The physics of side spin

[brechbt]

I've been trying to understand how side spin interacts with backspin or roll on the cueball. Imagine you have a geographic globe in your hand, and you spin it clockwise. Now imagine that, while it's spinning, you turn it upside down. It's now spinning counterclockwise. In this example, a 180 degree "roll" of the sphere has the effect of reversing the direction of the spin as well, relative to its surroundings.

My question is this: when you strike the cue ball with side spin and either top or bottom english, how is it possible to predict the effect of the side spin when the cue ball encounters a rail or another ball? For example, if you hit the ball with left spin and the cue ball rolls exactly 180 degrees before hitting a rail, you'd think it would behave as though you put right hand english on it instead, right? And yet, the effect of left or right english seems to be predictable regardless of cue ball roll or backspin.

I realize that this is a largely theoretical question that probably won't affect how anyone plays the game, but it's been bugging me. Come to think of it, though, I sometimes do have a shot where the cueball comes off the rail at an angle that seems to be opposite of what I would have predicted--I used to just pass it off to user error, but now I'm wondering. Can anyone explain this?

 

[Black-Balled]

This is your brain on drugs!

But, in more constructiveisity, Try playing billiards- no pocket pool- the big balls really act differently when they come off hails w/ hi or low spin. In pool, the effects are usually subtle, in billiards, dramatic.

 

[matta]

I've been trying to understand how side spin interacts with backspin or roll on the cueball. Imagine you have a geographic globe in your hand, and you spin it clockwise. Now imagine that, while it's spinning, you turn it upside down. It's now spinning counterclockwise. In this example, a 180 degree "roll" of the sphere has the effect of reversing the direction of the spin as well, relative to its surroundings.

I think this is where your confusion lies.

For my example, we'll play one tip of right one tip of bottom to get bottom right.

If you spin the cue ball, it is actually sliding across the table. It isn't rolling and flipping over. There is a gyroscopic affect trying to keep the ball's axis pointing in a constant direction. The ball does not want to roll.

So, in my example of equal parts bottom and right, you would get a sphere whose equator (I hope I can steal your earth analogy) travels between 10:30 and 4:30 (if you thought of the ball as a clock face). It would be spinning on an axis going through 1:30 and 7:30.

When struck well, even though the ball is traveling forwards, it is RARELY rolling until after contact and the friction of the cloth has killed the spin of the ball.

So in conclusion, your spin on the cue ball never "rolls" and gets reversed. The ball is sliding. And honestly, if it weren't for friction, it would spin just like you hit it, forever.

Hope that helps,

 

[brechbt]

I think this is where your confusion lies.

For my example, we'll play one tip of right one tip of bottom to get bottom right.

If you spin the cue ball, it is actually sliding across the table. It isn't rolling and flipping over. There is a gyroscopic affect trying to keep the ball's axis pointing in a constant direction. The ball does not want to roll.

So, in my example of equal parts bottom and right, you would get a sphere whose equator (I hope I can steal your earth analogy) travels between 10:30 and 4:30 (if you thought of the ball as a clock face). It would be spinning on an axis going through 1:30 and 7:30.

When struck well, even though the ball is traveling forwards, it is RARELY rolling until after contact and the friction of the cloth has killed the spin of the ball.

So in conclusion, your spin on the cue ball never "rolls" and gets reversed. The ball is sliding. And honestly, if it weren't for friction, it would spin just like you hit it, forever.

Hope that helps,

Thanks for the reply. I readily acknowledge that there will be instances where the cue ball is sliding with side spin as you describe. However, I believe that there will also be instances when the cue ball will be rolling or spinning backward with side spin, due to a more extreme application of top of bottom english along with the side spin. It is those instances that I'm curious about. It seems that the action of side spin will become unpredictable whenever the cue ball is NOT sliding.

 

[Andrew Manning]

Thanks for the reply. I readily acknowledge that there will be instances where the cue ball is sliding with side spin as you describe. However, I believe that there will also be instances when the cue ball will be rolling or spinning backward with side spin, due to a more extreme application of top of bottom english along with the side spin. It is those instances that I'm curious about. It seems that the action of side spin will become unpredictable whenever the cue ball is NOT sliding.

The geographical globe example confused you, and here's why:

The globe is fixed to the stand by pins at the north and south pole. It can only spin along this axis, due to the pins. Therefore when you turn it upside down, you're actually spinning it along two axes simultaneously; it's spinning around the poles, and you're also turning it by hand along a perpendicular axis.

