Bob Jewett Combinations and Throw Some surprising insights into the world of "throw."

In my column last April, I covered some of the details of throw. Here are two related and surprising experiments for you to try. As a reminder, a ball is said to be "thrown" when its path is not directly away from the spot where another ball contacts it. This deviation can be due to spin on the cue ball, or simply from the motion of the striking ball across the struck ball on a cut shot. Most beginners will shoot the shot in Diagram 1 wrong. The two object balls are frozen together and pointed about six inches away from the pocket. A novice will attempt to "cut" the second ball by playing to side A of the balls, perhaps expecting the first ball to move to the right before pushing the second ball towards the pocket. Of course, we all know that you have to hit the shot on side B, and let the friction between the balls drag the second ball towards the pocket. But how does the shot change if the balls aren't touching? With some separation, as in Diagram 2, there will be two effects, the throw from the sur- face friction, and the cut because the first ball does move to the side before it hits the second ball. Which effect will dominate? If the balls are separated by a hair's breadth, the shot hasn't changed much and you would expect nearly the same result as for frozen balls. With an inch of separation, the cut effect will probably dominate. Our goal in the experiment is to find the separa- tion at which the cut exactly cancels the throw, and the second ball goes straight up the table. In Diagram 2, a ball is placed on the far cushion along the line of the two balls, so we can easily see the amount of cut or throw. the right place, shoot the shot as an angle Of course, the results will depend on how For repeatability of ball placement, get combo as shown, with full contact on the sticky the balls are. When I tried this shot at some self-adhesive donut-shaped paper first ball, which in turn has a half-ball con- a local pool hall, I got cancellation for a reinforcements. There is a new style avail- tact on the ball that's driven up the table. half-ball hit when the separation was close able made of thin, tough plastic that can be Is there more throw or cut on the shot? to a quarter-inch. This is exactly the rule of lifted and moved several times for reposi- That is, where does the ball land on the far thumb that I've used for over 30 years, but tioning. A trick I use for minor tweaks is to cushion relative to the target ball? Is it the I had never measured it before. Common place a fingernail as a marker at the edge, same from the other side? If it's not, some- rule of thumb: "If the balls are a quarter- and then lift and replace the donut the thing is screwy with your setup or table. inch apart, there is no throw or cut, no mat- required distance from the nail. Next, try a fuller hit; place the cue ball clos- ter how you hit them." Is it a quarter-inch As a first guess, place die two balls one- er to the line of the shot, so the first ball is with your equipment? quarter inch apart. That's probably close to driven about 3/4 full into the second ball. When I tried a fuller hit, I got a surprise. half the diameter of your ferrule, in case What happens for a more extreme angle? The throw dominated. With a thinner con- you don't carry calipers. Place the rail ball Does speed change the shot? If you have tact, such as 45 degrees or 1/4-ball full, the on another donut, and shoot straight along the donuts on the table to replace the balls, cut dominates. The result of this experi- the combination line to be sure that all three you can try all of these changes in a few ment is that the simple rule of thumb isn't balls are in line. Once you have the target in minutes. accurate, and you need to do some testing 18 | BD-JANUARY 2001 Bob Jewett

under your own conditions. could be made consistently I've seen ball-to-ball friction even when the last ball was vary by a factor of two, and two diamonds from the this will surely change the pocket. For this case, the "zero-throw" spacing. If you error multiplication factor try the experiment, please without correcting throw is send me your results in care about 58, and the permitted of Billiards Digest. error at the end is only five The second experiment in degrees, so the simple theory throw was suggested by would require a tenth of a Hugh Hilden, who is a pro- degree accuracy in the aim- fessor of mathematics at the ing. This is a sixth of an inch University of Hawaii, and in the length of the table. who sometimes uses pool With the balls set two balls problems in his calculus apart, the percentage was courses. The setup is shown down, but the shot was still in Diagram 3, and is similar possible. With a one-ball to an ancient trick shot. Ten separation, the shot becomes balls are lined up straight to a unmissable, even with some pocket. The critical factor in the experiment error, and the shot is theoretically nearly intentional aiming error. This shot is fun to is the separation of the balls. In theory, if impossible. try, and it sounds like a machine gun when the balls are separated by one-ball diame- Where does throw enter? It turns out that you shoot it. Try it with all fifteen balls. ter, any small aiming error you have on the throw between successive balls, which is These experiments will improve your feel first pair — one degree — will be copied caused by the cut angle of the error, tends for combinations, and the next time you run exactly to each subsequent collision. to correct the error. This is partly due to the into either multi-ball or not-quite-frozen Suppose you space the balls by two ball balls being thrown back in line, and partly combos, you'll be ready. And if you're a diameters instead. Geometry says that any due to spin that the thrown ball picks up, in junior player deciding about college, con- initial error will be doubled in each colli- the direction which tends to cancel the sider math at the University of Hawaii. You sion, and with a one-degree error at the error. may have already done the homework. start, the sixth ball won't even hit the sev- Professor Hilden reports that when the Bob Jewett is an Advanced-level BCA enth. There is geometrical growth of the balls are one ball and a half apart, the shot Certified Instructor.

