Squirt (cue ball deflection) in Pool and Billiards

• aim compensation
• bridge length effects
• cue elevation effects
• cue natural pivot length
• effects summary
• endmass and stiffness
• low-squirt (low-deflection, LD) shafts
• miscue limit
• published data
• robot test results
• speed effects
• squerve
• squirt, swerve, and throw confusion
• straight-in shot with unintentional english
• tip hardness effects
• tip contact height effects
• tip size and shape effects

for more information, see Section 4.04 in The Illustrated Principles of Pool and Billiards
and Disc II of the Video Encyclopedia of Pool Shots

aim compensation

How can I easily adjust my aim to account for squirt (cue-ball deflection)?

"Squirt - Part IV: BHE, FHE, and pivot-length calibration" (BD, November, 2007) and "Throw - Part X: the big picture" (BD, May, 2007) cover aim-and-pivot techniques, which can be used to adjust your aim for squirt.

For more information, see:

http://billiards.colostate.edu/threads/aiming.html#compensation

bridge length effects

Does the bridge length or tighness have any affect on squirt (cue-ball deflection)?

No, unless the bridge length is really short and the bridge fingers are very bony and have a very tight grip around the cue (i.e., non human).

Even if the bridge were perfectly rigid, it would still have absolutely no effect for bridge lengths beyond about 6-8 inches. The following video shows and explains why visually (at the 2:32 point point in part 2): NV B.96 - Grip and bridge technique and advice. Here's a direct link to the pertinent point in the video.

And Diagram 4 in the following article gives some additional experimental proof related to endmass:

"Squirt - Part VII: cue test machine results" (BD, February, 2008)

cue elevation effects

What effect does cue elevation have on squirt or cue ball deflection?

This is a difficult question to answer in simple terms. With more cue elevation, the effective squirt angle increases. For example, with the cue elevated really high (almost 90 degrees) with right english, the CB actually squirts almost entirely to the left (i.e., squirt angle is almost 90 degrees). However, with more cue elevation, there is much more swerve. Also, some of the swerve occurs immediately as the CB bounces off the table with the downward hit. I like to call this "immediate swerve." This effectively reduces the amount of "apparent squirt."

Squirt really isn't that important alone (except for near-level-cue shots at fast speed or short distance, where swerve is not a significant factor). What is really important, especially with increasing cue elevation, is squerve (the combined effect of squirt and swerve). And this varies a lot with speed and conditions. And with higher cue elevations, the swerve effect dominates the squirt effect to the point where the squirt can be realistically ignored.

endmass and stiffness

How does shaft endmass affect squirt (cue ball deflection) and how is endmass related to stiffness?

See Diagram 4 in "Squirt - Part VII: cue test machine results" (BD, February, 2008). People who think extra stiffness is required to produce more squirt are incorrect. Added endmass alone (without added stiffness) produces significant increases in squirt. This supports the theory in TP A.31. The squirt of a shaft can be lowered by reducing the weight of the last 5-8 inches. This can be done by reducing the shaft's diameter, drilling out the core of the end of the shaft, and/or using a lighter (or no) ferrule.

Endmass is also related to stiffness. A stiffer shaft will typically be thicker and heavier at the end. Also, transverse elastic waves will travel faster in a stiffer shaft, effectively increasing the "endmass." For more info, see the paragraph after Equation 4 in TP A.31. A carbon-fiber shaft illustrates these principles well. The shaft end can be much lighter (which tends to reduce "endmass"), but it will also be much stiffer (which tends to increase effective "endmass").

For more information, see NV B.32 - Squirt and the effects of endmass, NV B.1 - Mike Page's squirt and swerve video, and "Return of the squirt robot" (BD, August, 2008). Also, to see how the amount of squirt can affect the miscue limit, see: HSV B.47 - effect of shaft endmass and squirt on miscue limit.

Here's a list of advantages and disadvantages of low-squirt shafts.

from iusedtoberich:

The Meucci shaft over the years has had features to reduce the endmass:

1. The ferrule has always been thin walled relative to most other cues. (the plastics used in ferrules is usually of higher density than maple)

2. The ferrule has been made of a less dense material than most other ferrules on competing cues.

3. On recent shafts (black dot), the tenon has been tapered like the end of a pencil (not that extreme), yet the internal walls of the ferrule have remained cylindrical. This further reduces endmass by introducing a tapered hollow region right behind the tip.

