ball. In the beginning, billiards was played with wooden sticks called maces as the pool cue wouldn’t be invented until the late 1600’s. The original tables had flat borders with the only goal to keep the balls on the table. However, they would soon resemble river banks and the borders we see today, coining ricochets as ‘bank shots’. It wouldn’t be until the industrial revolution that pool equipment and dimensions would be developed that resemble the game today. Throughout the history of pool, variations in games, styles, and strategies have shaped the culture of the sport. [1]
The Essential Equipment
The first piece of equipment essential to all billiards games is the table itself. The size and structure of billiards tables are highly dependent on the desired game. However, another important aspect of pool table design and play is the felt on the table. The felt is the quintessential factor in the frictional force that impacts the way the ball rolls on the table. A greater coefficient of friction the slower the ball will roll, a smaller coefficient of friction the faster a ball will go. And with an even smaller coefficient of friction, the ball may not even roll when struck, but slide like a hockey puck. Felt, as compared to other surfaces (ice, concrete, etc), provides the ideal coefficient of friction for consistent ball rotation and spin. In fact, competition grade fabric is made of worsted cloth where all the weave fibers are created the same size to ensure a consistent surface. [2]
The next major equipment component of billiards is the balls themselves. For a large portion of the history of pool, the balls were made from ivory. A single elephant tusk could only produce 3 to 4 balls, thus making them extremely expensive and fragile. It was not until the turn of the century that the modern composition of pool balls was developed. In 1907, a chemist by the name of Leo Baekeand developed the material bakelite, a type of phenolic resin that modern pool balls are made of today. The resin is heated and poured into a mold, the size of a pool ball and cured under extremely high pressure, condensing into a solid ball as depicted in Figure 1. [3]
Figure 1: The Composition of a Billiard Ball
The next essential equipment piece of billiards are the sticks, referred to as cues. The first pool cues were not developed until the late 1600’s and were not completely mastered until the 1800’s. Today, the best pool cues are made of straight-grain hard rock maple wood but other woods such as red ivory, ebony, rosewood, and olive wood are also used. Materials such as aluminum, titanium, and acrylic have also been used for pool cues but are often chastised by the pool playing community. A signature component of a quality pool cue is the tip. The pool cue tip is where the energy from your pool cue is transferred to the cue ball. The cue tip is the surface that makes contact with the ball and thus very important for consistency. An essential aspect of all cue tips is the convex shape and the hardness of the cue surface. Variations in tip hardness can affect the performance of the pool cue. Soft cue tips will absorb more impact force and stay in contact with the cue ball for longer, allowing more spin generation. Hard cure tips will allow more energy transfer for more powerful contact but generate less spin and are more susceptible to miscue hits. Generally, medium hardness cue tips are used because they combine consistency with cue ball control. [4]
In order to ensure consistent striking and control with a pool cue an often used material is pool chalk. Pool chalk is not like ordinary classroom chalk but is made of a special formula of silica that has a gritty texture. Pool chalk first originated in the 1800’s and has slowly evolved into the form we see today. Pool chalk color has also changed over time, from white to green to eventually the blue we recognize today. This evolution was all about finding the perfect formula to reduce miscuses and enhance gameplay. Pool chalk works by adding a frictional surface to the pool cue tip that ensures a consistent contact surface with the pool ball. Without a properly chalked cue tip, a miscue hit can occur in which the tip does not hit the ball squarely. In a miscue hit the ball will go in an unintended direction, which is every player’s worst nightmare. Beyond eliminating miscue hits, pool chalk is also applied to allow desired spin on the cue ball. Applying spin on the ball is an essential skill for all pool players as it allows a greater variety of shot selection and planning. Applying spin is also governed by the physical laws of the universe and if mastered can be repeated. [5]
The Physics of the Game
Mastering the physical laws of the universe can bring you one step closer to engineering the perfect pool shot.
The first fundamental physics property of pool is collision dynamics. Collision dynamics is the description of two objects colliding into each other. There are two forms of collision: elastic and inelastic collisions. In elastic collisions, the two objects collide and bounce off each other carrying their collective momentum with them (ex two billiard balls colliding). Inelastic collisions describe collisions in which two objects collide and combine mass, either continuing velocity or stopping completely. Inelastic collisions are not typically an applicable concept to billiards. Nevertheless, applying these concepts to pool is fundamental for angle shots as seen in Figure 2.
Figure 2: Elastic Collision Between Two Balls
The angle shot depicted in Figure 2 shows a moving ball (gray) colliding with a stationary ball (red) and the resulting deflection angles. A and B represent the resulting deflection angles of the two balls which always add up to 90 degrees. Mastering this deflection angle with the appropriate cut or slice is essential to a perfect pool shot. In doing so one can ensure the target ball goes where desired, ideally a pocket. Another important aspect of elastic collisions is predicting the response angle (A) of your cue ball after the collision. This is an important aspect for planning your next shot and preventing a scratch, or a violation by making the cue ball in a pocket. A more in depth diagram of the response angle can be seen in Figure 3.