20 BD-JANUARY 2001 Bob Jewett Newton on the Ball The flaws of the 90-degree rule.

Guest columnist (and fellow billiard- sion. The line from S to F gives the direction assumptions are often violated, and slightly physics fanatic) Dr. George McBane is a and speed of the cue ball. It's easy to see that different diagrams must be used. professor of chemistry at Ohio State as the cut angle (the angle from I to S to O) It's rare for there to be no change in the University, where he and his graduate stu- gets bigger, the object ball speed will get translational energy. Usually there is some dents study collisions between molecules. smaller and the cue ball speed will get big- change in the spins of the two balls during Tools used there can be applied to billiard ger, until finally for a perfect 90-degree cut their collision, so that translational energy is balls, as you will see. the object ball will not move at all and the converted to rotational energy or vice versa; cue ball will go straight forward without to prevent that, you have to either hit a Anyone who has played pool for more slowing down. If you remember your geom- straight — in stop shot, or you have to hit a stun than ten minutes has figured out that the etry, you might also be able to show that, shot with just enough outside english that thinner the cut, the slower the object ball with this diagram, the angle between the the surfaces of the two balls do not rub goes, and the faster the cue ball goes after final cue and object ball directions is exactly together when they collide. When the balls they collide. And the first thing most players 90 degrees, no matter what the cut angle is; do rub together, some energy changes from are told when they start to learn position play the "right-angle rule" is correct in this case. moving the balls along the cloth to making is "After the collision, the cue ball leaves them spin, or vice versa. Some also goes at right angles to the object ball's path." to producing the sound of the hit, and The first of those statements is true, the some warms up the balls; both of those second is only sometimes true. amounts are usually too small to worry People who study collisions—of plan- about. ets, of subatomic particles, of balls—use In the Newton diagram, changes in a simple diagram, called a Newton dia- translational energy change the size of gram (after Sir Isaac) or velocity vector the circle. In the majority of shots, trans- diagram, to help figure out what laws of lational energy is lost, and the circle gets conservation of energy and momentum smaller. This is true for shots where the require of a collision. throw tends to decrease the cut angle: The diagram is easy to draw. Cueists inside English, center ball, or can use it to show how fast the cue and little/enough outside English that the cue object balls will go in a cut shot, what the ball still "slips forward" on the object angle will be between the cue and object ball as it hits. If you use enough outside balls' paths after a collision and how the english that the cut angle is increased behavior of the balls will change if the (which is easiest for nearly straight-on cue ball is lighter or heavier than the hits), then some of the initial spin of the object ball. It can also occasionally dis- cue ball ends up as translational energy, prove plausible-but-incorrect statements and the circle can get bigger. about how balls behave, including the Diagram 2 shows how this works. The "right-angle rule." In carom games, one-pocket and safeties at two diagrams drawn there are both for 30- The simplest version is shown in Diagram pool, it is often important to control the degree cut shots to the right. On the left, the 1, along with the shot it corresponds to on speeds of both object ball and cue ball, and shot was hit with center-ball. At the moment the table. To draw it, start with a line along this diagram can show you how those speeds of contact, the balls rubbed together, and the the direction you will shoot the cue ball. The vary with the cut angle (The diagrams tell friction from that rubbing threw the object line's length represents the cue ball's speed you only about the collision between the ball to the left and imparted some clockwise just before the collision. balls, so they apply directly to stun shots. spin to each ball (See Tech Talk, April 2000). Mark the beginning of the line with S (for Follow or draw will affect the speed and The throw has no effect on the diagram, "stationary"), and the end with I ("initial"). direction of the cue ball; those effects must since the line from S to O was drawn in the At the midpoint of that line, put a dot (C). be "added on" to these). direction the object ball actually traveled. It Draw a circle with its center at C that passes What assumptions lie behind this picture? takes energy to makes the ball spin, though, through S. Now, starting at S, draw another First, these diagrams assume that all the and that energy comes from the initial trans- line, parallel to the path the object ball must action takes place in a single plane. If the lational motion of the cue ball; that makes take to the pocket; extend it until it touches cue ball is airborne, or is different in size the circle smaller, so that the line from O to the circle. Mark the point of its intersection from the object ball, the slate enters the pic- F is shorter than the line from S to I. Now the with the circle O ("object"). Draw a line ture in an intimate way and the diagrams are angle from O to S to F is less than 90 degrees. from O through C to the circle on the other not as useful. Diagram 1 also assumes that On the right, the same shot was hit with side; mark that intersection F ("final"), and the cue and object balls have the same mass, heavy outside (left) English (The player finally draw a line from S to F. and that the total translational energy (ener- aimed differently than on the left, so that the The line from S to O gives the direction gy of motion along the table) is the same object ball would still leave in the same and speed of the object ball after the colli- before and after the collision. These latter direction—toward the pocket). In this shot, 1 4 | B D - FEBRUARY 2001 Bob Jewett when the two balls came together, the rub- the cut, as is sometimes claimed. section with the object ball circle O. Draw a bing between them was in the other direc- If the cue ball and object balls do not line from O through C and on to the cue ball tion; the object ball was thrown to the right weigh the same, there is a dramatic effect on circle; its intersection with the cue ball circle and picked up a little counter-clockwise is F. Finally, draw the line from S to F that spin, and the cue ball lost spin. The trans- shows the final direction and speed of the lations! energy increased overall, so the cue ball. Diagram 3 shows a heavy cue line from O to F is longer than that from S ball (left) and a light cue ball (right). to I. Now, the angle from O to S to F is (Translational energy changes would larger than 90 degrees; the separation make both circles smaller or bigger; angle widens in this case. Diagram 3 shows the case where there is How big are these changes in separation no change.) angle? It's reasonable to think of them this If the cue ball is heavier, the separation way: the cue ball always leaves at right angle varies smoothly from zero for a angles to the line between the two ball straight — in hit to 90 degrees for a very thin centers at contact, while the object ball cut. A heavy cue ball produces "instant will be thrown to the right or left of the follow"; the cue ball will start out moving line between centers. So, the changes in sep- the cue-ball path. This situation is most com- forward of the right-angle line, even if it aration angle are the same size as the throw mon on coin-operated tables, but can also arrives with back spin, and before friction angles, and with clean balls those are rarely appear on other tables if the cue ball is mis- with the cloth has had any effect. bigger than five degrees. That argument is matched or worn. To draw this diagram, If the cue ball is lighter than the object ball, not exactly right; some energy is lost to heat instead of placing point C at the midpoint of then you get "instant draw." For a straight — in and sound, and the balls do move slightly the first line, you put it at the "balance shot, the cue ball will back up after contact during the time they are in contact so the point": the point where a light, stiff rod with even if it did not have any spin (Think of "line between centers" is not precisely its ends at S and I would balance if the cue throwing a soccer ball at a bowling ball). As defined, but it gives a good estimate of the ball was put at I and the object ball at S. In the cut gets thinner, the separation angle will maximum change from right angles. other words, the distance CI times the cue decrease from 180 degrees, and finally for You can occasionally use these changes in ball mass must equal the distance CS times very thin cuts it will approach 90 degrees. separation angle to maneuver around an the object-ball mass. Then, draw two cir- For both heavy and light cue balls, the obstructing ball in your path to the next shot, cles. One should have its center at C and most dramatic effects appear for shots near or even to take a free carom shot at the nine pass through I; that is the "cue-ball circle." straight in. Because the separation angle ball while still pocketing your main object The other, the "object-ball circle," has its changes dramatically with the cut angle, ball. The diagrams also show that it is not center at C as well, but passes through S. carom shots are much more difficult with possible to make a cut shot without having Then draw the line from S in the object ball mismatched balls. the cue ball move in the direction opposite travel direction as before, and label its inter- —George C. McBane Bob Jewett Weird Techniques Get a better grip on hard-to-reach shots.

