The physics of side spin

Jal said:
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
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Well, I'm certainly glad we were able to resolve that. Now we can move on to less important matters :D

-Andrew
 
Jal said:
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....
Click to expand...
Well, to the extent that 1/3 = 0.3(overbar) you might accept a similar notation for the result:

sqrt(2) = 1+1/(2+1/(2+1/(2+1/(2+1/(2+1/(2+1/(2+1/(2+1/(2+1/.....))))))))

where the overbar is placed above "1(2+".
 
I think the following video might help you better understand some of the pertinent effects:


Regards,
Dave

brechbt said:
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?
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Dr Dave,

Is it safe to say that, for all practical purposes, swerve occurs during this transition from one axis tilt to the other? Meaning that once the transition has taken place, there will be no additional swerve?

I have found that on many long soft cut shots with inside english that I don't have to hit them with low and inside, I can just hit softer and hit high and inside. This tremendously reduces or eliminates the swerve and I can aim straight at the shot without allowing for Swerve.


Royce Bunnell
www.obcues.com
 
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Bob Jewett said:
Well, to the extent that 1/3 = 0.3(overbar) you might accept a similar notation for the result:

sqrt(2) = 1+1/(2+1/(2+1/(2+1/(2+1/(2+1/(2+1/(2+1/(2+1/(2+1/.....))))))))

where the overbar is placed above "1(2+".
Click to expand...
Yes, I accept that, since it's a solution to:

y+1 = 2 + 1/(y + 1)

Is there a continued radical version of it which uses only whole numbers, as with the Golden Ratio?

Jim
 
RBC said:
Dr Dave,

Is it safe to say that, for all practical purposes, swerve occurs during this transition from one axis tilt to the other? Meaning that once the transition has taken place, there will be no additional swerve?
Click to expand...
That is correct. Swerve occurs only while the CB is still sliding (i.e., not rolling yet). FYI, I have much more detailed info in this topic here:


Regards,
Dave
 
Jal said:
... Is there a continued radical version of (square root of 2) which uses only whole numbers, as with the Golden Ratio?
Click to expand...
Since the golden ratio continued radical uses all minimum whole numbers (1), it seems unlikely, as the value of the CR is monotonic in each of its components, and sqrt(2) < GR. But 1+sqrt(2) = sqrt(3+sqrt(8)). The 8 can be expanded in several ways as a CR, i.e.: sqrt(2) = sqrt(3+sqrt(1+sqrt(42+sqrt(42+sqrt(42...)))-1
 
Bob Jewett said:
Since the golden ratio continued radical uses all minimum whole numbers (1), it seems unlikely, as the value of the CR is monotonic in each of its components, and sqrt(2) < GR. But 1+sqrt(2) = sqrt(3+sqrt(8)). The 8 can be expanded in several ways as a CR, i.e.: sqrt(2) = sqrt(3+sqrt(1+sqrt(42+sqrt(42+sqrt(42...)))-1
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If you guys keep this up, somebody might accuse you of liking math. And then you might get beat up after class. :wink:

Concerned,
Dave
 
Jal said:
I[...] 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.
[...]
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Hmmm.

So the diagonal of a 1X1 square has a length of sqrt(2)--and that line of mystical length is itself the side of a new square that has diagonal of exact length 2. So is it the side or the diagonal of a square that has no exact length?
 
RBC said:
... I have found that on many long soft cut shots with inside english that I don't have to hit them with low and inside, I can just hit softer and hit high and inside. This tremendously reduces or eliminates the swerve and I can aim straight at the shot without allowing for Swerve.

Royce Bunnell
www.obcues.com
Click to expand...
Hi Royce,

One simple result of the analysis is that the final path of the cue ball will be parallel to a line joining the bottom of the cue ball and the spot on the cloth that your stick is pointing at. For a given amount of side spin, a shot with draw points to a spot on the cloth much closer to the cue ball than a shot with follow (for most players). The angle of swerve goes down more or less directly with how far away the "spot on the cloth pointed at" is.

A corollary of this result is that if you manage to shoot with a truly level stick, there will be no swerve on side spin shots, as the cloth spot is infinitely far away.
 
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