Billiard Mechanics

[Elly Garnand]

Billiardsin this case referring to English Billiards) is a game that is popular not just in England but around the world thanks to its popularity during the time of the British Empire. Billiards is a cue sport that is played by two players and utilises one object ball (red) and two cue balls (yellow and white).

English Billiards can be played one-vs-one or two-vs-two with the singles version of the game being the most popular. The game is played on a table that has exactly the same dimensions (3569 mm x 1778 mm) as a snooker table, and in many places both games are played on the same table. Three balls must also be used, one red, one yellow and one white, and each must be 52.5mm in size.

Players have a cue each which can be made from wood or fibreglass and this is used for striking the balls. The last essential piece of equipment is chalk. During the game, each player will chalk the end of their cue to ensure there is good contact between the cue and the ball.

English Billiards is won when one player (or team) reaches the agreed amount of points needed to win the game (often 300). Despite their being only three balls on the table at any one time, it is a very tactical game which requires a tremendous degree of savvy gameplay as well as skill to ensure that you keep ahead of your opponent.

As well as thinking in terms of attack and scoring points, it is essential for anyone who wants to win a game of billiards to think defensively at the same time and make things as difficult as they can for their opponent.

Billiards games are divided into 2 types: carom billiards, played on a pocketless table in which the object is to bounce the cue ball off other balls or the table rails, and pocket billiards, played on a table with pockets in which the object is to sink the colored balls into the pockets by striking them with the cue ball -- aka pool.[1]XResearch source If you're looking for pocket billiards, wikiHow has a great How to Play Pool article, too. But here, we'll cover the basics of carom billiards -- and its variations -- in addition to equipment and strategy. Carom billiards involves serious skill, often incorporating angles and trick shots. If you already know pool, carom is the next step!

In fact, when the balls collide (or a ball collides with the bank), the momentum is conserved, along with the angular momentum, swapping spin and resulting in unexpected and dramatic results. To complete the master strokes, the balls (as well as the cues) must be perfectly calibrated.

In other words, if no external force intervenes in the system, a body keeps its own momentum (conservation of momentum), which is similar to the kinetic energy of a body travelling at a specific speed v1 and having a certain mass m1. The formula is as follows:

By its very definition, momentum is a constant measure for a body moving at a constant speed. In other words, a body retains its own momentum if no external force intervenes in the system (conservation of momentum), parallel to the kinetic energy of a body moving with a certain speed v1 and having a certain mass m1. The equation is:

As with other sports, studies and motion detection analysis are nowadays performed with special high-frequency cameras (up to 10000 fps). The rebound analysis is performed by observing the behavior of the ball hitting the side of a generic billiards table, made up of a particular type of elastic rubber with a triangular profile covered with fabric (see figure 2).

In the game of billiards, the collision theory is probably the most important (see figure 4). The collision phenomenon can be described as two bodies or two masses colliding with each other. During this phenomenon, the bodies exchange parts of their energy. A fraction of the kinetic energy is transformed into heat and deformation and the velocity vectors of the two bodies change. When two billiards balls collide, the bump is almost elastic. An elastic collision is one in which the kinetic energy of the system is conserved before and after the collision.

In the diagram, the vectors indicate the direction of movement of the bodies. The normal impact is the straight line of action on which the impact forces act, passes through the point of contact of the two bodies and is perpendicular to the tangent plane.

The physics of billiards predicts a point on a ball which, when hit, develops no frictional force between the ball and the billiard table (see figure 6). This makes it possible to make interesting shots.

Nice article. I think it would be helpful to the reader to explain that not developing friction implies that the struck ball will therefore simply roll immediately after contact with no slide (friction). This is called a follow shot, perhaps the most useful stroke in pool.

Hi, I am Salman, Owner of Pool Mentor. I read the article you shared and found it informative. The article explains that billiards is an excellent sport for testing physics and mathematics. In fact, professors at several universities use this game to explain the fundamental principles of physics. Billiard relies on bounces and bumps, and professionals are capable of performing prodigious, often strange and magical stunts, and they are probably oblivious to the calculations underlying them, relying solely on experience.

