Cueball Path = Vector Addition?

[TATE]

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 see two things when I'm shooting the shot, the object ball heading into the pocket and the cue ball going to where I want it to go. Then I figure out what spin to put on the cue ball to pull off the shot. Your aim point affects both OB and CB. There is rarely a single aim point on a shot, because it can be manipulated by speed, spin and pocket play.

Once you've decided what to do (don't shoot until you have) It's all feel and visualization. It's very difficult to say in your mind "I'm going to cut 1/3 of the ball at speed two on this tangent line with low left" and force your hand to do that. If you can't see it, you can't feel it. If you can't feel it, then I suggest just making the object ball and hoping like hell you get another shot.

Here's me playing position on the ghost last night:

2021 AZB Ghost Challenge - Official Thread

2021 AZB Ghost Challenge - Official Thread It’s a new year, and everyone is on a clean slate. Let's see who can back up their written posts with game play for bragging rights :);)o_O:LOL: If you have a video of your run, link it, and I will add it to this post. Neither video or skill are...

forums.azbilliards.com

 

[Black-Balled]

Didn't know Timothy Leary played pool.

He definitely does.

 

[bbb]

He definitely does.

You should see what his cue ball looks like with force follow

 

[PoolHallPaul]

Didn't know Timothy Leary played pool.

If I keep reading this junk I'll be doing drugs.

 

[Cornerman]

You might want to look at Dr Dave's recent video on carom angles. I'm sure he'll be posting it himself

 

[dr_dave]

... 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.

The math and physics derivation can be found here:

TP A.4 - Post-impact cue ball trajectory for any cut angle, speed, and spin​

The diagram on page 7 shows the simple vector-addition interpretation of the analysis.

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.

A complete summary and demonstration for all of these recent discussions can be found here:

Rolling Carom Angle (RCA) System​

Enjoy,
Dave

 

[MattPoland]

You might want to look at Dr Dave's recent video on carom angles. I'm sure he'll be posting it himself

I have seen that. It's a great resource. Dave does a great job of serving as a clearinghouse of information. I find much of it in this video to either (A) exclusively focus on rolling cueballs, (B) go deep on the math, (C) or include things you can do with your fingers, stick, or other physical-oriented techniques.

I guess the main thrust of the topic I'm raising here is around how people approach predicting cueball angles with any degree of cut, speed or spin in terms of mental systems. The stuff we do quickly in our heads as we move from shot to shot. In my case, I feel vectors blending together.

 

[PariahZero]

The math and physics derivation can be found here:

TP A.4 - Post-impact cue ball trajectory for any cut angle, speed, and spin​

I love your site, and books, Dr. Dave. But this made my head hurt. I’m happy to see it, though.

I haven’t had to do math like that in quite some time now. I’m kind of ashamed how much math I’ve forgotten from disuse, but I filled the space with other stuff, so...

I’m going to fall back to dark magic: ph'nglui mglw'nafh Cthulhu R'lyeh wgah'nagl fhtagn

 

[dr_dave]

The math and physics derivation can be found here:

TP A.4 - Post-impact cue ball trajectory for any cut angle, speed, and spin​

The diagram on page 7 shows the simple vector-addition interpretation of the analysis.




A complete summary and demonstration for all of these recent discussions can be found here:

Rolling Carom Angle (RCA) System​

Enjoy,
Dave

I love your site, and books, Dr. Dave.

I'm glad you like my stuff.

But this made my head hurt. I’m happy to see it, though.

I haven’t had to do math like that in quite some time now. I’m kind of ashamed how much math I’ve forgotten from disuse

I'm sorry I made your head hurt and reminded you of what you've lost. I should always post warnings with these TP links. Not many people on AZB have interest in such detailed math and physics. However, the second link (RCA System), is "sanitized" and includes only stuff useful to players (even those without knowledge or interest in math and physics). Check it out.

Enjoy,
Dave

 

[hang-the-9]

I have seen that. It's a great resource. Dave does a great job of serving as a clearinghouse of information. I find much of it to either (A) exclusively focus on rolling cueballs, (B) go deep on the math, (C) or include things you can do with your fingers, stick, or other physical-oriented techniques.

I guess the main thrust of the topic I'm raising here is around how people approach predicting cueball angles with any degree of cut, speed or spin in terms of mental systems. The stuff we do quickly in our heads as we move from shot to shot. In my case, I feel vectors blending together.

The same way we calculate air mass, distance, gravity and weight when throwing a basketball or catching a ball. Experience.

 

[Patrick Johnson]

The same way we calculate air mass, distance, gravity and weight when throwing a basketball or catching a ball. Experience.

Yes, attentive experience.

pj
chgo

 

[dr_dave]

You might want to look at Dr Dave's recent video on carom angles. I'm sure he'll be posting it himself

I have seen that. It's a great resource. Dave does a great job of serving as a clearinghouse of information. I find much of it in this video to either (A) exclusively focus on rolling cueballs, (B) go deep on the math, (C) or include things you can do with your fingers, stick, or other physical-oriented techniques.

I guess the main thrust of the topic I'm raising here is around how people approach predicting cueball angles with any degree of cut, speed or spin in terms of mental systems. The stuff we do quickly in our heads as we move from shot to shot. In my case, I feel vectors blending together.

FYI, this particular video focused on rolling-CB systems, but there are useful systems for predicting CB motion for all types of shots.

Concerning using vectors to "feel" the direction, the 5/7-2/7 principle applies to all draw and follow shots, with any amount of spin. From the bottom of page 4 of TP A.4, the final CB direction is always 5/7 of the tangent-line vector added to 2/7 of the spin vector. The difficult part is judging how the shot speed and cut angle affect the tangent-line vector and how the amount of spin affects the spin vector. And you also need to be able to visualize the vector addition. Ain't nobody got time for all that. That's why intuition built by countless hours of smart practice and successful experience is better. For people who don't have the patience for that, the easy-to-use systems can be very helpful and effective.

Regards,
Dave

 

[MattPoland]

FYI, this particular video focused on rolling-CB systems, but there are useful systems for predicting CB motion for all types of shots.

Concerning using vectors to "feel" the direction, the 5/7-2/7 principle applies to all draw and follow shots, with any amount of spin. From the bottom of page 4 of TP A.4, the final CB direction is always 5/7 of the tangent-line vector added to 2/7 of the spin vector. The difficult part is judging how the shot speed and cut angle affect the tangent-line vector and how the amount of spin affects the spin vector. And you also need to be able to visualize the vector addition. Ain't nobody got time for all that. That's why intuition built by countless hours of smart practice and successful experience is better. For people who don't have the patience for that, the easy-to-use systems can be very helpful and effective.

Regards,
Dave

Did you see the pictures I posted on page 1? That’s roughly how I visualize it.

I think it’s probably just my intuition telling me where the cueball will go except I hold in my mind the tangent line, initial cueball direction and spin.

 

[dr_dave]

Did you see the pictures I posted on page 1? That’s roughly how I visualize it.

I did. That's why I shared the info. I thought the theoretical vector interpretation might help with your vector-visualization intuition.

I think it’s probably just my intuition telling me where the cueball will go except I hold in my mind the tangent line, initial cueball direction and spin.