With perfect play, every shot is going of the pond, bridges are available that lock make the cue ball clear an obstructing ball to look the same: comfortable stance with- together for additional stability. by miscuing (scooping the ball). It is not out stretching; smooth, straight stroke; easy A more creative use of the bridge on this legal to shoot jump shots with just your position on the next ball using little or no shot is to place the head on rail A and the shaft. Shaft jumping is effective because spin; repeat. This can be dull. When players butt at rail B. The bridge handle will be the resulting very light stick stops on con- get into trouble, you get to tact with the cue ball and see some interesting tech- lets it rebound freely niques. You should learn from the table. It is not some of these — at least legal to use a very hard the legal ones — so you'll material such as phenolic be ready on those rare for a tip. Such "tips" occasions when you get seem to help the cue stick out of line. stop faster, but can be One common question is hard on the equipment. what to do when you can't Speaking of miscues, reach a shot normally. The Shot A in Diagram 2 standard techniques are to shows where some play- use a mechanical bridge ers are tempted to use an or shoot opposite handed, intentional miscue. The and both of these should cue ball and object ball be part of your practice. are pointed straight at a Suppose, though, that pocket, but are only a you're faced with the shot quarter of an inch apart. in Diagram 1, and your The problem is to avoid name isn't Shaquille. You hitting the cue ball a sec- need to hit the ball on the ond time as the cue stick cushion, and most of the follows through. If you rack is in the way. aim to hit the cloth and the ball at the same time, The standard method for a miscue will result, and this situation is to place the cue ball will hit the one mechanical bridge on object ball and jump straight up in the air. top of another to get added height — the high enough to clear the obstructing balls. Players who try this in tournaments protest top bridge's shaft goes in the slot where Now place your hand on the bridge handle the resulting foul call because they say they you would normally put your cue stick. It and form a more or less normal bridge for were not playing a jump shot, but the shot can also help to turn one or both bridges on the shot. This technique seems to be legal. is ruled a foul nonetheless. their sides to get more height. If lots of Another technique is useful when you balls are between you and the cue ball, the need to hit the ball pretty hard, and you A legal technique for 2A is to move your top bridge can be pushed forward to can- don't trust the mechanical bridge for that grip hand forward so that it will be at the tilever out over the obstructions. Be sure to much power. An example would be at bil- rail just before the tip hits the ball. If you grip both bridge handles firmly together for liards where you have to take the cue ball stroke with the stick rubbing the rail, your stability. As with most bridge shots, don't off the left side of the object ball in hand will smash into the rail and stop the be ambitious about what you are going to Diagram 1 and go six cushions for the stick before it hits the cue ball a second do with the cue ball; easy does it. If you score. The shot can be reached from the time — correct placement of the grip hand haven't practiced this one before you need side of the table, but you can't get your is critical to getting power without a foul. it, good luck. It is illegal to stack more than head over the cue stick to sight. Raymond This technique was said to be a favorite two bridges. It's also illegal to rest your Ceulemans has been known to place the proposition of Luther Lassiter. With prac- hand on top of the rack, even when playing cue stick on the correct line while standing tice, it doesn't hurt much. by "cue-ball fouls only." at the other end of the table, walk around to Diagram 2B shows a straight — in shot that There are several bridges on the market the side, carefully pick the stick up without requires draw. Being right-handed, you that help with this kind of shot. At snooker, moving it off line, and then stroke "blind- can't reach it, and the mechanical bridge is a bridge (snooker players call it a "rest") ly." Under Billiard Congress of America missing in action. Jerry Briesath has the with a long "swan's neck" that arches out rules, this is legal provided that you main- cute solution: lay your stick flat on the table over obstructions is available. Another tain contact with the cue stick. with the tip nearly at the cue ball. With your snooker bridge called the "spider" has feet Jump shots are so common now that they left hand, pinch under the stick just a little wide enough and long enough to straddle a hardly deserve mention, except for the at the joint so the tip is the right height on single ball — think bow-legged. On this side wrong ways to do them. It is not legal to the cue ball. Now jam the heel of your right

