Are rail sights in the correct place? Should the gutter line be 2:1 rather than the cushion nose?

[mr3cushion]

This video will 'Debunk' any Nonrealistic theories about, 'smaller' tables have 'shorter return angles.'

Video shows Frederic Caudron has a 'High Run' of 32 on a 4'x8' 3C table. Pay close attention to the 3rd/4th/5th rails returns. They are 'Identical' to a 5'x10' 3C table.

 

[justnum]

Mr3cushion great post. I went straight to measuring

Estimated playing area inside cushions 50 inches x 100 inches
Distance between diamonds on my AMF playmaster is 12 1/2 inches.
Distance from inside of cushions is 50 inches by 100 inches.
The diamonds 2 1/2 inches from the inside of the rail.

That means the diamond system is not a true bisector angle wise. Drawing lines through to the diamond is problematic.

The true diamond system would be along the inside rails. The diamonds should be located on the inside rails.

Those lines would be more accurate with what is happening on the table. There is also the offset for the radius of the ball to the rail.

 

[iusedtoberich]

It's their distance back from the cushion nose/gutter that makes them work for that.

pj
chgo

Do you really think whichever company first put diamonds on a table was thinking of this? And that is the reason they are pushed backwards into the wood rail? Or, rather, do you think putting them on the wood rail top simply makes sense from a practical standpoint? Where else could they possibly be placed from a manufacturing standpoint? Maybe the only way to place them on the "rail groove" or the "cushion nose" (if one deemed that a better location) is to draw them there with a paint mark, etc.

 

[iusedtoberich]

Here is a 4 rail bank with the ball dying on the 5th rail. First picture is a 100" x 50" table (pool 9'). Second picture is a 80" x 40" table (pool 7'). The angle of incidence and the angle of reflection are equal at each rail impact. You can see the angle dimensions on each "bounce" off the cushion is equal.

Look at the 5th rail, the distance difference between the big table and the small table where I have the yellow box. 3.74" vs 1.78". A difference in ball position of 1.96". This proves that different sized tables have different angles, because "the gutter line" is not a 2:1 rectangle, and instead the "cushion nose" is a 2:1 rectangle. This is perfect geometry, not accounting for physics, as I've said throughout this thread. Although I'd imagine the physics effects would be the same on different sized tables, so the overall difference would be similar when considering the physics effects.

Neither table is pointing at any diamonds. The diamonds are irrelevant. The angle into the first cushion is 30 deg. And each subsequent bounce is a perfect reflection. That's what's kept constant. If I make the same comparison between a 9' and 7' table, but adjust the table cushions so the gutter line is a 2:1 rectangle, both sizes should match where the ball ends up on the 5th rail.

 

[mr3cushion]

View attachment 720580

View attachment 720581


Here is a 4 rail bank with the ball dying on the 5th rail. First picture is a 100" x 50" table (pool 9'). Second picture is a 80" x 40" table (pool 7'). The angle of incidence and the angle of reflection are equal at each rail impact. You can see the angle dimensions on each "bounce" off the cushion is equal.

Look at the 5th rail, the distance difference between the big table and the small table where I have the yellow box. 3.74" vs 1.78". A difference in ball position of 1.96". This proves that different sized tables have different angles, because "the gutter line" is not a 2:1 rectangle, and instead the "cushion nose" is a 2:1 rectangle. This is perfect geometry, not accounting for physics, as I've said throughout this thread. Although I'd imagine the physics effects would be the same on different sized tables, so the overall difference would be similar when considering the physics effects.

Neither table is pointing at any diamonds. The diamonds are irrelevant. The angle into the first cushion is 30 deg. And each subsequent bounce is a perfect reflection. That's what's kept constant. If I make the same comparison between a 9' and 7' table, but adjust the table cushions so the gutter line is a 2:1 rectangle, both sizes should match where the ball ends up on the 5th rail.

