CTE aiming mathamatics

DCsquared,
I thought that the "1 tip offset" was supposed to be a parallel shift from the CTE position?

Like this:
img062.jpg
 
DCsquared said:
Please Note that in the following diagrams any letter with a ‘ (prime) is a length and any with out is a angle and capital letters are points. Also the green ball is the “ghost ball”.

Variables defined:

P = pivot point
E = edge of object ball

m’ = Distance from center of object ball to desired pocket
mx’ = x component of m’
my’ = y component of m’

x’ = radius of cue ball (indicated by all red lines)

b’ = bridge length (green line)

l’ = length from the pivot point (P) to the edge of the object ball (E) (purple line)

n’ = length from the center of the cue ball to the x’ the runs from the center of the object
ball to E

d’ = distance at the edge of the cue ball between b’ and l’

a = angle between m’ and my’ (vertical)

b = angle between the line from the center of the ghost ball to desired pocket and n’

c = angle between n’ and my’ (vertical)

d = angle between l’ and vertical

e = angle between n’/b’ and l’


CTE for Various Shots:

Shot #1: Low angle shot ( b < 30 degrees)

Image #1 is a full table view of this shot.

Image #2 shows the angles created upon cue ball impact with object ball.

Image #3 include from point P to object ball.


In this shot the desired angle that we wish to generate in order to make the shot is angle a. This is difficult because angle b is hard to measure as there are no physical reference points for it’s measurement.

Therefore we can use physical reference points to generate d and e which in turn will create angle b.

First how a is dependent on b, d and e by using similar angle laws. Z rule and opposite angle rule (high school math).

a = b + c [1]
c = e + d [2]

rearranging and solving for a gives:

a = b + (e+d)
= b + e + d [3]

Using CTE you initially set up distance d’ off the center of the q ball creating a straight line between P and E. This takes the measurement of angle d.

You then pivot distance d’ about point P to the center of the cue ball (inline with n’). This generates angle e.

The collision of the object ball and the cue ball produces angle b.

You now have the 3 pieces of information needed to generate angle a.

The other variable that you need to know is distance d’. The correct d’ is proportional to b’. As your bridge length increases so must your d’. This is why you must practice with CTE to figure out what d‘ correlates to your comfortable bridge length.

Shot # 2 No angle shot (DEAD straight)

Image #4 is a full table view of this shot.

Image #5 shows the angles created upon cue ball impact with object ball.

Image #6 include from point P to object ball.

As you can see in the this shot angle b goes to zero. That is why this is much easier to picture.




Therefore equations #1, #2 and #3 become

c = e + d
c = a
a = e + d

Measure d pivot distance d’ about P to measure e. This then gives you angle c which in turn generates angle upon impact.

Shot #3 Half ball Hit ( b = 30 degrees)

Image #7 is a full table view of this shot.

Image #8 shows the angles created upon cue ball impact with object ball.

Image #9 include from point P to object ball.

In this shot angle c has gone to zero.

Therefore equations #1, #2 and #3 become

a = b
0 = e + d
a = b

In this shot no measurements of e and d are not required as they both equal 0. Therefore you can line the center of the ball at the edge to generate b which in turn generates a upon impact.

Shot #4 acute angle cut (b > 30 degrees)

Image #10 is a full table view of this shot.

Image #11 shows the angles created upon cue ball impact with object ball.

Image #12 include from point P to object ball.


Also not that I have added 3 Points:

A: Center of object ball
B: Center of ghost ball
C: End of red (length = 2 x’) segment

Line AB is equal in length to BC
Line BC is the projection of AB across the vertical axis of the ghost ball such that the angle ABC is 90 degrees. This is important so that the angle laws still work. It also shows why on shots when b > 30 degrees you l’ is on the opposite side of n’ then in shots when b < 30 degrees.

In this case everything works the same. Angles d and b’ are also projected across P’s vertical axis.

Equations 1 and 2 remain the same:

a = b + c
c = d + e

measure d using by lining up P to E. Pivot d’ to center of cue ball to generate e. b is generated by the collision between object and cue balls. The results is angle a.

Pretty sure that should cover every shot on the table while using CTE. Of course spin and throw and all of that fun stuff are not taken into account.

Enjoy!
Click to expand...


