# Cueball Path = Vector Addition?

#### MattPoland

##### AzB Silver Member
Silver Member
I don’t do any actual math. But I visualize the cueball path after contact with an object ball as the addition of two vectors. The first vector is the tangent line with a magnitude proportional to how hard I hit the shot. The second vector is the original cueball path with a magnitude relative to the amount of action on the cueball. My mind just sees both vectors and merges them into the predicted path. I see a lot of talk about things like the peace sign for predicting some rolling cueball trajectories. I was just wondering if others went off pure feel /familiarity or if they similarly had a mathematical visualization in mind.

#### justnum

##### Principal Investigator of Magic Trick Shots
Silver Member
I don’t do any actual math. But I visualize the cueball path after contact with an object ball as the addition of two vectors. The first vector is the tangent line with a magnitude proportional to how hard I hit the shot. The second vector is the original cueball path with a magnitude relative to the amount of action on the cueball. My mind just sees both vectors and merges them into the predicted path. I see a lot of talk about things like the peace sign for predicting some rolling cueball trajectories. I was just wondering if others went off pure feel /familiarity or if they similarly had a mathematical visualization in mind.
i keep my eyes open to see the mathematical model when shooting

when the game was designed what purpose does 15 balls have?
I am fascinated by ancient math. Pyramids had purpose.
perfect spheres must have been a recent invention to experiment with back then.

designing a truly flat surface a major challenge as well. and developing the rest of the game, cloth. rails, ...

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#### jsp

##### AzB Silver Member
Silver Member
I don’t do any actual math. But I visualize the cueball path after contact with an object ball as the addition of two vectors. The first vector is the tangent line with a magnitude proportional to how hard I hit the shot. The second vector is the original cueball path with a magnitude relative to the amount of action on the cueball. My mind just sees both vectors and merges them into the predicted path. I see a lot of talk about things like the peace sign for predicting some rolling cueball trajectories. I was just wondering if others went off pure feel /familiarity or if they similarly had a mathematical visualization in mind.
Actually, the CB path after contact is solved through vector subtraction. You take the vector of the CB path before contact and subtract from it the vector of the OB post contact to solve for the vector of the CB path post contact. But I understand what you mean.

#### Bob Jewett

##### AZB Osmium Member
Staff member
Gold Member
Silver Member
I don’t do any actual math. But I visualize the cueball path after contact with an object ball as the addition of two vectors. The first vector is the tangent line with a magnitude proportional to how hard I hit the shot. The second vector is the original cueball path with a magnitude relative to the amount of action on the cueball. My mind just sees both vectors and merges them into the predicted path. I see a lot of talk about things like the peace sign for predicting some rolling cueball trajectories. I was just wondering if others went off pure feel /familiarity or if they similarly had a mathematical visualization in mind.
Yes, there are easy, accurate ways to use vectors to describe where the cue ball is going, but you are leaving out some details.

First, the speed and direction of the cue ball off the object ball is given by a right triangle. The incoming speed and direction is the hypotenuse of the triangle and the two perpendicular legs are in the directions of the object ball and the cue ball. That triangle will give you the relative speed of the cue ball and object ball relative to the incoming speed.

Second, the follow/draw on the cue ball can be described as a vector. It's forward along the incoming path of the cue ball and back if you have draw. The length of that spin vector should be scaled so that if the cue ball is rolling smoothly, the length is the same as the hypotenuse above and in the same direction.

Finally, the final path of the cue ball is a mixture of the speed vector coming off the object ball (90-degree rule) and the spin vector where they are combined in the ratio of 5/7 of the speed vector to 2/7 of the spin vector.

The spin part may sound like magic, but in fact it was all worked out nearly 200 years ago. I'm sure Dr. Dave has an explanation of it somewhere on his site. I have a column or two I wrote about it somewhere in my online column archive.

The 2/7 and 5/7 mixture is the basis of the follow angle system that has been discussed extensively here recently.

The vector idea leads to several useful conclusions.

#### PariahZero

##### Member
The spin part may sound like magic, but in fact it was all worked out nearly 200 years ago. I'm sure Dr. Dave has an explanation of it somewhere on his site. I have a column or two I wrote about it somewhere in my online column archive.

Very well put.