Why didn't You show an example of the 1st cushion contacted being the 'Long' cushion? You chose to example a, 'Plus 2' example, Not a 'Normal' 3 or 4 rail 'Diamond/Non diamond system shot. (3 rail) Long, short, long, (5 rails) long, short, long, short, corner or short/long.

 

[bbb]

Do your diagrams take into account
A ball picks up running English as it goes around the rails
Do your lines account for that ?

 

[justnum]

Mathematical boundaries that will be useful for future computer applications.

The red line is the physical boundary for a balls center of mass.
The purple line is the nose cushion.
A unique table profile is defined as the ratio for red/purple for the total distance along the short rail, 5 diamonds length.

Some situations will require nose cushion aiming.
Other situations require ghost ball tracking.

 

[iusedtoberich]

Why didn't You show an example of the 1st cushion contacted being the 'Long' cushion? You chose to example a, 'Plus 2' example, Not a 'Normal' 3 or 4 rail 'Diamond/Non diamond system shot. (3 rail) Long, short, long, (5 rails) long, short, long, short, corner or short/long.

It’s an arbitrary example. Any angle chosen would produce a similar result. I picked this because it was simpler to draw. I know a real shot would not follow this path exactly. Geometrically this part is correct and proves what I’ve been saying.

 

[iusedtoberich]

Do your diagrams take into account
A ball picks up running English as it goes around the rails
Do your lines account for that ?

No. That’s the whole point. The lines are a perfect mirror. They are geometrically correct. Not correct from a physics standpoint (spin, compression, friction, etc).

 

[iusedtoberich]

Why didn't You show an example of the 1st cushion contacted being the 'Long' cushion? You chose to example a, 'Plus 2' example, Not a 'Normal' 3 or 4 rail 'Diamond/Non diamond system shot. (3 rail) Long, short, long, (5 rails) long, short, long, short, corner or short/long.

Also you may be reading the bank backwards upon rereading your post. The ball starts in the lower left corner of the picture and does strike the upper long rail first.

 

[Patrick Johnson]

Do you really think whichever company first put diamonds on a table was thinking of [placing them the right distance from the nose to make rolling kicks/banks work]?

Who knows? I just said that's how they work.

pj
chgo

 

[mr3cushion]

Also you may be reading the bank backwards upon rereading your post. The ball starts in the lower left corner of the picture and does strike the upper long rail first.

Ok, my bad! Now for the Bad news. There is NO 3C table in the world that would create these angles as diagramed, with or without side effect! Unless it was 'reverse' English.

 

[bbb]

No. That’s the whole point. The lines are a perfect mirror. They are geometrically correct. Not correct from a physics standpoint (spin, compression, friction, etc).

So since this is merely hypothetical and not real world
Why bother making a big deal about it ?

 

[justnum]

The 2 to 1 ratio should exist in multiple ways.

Creating a special multirail bank is interesting.

This diagram shows the intersections between pockets that are not on the same line.
Notice the square formed by the intersections of the corner to the side pockets.
The 2x4 rectangle is the intersection between opposing corner pockets.

A fun game to play is for the grid below how many squares can you count?
The fun story to talk about is how does a system based on 2 to 1 proportion preserve other relationships.

The terminating points for the "discountinuities" are always placed at regular 2 to 1 intervals, just like rational numbers.

Chess knights move with a 2 steps forward and 1 side step. The 2 to 1 ratio is worth preserving in a game as designed by the ancients.

Sadly the most famous right triangle is not 2 to 1, it is a 30, 60. The confusion about ratios versus angles is common.

Angles preserve similarities in triangles. In rectangles the dimensions being proportional preserve a lot more properties than similar triangles.

Proportional rectangles are more interesting than similar triangles.

Enjoy the pretty picture.