I used to have this recurring dream about Fr. Jacobs, trig class, and a pop-up exam... basically, you just made me break into a cold sweat :-o

Lou Figueroa
 
lfigueroa said:
I once had a dance instructor who once told me the same thing.

Lou Figueroa
*never*
give your wife
dance classes
for a present
Click to expand...

Lou- I did that ONCE with an ex-gf. Never again. Between me sucking on my albuterol and my hamstrings cramping, it was the worst experience ever.
 
SpiderWebComm said:
Lamas- no parallel shift. It's an arc.
Click to expand...

Where then is the pivot point/axis of said arc? Is it at a different location than the pivot point/axis established by the CTE bridge placement - otherwise you would only pivot back to the same center of the CB?

Kinda reminds me of the instructions I got on my honeymoon.
 
LAMas said:
Where then is the pivot point/axis of said arc? Is it at a different location than the pivot point/axis established by the CTE bridge placement - otherwise you would only pivot back to the same center of the CB?

Kinda reminds me of the instructions I got on my honeymoon.
Click to expand...

Your bridge can be anywhere from 10-12" --- that allows for shots longer than a diamond apart. If you imagine your bridge as the center of a circle and the OB as the edge of the circle - pivot along that arc. Focus solely on moving your tip while rotating your upper torso / pivoting from your back hip. This calibrates the pivot point in your cue.
 
SpiderWebComm said:
Why perceive bases of ghost balls 1 1/8" when perception can by skewed?
Click to expand...

D,
I had to give up the CTE when my instructors (all fairly high level pro players) insisted I begin targeting specific portions of the pocket, to make my position play better. I just couldn't incorporate CTE into a system that would reliably hit the exact point in the pocket I chose.

I will say that all of the pro's that I have discussed it with believe that pocketing is the easiest part of the game (most of them started with ghost ball, and now just aim by feel once they identify the contact point on the object ball that will pocket the ball in the specific portion of the pocket); and that the fine control of the white ball can only be attained if they are quite exact in their pocketing target. I don't think they would mind if I used CTE as long as I could hit specific portions of the pocket (actually my pocketing is getting good enough now, I'm not really sure I need any system; but I sure could have used it a couple of years ago).

Do you know any CTE'ers that have figured out how to attain such precision in their pocketing? I think the math for THAT would be a bit more complicated; but surely someone can do it with CTE. I couldn't pin Hal down on how to achieve it using CTE (a year or two ago).
 
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LOL this is all very funny :thumbup:. You guys are making aiming way to difficult. Just get out there and practice....

It seems like there are a lot of people on here trying to find that one thing that will instantly improve their game or make them pro.
 
Why do I punish myself? But no, it's ok. It's karma for a squirrel I ran over a year ago or something.

So:

There's some correlation between bridge length and distance between the balls but let's forget that for the moment and assume we have more than a diamond between them.

1. Address ball (using best guess/common sense where to tentatively line up, and bearing in mind the tip offsets for half-ball, over half-ball, and under half-ball).

2. Plant your bridge in such a way that the cue points directly at the edge of the OB.

3. Imagining that the OB is the center of a clock, and the cue is the second hand, "sweep" the cue along an arc. Sweep until the tip appears to be pointing through the center of the CB(?). Different people may need different amounts of sweep/pivot(?) You can replant your bridge or just twist slightly to make the sweep/pivot while maintaining a straightish shooting alignment. Or you plant knowing ahead of time (through experience) about where your bridge will be planted post-pivot.

4. Shoot.

Any of the above incorrect? Any major chunk missing?
 
CreeDo said:
Why do I punish myself? But no, it's ok. It's karma for a squirrel I ran over a year ago or something.

So:

There's some correlation between bridge length and distance between the balls but let's forget that for the moment and assume we have more than a diamond between them.

1. Address ball (using best guess/common sense where to tentatively line up, and bearing in mind the tip offsets for half-ball, over half-ball, and under half-ball).

2. Plant your bridge in such a way that the cue points directly at the edge of the OB.

3. Imagining that the OB is the center of a clock, and the cue is the second hand, "sweep" the cue along an arc. Sweep until the tip appears to be pointing through the center of the CB(?). Different people may need different amounts of sweep/pivot(?) You can replant your bridge or just twist slightly to make the sweep/pivot while maintaining a straightish shooting alignment. Or you plant knowing ahead of time (through experience) about where your bridge will be planted post-pivot.

4. Shoot.

Any of the above incorrect? Any major chunk missing?
Click to expand...

