When can you no longer cross the tangent line??

MOJOE

MOJOE

Work Hard, Be Humble. jbk
Silver Member
I was watching a DVD on CB control. It talks about the tangent lines which I comletely understand. Also talks about using 12:00-1, 12:00-2 etc. on the CB strike to get the CB to move forward X amount to get to your desired location on the table.

Obviously this works ONLY depending on the initial cut angle. When (at what angle), does it become impossible to get forward of the tangent line. I know with inside enlish you can get there after rail contact, but not before, obviously.

I am just curious how others figure how far they can go forward depening on their angle. I want systems here, not just I do it by feel? What is your basis for figuring this out.

I also posted this on the Cuetable site but thought I may get some different methods on figuring this on this site.

CueTable Help

 
I'll take a stab at it...

I usually consider the point of no return with regard to high/low english on a cut to be when I am cutting 'half' of the object ball or more. I have found that high and/or draw english does not 'take' when cutting a ball more than half...I would estimate the angle of the cut at somewhere between 22 1/2 to 30 degrees. Anything thinner and I don't beleive any english will affect the path of the cue ball to any reliable degree.

My reasoning is that thinner than half, it is more of a glance off the object ball and less than half, you are actually making more direct contact form cue ball to object ball and the cue ball will 'slow down' enough for the high/low english to 'take' on the felt.

Confused? Me too:rolleyes: ...but that's my theory and I'm sticking to it:) .

I hope this is what you were looking for. I tried to explain it so that it's more than just a 'feel' thing the best I could.

I am interseted to see if anyone else tackles this. Maybe we have a physisist out there.

L8R...Ken
 
Using the 30 degree rule, it's hard to reverse-calculate the spot you're mentioning. I mean, we could find it for this particular position of the OB, but what good what that do? The OB's never in the same exact spot when you need it. The rule will, however, let you be able to measure whether one will work or not.

Keep in mind that the 30 degree rule applies to (1/4-3/4) ball hits, and only works perfectly if you hit it SOFT. Any harder and you have to start drawing parabolas...

If you don't know the rule I speak of, do some research.

-s

(I guess what I'm getting at is, you're looking for a hard-and-fast 'point of no return' when you'd be better off knowing how to judge each shot, as each shot is different)
 
I guess I'm not understanding the question.

Using follow english on the cb will always cause it to roll forward from the 90 degree tangent line.
 
Sometimes you can be too systematic. There's nothing wrong with taking extra measure in thought. But when it comes down to it you have to go with experience.
 
MOJOE said:
Obviously this works ONLY depending on the initial cut angle. When (at what angle), does it become impossible to get forward of the tangent line.
Click to expand...

Keep the line from the CB to the contact point on the OB (the initial line of aim) in mind. Your CB spins in that direction using follow. After contact, the CB starts along the tangent line and the spin then changes its direction to some degree.

But, if the tangent line and the spin are in almost the same direction, the spin will not have much effect at all, since the direction it's pushing is the direction the ball's already going. I like to visualize this spin just after contact, and picture how much it will cause the CB to curve by visualizing the direction of spin and the direction of CB travel together. I know that's not really an answer to your question, but I find thinking about it this way allows me to reliably predict how far I can bend the CB with follow or draw given the cut angle of the shot.

-Andrew
 
MOJOE said:
... I am just curious how others figure how far they can go forward depening on their angle. I want systems here, not just I do it by feel? What is your basis for figuring this out.
...
Click to expand...

Here is a system for calculating the follow angle that works pretty well for all angles but is easiest to apply for fairly thin cuts. Imagine the tangent line. Take the cue ball position and drop a perpendicular to the tangent line from the cue ball. Go from the the cue 3/4 of the way along that perpendicular to the tangent line. Put a coin there. Sight from that coin through the center of the ghost ball and that will give the direction of the cue ball after it follows off the object ball.