That kind of spin never occurs on a pool table; i.e. a pool ball only spins around one axis at a time. If I hit with low left, the ball isn't simultaneously spinning left and turning backwards; instead it's spinning along a tilted axis. The side spin and backspin are actually just one "spin", and the direction of that spin is somewhere in between what it would be for pure draw or pure side. The friction of the cloth does decay this spin during the shot, but there's none of the reversing of direction you see in the globe with its fixed axis.

-Andrew

 

[Patrick Johnson]

I've been trying to understand how side spin interacts with backspin or roll on the cueball. Imagine you have a geographic globe in your hand, and you spin it clockwise. Now imagine that, while it's spinning, you turn it upside down. It's now spinning counterclockwise. In this example, a 180 degree "roll" of the sphere has the effect of reversing the direction of the spin as well, relative to its surroundings.

My question is this: when you strike the cue ball with side spin and either top or bottom english, how is it possible to predict the effect of the side spin when the cue ball encounters a rail or another ball? For example, if you hit the ball with left spin and the cue ball rolls exactly 180 degrees before hitting a rail, you'd think it would behave as though you put right hand english on it instead, right? And yet, the effect of left or right english seems to be predictable regardless of cue ball roll or backspin.

I realize that this is a largely theoretical question that probably won't affect how anyone plays the game, but it's been bugging me. Come to think of it, though, I sometimes do have a shot where the cueball comes off the rail at an angle that seems to be opposite of what I would have predicted--I used to just pass it off to user error, but now I'm wondering. Can anyone explain this?

Imagine tilting a 50-gallon barrel and rolling it along on its bottom edge (you might have done this with a garbage can). Now imagine the barrel contained within a large ball so that its top and bottom edges press tightly against the ball's surface, forming circles around the ball like latitude lines at the Earth's Arctic and Antarctic Circles. Now imagine rolling the ball with the barrel contained inside it and tilted so that the Antarctic Circle rolls along the ground like the edge of the barrel would if the ball wasn't there.

That's how a ball rolls with sidespin - it rotates around the barrel's axis, which is tilted, and it contacts the surface of the table along the ball's "Antarctic Circle", which is also tilted. There's only one (tilted) axis of rotation and it doesn't flip over the way you imagine (although it does gradually change its tilt).

pj
chgo

 

[brechbt]

Patrick and Andrew, good explanations. You've cleared this up for me. Thanks.

 

[matta]

Patrick and Andrew, good explanations. You've cleared this up for me. Thanks.

Well, it looks like you have it now that I am finished with my little drawing... Either way, here it is.

The blue circle is the cue ball.
The red circle is the contact point.
The line going through the cue ball is the axis of rotation.
The arc going around the cue ball is the direction in which the ball is spinning.

A picture is worth 1000 words? Let's see.

 

[Andrew Manning]

Well, it looks like you have it now that I am finished with my little drawing... Either way, here it is.

The blue circle is the cue ball.
The red circle is the contact point.
The line going through the cue ball is the axis of rotation.
The arc going around the cue ball is the direction in which the ball is spinning.

I picture is worth 1000 words? Let's see.

Your picture is worth all the words I wrote on the topic, but I don't think I reached 1000.

Anyway, good diagram to clearly illustrate what's happening.

-Andrew

 

[Patrick Johnson]

Well, it looks like you have it now that I am finished with my little drawing... Either way, here it is.

The blue circle is the cue ball.
The red circle is the contact point.
The line going through the cue ball is the axis of rotation.
The arc going around the cue ball is the direction in which the ball is spinning.

A picture is worth 1000 words? Let's see.

That picture is worth at least 1,000 words.

Here's the same picture with a few lines added to illustrate how tilted spin is actually a combination of side spin and follow (it has a "component" of each):



If the axis of rotation is tilted at 45 degrees, as shown, the total spin is divided equally between side spin and follow, with each being half as much as if the axis was either fully vertical or fully horizontal.

pj
chgo

 

[Andrew Manning]

That picture is worth at least 1,000 words.

Here's the same picture with a few lines added to illustrate how tilted spin is actually a combination of side spin and follow (it has a "component" of each):

If the axis of rotation is tilted at 45 degrees, as shown, the total spin is divided equally between side spin and follow, with each being half as much as if the axis was either fully vertical or fully horizontal.

pj
chgo

I think you mean draw when you say follow. The CB is travelling away from the viewer in the picture; you can tell by the below-center tip contact.

-Andrew

 

[Jal]

...If the axis of rotation is tilted at 45 degrees, as shown, the total spin is divided equally between side spin and follow, with each being half as much as if the axis was either fully vertical or fully horizontal.

Nice diagrams!

I think the bold part should read "with each being 1/sqrt(2) as much...", which is equal to 0.707... This can only be approximated because of the nature of the the square root of 2. There is no exact value for it.