The cue tip is now at the center of the CB and the cue is aimed at the edge of the OB.....shoot.....30 degree cut accomplished...but how about 45 degrees, 60 degrees or 85 degrees?:confused:

"Any major chunk missing?"
CTE requires a lateral shift away from the CTE Line (CTEL). Some say 1 tip diameter to the side.....some say laterally and parallel to the CTEL....SpiderWeb Dave says not parallel but in an arc, but from the bridge or while pointed to the edge of th OB like your clock analogy? But how far for a given cut angle....some say it doesn't matter - works for all angles?
 
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CreeDo said:
Why do I punish myself? But no, it's ok. It's karma for a squirrel I ran over a year ago or something.

So:

There's some correlation between bridge length and distance between the balls but let's forget that for the moment and assume we have more than a diamond between them.

1. Address ball (using best guess/common sense where to tentatively line up, and bearing in mind the tip offsets for half-ball, over half-ball, and under half-ball).

2. Plant your bridge in such a way that the cue points directly at the edge of the OB.

3. Imagining that the OB is the center of a clock, and the cue is the second hand, "sweep" the cue along an arc. Sweep until the tip appears to be pointing through the center of the CB(?). Different people may need different amounts of sweep/pivot(?) You can replant your bridge or just twist slightly to make the sweep/pivot while maintaining a straightish shooting alignment. Or you plant knowing ahead of time (through experience) about where your bridge will be planted post-pivot.

4. Shoot.

Any of the above incorrect? Any major chunk missing?
Click to expand...

Your bridge is planted pre-pivot at your standard 10-12" bridge length with no care of the arc. When your bridge is locked in, hip pivot along the shot arc.
 
LAMas said:
The cue tip is now at the center of the CB and the cue is aimed at the edge of the OB.....shoot.....30 degree cut accomplished...but how about 45 degrees, 60 degrees or 85 degrees?:confused:

"Any major chunk missing?"
CTE requires a lateral shift away from the CTE Line (CTEL). Some say 1 tip diameter to the side.....some say laterally and parallel to the CTEL....SpiderWeb Dave says not parallel but in an arc, but from the bridge or while pointed to the edge of th OB like your clock analogy? But how far for a given cut angle....some say it doesn't matter - works for all angles?
Click to expand...

I think you guys are reading the Dr. Dave page. Offset your tip 1/2 ball with your cue parallel to the CTEL with your tip pointing at nothing at all. If you point at the OB edge, it's 100% not parallel to the CTEL. Pivot along the arc and re-think. It's physically impossible to be at a 1/2 ball hit unless you're bridging on the CTEL itself.
 
Thank you so much, this is so simple a child could get it. Now my game will be so much easier. It sure beats a sharp stick in the eye. This is something like E=MC sq. Thanks Again
 
The first post in this thread finally broke my back. I'm all done.

Even if I didn't grasp the trigonometry and the calculus, I could at least follow along with the geometry by Pat Johnson, JAL, Mike Page and of course Dr. Dave but you have finally done me in DCsquared. My spirit is finally broken. I'm all done with the academics........well, at least their math.

I'm going to try some hypnosis and maybe even Buddhism to improve my game. Are there any Buddhist pool players on the pro circuit?

Lucky Joe
 
SpiderWebComm said:
I think you guys are reading the Dr. Dave page. Offset your tip 1/2 ball with your cue parallel to the CTEL with your tip pointing at nothing at all. If you point at the OB edge, it's 100% not parallel to the CTEL. Pivot along the arc and re-think. It's physically impossible to be at a 1/2 ball hit unless you're bridging on the CTEL itself.
Click to expand...

Is this 1/2 Ball offset to the side - parallel to CTEL?

CTE_OFFSET.jpg
 
Sorry dudes, my solar panels arrived today meaning that I have lots of work to do in the next couple days. I will have to answer all of the questions regarding my first post on friday. Untill then keep asking away, I'll try to answer them as simply as possible then.

Another thing that is bothering me is how to determine point P. I'm pretty sure that I have figured a way to pin point it's location with respect to each shot, but I need to figure it out on paper before I figure out what that is.

Also for the dudes who are having a hard time grasping the math inside my first post, I will do a quick tutorial of the super super super super super easy math that was used. Don't worry no trig calculations or calc involved. Trust me I hate breaking backs!
 
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