How much of an effect does added or removed endmass have on the resulting squirt of a shaft?

Based on the theory in TP A.31 and the data in "Squirt - Part VII: cue test machine results" (BD, February, 2008), a typical cue might have a ball-to-endmass ratio of about 30, corresponding to an effective endmass of about 5 grams. Any endmass added to or taken away from this would affect the amount of squirt proportionally. For example, for the 0.3 gram and 1.3 gram added masses in Diagram 4 of the article, the total endmass would be 5.3 with 0.3 grams added close to the tip and would be 6.3 with 1.3g added close to the tip.  This comparison corresponds to an endmass ratio of 6.3/5.3=1.2.  The robot measurements for squirt angle were 3.9 degrees with the larger added mass and 3.3 degrees with the smaller added mass. This is directly related to the endmass ratio: 3.9/3.3 = 6.3/5.3 = 1.2.

miscue limit

Does the miscue limit depend on the shaft's squirt?

See: HSV B.47 - effect of shaft endmass and squirt on miscue limit. It appears that a cue with more endmass (a lot more in the video) allows greater tip offset. With more tip offset, you would expect to get more english. You would also expect to get more squirt than you would get even with the same endmass. If you watch all of the shots in the video, you will see that the cue with the added endmass had much more squirt than the cue without the added endmass, much more than can be explained by a small difference in tip offset. Also, with more squirt comes less english (for a given tip offset), because the effective offset is less. If you look at the stripe on the ball in the super-slow-motion clips, you will see that the CB actually has slightly more english (spin per distance) with the low-squirt cue (due to a larger "effective tip offset"), even though the "actual tip offset" is slightly greater with the added-endmass cue!

For more info, see:

• getting more spin with low-squirt cue
• maximum english

Can the type or brand of chalk affect the amount of squirt?

I personally think that all commercially available pool chalk, assuming the tip is holding it, grabs the CB without any slipping whatsoever.  When the tip slips, a miscue results.  Now, "partial" miscues are possible, where the tip mostly grabs and just slips a little.  With any miscue (partial or full), there is significantly more squirt because the tip moves sideways more as it slides over the edge of the CB (see example videos here).  With more tip sideways motion (which requires force), the CB will experience more equal-and-opposite-reaction sideways force, resulting in more CB squirt.  Also, I would expect the amount of squirt would be very inconsistent if there were partial or full slip due to the complicated nature of impact-induced slip.  That's why the tip probably doesn't slip with most shots, because with most shot (assuming the tip is well chalked), CB squirt is very consistent.

published data

Where can I find published data on squirt values for various cues?

Platinum Billiards did some tests a while back and posted a collection of extensive data (see below). Meucci has also done some testing measuring the combined effects of squirt, swerve, and throw, so no reliable squirt data is available (videos and results are available here). Ron Shepard's squirt paper reports a squirt angle range of about .5 to 2.3 degrees for low- to high-squirt cues, corresponding to a pivot point range of about 50" to 10". Platinum's data (see below) ranges over 1.3 to 2.3 degrees of squirt angle and 7.6" to 14.1" for pivot points. Some other data is available on the cue natural pivot length resource page. These numbers seem to fall in between the ranges reported by Shepard and Platinum.

from Platinum Billiards (results from tests on a cue-testing robot called "Iron Willie"):

HOW AND WHAT WE TEST
We ask the question “which shaft deflects least?” because the butt of the cue has little effect on cue ball deflection. However, shafts are generally tested on the same brand of butt and the test weight for all is kept close to 19 ounces. All shafts are tested as sold by the manufacturer including tip type and tip curvature as noted. All tests are performed using a robot which makes precisely the same stroke with each cue, and for this test the machine is set to produce cue ball speeds of around 15mph. A series of four shots is made with each cue and the resulting cue ball deflection is recorded on a target 50” away which is exactly the distance between the foot string and the head spot on a 4 ½ x 9 pool table. The four shots are 6mm (about ¼”) and 12mm left of center, and 6mm and 12mm right of center, and these offsets are measured from the center of the cue ball to the center of the shaft. The actual cue ball deflection produced by each shot is measured and the average for the series is given in the chart below in millimeters and inches.