Figure 3: Inelastic Collisions over Various Cut Angles
In Figure 3, the deflection angle and response angle are depicted over various cut angles. An important constant identified in the figure is that the angle between the defection path and response path again is always 90 degrees. This allows prediction of your response angle to be calculated and mastered. [6]
The next fundamental physics property to apply to pool is the bank shot. The bank shot is a play in which the side of the table, or rail, is used as a collision point to bounce a ball off. Bank shots add great versatility to a player’s game as they can be used with the cue ball or with the target ball. Beyond the added versatility of the play, bank shots are also extremely predictable with a proper understanding of physics and geometry. The approach angle that a ball collides with a rail will always be reflected symmetrically as depicted in Figure 4. [7]
Figure 4: Bank Shot Symmetry
The symmetric nature of bank shots allows aiming for a collision shot possible with a different cue ball deflection angle and the ability to avoid balls in the way of traditional shots. Traditional uses of bank shots are when the desired ball or pocket are blocked by other undesired balls. Expanding the bank shot to plays across the table can be achieved using the dots on the side of pocket billiard tables. An example of the different possible bank angles from a cue shot in the corner can be seen in Figure 5. [7]
Figure 5: The Bank Angles from Table Dots
Figure 5 displays the bank angle of a single ball off multiple rails (cushions) when aimed at the dots on the sides of a typical table. The dots are critical markers to making bank shots as they are consistent markers used for aiming.
The last, arguably the hardest to master, fundamental physical principle in billiards is applying spin to the cue ball. Spin is placed on the ball when the player hits the ball at a location outside of the direct center of the ball. An overarching description of different spins applied to the cue ball can be seen in Figure 6.
Figure 6: Target Spin Locations on Cue Ball
A follow shot results in the cue ball continuing to roll forwards after the shot, whereas a draw shot results in the cue ball rolling backwards after the collision. A stun shot meets the two right in the middle, with the cue ball staying stationary after the collision. These shots are critical to controlling the resulting placement of the cue ball and setting up one’s next shot. But how does hitting the ball at these locations actually create the resulting cue ball movement? By adding spin to the ball, the frictional force of the pool table felt applies additional forces to the ball as depicted in Figure 7. [8]
Figure 7: Top Spin, Bottom Spin, and Stun Shots
Figure 7 outlines the follow shot, and draw shot, and a stun spot in terms of the specific spin applied to the ball. The frictional force on the table is labeled to show how the table affects the spin on the ball. These shots are desired for billiards players because they allow control of the resulting placement of the cue ball. A common situation to use a draw or stun shot is when a target ball is very close to a pocket. In order to avoid a scratch the cue ball is stopped or spun backwards away from the pocket after making contact with the target ball.
Furthermore, a right English shot and left English shot apply sidespin to the cue ball. This does not necessarily cause the ball to curve but insteads results in a varied deflection angle for both the cue ball and the target ball. This is particularly helpful for rail shots, in which the target ball is touching the rail and would normally bounce off, instead the target ball can be aimed to stay along the rail. English shots, or spin shots, can vary in strength depending on the variance from center the player hits the cue ball. To maximize the spin placed on a ball, the ideal contact point is half a radius away from the center of the ball. This contact point is depicted in Figure 8. [8]
Figure 8: Maximum Spin Location Striking Point
By maximizing the spin on the ball, the effects on the cue ball are maximized. Varying the amount of spin placed on the cue is essential to engineering the perfect pool shot.
Game Variations
Now that you have learned how to engineer the perfect pool shot, you must also master the rules of the game. Today there are 3 main ‘cue’ sports categories: pocket billiards (pool), English billiards (snooker), and carom billiards. Billiards refers to all three variations, but pool only refers to pocket billiards.
The most familiar to Americans is pocket billiards or ‘pool’ which is played on a 6 pocket table with games such as 8 ball or 9 ball pool. 8 ball pool is the most popular variation today in the United States which comprises 15 solid and striped balls as seen in Figure 9.
Figure 9: The Standard Racking of 8 Ball Pool
Figure 9 depicts the standard racking setup with the 8 ball in the center and a striped and solid ball in opposite corners. The objective of 8 ball pool is to make all of the balls of your type (striped or solid) in a pocket before your opponent and then the 8 ball in a pocket; hitting in the 8 ball prior results in a loss. In 8 ball pool the mastery of collision, deflection, and rotation dynamics are essential. [9]
However, another popular pocket billiards variation is 9 ball. 9 ball uses the same balls as 8 ball pool but only balls labeled 1 through 9. The initial set up racking procedure resembles a diamond and can be seen in figure 10.