12 | BD-MARCH 2001 Bob Jewett

hand into the rubber bumper on your stick. Jerry can draw the cue ball the length of the table. Can you? I suppose a pencil under the stick would also work to raise the tip to the right height, but that would be Illegal Use of a Device. One technique for getting a lot of side spin is to aim as if for no English and then swerve to the side on the final stroke. Some players claim this works but I doubt that it gets more spin that coming straight through, and I can't think of a better way to destroy consistency. Semih Sayginer and Mike Massey seem to get enough spin without this technique. The only benefit of this method is that it can compen- sate for squirt under some condi- tions. centered. owner of the table asks, you don't know A related technique some professional Masse shots give plenty of room for me. players use is to always set up at the bottom "interesting" techniques. Grips include the Have you seen something really strange of the cue ball and then hit high, low, left, regular, the "dart" grip, and "The Claw." on the pool table? A technique, that is. If so, right, center or anywhere. The rumor is that For this last grip, get into full masse posi- let me know about it, in care of this maga- old-time players used this to baffle their tion, and make a "V for victory" sign with zine, and I'll describe it in a future article. opponents. There is one thing it will help your grip hand, palm down. Put the stick In the meantime, perfect the above tricks. with: If you have a problem seeing where into the V and then curl your two fingers to You won't need them often, but they're the center of the cue ball is, starting at the grab the stick between them. You can get interesting to try, and it's good to be pre- bottom is the best place to see if you are surprising power with this grip. If the pared.

14 BD-MARCH 2001 Bob Jewett Three Draw Drills Something old and something new.

How's your draw? I recently was will throw the object ball into the pocket so you place the cue ball on the A side for working on mine to improve my finesse that not as much cut angle is needed. It will draw or the B side for follow? Try each way position for one-pocket and 14.1. The fol- take you a while to get the feel for this. 10 times to see which works best for you. If lowing drills have something new and chal- Accurate aim is mandatory, since you will you have trouble with the fallow shot, the lenging even for the old hands. still have to cheat the pocket. most likely problem is failure to hit high I saw the first drill nearly 40 years ago in Diagram 1C shows the opposite prob- enough on the cue ball; the higher you hit, Willie Mosconi's Winning Pocket Billiards. lem; the cue ball has wandered too far and the less speed is needed for the position. Place a number of balls in a semi-circle is on the wrong side of the 3 ball. You need Next try placing the 1 ball at A. Is draw bet- around the side pock- ter than follow now? et and shoot them in Finally, place the one order. Where the ball at B. There is a balls start is up to rule-of-thumb that you; I find it's best to says with ball in put the balls as close hand, you should to the pocket as pos- never place the cue sible without block- ball for a draw shot. ing a shot. You are Is any of these shots not allowed to touch an exception for you? any cushion with the Finally, Diagram 3 cue ball or to bank an is an interesting draw object ball. Reset all drill that can be used the balls as soon as as a challenge. The you have missed a goal is to pocket the 9 shot. ball in Pocket X with Diagram 1A shows a draw-carom after how the start of a perfect run looks. The cue pocketing the 3 ball. You don't have to get ball follows a zig-zag path; after each shot the 9 all the way there in one shot, though; it comes to rest about eight inches from the leave it where it rolls to and try again. The next ball, and lined up so that a shot to the 3 ball comes back up to the same position, center of the pocket gives just enough angle and the cue ball is in hand for each try. The to get to the next ball. You will quickly positions A, B and C show possible succes- learn what that angle is, but a good rule-of- sive positions of the 9 if you shoot softly. thumb is to leave the cue ball so that shoot- And it is good to land softly on the 9, since ing full at the object ball will barely put the this will teach you precise finesse position. ball in on the right side of the pocket. Softer shots also tend to keep the 9 near the Now for a new wrinkle on this old drill: if cushion where it is easy to get to. If you fail you make all the balls without a miss, add to touch the 9, start the drill over. one ball to the semi-circle for the next run, While you work on this drill, try to get a but if you fail, subtract one ball from the feel for the angle the cue ball draws to for a next set. This is now a form of "progressive to hit the object ball on the left side and get particular cut angle on the 3 ball. With a lit- practice" and you can keep track of how the cue ball to come to the right. tle practice, you'll be able to pull the cue you are doing by simply noting how many Amazingly, the answer is once again right ball right along the end rail even with a balls are in the present semi-circle. If you side-spin. The trick is to elevate to about 45 starting angle over 30 degrees. For this need a grade for motivation, three is a C, degrees and play a half — masse shot. The cue drill, you will probably want the tip as low six is a B, and nine is an A. ball will curve before and/or after hitting as possible on all shots to minimize the Diagram IB shows a problem you will the 3 ball, and with the right touch will get cue-ball speed. In the first drill in Diagram likely encounter. The cue ball stopped too back in line for the 4 ball. This shot calls 1, it is often useful to take a little draw off soon for a good shot on the 3 ball as shown for a solid raised V — bridge and finesse. the ball to keep from pulling back to far. by the dashed line, which points down the Don't shoot it like you're killing snakes; One variation is to go for as many con- rail several inches past the pocket. If you instead, it should be more like kissing your tacts as possible. For this, soft shots are have perfect soft draw and cheat the pocket Grandma. mandatory, and hitting the cushion with left to the verge of missing, you may be able to In Diagram 2 is a chance for you to test side spin seems to keep better control of the keep the cue ball from going past position the idea that follow is better than draw for cue ball. My record is about 18 shots before for the 4 ball. In this situation, try using as position. You have ball in hand on the 1 ball pocketing the stripe. Another variation is to level a cue as possible and right English at a game of 9-ball, and need to get to the go for the fewest shots, but you'll see that with the draw. The idea is that the side spin shaded area for a shot on the 2 ball. Should much better accuracy is required.

