## The Physics of Billiards

Center ball: When you hit center ball, the cue ball (illustrated with a striped ball, here) slides for a ways, and then rolls. Actually, the ball starts to roll immediately, but slide predominates over roll, at first. The harder you hit the ball, the farther it slides before the ball is rolling.

Draw: On the right we see draw, which is achieved by hitting the cue ball below center. First the ball rotates backward. This rotation slows as the ball slides, and then the ball rolls forward as it does on other shots. The harder you shoot, the farther the ball will travel with this backward spin. And the lower you cue the ball, the farther the ball will travel with this backward spin. If the cue ball hits another ball solidly (more or less), when it still is spinning backwards, then this backward spin will make it come back toward you, after the collision. This is the classic draw effect.

Follow: The opposite of draw is follow. This is achieved by hitting the cue ball above center. The cue ball then rotates forward. If the cue ball then hits another ball, it will roll forward after the collision. But the cue ball has natural follow, just because it rolls on the cloth (first diagram). So you can achieve the follow effect with center ball (or even draw) if you allow the cue ball to start rolling before it hits another ball. When a cue ball with draw or follow strikes another ball solidly, it will pause for an instant (still spinning) before the draw or follow takes hold.

Stop shot: One of the most useful shots in pool is the stop shot. When the cue ball is very close to the object ball, this can be accomplished with center ball. The cue ball slides to the object ball and stops dead as the object ball shoots ahead because of the collision. But most stop shots are done with draw. You use just enough draw that the cue ball stops sliding just as it strikes the object ball. This may sound difficult to judge. But it is fairly easy with practice. You soon learn to adjust your speed and amount of draw, depending on the shot (distance and other requirements of the pool situation).

Paths after a collision: When a cue ball (or some other ball) strikes an object ball, the object ball then moves away along the line between the centers of the two balls. In the diagram on the left, we see the cue ball about to strike the red ball. The black circle is the image of the cue ball as it strikes the red ball. You can imagine this image, whenever you shoot, if it will help you aim the cue ball. In this diagram, the red ball then moves to the upper left, along the line between its center and the center of the cue ball's image. If the cue ball had center ball (when it hit the red ball) then it will move off to the right (as shown in the diagram) at right angles to the path of the red ball. This right angle is not perfect, as the two balls are not perfectly elastic, but it is very close to being perfect. With follow the cue ball will curve forward, and with draw the cue ball will curve backward, as shown. People don't always notice the curving effect, but it can be dramatic if you watch for it.

Aiming: The above diagram (showing the paths after collision) shows the famous ghost ball (the black circle) which many people visualize when aiming. They aim directly at the ghost ball. I guess there are several alternative tricks. One is to concentrate on the cue ball hitting the exactly correct contact point (where the object ball and ghost ball touch); I think most people do this. Another is to just adjust your aim until the shot "feels right" subconsciously; I think most pros do this. Another is to have several kinds of standard hits that you can shoot at any time: 1/2 ball hit, 1/4 ball, 3/4 ball, and maybe various 1/8, and decide which of these to shoot, and then shoot it. Another is to aim for a 1/2 ball hit (practice, so you'll know at what angle a 1/2 ball hit goes), and then adjust slightly to make it thicker or thinner, whatever is required (however you make that decision). All of these require practice. A 1/2 ball hit, by the way, is the easiest, most accurate cut, as the center of the cue ball goes directly toward the very edge of the object ball, giving you an easy target. It is less prone to error than thin or thick hits. For accurate aiming, it also helps to have a consistent, level stroke.

Side English: American's call it English. The British call it side. I call it side English to make sure I am understood. It is side spin on the ball. On the right is a diagram in which the cue is imparting left English (as seen from above). The situation is not as simple as shown here, as the ball also starts rolling, and the various spin axes change, causing a small amount of curve in the path of the ball. Side English complicates the game a lot, and makes many shots possible which would not be possible otherwise. The main effect of side English is the angle that the cue ball (and to a lesser extent, other balls) bounces off the rail (see Kicks and Banks - Part II (complications), complication #3). The second most important effect of side English is squirt; the cue ball does not go straight in the direction that the cue is pointing, it squirts off to the side a little. Left English makes the ball squirt to the right. The greater the side English, the greater the squirt. And squirt causes you to miss shots, and is the main reason that the pros tell you not to use side English unless you have a good reason. The third most important effect of side English is Throw. There is also accidental side English, caused by a bad stroke. And other balls gain side English, mainly by banking off rails (but also because of throw).

Curve: See "paths after a collision," above, concerning curve using draw or follow. The curve caused by side English is very small, and quite a few people think that a level stroke cannot make the cue ball curve. The physics is quite clear, however; a level stroke with side English does cause a small amount of curve in the path of the cue ball. Elevating the butt of your cue will increase the curve dramatically, and will cause you to miss shots. Even higher elevation of the cue is called a masse (massé) shot, which can produce amazing effects, and tear the cloth.

Banks and kicks: See Kicks and Banks - Part I (calculating), and especially Kicks and Banks - Part II (complications) (as well as Kicks and Banks - Part III (putting it all together), Two Rail Kicks and Banks, and Three Rail Kicks and Banks).

Miscue: If you try to get extreme side English or draw or follow, you may miscue. This is when the cue slides off the side of the cue ball, instead of hitting it solidly. The sound you hear is the cue vibrating.

Jump shot: Besides imparting extreme spin on the cue ball, greatly elevating the cue can make the cue ball jump. If you shoot your break shot (in 8 ball or 9 ball) with an elevated cue, you probably jump your cue ball off the table often. Hit down on the cue ball, with center ball or some draw. A shorter jump cue makes this even easier, and makes the jump higher and more dramatic; there is a legal limit to how short a cue can be. The type and thickness of the cloth may be a factor in how high the cue ball jumps. Beginners often shoot a jump shot by hitting the cue ball very low and miscuing, which is illegal if done intentionally. A jump shot over another ball is illegal in snooker. It is difficult to aim a jump shot.

Ball speed: Ball speed has several effects. When two balls collide, ball speed changes the angle because it delays the curve in the paths of the balls, as in the diagram on the left. So, to maximize the effect of draw or follow, a slow speed may be necessary. Conversely, to get a straighter ball path, a fast speed may be necessary. Also a faster speed makes the ball slide farther before friction causes natural follow to take hold. Throw is more effective at a slower speed. The curve of a masse shot happens sooner at a slower speed, but the spin is greater at a faster speed, and so it is particularly difficult to get the speed of a masse shot right. And ball speed dramatically changes the angles of kicks and banks (see Kicks and Banks - Part II (complications)).

For "squirt," see "side english," above. See Illegal Double Hit In 99 Critical Shots In Pool and Double Hit Animation (takes a few seconds to load). Also see Amateur Physics for the Amateur Pool Player by Ron Shepard (pdf file).
{"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0}