This system assumes that the cue ball is rolling smoothly on the cloth, which is as much follow as you will normally ever see.
 
Thanks Bob!

Thanks Bob,

That was exactly the kind of info that I was looking for. I believe that I understand. I have a really good idea normally, but sometimes my gut just is not accurate enough. I will expriment with what you say here tonight.

Thanks to all else who have given opinions as well. I have experimented with this quite a bit, I just wanted to know if there was a formula that was pretty safe to rely on.

Mojoe

Bob Jewett said:
Here is a system for calculating the follow angle that works pretty well for all angles but is easiest to apply for fairly thin cuts. Imagine the tangent line. Take the cue ball position and drop a perpendicular to the tangent line from the cue ball. Go from the the cue 3/4 of the way along that perpendicular to the tangent line. Put a coin there. Sight from that coin through the center of the ghost ball and that will give the direction of the cue ball after it follows off the object ball.

This system assumes that the cue ball is rolling smoothly on the cloth, which is as much follow as you will normally ever see.
Click to expand...
 
Bob, Would the exact opposite be true for a CB that is drawing with maximum backspin when it comes in contact with the OB? I would think it would be close.

JBK
 
MOJOE said:
...
I am just curious how others figure how far they can go forward depening on their angle. I want systems here, not just I do it by feel? What is your basis for figuring this out.
Click to expand...
The CB's direction after it reaches natural roll can be determined using this:

http://ww2.netnitco.net/users/gtech/CBDirection4.jpg

This is a graphical depiction of the following formula, which gives its final direction, V', in terms of its initial direction, V, and spin, W. The vector R is the displacement vector from the center of the ball to the contact point on the cloth.

V' = (5/7)[V - (2/5)W X R]

For the diagram, the V that's plugged into the formula is the cueball's immediate velocity after the collision. Its magnitude is (Vi)sin(C), where Vi is its pre-impact speed, and C is the cut angle. Its direction is along the tangent line.

For some tip offset (contact point) from centerball, B, as seen from the shooter's perspective, the spin on the cueball, W, is given by:

W = (5/2)(1/R^2)B X Vi

so the term (2/5)W X R becomes:

(1/R^2)(B X Vi) X R

This method of predicting its final direction, as with all methods, loses accuracy where spin is lost (or gained) on the way to the object ball, and/or during the collision with it. The spin loss due to friction during the collision can be considerable, up to 35.7% in some cases. The effective length of b in the diagram has to be adjusted accordingly.

Unless you're familiar with vectors, the math isn't going to mean much to you... but you did ask for justification. The short of it, as the other posters have pointed out, is that you can always get the cueball to move forward of the tangent line. The only exception I can think of would be at a very severe cut angle with a very underweight cueball.

Jim
 
MOJOE said:
Bob, Would the exact opposite be true for a CB that is drawing with maximum backspin when it comes in contact with the OB? I would think it would be close.

JBK
Click to expand...
There is a similar construction for draw, assuming "unit draw" in which the top of the cue ball is motionless. (Some may have trouble visualizing a ball with the top motionless, but for a smoothly rolling ball, the bottom is motionless, and if you stand on your head, I think it will be clear.)

For nearly full follow shots, a simple rule of thumb is that if you cut the object ball one degree to the right, the cue ball will go three degrees to the left of its original path, or four degrees to the left of the object ball's path.
 
draw "trisect" system

MOJOE said:
Bob, Would the exact opposite be true for a CB that is drawing with maximum backspin when it comes in contact with the OB? I would think it would be close.
Click to expand...
For a draw shot with a typical amount of "good" action, the "trisect" system is very effective. For illustrations and a detailed explanation, see my March '06 article. Also, FYI, I have advice on how to predict CB direction for all types of shots here:
Regards,
Dave
 
full and thin hits

Bob Jewett said:
There is a similar construction for draw, assuming "unit draw" in which the top of the cue ball is motionless. (Some may have trouble visualizing a ball with the top motionless, but for a smoothly rolling ball, the bottom is motionless, and if you stand on your head, I think it will be clear.)