The spin part only looks like magic until you start doing the math. The math typically results in an overwhelming desire to return to believing in magic, the blacker the better. The stuff isn’t something many would do for fun.

It’s a whole lot easier to read Dr. Dave’s articles on the 30-90 rules, and then build an intuition for how spin and speed changes the rebound angles.

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#### MattPoland

##### AzB Silver Member
Silver Member
Yes, there are easy, accurate ways to use vectors to describe where the cue ball is going, but you are leaving out some details.

First, the speed and direction of the cue ball off the object ball is given by a right triangle. The incoming speed and direction is the hypotenuse of the triangle and the two perpendicular legs are in the directions of the object ball and the cue ball. That triangle will give you the relative speed of the cue ball and object ball relative to the incoming speed.

Second, the follow/draw on the cue ball can be described as a vector. It's forward along the incoming path of the cue ball and back if you have draw. The length of that spin vector should be scaled so that if the cue ball is rolling smoothly, the length is the same as the hypotenuse above and in the same direction.

Finally, the final path of the cue ball is a mixture of the speed vector coming off the object ball (90-degree rule) and the spin vector where they are combined in the ratio of 5/7 of the speed vector to 2/7 of the spin vector.

The spin part may sound like magic, but in fact it was all worked out nearly 200 years ago. I'm sure Dr. Dave has an explanation of it somewhere on his site. I have a column or two I wrote about it somewhere in my online column archive.

The 2/7 and 5/7 mixture is the basis of the follow angle system that has been discussed extensively here recently.

The vector idea leads to several useful conclusions.

I definitely appreciate the actual physics model will be more complex given some of those affects are changing over time, e.g. bending a draw or follow shot because the spin hasn’t grabbed yet.

I was more curious whether people practically use a simplified vector model mentally (while playing) for visualizing the final cueball path. I picture the tangent direction and feel a magnitude... then I picture the original CB direction and feel a magnitude based on action (draw, stun, rolling, or follow)... blend them together without thinking too hard about it... and I can see a resulting path.

Something I do similar but as an alternative is to just think exclusively in terms of tip position. Once I can feel what will stun, I’ve got the tangent line. From there I can feel minor increments of raising my tip equivalently pushing my cueball forward of that line. And I can feel lowering my tip position to incrementally pull me back from that line.

It’s kind of like doing the wagon wheel drill. Sometimes that vector math gives me a clear picture of the path. Sometimes the tip position gives me a clear picture. And of course other times I don’t need to think about it at all and the ball just goes where I will it to. That’s probably most of the time. But I pull out the other two approaches on occasion when I feel like I really need to maneuver in tight positions, get a meticulous breakout, or carom a ball into the pocket.

#### straightline

##### AzB Silver Member
Silver Member
I don’t do any actual math. But I visualize the cueball path after contact with an object ball as the addition of two vectors. The first vector is the tangent line with a magnitude proportional to how hard I hit the shot. The second vector is the original cueball path with a magnitude relative to the amount of action on the cueball. My mind just sees both vectors and merges them into the predicted path. I see a lot of talk about things like the peace sign for predicting some rolling cueball trajectories. I was just wondering if others went off pure feel /familiarity or if they similarly had a mathematical visualization in mind.
I approximate the cue ball break by taking the front of the ball exit line and adding the amount of ball displacement weighted for speed of hit. You can refine this by taking measurements in concentric areas around the collision event. I don't bother anymore - no facilities but it's pretty accurate for all feel.

#### Patrick Johnson

##### Fish of the Day
Silver Member
I don’t do any actual math. But I visualize the cueball path after contact with an object ball as the addition of two vectors. The first vector is the tangent line with a magnitude proportional to how hard I hit the shot. The second vector is the original cueball path with a magnitude relative to the amount of action on the cueball. My mind just sees both vectors and merges them into the predicted path. I see a lot of talk about things like the peace sign for predicting some rolling cueball trajectories. I was just wondering if others went off pure feel /familiarity or if they similarly had a mathematical visualization in mind.
Pure feel/familiarity (and focused practice) for me - although I like the “math” and use it occasionally to confirm/refine my feel, especially if I can simplify it somehow (like by visualizing right triangles as Bob mentions).

pj
chgo

#### garczar

##### AzB Silver Member
Silver Member
You guys make me feel like an idiot. How did i ever learn to play without knowing(or caring) about this stuff? I guarantee you if Bob ever played in the rooms i played in he could win 90% of his matches just by talking. His opponent would be so confused he wouldn't make a ball. Just kiddin' guys, carry on. I'm learning something. I think.