1 4 | B D - APRIL 2001 Bob Jewett

One last word on this drill. If you different to you when it's reversed. Of over-do it and run the 9 ball to Y, not all course, the shots in Diagram 2 may need is lost. Very carefully line the cue ball a bridge on one side for players who don't up between the 3 and the upper edge of switch hands. Draw is always a good skill the 9, and then do your best to draw the to have ready for position play. Finesse- cue ball perfectly straight back to hit the draw is even better. 9 on the upper edge. This shot is worth a couple of tries even if you miss the Bob Jewett is an Advanced-level Billiard first time, just to get a feel for this very Congress of America-certified instructor precise skill. and partner in the San Francisco Billiard For all of these drills, remember to Academy, which is BCA-certified for change sides. The shot may look a lot instructor training.

BD-APRIL 2001 15 Bob Jewett Charting the Course Converting spin to speed.

This month we're going to look into ond or two afterwards? We all know from first surprising result that we can see from details of the physics of straight draw and experience that the object ball will pick up these diagrams is that for our full-follow- follow shots. Don't worry about equations smooth forward roll, while the stopped cue shot case, the cue ball and the object ball and algebra — most of the work is going to ball will accelerate forward with its excess will reach smooth rolling at the same be done by a simple graphical tool. Next top spin until it too is again rolling smooth- instant, because the two sets of arrow heads month the study will be extended to cut ly on the cloth. The two arrows for each begin with the same separation. shots with draw and follow, and the tool ball will match when each ball reaches that Also note in the diagram that the object will show us immediately the angle the ball ends up with more speed than the cue ball will take for any cut angle and cue ball. This is because of the 2.5:1 any amount of draw or follow. ratio of how quickly the arrow heads The basic notion of the tool is that any change. This ratio is determined by how ball has a speed and a roll, and these can efficiently a solid sphere (like a pool be shown on a diagram with two arrows. ball) stores energy in rotation compared A simple rule will tell us how the speed to simple forward motion. The ration of and spin change if they don't "match." final speeds is also 2.5:1, and if we Consider a cue ball rolling smoothly on square this we get the ratio of how far the cloth. From its center, we draw an the balls will travel, or 6.25:1. This fac- arrow in the direction of its movement tor was discussed here in December of with a length that shows its speed. last year and is useful to know when Physicists call such an arrow a vector, playing soft-follow shape; the cue ball but we'll stick with "arrow." will go forward about 1/6 as far as the object ball is driven. We will also represent the follow or draw on the ball with another arrow. Of course, if the cue ball had no follow Let's call this the spin arrow, while the or draw when it hit the object ball, it first one will be the speed arrow. The would have neither speed nor spin after speed arrow is shown as a solid arrow, the collision, and it would have no rea- while the spin arrow is shown with a son to move. Suppose the cue ball had dashed line. Since rolling smoothly on "perfect" draw. Then its spin arrow the cloth is the natural state of the cue would be back away from the object ball, let's make the two arrows equal in ball, and would be just as long as its that case. speed arrow at impact. The spin-to- The arrow diagram for our rolling cue speed transformation would take place ball is in Diagram 1. The two arrows are just as before, but in the opposite direc- the same length and in the same direc- tion. (Remember that "perfect" draw is tion. How fast is the ball going? That defined as just as much spin as a rolling depends on the scale of the arrows. As we'll state, but what happens in the interim? ball but back spin rather than follow. It is see below, most of the results give ratios of The amazingly simple rule that describes about the limit of what you put on the cue speeds, so each diagram will apply to all how spin and speed change to match is this: ball with a level stick.) balls in a particular situation without regard the tips of the two arrows move towards What would happen if the cue ball had to the actual speed or spin. For example, all each other at a constant rate, and the spin only partial natural roll when it struck the smoothly rolling balls have an arrow dia- arrow moves two and a half times faster object ball? If you knew how much follow gram like Diagram 1, regardless of speed. than the speed arrow. Diagram 3 shows it had, you could draw the spin/speed It's pretty clear that a smoothly rolling how the arrows change with time — per- arrows for it and find the final result. Try an cue ball will remain like that until it hits haps in each tenth of a second. On the top, example with "half-follow" on the cue ball, something, so the two arrows will remain the object-ball speed decreases while the which you can get by striking the cue ball matched. Suppose this cue ball hits an spin (forward roll) increases. Similarly, the at about 6 mm above its center. For bonus object ball full. What is the arrow diagram cue-ball spin partly turns into speed. Note credit: how far will the cue ball move for- for each ball right after the collision? In that the spin changes more than the speed ward compared to the object ball for this Diagram 2, the object ball is shown on the on each ball, by that factor of two and a half-follow case? right and the cue ball on the left. At first, half. Where is side spin in all of this? Hiding. the object ball has a speed equal to the orig- The actual rate at which spin and speed Until the cue ball hits a cushion, side spin inal speed of the cue ball and no spin; it's balance is determined by the friction has almost no effect. The dynamics of draw sliding on the cloth. The cue ball is the between the cloth and the balls. On sticky and follow shots are unchanged by the opposite; it has no speed but retains all of cloth, the transition period will be shorter; presence of side spin on the cue ball. the follow it had just before the collision. on slippery cloth, or with waxed balls, the As a last example, consider a cue ball How do these diagrams change the sec- equilibrium will take longer to occur. The that's struck with perfect draw, but without

