Spin axis and carom angles

[pagaspoling]

Lately I've been playing a lot of 3-cushion and I've thought a lot about carom angles and how to create angles. When I read the Technical Proof section at Dr Daves site and the Physics Resources I have a hard time to find any explanation on how spin axis affects the carom angles.

First lets assume that the CB is traveling in exactly the same direction just before impact with the OB for all different scenarios. Secondly lets assume the CB has the same spin rate factor for all shots.

If the CB hits the OB with a spin axis that is vertical the CB will travel down the tangent line and follow the 90 degree rule. If the spin axis is horisontal when the CB hits the OB the CB will swerve into: "The final ball direction is at 2/7 of the distance x between the tangent line and aiming line, measured perpendicular to the tangent line (i.e., parallel to the impact line)." (from TP_A-4).

With a spin axis that is tilted 45 degrees what will the final CB direction be? In the spin axis flip video the ball seem to start to roll with its spin axis approximately 45 degrees thats why i chose that angle. How can I predict carom angle from spin axis?

 

[Patrick Johnson]

Interesting question, but…

I think the “spin axis” is normally perpendicular to the direction of spin (i.e., with only vertical spin the spin axis is horizontal).

pj
chgo

 

[pagaspoling]

I think the “spin axis” is normally perpendicular to the direction of spin (i.e., with only vertical spin the spin axis is horizontal).

Oops, i changed it now! Thank you

 

[garczar]

Lately I've been playing a lot of 3-cushion and I've thought a lot about carom angles and how to create angles. When I read the Technical Proof section at Dr Daves site and the Physics Resources I have a hard time to find any explanation on how spin axis affects the carom angles.

First lets assume that the CB is traveling in exactly the same direction just before impact with the OB for all different scenarios. Secondly lets assume the CB has the same spin rate factor for all shots.

If the CB hits the OB with a spin axis that is vertical the CB will travel down the tangent line and follow the 90 degree rule. If the spin axis is horisontal when the CB hits the OB the CB will swerve into: "The final ball direction is at 2/7 of the distance x between the tangent line and aiming line, measured perpendicular to the tangent line (i.e., parallel to the impact line)." (from TP_A-4).

With a spin axis that is tilted 45 degrees what will the final CB direction be? In the spin axis flip video the ball seem to start to roll with its spin axis approximately 45 degrees thats why i chose that angle. How can I predict carom angle from spin axis?View attachment 724955

No offense but if had to think in these terms i'd quit. Game is not that complicated. As much right-brain art as left-brain science.

 

[Bob Jewett]

It was shown a long time ago the the spin about the vertical axis does not change the path of the cue ball to any significant extent. It is only the spin around the other two axes -- the ones parallel to the table -- that cause the cue ball to curve change speed on the cloth.

There are many people who believe there is some effect like the very strange effects you see in fixed-axis gyroscopes. There is none of that for pool balls.

 

[bbb]

It was shown a long time ago the the spin about the vertical axis does not change the path of the cue ball to any significant extent. It is only the spin around the other two axes -- the ones parallel to the table -- that cause the cue ball to curve change speed on the cloth.

There are many people who believe there is some effect like the very strange effects you see in fixed-axis gyroscopes. There is none of that for pool balls.

besides the horizontal axis
what is the second axis that is parallel to the table?

 

[Patrick Johnson]

besides the horizontal axis
what is the second axis that is parallel to the table?

There are two horizontal axes: one aligned "north/south" (spin around this one produces masse) and the other aligned "east/west" (spin around this one produces follow/draw). You can think of the horizontal axes as "length and width" and the vertical axis as "height".

pj
chgo

 

[bbb]

There are two horizontal axes: one aligned "north/south" (spin around this one produces masse) and the other aligned "east/west" (spin around this one produces follow/draw). You can think of the horizontal axes as "length and width" and the vertical axis as "height".

pj
chgo

I’m still confused like with a Compass
isn't North South vertical and east west horizontal?

 

[Patrick Johnson]

I’m still confused like with a Compass
isn't North South vertical and east west horizontal?

Compasses are designed to work horizontally like the Earth's magnetic field (north/south is forward/back; east/west is right/left). The third axis is perpendicular to those (up/down).

But, like you, I do think of north as being "up" because of how a globe looks to me.

pj
chgo

 

[pagaspoling]

It was shown a long time ago the the spin about the vertical axis does not change the path of the cue ball to any significant extent. It is only the spin around the other two axes -- the ones parallel to the table -- that cause the cue ball to curve change speed on the cloth.

There are many people who believe there is some effect like the very strange effects you see in fixed-axis gyroscopes. There is none of that for pool balls.

But the ball can only spin on one axis. And how this axis is tilted will affect how much of the spin that will be able to curve the cueball after impact with the object ball. If the spin axis is completely vertical there will be no curve since the ball is not moving at the resting spot on the table.

It seems that you talk about spin as it would be happening around many axes at the same time?