My unique advice for playing billiards is to practice your aiming skills. Aiming is one of the most important skills in billiards, and it can take some time to master. You can practice your aiming skills by playing the game regularly and experimenting with different angles and shot power.

The article nicely explains the dynamics of billiard balls, without getting into the complexity of the rigid-body dynamics and many parameters with empirical values, such as friction coefficient, coefficient of restitution.

Further to my previous comment, I found a derivation for h/r = 1.4 in -world-physics-problems.com/physics-of-billiards.html. As a result, I can ascertain that the information in your article is correct!

8-ball is the most popular and widespread game variation in pool. It is played with all 15 object balls, which are divided into the groups of solid (1-7) and striped balls (9-15) and the black eight. The first regularly pocketed ball after the break decides which player plays which group.

8-ball is a called-shot game. Therefore, in order to pocket a ball correctly and continue to play, it must be called beforehand which ball is to be pocketed in which pocket. Combinations are generally allowed. A player must always hit one ball of his group first in order to make a correct shot. In the case of obvious shots, no call needs to be made.

The objective of the game is to pocket all the balls in your group and then the black eight ball. The pocket for the eight ball must be called, but may be re-selected for each attempt. According to the official rules of the WPA (World Pool Association), the eight ball does not have to be played into the same or opposite pocket of the last pocketed ball. However, such rule variations are quite possible and common.

At the break, the cue ball may be placed anywhere in the kitchen. No particular ball must be hit first, and no ball must be called. If a ball is pocketed during the break, the break is automatically valid and the player breaking remains at the table. If no ball is pocketed, at least four object balls must hit one or more rails after the first contact of the cue ball with the rack for the break to be correct. If this is met, the shot changes and the other player takes over.

If both the cue ball and the black eight ball are pocketed, the opponent decides whether to re-rack or to take over the position with the black ball re-spotted. In this case, he then has ball-in-hand from the kitchen.

After the break shot, the player entitled to take over the position is basically free to choose which group he wants to take over. Even if only stripes is pocketed at the break, the player can choose the solids if he thinks they are better. The groups are only finally assigned when the player has pocketed a ball in accordance with the rules. As long as the groups have not been assigned, mixed combinations may be played, e.g. a solid may be played first and a called stripe may be pocketed in a called pocket. The eight may never be played first.

After a foul, the other player always has ball-in-hand and may place the cue ball anywhere on the table for his next shot. The only exception is at the break. If the player commits a foul here, the other player may only move the cue ball inside the kitchen and may only play balls first that are outside the kitchen.

The winner of a 9-ball game is the player who sinks the 9 ball with a correct shot. It does not matter whether it is the last object ball to drop with a normal shot, a valid combination over another ball, or by pure chance, as long as the rules for a correct shot are met. Potting the 9 ball on the break also automatically leads directly to winning the game if the break was executed correctly. Furthermore, a game can be won if the opponent commits a foul in three consecutive shots (see Three-Foul Rule).

If an object ball is pocketed during the break, the break is automatically valid and the player making the break remains at the table. If no ball is pocketed, at least four object balls must hit one or more rails after the first contact of the cue ball with the rack for the break to be correct. If this is met, the shot changes and the other player takes over as it lies.

In addition to the standard rules, many 9-ball events use the Kitchen Rule or 3-point rule. According to this rule, after the break, at least three object balls must run back into or through the kitchen for a correct break to occur. It is sufficient if the head string is touched, the ball does not have to cross it completely. Pocketed balls are automatically deducted from the 3-point rule. So if one ball is pocketed, only two have to go into the kitchen. If two balls are pocketed, only one has to go into the kitchen. If three or more balls are pocketed, the Kitchen Rule is automatically fulfilled. All other combinations mean an Illegal Break. If such an illegal break occurs, the player entitled to take over can decide whether to take over the situation or to let the player who caused the illegal break continue to play. If the player takes over, a correct shot must then be made on the lowest ball remaining on the table. If the shot is returned, the person who caused the illegal break may also continue the game with a push-out.

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