14 BD-MAY 2001 Bob Jewett

an object ball close by. Its arrow diagram In next month's column, we'll extend this is shown in Diagram 4, as is the time idea to cover draw and follow with cut development of the spin and speed. If you angles included. This will let you plan any go through the ratios, you'll discover that carom with any amount of draw or follow the cue ball ends up rolling at only 3/7 of — theoretically, at least. The diagrams will its initial speed, and it will go only about help explain the working reasons for sever- 20% as far as a ball that's been struck for al draw and follows systems that have been "perfect" follow at the same stick speed. covered in previous columns. This explains the working of the "drag" shot, in which you shoot a long shot hard- Bob Jewett is a partner in the San er but with draw so roll-off can't hurt you Francisco Billiard Academy, which offers so badly but you can still land softly on the classes at all levels from beginning players distant shot. to advanced instructors.

BD-MAY 2001 15 Bob Jewett Drawing Draw Part 2 of charting the cue ball's path.

Last month I described a graphic tech- requirements. What sort of path does the cue ball follow nique for understanding how draw and fol- The new speed arrow of the cue ball is during this time? It is easy to get a close low interact with the forward speeds of the exactly the side CA, and the speed arrow of approximation of the path by joining the cue ball and object balls, and how speed is the object ball is side CB. This is a strange speed arrows head-to-tail in order. converted to spin and vice versa. The basic situation for the cue ball. The speed and the Diagram 4 shows what this looks like; the idea is shown in Diagram 1, where the cue spin are no longer in the same direction (or path shown is roughly a curve. If we used ball is struck with draw. If twice as many times, with the there is no object ball in the times more closely spaced, cue ball's path, the speed and the ten arrows would form an spin arrows evolve as shown, even smoother curve. with the spin (draw) arrow, Technically, the ideal curve is getting shorter and finally a parabola, which is also the turning into follow as the path a ball follows when speed arrow decreases from thrown. At the end of the the initial value due to the curving part of the path, the drag from the draw. An Spin (draw) Speed cue ball will continue to roll important point is that the along the direction of Arrow spin arrow changes five units 1 5, since by then the speed and for each two units that the spin have reached their happy speed changes. Another is 2 common equilibrium. that the two arrows move at a constant rate towards each This draw shot repays time other. That constant rate is spent in practice. Notice that the final path of the cue ball determined by how slippery Spin (follow) the cloth is. is a little past the perpendicu- lar to the initial path. (The While this analysis is both calculated angle is about five interesting and useful, the Speed degrees.) Previous columns, real action starts when the including Dr. George cue ball hits an object ball at Onoda's column in May an angle. At that instant, the 1989, suggest that it is hard speed of the cue ball, which to pull the cue ball back was in line with the draw or behind the perpendicular. follow arrow, is knocked by How does the shot work for the collision to a different you? (It's no fair if you cheat line with a different speed. In by hitting more than half the Diagram 2 the cue ball that object ball.) If the perpendic- we loaded up with draw is ular is your limit, what are seen from above as it hits an some reasons you might not object ball for a half-ball hit. be getting the angle predicted The initial speed and spin are Draw for "perfect" draw? equal, and in opposite direc- Usually the final direction tions. Remember that we of the cue ball is far more called this amount of draw important than the exact "perfect," as there was just as curve it takes before it settles much draw as a smoothly rolling ball along the same line) — what happens to into that path. A simple case is shown in would have follow. each, and where does the cue ball go? Diagram 5. This is the same shot as in What does the speed of the cue ball The two arrows still move according to Diagram 2, but with follow rather than become? To find it, draw a rectangle as the rule given earlier. They move towards draw. The speed is the same, but the spin is shown in the diagram. One corner is at the each other (along a straight line) with the in the opposite direction. The final direc- center of the cue ball, and one side is along spin arrow changing 2 1/2 times as fast as tion can be found by joining the speed and the line joining the centers of the cue ball the speed arrow. This is shown in Diagram follow arrows, and then finding the point and object ball. The final detail that com- 3, where the successive arrows are shown along that line that divides it in the ratio of pletely sets the rectangle is that the speed for five different times in sequence. At 5th- 2:5. arrow of the cue ball is a diagonal of the time sequence, the arrows are the same The angle between the initial and final rectangle. Believe it or not, there is only length and in the same direction, so the paths in this case is a very important one to one rectangle that satisfies these three change stops at that point. know; it is the natural angle for a half-ball

14 BD-JUNE 2001 Bob Jewett

hit. Position play that involves grabbing the rim, but if all the lead were in anything close to half-ball (a the hub, the spin would be much easier to 30-degree cut) and a rolling stop with that long lever arm from the cue ball will produce a deflec- spokes. How large is the effect for cue tion angle very close to this balls? It seems to be no larger than the (about 34 degrees). effect of the cue ball's being small and light The geometry of the rectan- from wear. gle and the arrows can be used In theory, this graphic system for figuring to develop various systems for out where the cue ball will go can give you cue-ball control. For example, precise results. Since it depends on know- you can show that if you play ing how much spin the cue ball has, the eas- a follow shot with a small cut iest case is when the cue ball is rolling angle to the left, the cue ball will be deflect- smoothly on the cloth. Fortunately, playing ed to the right by 2 1/2 times the angle. In with a smoothly rolling cue ball is the eas- a previous column, I suggested 3 as the iest way to play position, next object ball ratio. See what happens for you with real willing. This system may also be useful for balls on real cloth. letting you know which shape shots are Where does this factor of 2:5 come from? impossible — the speed arrowhead can be Roughly stated, it says how much more pulled over only so much by the spin arrow. effective the simple movement of the mass This system can even be applied to masse of the ball is than the movement you get shots, and for a given stick elevation and from the spin rubbing on the cloth. offset, you can draw out the curved part of Physicists call this the "moment of inertia." the path as in Diagram 4. That extension The usual assumption is that the ball is uni- will have to wait for a future column. form, but this is not always the case. Some cue balls have heavier centers, and the Bob Jewett is an advanced-level Billiard effectiveness of spin on such balls is small- Congress of America Certified Instructor er; they would be more lively if they were and a partner in the San Francisco Billiard hollow with a heavy shell. Think about it Academy, which offers classes at all levels this way: if you had a bicycle tire made out from beginning players to advanced of lead, it would be hard to stop its spin by instructors.