For nearly full follow shots, a simple rule of thumb is that if you cut the object ball one degree to the right, the cue ball will go three degrees to the left of its original path, or four degrees to the left of the object ball's path.
Click to expand...
Bob's posts reminded me of an article by George Onoda that has good illustrations of the thin-hit and full-hit approximations. I just added the following to my "where the CB goes" document:

For roll shots, there are good approximations for the CB deflection angles. The math and illustrations can be found in a 1988 technical article by George Onoda.

For a fairly full hit (less than a 1/4-ball hit), the CB will deflect about 2.5 times the cut angle (e.g., for a shot with a cut angle of 10 degrees, the CB will deflect about 25 degrees).

For a fairly thin hit, with a ball-hit-fraction greater than 3/4, the CB will deflect about 70% of the angle between the aiming line and the tangent line.

See Figures 4 and 5 in the article for illustrations.

As with the 30 degree rule and trisect system, the full-hit and thin-hit rules apply to the final direction of the CB. The actual final path of the CB is shifted down the tangent line with higher speed.
​
I think the document is now a useful summary of systems for predicting CB motion for most pool shots.

Regards,
Dave
 
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dr_dave said:
As with the 30 degree rule and trisect system, the full-hit and thin-hit rules apply to the final direction of the CB. The actual final path of the CB is shifted down the tangent line with higher speed.
Click to expand...

I think there is a fine point here that is being missed (or at least underemphasized). For a rolling ball, the initial path is a portion of a parabola. With higher speed the scale of the parabola increases, but it is still a parabola. I often see people here say in posts things like "the CB stays on the tangent line longer" for shots hit at higher speed. As I understand it, this is false. The path of the CB leaves the tangent line immediately. The better wording would be "the CB stays NEAR the tangent line longer". Please correct me if I am wrong.

Mark
 
mbvl said:
I think there is a fine point here that is being missed (or at least underemphasized). For a rolling ball, the initial path is a portion of a parabola. With higher speed the scale of the parabola increases, but it is still a parabola. I often see people here say in posts things like "the CB stays on the tangent line longer" for shots hit at higher speed. As I understand it, this is false. The path of the CB leaves the tangent line immediately. The better wording would be "the CB stays NEAR the tangent line longer". Please correct me if I am wrong.

Mark
Click to expand...
You are right. Of course, with a follow shot, the cueball is lifted off the surface a bit, so there is a little delay to its forward curve.

Jim
 
Jal said:
You are right. Of course, with a follow shot, the cueball is lifted off the surface a bit, so there is a little delay to its forward curve.

Jim
Click to expand...

I disagree with the ball leaving the surface. Its all about the spinning ball and friction. After equal masses collide forward inertia is stopped momentarily yet the ball spins and acceleration is gradual.
 
When can you no longer cross the tangent line??
Click to expand...

You've got some good information, but I don't think anybody has answered this question directly. The answer is the CB will always cross the tangent line if hit with follow, and it will do it more or less immediately after contact with the OB.

But the tangent line isn't like the one in your drawing. It passes through the center of the CB, not the OB - like the blue line in your drawing, not the yellow one. Maybe that's what has confused you?

pj
chgo
 
Thanks to everyone with some great info for me to chew on. You all have been very helpful. As PJ mentioned, I understand that the tangent line is actually through CB center, my illustration was incorrect.

Rep to all who have helped with my question.

Peace, Mojoe
 
Patrick Johnson said:
But the tangent line isn't like the one in your drawing. It passes through the center of the CB, not the OB - like the blue line in your drawing, not the yellow one. Maybe that's what has confused you?

pj
chgo
Click to expand...

That's not correct either. The tangent line does not pass through the center of either ball, but is tangent to both balls. It's halfway between the yellow line and the blue one.

Mark
 
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