Regarding pocketing balls, is the corner-pocket's effective size the same whether object ball is frozen to the short rail or on the table spot?

[Paul_#_]

Jack Koehler writes in The Science of Pocket Billiards that the pocketable size of corner pockets is the same size regardless of object-ball position:

“The unique thing about corner pockets is that the effective pocket size remains the same regardless of approach angle. The target area shifts so that it is always perpenducular to the path of the object ball.”​

Koehler provides figures of the pivotable-target area (see pages from book below). In figure 4-6, he shows an object ball frozen to the long rail and three inches from the corner pocket. The cue ball, a few inches back of object ball, is aimed at the long-rail cushion and object ball's center. This despite the fact that this aiming pushes object ball into the cushion ---not the pocket. Because of Koehler’s pivotable corner-pocket targetable area, however, its pocketable since the object ball is aimed within the pivoted target area, object ball banks and pockets.

See photos below from a pool table of Koehler's targetable area of a corner pocket. Just like figure 4-6, a cue ball is aimed at a frozen-to-rail object ball and aimed at cushion but still within the pivoted-targeablet area of the corner pocket as Koehler stated.

Koehler discusses this in the one paragraph below. What more can be said? When does corner-pocket target size NOT remain the same regardless of object-ball approach angle? How does object-ball speed and position, and pocket type affect a corner pocket’s effective pocket size?

Others have mentioned Koehler's book at https://forums.azbilliards.com/threads/good-books-to-learn-from.579785/

I liked "the science of pocket billiards" Jack. E. Koehler.

I liked it also, but I've had a top instructor years ago say there's some errors in it.

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[Patrick Johnson]

Geometrically, a corner pocket opening from along an adjoining rail is only about 70% as wide as it is from the nearest spot.

But I suspect that's not your only question about it...

pj
chgo

 

[Bob Jewett]

Dr. Dave did an extensive theoretical analysis of this including rattling before dropping. He and I also did measurements. As I recall -- too lazy to look up the material on his website -- there is a "best" angle of approach that is about 4 degrees off the rail for which the pocket is largest.

In addition, speed changes the size. It is well known that for shots along the rail, the pocket tightens for power shots. Less well known is that from 45 degrees, the pocket is slightly larger for power shots.

 

[Patrick Johnson]

…there is a "best" angle of approach that is about 4 degrees off the rail for which the pocket is largest.

Is that because of the more-exposed opposite pocket facing helping to “turn” the ball into the pocket?

pj
chgo

 

[Bob Jewett]

Is that because of the more-exposed opposite pocket facing helping to “turn” the ball into the pocket?

pj
chgo

Yes, most often seen on soft shots. It causes viewers to declare that the tournament pockets (slick cloth) are too sloppy. I think it's also important that a rolling ball comes off the rail longer than it goes in for shallow angles.

 

[Bob Jewett]

Related to this discussion, there is a single point in the pocket that is pretty close to the center of the pocket for all angles of shots into that pocket. It is at the intersection of the rail grooves. Put a donut there when working on your pocketing.

 

[Paul_#_]

Geometrically, a corner pocket opening from along an adjoining rail is only about 70% as wide as it is from the nearest spot.

So, with five-inch pockets, an object ball at the table spot sees a five-inch corner pocket but for the ball frozen to the rail, its a 3.5 inch corner pocket.

Dr. Dave did an extensive theoretical analysis of this including rattling before dropping. He and I also did measurements. As I recall -- too lazy to look up the material on his website -- there is a "best" angle of approach that is about 4 degrees off the rail for which the pocket is largest.

In addition, speed changes the size. It is well known that for shots along the rail, the pocket tightens for power shots. Less well known is that from 45 degrees, the pocket is slightly larger for power shots.

I will have to find those reports.

Koehler intuitively is wrong. Newer players joke the slow-hit ball pocketed off the cushion near the pocket is a lucky or sloppy shot.

I thought the pocket-size-is-the-same-size contention was too fanciful and too mathematically pretty. Its more accurate to say it’s the same size for slow-hit balls but his phrasing is cooler: The unique thing about corner pockets is that the effective pocket size remains the same regardless of approach angle.

I wonder, too, about the cue ball. On a narrow-angle shot, I have hammered an object ball frozen to the rail a couple inches from the corner pocket and scratched. Shouldn’t the cue ball have gone off on a tangent and not in the pocket? Is this Koehler related, CIT, I actually first hit the cushion instead of object ball, or something to do with what Bob posted:

a rolling ball comes off the rail longer than it goes in for shallow angles.

 

[Not Dead Ted]

If you want the full math: https://drdavepoolinfo.com/technical_proofs/TP_3-6.pdf.

Related proofs: https://drdavepoolinfo.com/technical-proof/


However, if you have a copy of The Illustrated Principles of Pool and Billiards, see figures 3.37 and 3.39 which are more tractable versions of the technical proofs.

The practical result for slow shots is that the effective corner pocket size maximizes for shots down the rail, 45 degrees (or close to it), minimizes at about +/- 30 degrees from straight in, and is fairly flat in-between.

For fast shots, the corner pocket size is maximal at 0 degrees, and drops off gradually to reach it's minimum at 45 degrees. The drop off in pocket size from straight in to rail shot is maybe 20-25%, so from a practical viewpoint, Koehler is not far off.

The moral of all this is that speed down the rail causes rattles.

 

[Bob Jewett]

Another thing to note is that not all pockets can be judged just by their width at the points. There are wide pockets that rattle due to the facing angle.

Also... Years ago I tested the concept of "get-in english", which states that if the object ball has side spin from the cue ball, and the ball starts close to a cushion, the spin can help turn the object ball into the pocket off the facing. During the tests, I found that the pocket I was testing had a "hole" in it. A certain line of approach near the rail would hit the nearer pocket liner at the point and miss. A shot that hit the rail farther up the cushion would not hit the projecting point and go in. Of course, perfectly to the center of the pocket without contacting the cushion went in. I don't think pockets should behave like that.

As for the result of the test, get-in english made the pocket about 20% wider for some shots.

 

[Paul_#_]

if you have a copy of The Illustrated Principles of Pool and Billiards, see figures 3.37 and 3.39 which are more tractable versions of the technical proofs.

SEE BELOW

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[Paul_#_]

Koehler claimed a corner pocket’s effective target size is the same regardless of object-ball angle to corner pocket. Koehler’s finding is not what you see — actual pocket and target size decreases with increasing ball angle to corner pocket (ball sitting on table spot would have zero-degree angle to corner pocket and ball frozen to cushion, 45 degrees).

Dr Dave outdoes Koehler. Dr Dave compared shot difficulty — the effective corner-pocket target size — of two object balls near the side-rail cushion (see figure 3.38 below). One ball was nearly hugging the short-rail cushion while the other was a few ball-width distances from the same cushion. Both were about three diamonds from the corner pocket.

He found it was 30% more difficult to pot the more-distant-to-cushion object ball than the object ball nearly hugging the cushion (figures dotted line in fig. 3.37). For the two balls in figure 3.38, effective target size increased as actual target size decreased — this differs from what your eyes see and Koehler found. Here, effective target size increased as ball came closer to the cushion. It increased so much that there was a larger effective target size for the ball nearly at the cushion (43 degrees) than for a ball sitting on the table spot, perpendicular to the corner pocket, and zero degrees to the corner pocket.

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