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#### Black-Balled

##### AzB Silver Member
Silver Member
You guys make me feel like an idiot. How did i ever learn to play without knowing(or caring) about this stuff? I guarantee you if Bob ever played in the rooms i played in he could win 90% of his matches just by talking. His opponent would be so confused he wouldn't make a ball. Just kiddin' guys, carry on. I'm learning something. I think.
Haha...the math was added after the game, not before it.

Meaning dumb and happy are still ok for pool fun. I can prove it.

#### justnum

##### Principal Investigator of Magic Trick Shots
Silver Member
Haha...the math was added after the game, not before it.

Meaning dumb and happy are still ok for pool fun. I can prove it.

the math always existed, the game helped make it easier to visualize and identify different aspects of math.

each stroke or shot played is a demonstration that it isnt going to change its mind because it counted it the wrong way, but the totals still match

#### hang-the-9

##### AzB Silver Member
Silver Member
I don’t do any actual math. But I visualize the cueball path after contact with an object ball as the addition of two vectors. The first vector is the tangent line with a magnitude proportional to how hard I hit the shot. The second vector is the original cueball path with a magnitude relative to the amount of action on the cueball. My mind just sees both vectors and merges them into the predicted path. I see a lot of talk about things like the peace sign for predicting some rolling cueball trajectories. I was just wondering if others went off pure feel /familiarity or if they similarly had a mathematical visualization in mind.

This is what I call Pool Vision, we develop that after a lot of playing where the table becomes a collection of shots and angles vs just a mess of random balls that seem confusing. You see all the angles automatically after a while.

#### The_JV

##### 'AZB_Combat Certified'
Pure feel/familiarity (and focused practice) for me
This.... years of playing
I wonder as well... I'll always stand by my assertion that the best way to figure out this game is to play it. When the tires hit the road, and the math didn't manifest like it was expected to after playing the shot. Do you stop playing and break out you calculator, or set it back up and adjust...?

#### bbb

##### AzB Gold Member
Gold Member
Silver Member
I don’t do any actual math. But I visualize the cueball path after contact with an object ball as the addition of two vectors. The first vector is the tangent line with a magnitude proportional to how hard I hit the shot. The second vector is the original cueball path with a magnitude relative to the amount of action on the cueball. My mind just sees both vectors and merges them into the predicted path. I see a lot of talk about things like the peace sign for predicting some rolling cueball trajectories. I was just wondering if others went off pure feel /familiarity or if they similarly had a mathematical visualization in mind.
The 1960’s must have been good to you...

#### garczar

##### AzB Silver Member
Silver Member
The 1960’s must have been good to you...
Didn't know Timothy Leary played pool.

bbb

#### justnum

##### Principal Investigator of Magic Trick Shots
Silver Member
This.... years of playing

I wonder as well... I'll always stand by my assertion that the best way to figure out this game is to play it. When the tires hit the road, and the math didn't manifest like it was expected to after playing the shot. Do you stop playing and break out you calculator, or set it back up and adjust...?
that is why trickshots should be part of olympics. multiple attempts promote second and third chances.

#### MattPoland

##### AzB Silver Member
Silver Member
Here's some visuals to see if it helps. This is what basic vector addition is....

#### MattPoland

##### AzB Silver Member
Silver Member
So apply that in a very layman's way to a pool shot can look like this...

#### MattPoland

##### AzB Silver Member
Silver Member
But in my head it more looks like this when I'm visualizing the shot.

Basically the tangent line is my anchor point and the amount of spin tells me how far forward or backward of that line I'm sending the cueball. And I think of it in terms of vector addition even though I'm not specifically doing any calculations.

#### MattPoland

##### AzB Silver Member
Silver Member
Maybe that makes sense in a more simplified manner. It's not some crazy rocket surgery nor is it some crazy psychedelic visual trip. It's just mentally visualizing arrows and thinking how they blend together in a practical way that I can bring to the table. It just happens that the vocabulary of math has the terms to describe it.