Platinum Billiards is an independent company and has no affiliation with any billiard product manufacturer. The performance information we provide is based on careful scientific testing and observation. We are highly experienced at testing the performance of cues and we believe that our methods are sound and accurate. However, we do not claim that our findings are absolute. We are aware that cues of a same model vary slightly and as we test more samples of each, the numbers will become more refined. If any manufacturer is unhappy with our results and/or feels that the ratings are unfair, we encourage them to contact us and we will be happy to answer questions about our methodology and/or arrange for the testing of any cues they would like to send us, and if warranted, we will adjust the numbers accordingly. We can only offer testing of cues, shafts, products that are currently on the market. We do not offer testing for prototypes or products that have yet to be made available to the general public.

robot test results

Where can I find information on experimental results from squirt-testing robots?

See published data for some cue-comparison results from Platinum Billiards resulting from cue tests with "Iron Willie" (a cue-testing machine). The Jacksonville Project also did some work with "Iron Willie."

The following articles document work with a cue-testing machine developed at Colorado State University:

"Squirt - Part VII: cue test machine results" (BD, February, 2008)
"Return of the squirt robot" (BD, August, 2008)

NOTE - when using a machine to test cues, the "grip" needs to be flexible, like the flesh in a human hand (e.g., by lining the mechanical "grip: with silicone rubber).

The problem with a non-human, extremely-firm robot grip is that it can add significant effective weight to the cue. If the grip is totally rigid, the weight of the machine's "hand" and "arm" completely add to the weight of the cue. For example, if you put an 18 oz cue in a rigid machine grip, and the weight of the machine's "grip" is 20 oz, the cue will act like a 38 oz cue! The result of this is that the CB will not leave fast enough to clear the tip with an off-center hit. The tip will either remain in contact with the CB or catch up after initial contact, creating either a push or double hit. The hit will look and sound normal, but the CB will have more squirt (CB deflection) ... sometimes a lot more (as if there where a miscue).

Lot's of care must be taken when using a machine to test and characterize equipment that will be used by non-machine humans.

speed effects

Does squirt change with speed?

"Cue ball deflection" or "squirt" refers to the angular deflection of the CB immediately off the tip. Squirt does not vary with speed. Proof, from careful experiments with cue-testing robots, can be found here:

"Squirt - Part VII: cue test machine results" (Billiards Digest, February, 2008)

"Squirt - Part II: experimental results" (Billiards Digest, September, 2007)

NV A.17 - Effective squirt vs. speed

And here's another from Disc II of the Video Encyclopedia of Pool Shots demonstrating the combined effects of squirt and swerve:

Again, squirt doesn't vary with speed, but swerve and squerve do.

squirt, swerve, and throw confusion

What is squirt (CB deflection) and how is it different from swerve (CB curve)?

From the online glossary:

squirt (same as "cue ball deflection"): angular displacement of the cue ball path away from the cue stroking direction caused by the use of english. Squirt increases with the amount of english.

effective squirt: (same as "squerve"): the net effect of squirt and swerve (i.e., the cue ball deflection off the aiming line at object ball impact).

swerve: curve of the cue ball’s path due to cue elevation and english.

Here are some video demonstrations and explanations of squirt, swerve, and throw:

• NV A.17 - Effective squirt vs. speed
• NV B.1 - Mike Page's squirt and swerve video
• NV B.70 - Squirt, swerve, and throw, from VEPS II
• NV B.86 - Cut-induced throw (CIT) and spin-induced throw (SIT), from VEPS IV

A complete summary of all squirt, swerve, and throw effects can be found here.

How can you predict the directions and amounts of squirt, swerve, and throw with various types of shots?

I’ve gotten several e-mail questions concerning Diagram 3 in "Squirt - Part I: introduction" (BD, August, 2007). Here's the diagram:

Several people have suggested the throw direction is wrong due to collision- or cut-induced throw (CIT). Tthink about it yourself and decide if you think the diagram is correct or not. Many people seem to be confused by the real effects of squirt and swerve. Diagram 4 from the article (see below) helps clarify things.

The phrase "effective squirt" is used for the net effect of squirt and swerve. The term "squerve" (SQUirt + swERVE) means the same thing. The following series of instructional articles dealing with squirt covers all of the details of squirt and swerve:

"Squirt - Part I: introduction" (BD, August, 2007).
"Squirt - Part II: experimental results" (BD, September, 2007).
"Squirt - Part III: follow/draw squirt and swerve" (BD, October, 2007).
"Squirt - Part IV: BHE, FHE, and pivot-length calibration" (BD, November, 2007).
"Squirt - Part V: low-squirt cues" (BD, December, 2007).
"Squirt - Part VI: tip shape" (BD, January, 2008).
"Squirt - Part VII: cue test machine results" (BD, February, 2008).
"Squirt - Part VIII: squerve effects" (BD, March, 2008).
"Squirt, swerve, and throw wrap-up" (BD, April, 2008).

