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08-05-2020, 04:54 PM

yes, you are right. I see that now. My mistake. Thanks for the explanation.
  
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Bob Jewett
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08-05-2020, 05:39 PM

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Originally Posted by AimPro Billiards View Post
yes, you are right. I see that now. My mistake. Thanks for the explanation.
BTW, I used to take the perpendicular as in your calculation but many years ago someone (here? RSB?) pointed out that the base of the isosceles triangle has less error -- and is easier to use on the table.


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08-05-2020, 06:24 PM

I'm embarrassed to remember that I learned how to do this exact problem correctly in high school math -- and apparently forgot! I also forgot the basic approach of drawing a diagram before writing any equations, thinking it was too simple a problem to need that.

But I'm intrigued by your comment that the correct method is easier to do on the table. Could you explain that. To me, it's just estimating the distance between the two endpoints. [Put finger down to mark starting position; move cue to other position and estimate the distance.] You are suggesting to estimate half the distance and doubling it is somehow easier as well as more accurate?
  
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Bob Jewett
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08-06-2020, 01:13 PM

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Originally Posted by AimPro Billiards View Post
... You are suggesting to estimate half the distance and doubling it is somehow easier as well as more accurate?
No. The division into two separate distances is only in the analysis. The measurement is of the base of an equilateral triangle for which the two sides are your cue stick. Just like in the original diagram. Only the entire distance is measured. From the position of the bumper to the new position of the bumper. That distance is the number of degrees directly. No division or multiplication. Just take the distance.

(For angles over 45 degrees, you measure the complement and subtract, as described above. But that is only for such thin cuts.)


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Yesterday, 08:08 AM

OK, thanks. I get it.

I'll comment that in the past, I've tried measuring the complement angle for thin cuts. It's the obvious approach. But it didn't work for me generally, because I found that estimating the line of the complement (the tangent) was not easy for me to do accurately enough (within one degree). Do you have any suggestions of an easy way to get the tangent direction accurately?

My only method is using "Table Geometry" (see my video https://www.youtube.com/watch?v=4PGSQiq5b9g&t=186s) and getting the "Object ball angle", to which I can add 90 degrees. But at that point, I'd rather just get the "Cue ball angle" and compute the cut angle.
  
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Bob Jewett
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Yesterday, 11:15 AM

Quote:
Originally Posted by AimPro Billiards View Post
O ... Do you have any suggestions of an easy way to get the tangent direction accurately?
...
The best I know of, other than to use a fixture is to place my cue stick as in response 28.


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Dr. Dave and Bob J to the rescue
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Dr. Dave and Bob J to the rescue - Yesterday, 10:52 PM

Quote:
Originally Posted by AimPro Billiards View Post
OK, thanks. I get it.

I'll comment that in the past, I've tried measuring the complement angle for thin cuts. It's the obvious approach. But it didn't work for me generally, because I found that estimating the line of the complement (the tangent) was not easy for me to do accurately enough (within one degree). Do you have any suggestions of an easy way to get the tangent direction accurately?

My only method is using "Table Geometry" (see my video https://www.youtube.com/watch?v=4PGSQiq5b9g&t=186s) and getting the "Object ball angle", to which I can add 90 degrees. But at that point, I'd rather just get the "Cue ball angle" and compute the cut angle.
One comment stuck in my mind. It had to do with why would a player want to know an angle to pocket a ball? None of the aiming systems I know are based on a way to target based on degrees. But there is one area of the game where knowing the angle is beneficial, position. The benefit of knowing the cb path in degrees after contact tells us how to avoid scratches, whether the cb will miss or hit a ball off contact or If the path into a rail will result in position.

“Rolling Cue Ball Deflection Angle Approximations” ILLUSTRATED PRINCIPLES David Alciatore, PhD (“Dr. Dave”) https://billiards.colostate.edu/bd_a...2011/nov11.pdf is a great place to start. While Dr. Dave’s peace sign can be used from the cue ball side of the collision to estimate where the rolling ball will deflect after contact, the fact that it is known to approximate 30° can be used from the opposite side of the shot. Line the ghost ball centre to the cb centre with the cue. My shaft on my cue is 29 inches. Pivoting my cue joint, from the gb centre through ~15 inches equals about 30°. That applies on the ¼ through ¾ ball cuts. On thinner cuts the formula used is about 70% of the angle from cue line to tangent line. This allows a player at the table to simply use the cue to find the natural rolling path off contact on these thin shots.
  
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Yesterday, 10:58 PM

Quote:
Originally Posted by Imac007 View Post
Pivoting my cue joint, from the gb centre through ~15 inches equals about 30°.
This is equivalent to Bob’s technique of moving the butt 30 inches.

pj
chgo
  
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Today, 12:28 PM

Quote:
Originally Posted by Patrick Johnson View Post
This is equivalent to Bob’s technique of moving the butt 30 inches.

pj
chgo
Exactly the point of the perceptual move to the joint, especially when the surroundings make it easier. The cue can be used at the table to measure both 58” and half that amount 29”. Thinking inside the box, working with what’s there.

Paths into a rail also remain the same regardless of which end you look at them. A good example, I teach, has to do with spot on the wall. The concept is explained here. https://billiards.colostate.edu/bd_a...2011/feb11.pdf

It can be combined with another concept called Magic Spot. The 3 cushion diagram 1 in the Dr. Dave spot on the wall pdf goes over the spot, for that table. The idea is explained here. https://billiards.colostate.edu/reso...image_kick.pdf

Once the mirror contact point is decided, the line from the starting point through the magic spot tracks to the mirror. Of course, the cb is seldom in the reflective position at the table. By extending the original cue line, as in the spot on the wall idea, a new spot on the wall is established.

But there is almost never a convenient wall. The trick is for the player to become the spot. From the spot, the player can pivot to the cb location. Where that line crosses the rail becomes the new cue line. The point is the line crosses the rail at the same location regardless of which end of the line you look from.

Sometimes you need to calibrate for the magic spot. Tables are different. The method is quite simple. Starting from the corner, discover the line to the first rail that ends up, using running side, as 3 to the corner (the mirror). Once that track is known the trick is to find another mirror track to the third cushion. A good place to begin is from the second diamond up the long rail from the original corner start. Pick a starting point on the rail. The contact point on the opposite rail off 3 cushions through the magic spot with running follow should mirror the starting position. For the table you are calibrating, the magic spot must lie somewhere along that line or the table won’t work.

Where the two mirror image shot lines cross is the calibrated magic spot for the table.
  
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