 

[iusedtoberich]

The point is smaller tables would inherently bank the ball differently than larger tables. Due to no other difference except table size. The pictures in post 44 prove it. (Unless I made a drawing error). On the multi rail bank the difference was significant of almost 2". That's enough to miss a kick in pool or a carom in 3 cushion. The physics effects (friction, spin, compression, slide, etc) are cumulative on each cushion. All I'm showing here is the underlying geometry. (like when we discuss ghost ball in pool, yet everyone under the sun knows ghost ball is bull shit, but its still the starting reference).

We talk about so much "tiny detail stuff" on here, this falls into that category. I'm frankly surprised I'm the only one here who finds this interesting?

That's all.

 

[justnum]

All pool tables should let an ideal ball maximum being a ball of light to travel in the butterfly pattern within the pool playing area.

If light was a train and could travel along the bouncing path infinitely, then that grid would light up forever. Non terminating reflections or infinite reflections, something fun for the math people.

In terms of billiards a two dimensional area bounding a three dimensional sphere provides other math two calculate.

Billiards is an interesting phenomena that models all types of actions.

If you find other symmetric shapes, then in my past life I would've submitted to a journal.

For now symmetric shapes within the grid will be called infinite reflections, they will be used in AI simulations to avoid over calculating.

This is a great thread.

 

[mr3cushion]

The point is smaller tables would inherently bank the ball differently than larger tables. Due to no other difference except table size. The pictures in post 44 prove it. (Unless I made a drawing error). On the multi rail bank the difference was significant of almost 2". That's enough to miss a kick in pool or a carom in 3 cushion. The physics effects (friction, spin, compression, slide, etc) are cumulative on each cushion. All I'm showing here is the underlying geometry. (like when we discuss ghost ball in pool, yet everyone under the sun knows ghost ball is bull shit, but its still the starting reference).

We talk about so much "tiny detail stuff" on here, this falls into that category. I'm frankly surprised I'm the only one here who finds this interesting?

That's all.

And these 'tiny details' is what separates 2 dimensional (diagram) players from 3D (Real) world players. Real players, any cue game know what to do. Whether it be systemically or instinctively.

 

[iusedtoberich]

And these 'tiny details' is what separates 2 dimensional (diagram) players from 3D (Real) world players. Real players, any cue game know what to do. Whether it be systemically or instinctively.

I agree completely. I don't even use diamonds personally, I play angles completely by feel, including the rare occasions I play 3C.

 

[iusedtoberich]

Here is one more group of pictures I just made. This is much more realistic. This is the corner 5 system, shooting through the 3rd diamond, which is supposed to take you to the corner on a heated 10' carom table. (thru the second diamond instead for a 9' GC pool table). I got the rough track from Dr Dave's site. It does not matter if I'm off a bit on the "true track" for the purpose of this discussion. Clearly this track is way more realistic than the one in post 44. Anyway, the first picture is a 100x50 table and I used the corner 5 system and made the lines follow the diamonds. Each line has its angle measured, and underlined in blue. But those angles are not "driving" the lines, the 3rd diamonds on the two longs rail are (which I got from Dr Daves site). The second picture is a 80x40 table. On this one, I kept the same angle dimensions, but did not align to the diamonds. The angles are driving the lines, not the diamonds. You can see when the ball got to the 4th rail (the end corner) it has a .81" difference in position between the 9' table and the 7' table. The balls don't know where the diamonds are. The balls will react off the cushions the same way across different tables. So keeping the angles underlined in blue the same across both tables is more real world IMO than aligning to the diamonds. I also know the balls arc after contacting the rails. Of course that's not shown here. But again, all those affects are cumulative, and I would still expect a difference between table sizes.

 

[straightline]

This video will 'Debunk' any Nonrealistic theories about, 'smaller' tables have 'shorter return angles.'

Video shows Frederic Caudron has a 'High Run' of 32 on a 4'x8' 3C table. Pay close attention to the 3rd/4th/5th rails returns. They are 'Identical' to a 5'x10' 3C table.

Given the constant ball size, the smaller table requires less ball speed to produce "larger table" results. People claim differences because many, many shots require shot dynamics that are "non-negotiable".