Figure 10: The Standard Racking of 9 Ball Pool
In 9 ball pool, the 1 ball is at the front and the 9 ball in the middle of the rack. The goal of 9 ball is to hit the 9 ball in before your opponents. However, one must hit the lowest ball on the table with the cue ball first. Ricochet or carom shots into the 9 ball are allowed and are a common strategy of this variation. Therefore, understanding collision and reflection dynamics are essential for this game play. [10]
The next major variation of billiards is English Billiards or Snooker. Snooker is also played on a 6 pocket table, however they are much bigger 10 feet by 6 feet compared to 9 feet by 4.5 feet for pool tables. Additionally, snooker tables have smaller pockets and slightly smaller balls with 15 red, 6 colored, and 1 cue ball. The typical breaking set up of snooker can be seen in Figure 11.
Figure 11: The Standard Racking of Snooker
The goal of snooker is to make a red ball first followed by a colored ball then red then colored, and so forth. This red-colored sequence continues until all of the balls have been pocketed. If you fail to pocket the right ball, then it becomes the opposing player’s turn. Pocketing a colored ball earns oneself points, and the one with the most points once all the balls have been cleared wins. The scoring scheme can be seen in Figure 12.Similarly to 8 ball pool, snooker encourages the mastery of collision, deflection, and rotation dynamics for effective play. [11]
Figure 12: The Standard Racking of 9 Ball Pool
The last form of billiards is carom billiards. Carom billiards is played on a pocketless table with 3 or 4 balls. The balls are typically colored white, yellow, and red (2 for four ball) as depicted in Figure 13.
Figure 13: Set Up for 3 Ball Pool
The goal of the game is to score more points than your opponent by caroming your cue ball off the other balls on the table. A point is scored when a shooter’s cue ball caroms on any two other balls in the same shot. Two points are scored when the shooter caroms on each of the three object balls in a single shot. A carom on only one ball results in no points, and ends the shooter’s turn. Due to the scoring method of the game, the mastery of collision and deflection dynamics are essential skills for carom billiards. [9]
Conclusion
Engineering the perfect pool shot requires mastering the multiple physical laws that govern the game. It also requires understanding the various manufacturing processes developed to shape the game we know today. From European monarchs to the pool halls of your town, the game of pool has transformed over the generations. Now with all of this knowledge, you can be on your way to the perfect pool shot.
Work Cited
[1] “History of billiards (or pool),” The Billiard Shop, https://www.thebilliardshop.com/history-of-pool-and-billiards (accessed Mar. 7, 2024).
[2] W. P. B. 1963, “Choosing a pool table felt for your table,” West Penn Billiards, https://westpennbilliards.com/choosing-a-pool-table-felt-for-your-table/ (accessed Mar. 7, 2024).
[3] “What are billiard balls made of?,” Poolmania, https://poolmania.com/en/blog/post/what-are-billiard-balls-made-of/317 (accessed Mar. 7, 2024).
[4] “What Pool Cues Are Made Of (And Why It Matters),” BorderBilliards.com, https://borderbilliards.com/what-cues-are-made-of/#:~:text=Customarily%2C%20a%20pool%20cue%20of,maple%20wood%2C%20especially%20the%20shaft. (accessed Mar. 7, 2024).
[5] FCI Billiards, “What does chalk do in pool? understanding the magic of chalk and getting the perfect cue tip grip,” FCI Billiards, https://fcibilliards.com/blog/what-does-chalk-do-in-pool (accessed Mar. 7, 2024).
[6] Billiards and collisions | let’s talk science, https://letstalkscience.ca/educational-resources/stem-explained/billiards-and-collisions (accessed Mar. 8, 2024).
[7] wikiHow, “How to play pool like a mathematician (with pictures),” wikiHow, https://www.wikihow.com/Play-Pool-Like-a-Mathematician (accessed Mar. 7, 2024).
[8] D. G. Alciatore, “Pool and Billiards Physics Principles by Coriolis and Others,” pdfslide.net, https://pdfslide.net/documents/pool-and-billiards-physics-principles-by-coriolis-and-others-alciatore-ajp.html (accessed Mar. 7, 2024).
[9] “Billiard vs pool vs snooker,” Wild Billiard, https://wildbilliard.com/guides/billiard-vs-pool-vs-snooker/ (accessed Mar. 7, 2024).
[10] R. James, “All types of billiard games; a comprehensive guide,” Pool Game Guide, https://poolgameguide.com/all-types-of-billiard-games/ (accessed Mar. 7, 2024).
[11] “Snooker rules – how to play the right way,” Game Tables and More, https://www.gametablesonline.com/blog/snooker-rules-play-right-way/ (accessed Mar. 7, 2024).