 

[Patrick Johnson]

... the ball can only spin on one axis. And how this axis is tilted will affect how much of the spin that will be able to curve the cueball after impact with the object ball.

The CB curves when its surface moves crosswise on the cloth compared with its main ("forward") direction of travel, i.e., "masse" rotation. A tilted axis of rotation doesn't cause that - think of rolling a tilted barrel in a straight line, with the barrel exactly fitted within the CB so its upper and lower rims touch the CB's surface. That barrel's axis of rotation is the same as the ball's, and the part of its lower rim that's touching the surface moves parallel with the direction of travel.

pj
chgo

 

[pagaspoling]

The CB curves when its surface moves crosswise on the cloth compared with its main ("forward") direction of travel, i.e., "masse" rotation. A tilted axis of rotation doesn't cause that - think of rolling a tilted barrel in a straight line, with the barrel exactly fitted within the CB so its upper and lower rims touch the CB's surface. That barrel's axis of rotation is the same as the ball's, and the part of its lower rim that's touching the surface moves parallel with the direction of travel.

pj
chgo

....curve the cueball after impact with the object ball.

 

[pagaspoling]

The barrels are a good picture of what I'm wondering. It feels like a barrel with an smaller radius would, after the CB hits the OB, cause the cueball to move less forward than a barrel that is fatter and shorter.. Im wondering how much?

 

[Patrick Johnson]

....curve the cueball after impact with the object ball.

Before or after impact, same principle.

pj
chgo

 

[Patrick Johnson]

It feels like a barrel with an smaller radius would, after the CB hits the OB, cause the cueball to move less forward than a barrel that is fatter and shorter..

Yes, the barrel gets fatter/shorter as its rotation axis leans over more and more horizontal and its spin direction gets more and more vertical. When its axis is completely horizontal the "barrel" is just a flat vertical circle and there's only vertical rotation.

pj
chgo

 

[pagaspoling]

Yes, the barrel gets fatter/shorter as its rotation axis leans over more and more horizontal and its spin direction gets more and more vertical. When its axis is completely horizontal the "barrel" is just a flat vertical circle and there's only vertical rotation.

pj
chgo

Yes! How will it affect the carom angle?

 

[Patrick Johnson]

When its axis is completely horizontal the "barrel" is just a flat vertical circle and there's only vertical rotation.

Yes! How will it affect the carom angle?

With only vertical rotation the initial carom angle would be 90°, of course, and the follow on the CB would curve it forward of that, as usual. Are you thinking of something else?

pj
chgo

 

[Bob Jewett]

,,, It seems that you talk about spin as it would be happening around many axes at the same time?

Three axes, not many axes. The problem is a three-dimensional one. This is absolutely standard practice in physics. You resolve something that's in a random 3D direction into components along useful directions -- two horizontal and one vertical. (Or however you want to deal with them in the coordinate system you are using.)'

In the particular case of a uniform sphere, things are much simpler than for a shape like a top and it turns out that the spins along the three axes you have chosen do not interact with each other.

It turns out the because the spins don't really interact, the spin around the vertical axis does not affect the follow/draw/masse axes which are horizontal (and perpendicular to each other).

 

[pagaspoling]

Three axes, not many axes. The problem is a three-dimensional one. This is absolutely standard practice in physics. You resolve something that's in a random 3D direction into components along useful directions -- two horizontal and one vertical. (Or however you want to deal with them in the coordinate system you are using.)'

In the particular case of a uniform sphere, things are much simpler than for a shape like a top and it turns out that the spins along the three axes you have chosen do not interact with each other.

You can resolve the spin axis into three axes in order to understand what spin the ball has and how it will affect the path. But this doesn't mean that the ball is spinning on different axes it only spins around one axis that changes tilt during the shot.

If this axis is vertical there cant be any spin in the horisontal axis and vice versa (I will ignore any spin in the depth axis for now). I just want to now how to resolve all axes between vertical and horisontal into horisontal and vertical spin components in order to understand how much of the spin will affect the path (the spin component that is in the horisontal direction) from the tangent line into the final cue ball direction after collision with the cue ball.

 

[Bob Jewett]

.... I just want to now how to resolve all axes between vertical and horisontal into horisontal and vertical spin components in order to understand how much of the spin will affect the path (the spin component that is in the horisontal direction) from the tangent line into the final cue ball direction after collision with the cue ball.

I think any explanation of 3D angular momentum for a sphere will include this. The actual axis of rotation of a ball can simply be decomposed into its components along the major axes. You just take the x, y, and z components of the spin. It is very, very simple. You take the projection of the physical axis onto the analysis axes. That is the length of the spin vector multiplied by the cosine of the angle between the spin vector and the axis.

Examples: a ball that is rolling north without side spin has a spin vector that points west (the line of its axis by the right-hand rule). A ball that is spinning in place with left side spin has a spin vector that points straight down. A ball that is rolling northeast has a spin vector that points northwest which can be resolved into north and west.