Speed after collision
Remember in part 3 of this series we discussed the importance of being able to control the speed of your shooting arm? In today’s post we take what you learned in part 3 and add a slight complicating factor to the equation: the object ball. Remember, the ultimate goal in this game is to be able to control the final resting spot of the cue ball, and parts 3 and 6 of this series both deal with the speed of the cue ball.
For today’s post, I will first present some theory about energy transfer between cue ball and object ball. Next, I will tell you how to make adjustments to your arm speed to compensate for the energy loss that occurs when the cue ball collides with the object ball. Armed with this new information, you will have all the information necessary to make the object ball in a pocket, and subsequently move the cue ball around the table for a specific distance.
Okay, here’s the theory part. When the cue ball strikes an object ball, a certain amount of the energy contained in the cue ball is transferred to the object ball. For the purposes of this discussion, we will assume the cue ball is a naturally rolling ball with no English. Depending on the angle of the collision, the amount of energy transferred between the two balls changes. Pool players often have limited control over the angle of the shot they are taking (i.e. they have to play what the table gives them or their opponent gives them); therefore, it is important to know for a variety of angles (or ball hit fractions) how much energy will be contained in the two balls after impact. Once again, thanks to our mechanical engineering friends at Colorado State University, we don’t have to derive any of the math; we can just review the answer and implement the information learned. See the graph in Figure 1.
Figure 1
Here’s how you read the graph. The bottom row of numbers is the ball hit fraction, which tells you how “Full” the cue ball hits the object ball. The top row of numbers tells you the ratio of energy contained in each ball after the collision. All of these calculations assume a normally rolling cue ball (no English). Let me walk you through a few examples:
(1) If you aim the cue ball directly at the center of the object ball (a full hit), the ball hit fraction will be “1” and after collision the object ball (OB) will travel seven times further than the cue ball (CB)
(2) If you aim the cue ball directly at the outer edge of the object ball (a half ball hit), the ball hit fraction will be ½ and the object ball (OB) will travel 4 units of distance for every 3 units traveled by the cue ball (CB)
(3) If you aim the cue ball directly at the ¼ fraction hit mark, the cue ball (CB) will travel twice as far as the object ball (OB).
How is this information useful to us? By knowing how much energy is lost in the collision, we can make adjustments to our arm speed (increase it) to compensate for the loss of energy, and still be able to place the cue ball exactly where we want it after the shot. If you remember back to part 3 of this series, we were hitting the cue ball directly up and down the table without any interfering balls, and we were able to make the cue ball stop within certain zones of the table. In my final post of this series, we will repeat the exercise from post 3, but add an object ball to make it a little more interesting. In order to control the cue ball and make it come to rest in the appropriate zone of the table, we will be forced to make adjustments for the energy lost in collision. In the next post, I’ll pull together all that we’ve learned in this series, and show you how to make a shot, then control the final resting spot of the cue ball.
Angle of Reflection 