A major part of being a good pool shooter is an understanding of the tangent line, and the ability to position the cue ball in an ideal position for the next shot. This is commonly called "playing position" in pool and billiards lingo. An exceptional position player will always do well on the pool table.
There are several components to being able to place the cue ball where you want it after a shot. Among them are speed of the hit, the user of follow, draw, and english, and the observance of the tangent line.
The tangent line is the path that the cue ball will travel after it makes contact with the object ball during a pool shot. This path is quite predictable, and can be used to your advantage if you are aware of it and how it works.
There are two basic forms of tangent lines - the 90 degree and the 30 degree lines. The following explanation will describe the differences and similarities between the two varieties:
When the cue tip hits the cue ball in the center of the ball, and with a fair amount of power, it slides or skids, but does not roll, across the surface of the pool cloth for some distance. This is called a stun shot, and it can be used quite often in a pool game. The cue ball will eventually start to roll naturally as the energy of the hit dissipates.
A softly hit ball may begin to roll immediately, while a ball that is hit hard enough can skid across the entire length of the table without ever rolling. Whether the cue ball is rolling or not determines the angle of the tangent line.
A cue ball that hits the object ball perfectly straight with no cut angle, whether it is skidding or rolling, will naturally follow the same line of travel as the object ball after the shot if no stop or draw is put on the cue. A cue ball that hits the object ball at any angle other than straight on will rebound off the object ball at a set angle.
When the cue ball is skidding or sliding across the table and it hits an object ball, it will rebound off the object ball at a 90 degree angle FROM THE IMPACT DIRECTION LINE OF THE OBJECT BALL. The impact direction line is the line the object ball travels after it is hit by the cue ball.
On a correctly hit object ball, the direction line would be the line of travel the object ball follows to the desired pocket. Except for shots with intentional english, the cue ball will rebound 90 degrees from this direction.
The following diagram illustrates the direction the cue ball will travel after impact in a stun shot. See also this video.
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