The tangent line is the basic understanding of how the cue ball will react after hitting a stationary ball. To be even more specific, it is a simplification of the geometry and physics that occurs when a moving ball hits a stationary ball. Understanding the tangent line in pool will allow you to predict the direction your cue ball will go after impacting your object ball.
When you combine the understanding of the tangent lines with basic english and speed control, you can control the cue ball to a very high level of accuracy. This will allow you to maneuver the table at will.
The Tangent Line
If you took geometry and/or calculus in school, you probably learned about tangent lines, but don’t worry if you forgot. I completely forgot what a tangent line was the second I finished my final exams.
The tangent line is the line that goes perpendicular to any specific point on a curve, in our case a sphere.
The way I’ve taught this to people in the past is to imagine you have a billiard ball and a piece of paper. If you actually have a billiards table accessible and a paper, try this for yourself.
Hold the piece of paper up so that it is erect with one edge on the table. Now push the flat side against a ball with the paper still erect.
The picture below is a top-down view of what this would look like where the white line labeled tangent line is the piece of paper. The paper is now creating the tangent line of the ball.
This tangent line shows the two default directions the cue ball can deflect off the 1 ball when you hit the spot labeled “This Exact Spot”
The tangent line can be used to predict where the cue ball will go after impact. The tangent line is very accurate as long as the cue ball is sliding when it hits the object ball and it isn’t a straight shot. The slide of the cue ball is explained in the article here.
Using The Tangent Line In Practice
Now we understand what the tangent line is, but how is it actually used?
The tangent line explains how the cue ball or any ball will react when it collides with a stationary ball.
The only times that the tangent line is not effective for predicting where the cue ball will go are when the cue ball isn’t sliding or when you’re shooting a straight in shot.
When you put high or low english on the ball, it is not sliding. So, I just want to restate putting english on the ball will affect the accuracy of the tangent line. So, when learning the tangent line refrain from using english at first.
When the cue ball isn’t sliding or when there is english on the cue ball, you can still use it to predict the trajectory, but you have to make adjustments. For now we are only going to cover the tangent line without english, this means when the cue ball is sliding.
How to Use Tangent Lines With Straight Shots
Pictured below is an example of a straight shot. In this situation, without using english, there are 2 options for the cue ball. The cue ball will follow behind the 1 ball or it will stop in place on impact.
This diagram doesn’t explain too much in regards to the tangent line, but it is worth noting that the tangent line doesn’t apply on straight shots as shown above.
Next, we’ll cover what happens when you move away from a straight shot.
Even the slightest adjustment to the right or left, away from a straight shot, will cause the tangent line to apply.
Cutting From Left Side of Object Ball
If we move the cue ball to the right in the picture above, then the cue ball will follow the tangent line on the right side of the ball with respect to the shooter.
For example, in the picture below, we’re cutting the 1 ball in the side pocket from the left side of the ball. This means that the cue ball will follow the tangent line on the opposite side of the ball, illustrated by the red line. This allows us to predict where the cue ball will go before we even shoot.
It will allow you to avoid scratches and see positioning from a new stance. Something interesting to note is that no matter how far to the right you go the tangent line stays the same as long as you hit the same spot.
Cutting From Right Side of Object Ball
This logic works the same on the opposite side of the ball just all the effects are flipped. If we move the cue ball to the left in the picture and cut the 1 ball on the left side then the cue ball will follow the left side tangent line with respect to the shooter.
Understanding how the tangent lines work is the first step in understanding where the cue ball will go on any given shot. If you have a good grasp of tangent lines and combine that with good speed control, you can maneuver the table with very little english.
Sliding Cue Ball Review
The tangent line is almost 100% accurate when the ball is sliding on impact. There are 2 ways that the ball will be sliding on impact.
First, when you hit a ball it slides for a second before the friction of the table’s felt causes the ball to roll forward. This forward roll is similar to high top english. You can keep it from rolling forward for a longer distance by hitting the ball harder. However, hitting a ball hard makes it very hard to control. So, there is another way to make sure that the ball is sliding on impact.
The second way is a bit more difficult than hitting the ball hard. It can be difficult for even experienced players to get perfect. The better but more difficult way is to put just enough backspin or low english on the cue ball so that right when it impacts the ball, it is switching from a backward roll or backspin to topspin or a forward roll. This requires high-level english control and a lot of practice.
If you put too much low english, you will draw the ball back a little and not enough english will cause it to start rolling forward potentially following the ball in the pocket.
This method of sliding is very difficult because every shot is different and the amount of english needed differs depending on the distance to the object ball and how hard you shoot.
The tangent line is a great indicator of where the cue ball will go after impacting a stationary ball. If you master the tangent line and speed control, you can become very good at positioning your ball even without english.
The tangent line is only a perfect indicator of the ball’s trajectory if the ball is sliding when it impacts the stationary ball. This can be achieved in one of 2 ways. Either hit the ball hard or use the perfect amount of backspin to make it hit the stationary ball just as the backspin switches to forward spin. This is very hard to do but when mastered can greatly improve your game.
I hope this has helped you better understand controlling the cue ball. Please leave questions and comments below. I’ll reply ASAP!