BD-JUNE 2001 15 Bob Jewett The Rack It's more than a torture device.

One way or another, a major change is again. rack, the chance of getting a rack with min- coming to pool. The advent of the Sardo In other games, the number of gaps imum gaps by using a wooden triangle was Tight Rack is forcing players and officials varies. At 6-ball, you can obviously always nil. On new cloth and with a good set of to re-examine what a rack should be and do a perfect rack: start with a triangle of balls, you can get close, and players often how to deal with a nearly perfect framing of three balls, and then put the "corners" on — remark on how well the balls break under the balls. At least one rule has already everything can be frozen. At the 15-ball such conditions. As the cloth wears and changed, although you might not have gets small craters in the rack area, and espe- noticed. cially as the rackers move the rack around Let's begin by asking a question: Should and spread out the craters, the chances get the rack be tight? The norm for many lazy slim, and soon Slim leaves town. and/or cheating rackers is to leave a sloppy, Several things help the Sardo rack pro- loose grouping of balls on the table, result- duce nearly perfect racks. In tournaments, ing in a break that is unpredictable and the cloth is marked to show exactly where often ineffective. The rules require — and I to put the edges of the rack, so the chance think it's only fair — that the balls be of "crater spreading" is reduced. Compared racked as tightly as possible, but how tight to the typical wood triangle, it is far more is that? accurate mechanically — just think about It is not theoretically possible to freeze all how often you have to turn an standard tri- the balls in a rack. Here, we're talking angle to find the one good corner. Finally, about real pool balls that are all slightly dif- the top part of the rack that comes down to ferent sizes. A new set of good balls will be position the balls pushes them gently the same diameter (and round) within one together, rather than forcing them into spe- thousandth of an inch. The rules permit five cific positions, so any mismatched ball is times that deviation in each ball. With real accommodated as well as possible. balls, it is usually impossible to get every- What happens differently with a near-per- thing frozen. Start with the 9 ball in a 9-ball fect rack? At 14.1, the ideal break is for the rack. Assemble the rack by putting the 9 in two corner balls (the 1 and 5 in Diagram 2) position, and then freezing the 2 ball to its to go to cushions and return to the rack with side. Freeze the 3 ball to those two, and so no other ball moving — a perfect rerack. on around the 9, forming a ring of six balls With a good rack, this shot is impossible. with the 9 in the middle, as shown in As shown, the cue ball will hit the 1 ball Diagram 1. With the addition of each ball, into the 4. The 4 will move to the right and there is no choice about where to put it, it will contact both the 9 and 3. The energy since it must be frozen to the two other transmitted to the 9 will eventually emerge balls. Suppose the 7 ball is a little small, but with the 10, 14 and 11 balls leaving the all the other balls are perfect. The result is rack. If you want to do the perfect 14.1 as shown. The 7 can be frozen to the 9 and games, you can work from our 9-ball rack break, just leave gaps between the 4-9, 3-15 2, or the 9 and 6, but it cannot be frozen to by putting three-ball "corners" against the and 2-12. If those balls are frozen, extra all three of its neighbors. 8-4-5 and the 8-3-2 sides. With a little balls are guaranteed to move. Suppose the 7 was larger than the other thought, it's clear that each set of three balls What happens differently at 9-ball? The balls. Then the hole the 7 is supposed to fit might require one additional gap, giving first thing that a lot of players noticed with in would be too small, and while you could three required gaps in any 15-ball rack. the new Tight Racks is that if you find the freeze it to both the 6 and 2 balls, it could Pat Fleming has pointed out a way to get correct spot for the cue ball, one of the not also touch the 9 without forcing some rid of these "necessary" gaps that uses the wing balls (5 or 2 in Diagram 1) is almost ball away from the 9. fact that most pool balls aren't round. On guaranteed to go in, even with a moderate You complete the rack by adding the 1 many sets of old balls, the "eyes" of the speed (and well-controlled) break shot. For ball and the 8 ball at top and bottom, and balls — where the numbers are — bulge at least a year, the solution in tournaments both of those can be frozen easily to the 6- out. In our example above, you might make has been to move the rack position so that 7 and the 3-4, respectively. This means that the 7 ball "wider" by rotating it until its the nine ball rather than the one is on the for any normal set of pool balls, it is possi- eyes are against the 6 and 2 balls. If that spot. This makes the wing balls much hard- ble to rack nine balls with only one gap, doesn't quite close the gap, you could er to make, as they must be driven more and because balls are never exactly the rotate the eyes on the other balls into ser- through the balls behind them. same size, it is almost certain that there will vice. This is all a little far-fetched, but it's I noticed a second difference in one of be one gap among the balls around the 9. If something to keep in mind if you just can't Allison Fisher's matches at the Hopkins' there are two gaps, the rack could be better, get a normal rack tight. Super Billiards Expo this year. When she and it is reasonable to ask the racker to try Until the recent introduction of the Sardo broke, the 1 ball reliably found the side 14 BD-JULY 2001 Bob Jewett