Jim

 

[Andrew Manning]

Nice diagrams!

I think the bold part should read "with each being 1/sqrt(2) as much...", which is equal to 0.707... This can only be approximated because of the nature of the the square root of 2. There is no exact value for it.

Jim

Sure there is. It just can't be expressed in decimal.

-Andrew

 

[mbvl]

That picture is worth at least 1,000 words.

Here's the same picture with a few lines added to illustrate how tilted spin is actually a combination of side spin and follow (it has a "component" of each):

View attachment 82861

If the axis of rotation is tilted at 45 degrees, as shown, the total spin is divided equally between side spin and follow, with each being half as much as if the axis was either fully vertical or fully horizontal.

pj
chgo

As has been pointed out the example is a draw/spin shot, so it is not initially in accord with your (very appropriate) rolling/spinning barrel analogy. In this example the ball starts out sliding. But to carry the example a bit further, suppose this is a drag/draw shot with the intent of hitting it softly enough so that it will be rolling (along the antarctic circle) by the time it hits the object ball. At the time it achieves a rolling state, the spin axis will be tilted not to the right, but to the left.

Mark

 

[Jal]

Sure there is. It just can't be expressed in decimal.

It's an irrational number, which means it can't be expressed as:

sqrt(2) = a/b

where a and b are both whole numbers or themselves rational. It's unlike the number 1/3, for instance, which although in decimal form has an infinite number of fractional digits, can (obviously) be expressed as the ratio of 1 and 3.

The fact that it's irrational means that it can't be expressed with a finite number of digits. If it could, it would be rational. And if it can't be expressed with a finite number of digits, or as a ratio of two rational numbers, it means it can only be approximated. If the sides of a square are exactly one unit in length, for instance, the diagonal has no exact length, at least not measurably so.

But maybe my use of the term "exact" is a little muddy or different than yours. Please clarify if so.

Jim

 

[Patrick Johnson]

Andrew:
I think you mean draw when you say follow.

Jim:
the bold part should read "with each being 1/sqrt(2) as much..."

Mark:
At the time it achieves a rolling state, the spin axis will be tilted not to the right, but to the left.

LOL. Well, I think I got the punctuation right...

pj
chgo

 

[Patrick Johnson]

I think you mean draw when you say follow.

I don't know what you're talking about. Looks like follow to me:



pj
chgo

 

[Andrew Manning]

I don't know what you're talking about. Looks like follow to me:

View attachment 82942

pj
chgo

I stand corrected.

-Andrew

 

[Andrew Manning]

It's an irrational number, which means it can't be expressed as:

sqrt(2) = a/b

where a and b are both whole numbers or themselves rational. It's unlike the number 1/3, for instance, which although in decimal form has an infinite number of fractional digits, can (obviously) be expressed as the ratio of 1 and 3.

The fact that it's irrational means that it can't be expressed with a finite number of digits. If it could, it would be rational. And if it can't be expressed with a finite number of digits, or as a ratio of two rational numbers, it means it can only be approximated. If the sides of a square are exactly one unit in length, for instance, the diagonal has no exact length, at least not measurably so.

But maybe my use of the term "exact" is a little muddy or different than yours. Please clarify if so.

Jim

I guess when I said it can't be expressed in decimal, what I really meant is it can't be expressed numerically (regardless of radix). Also, as you point out, it can't be expressed rationally. However, its value is "exact" as I use the word exact; its value isn't a range, nor a variable, nor an approximation.

sqrt(2) - sqrt(2) = 0,
NOT
sqrt(2) - sqrt(2) ~= 0.

Of course this is an irrelevant semantic quibble, but that's what I meant by my comment.

-Andrew

 

[Jal]

I guess when I said it can't be expressed in decimal, what I really meant is it can't be expressed numerically (regardless of radix). Also, as you point out, it can't be expressed rationally. However, its value is "exact" as I use the word exact; its value isn't a range, nor a variable, nor an approximation.

sqrt(2) - sqrt(2) = 0,
NOT
sqrt(2) - sqrt(2) ~= 0.

Of course this is an irrelevant semantic quibble, but that's what I meant by my comment.

-Andrew

I think I get what you're saying. I mean I agree with the equations and that its value isn't a variable covering a range of numbers. And we both agree that it can't be written out, may I use the word "exactly", in positional notation.

Whether or not it has an exact value, as opposed to there being a unique procedure for generating its digits, I'm not completely sure. But since the diagonal of a 1X1 square certainly seems to have exact length, in that spirit I think I agree with you and that my language was sloppy.

Jim