Also, here's a video excerpt from Disc II of the Video Encyclopedia of Pool Shots that explains and demonstrates things:

Now back to Diagram 3. Throw direction depends on the direction of the relative motion of the surface of the cue ball in contact with the object ball. This direction is affected by both cut angle and spin. "Throw - Part VI: inside/outside english" (BD, January, 2007) and "Throw - Part VII: CIT/SIT combo" (BD, February, 2007) illustrate the different possibilities quite well. The throw direction shown in Diagram 3 of "Squirt - Part I: introduction" (BD, August, 2007) is appropriate given the amount of english.

Object ball throw depends on cut angle, shot speed, type and amount of english, and the amount of vertical plane spin (draw, follow, stun). The following series of instructional articles elaborate on all of these factors:

"Throw - Part I: introduction" (BD, August, 2006).
"Throw - Part II: results" (BD, September, 2006).
"Throw - Part III: follow and draw effects" (BD, October, 2006).
"Throw - Part IV: spin-induced throw" (BD, November, 2006).
"Throw - Part V: SIT speed effects" (BD, December, 2006).
"Throw - Part VI: inside/outside english" (BD, January, 2007).
"Throw - Part VII: CIT/SIT combo" (BD, February, 2007).
"Throw - Part VIII: spin transfer" (BD, March, 2007).
"Throw - Part IX: spin transfer follow-up" (BD, April, 2007).
"Throw - Part X: the big picture" (BD, May, 2007).
"Throw - Part XI: everything you ever wanted to know about throw" (BD, June, 2007).
"Throw - Part XII: calibration, and hold shots" (BD, July, 2007).

Collision-induced throw (CIT) and spin-induced throw (SIT) are just different names for throw, depending upon the primary cause of the throw, but the effects don't really combine as separate factors.

straight-in shot with unintentional sidespin

What effects do squirt, swerve, and throw have with a straight-in shot hit with unintentional sidespin?

There are two possible cases here:

1.) The cue is aligned in the proper aiming line direction but shifted to the left a little, creating unintentionally left sidespin, but the stroke is straight. In this case, the CB will squirt to the right (the amount depends on the cue and the amount of tip offset), the CB will swerve back some to the left (the amount depends on shot speed, cue elevation and ball/cloth conditions), the contact point might be to the left or right of the initial target depending on the relative amounts of squirt and swerve, then the sidespin will throw the OB a little to the right of what the contact point suggests.

2.) The cue is aligned in the proper aiming line direction and the cue tip is aligned with the center of the CB, but the stroke is not perfectly straight, resulting in slight unintentional left sidespin. In this case, the aiming line is now pivoted to the left a little, so the CB will tend to head to the left a little (the amount will depend on bridge distance). Everything else is the same as with "1," but now relative to this new aiming line direction.

tip contact height effects

What effect does tip contact height (for draw and follow) have on squirt or cue ball deflection?

With a near level cue, squirt is maximum with pure sidespin. This is because squirt acts completely in the horizontal direction when the tip is on the horizontal centerline of the CB. When the tip is above or below the horizontal centerline (e.g., with draw and follow shots with sidespin), the squirt direction is no longer horizontal. Squirt always acts in a plane through the cue and the center of the ball. When this plane is not horizontal, a portion of the squirt acts in the vertical direction, and the horizontal component is less than with a pure sidespin shot. Therefore, for a given amount of sidespin, squirt will be slightly less when the tip strikes the CB above or below center as compared to a pure sidespin shot.

Cue elevation can also change slightly with tip contact height. The cue can be slightly more level with a topspin shot as compared to a bottom-spin shot. Squirt (and swerve) also change with cue elevation (see squirt cue elevation effects).

from Jal AZB post:

You do get some squirt reduction in the horizontal direction - the direction we have to adjust for - when combining follow or draw with sidespin. For instance, if you make contact along the line going from the center of the cueball to the two o'clock mark, you'll get just as much squirt as with pure sidespin, but directed toward the eight o'clock mark instead of nine o'clock. The horizontal component is thus reduced to 87%. If you hit along the one o'clock line, the horizontal component is reduced by 50% (squirt is now directed toward the seven o'clock mark).

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