The Angle of Deflection
Today we are going to address one of the greatest mysteries, and provide one of the most valuable pieces of information, from the world of pool. I am often asked, “How do you know where the cue ball is going to go after it hits the object ball?” Before I explain the answer, let’s first define a couple of terms:
Angle of Deflection – When the cue ball strikes an object ball, the cue ball will be deflected from its original path by a very predictable angle. That angle is called the angle of deflection. Why is it important to know this angle? Because knowledge of this angle will allow you to predict with great accuracy the path the cue ball will take after it collides with an object ball.
Ball hit fraction – From the shooter’s point of view, ball hit fraction is defined as the point that you are aiming your cue stick at when you shoot the cue ball into the object ball. It’s easier to explain with the help of a simple diagram, like the one shown in Figure 1 below. Let me help clarify by walking you though three examples: (1) If you aim the cue ball directly at the center of the object ball, your ball hit fraction will be one; (2) If you aim the cue ball directly at the center of the ghost ball, the ball hit fraction will be zero. In other words, the cue ball will just barely miss the object ball; (3) If you aim the cue ball directly at the outer edge of the object ball, the ball hit fraction will be 1/2. In pool parlance, this is often referred to as a “Half Ball” hit.
Figure 1
Figure 2
For the purposes of our discussion today, let’s assume the cue ball is rolling naturally down the table with no side spin. How do you determine the angle of deflection? The folks at the Colorado State University Mechanical Engineering department have taken on the arduous task of calculating the math for us, so there’s no need for us to get into the details. The graph in Figure 2 that tells you exactly what the angle of deflection will be for any ball hit fraction.
Figure 3
Hummm…that’s not a very friendly graph is it? I don’t know about you, but there’s no way I will be able to remember that when I’m shooting! Let’s get away from the exact theoretical numbers, and simplify the graph so we can remember it and apply it in a practical setting. You will notice in Figure 3 I’ve greatly simplified the graph by drawing two vertical lines at the ¼ and ¾ ball fraction points and inserting a flat red line between these vertical lines. This of course is an approximation of the original chart, but it is very useful information nonetheless. The reason is because in most situations when you are moving the cue ball around the table to get into position for your next shot, you will want the cue ball to approach the next object ball at an angle that falls between these two lines. Why? Because the angle of deflection is relatively flat and predictable between these two lines: approximately 30 degrees. For ball hit fractions between 0 and ¼, and between ¾ and 1, the angle of deflection is roughly linear and proportional. Huh? Don’t worry about the language; just take a look at the simplified graph in Figure 3.
Figure 4
As discussed earlier, we want most of our shots to have ball hit fractions to be between ¼ and ¾. If we do, the angle of deflection will be relatively robust and predictable, at around 30 degrees. Why is this so special? Because if you have to deal with the same angle of deflection on every shot, you will get much better at predicting the path of the cue ball, and the key to winning pool is being able to control the cue ball. The next logical question is: “How do I know what 30 degrees looks like when I’m at the table shooting?” Good question! Here’s a very easy way to estimate a 30 degree angle. Just make relaxed a peace sign with your fingers. Guess what? The angle is approximately 30 degrees! (Figure 4)
Enough info for one day? Yes, my brain hurts also. How are you going to use this information to improve your game? Heck if I know. Why don’t we both take a break and come back tomorrow, where we will be discussing a much simpler topic, the Angle of Reflection.
Angle of Reflection 