all frozen — it's always possible to get this the 9. In a minor miracle, the 6 hit the 9 just — and one with the one ball slightly sepa- right to send it into the corner pocket. rated from the balls behind it. I think you'll Tough luck for Dominguez; if any ball had find that a millimeter can make all the dif- touched either the 6 or 9, Ortmann would- ference in the world to this shot. What was n't be "on the hill." Ortmann broke again, remarkable was not that Allison played the and as if it were on tracks, the 6 came 1, since that is the most predictable ball to around four cushions, hit the waiting 9 ball, make with the "forward-spotting" rule in and the match was over. force. What caught my eye is that she If we are going to accept tight racks at 9- played the shot at moderate speed and ball, how should the rules change? Here's seemed to be playing position on the 2 ball. one possibility for your consideration: The routes of the other balls in the rack After the break, all balls that were made start to be predictable if the rack is the same will spot, and the breaker gets the next shot. every time. A 50-mph break will no longer be useful, A final difference at 9-ball is that the 9 but the knowledge and skill to play specif- almost never moves. Although the two balls ic position on the 1 ball will be essential. in front of it will push on it, the two balls The 1 ball could go back on the spot, since behind will take up the energy, just as for it would actually be a disadvantage to make the middle ball in a three-ball combination. a ball on the break. I think it would be a If the nine isn't kissed — and on many better sort of 9-ball. breaks it isn't — it will still be in place If you would like to see what a very tight when the commotion dies down. This can rack at 9 ball plays like, send me email lead to some interesting shots. At the recent ([email protected]) and I will send back Billiard Congress of America Open 9-Ball a "PRN" attachment that will let you make Championship at the Riviera Hotel & your own racking template. You will need a Casino in Las Vegas, Oliver Ortmann was computer printer and a paper-hole punch. playing Ernesto Dominguez, and he needed two more games for the match. On his Bob Jewett is an Advanced-level Billiard pocket. Try this yourself: break from the break, the 9 stayed at home, as expected, Congress of America Certified instructor side cushion and hit the one ball nearly full. and the back ball, shown as the 6 in and was the National Collegiate Champion Test two cases, one with the front six balls Diagram 3, came four cushions directly at in 1975.

BD-JULY 2001 15 Bob Jewett When Spheres Collide More here than meets the eye.

In last month's column, I mentioned in the spherical shape of the balls. As they tion (that's the hard part) and then measur- passing that pool balls compress during move together, flat spots develop on each ing the time of the contact (that's the easy collisions. This seems to be contrary to one as the plastic in the contact area com- part). His typical result was 200 millionths what you see on the table: the balls appear presses. The cue ball continues to move of a second. It is important that this time is to be hard, incompressible spheres. In fact, forward as the compression starts to move much longer than the time it takes for there must be some "give" to the surface, or the object ball. As the object ball picks up sound to travel from one side of the ball to they would not behave nearly as perfectly speed, at some point it is moving just as fast the other, or just as for the cue stick, the as they do. as the cue ball. "echo" of energy from the far side of the In July 1998, I explained that to study a ball couldn't take part in the shot. cue stick, you should think of it as small The ball-ball collision is hiding a further lumps of mass joined by short, stiff springs. subtlety that can be important in play. As Since the naked eye can't see the stick com- the balls compress together, the interaction pressing along its length during a shot, you is not like a simple spring. Instead it is a might conclude that the stick was perfectly sort of compound spring, because as the stiff, did not compress, and delivered its flat spot gets larger, more and more surface energy through the tip to the ball nearly area gets involved. This means that the instantaneously. In fact, what happens is "spring" gets "harder" the more the balls that ball pushes on the tip and compresses are compressed. For a normal cue-ball-to- it, the tip pushes on and compresses the fer- object-ball collision, this makes little dif- rule, which pushes on the shaft, which then ference, but when another object ball is pushes through the joint, into the butt and This "equal-speed" point happens to be at behind the first object ball, as when two finally to the back end of the cue. As the the time of maximum compression, when balls are spotted on the long string, the ball comes off the tip, all this compression the flat spot is largest, and when half of the exact nature of the collision becomes is relaxed, and the energy stored in the energy of the shot is stored in the compres- important. compression of both the tip and the stick sion of the surfaces of the two balls. After What happens during the shot is illustrat- itself is mostly released into the cue ball. I this point, the compression releases like a ed in Diagram 2. This is for balls that are say "mostly" because both the stick and the spring, and that stored energy is put back perfectly springy (elastic) and the predic- tip are not perfectly springy. Some energy into the object ball. If no energy is lost in tion is a little surprising. Theory says that is lost into the stick/tip combination, but if the balls — and they are really quite close for perfect balls, the cue ball is expected to there were no springiness at all, the cue ball to perfect — the push-off of the object ball bounce back from the two-ball collision would have only about 60% of the speed from the compression will stop the cue ball with some speed. For the "progressive we see. dead. spring," the speed back is expected to be Do you remember from high school what I bet you didn't know that all of that goes about 8% of the incoming speed. If the sound waves are? They are a similar com- on when you shoot a stop. balls behaved like regular springs, gov- pression of the air by something vibrating. How big is the flat spot? You can find it erned by Hooke's Law, the bounce-back is Usually the sound energy doesn't come yourself by putting a piece of carbon paper expected to be twice that large. back, but when it does, it's an echo. You can (if you can find one) in front of an object Why do three balls behave so much dif- think of the compression of the stick as ball and then noticing the size of the mark ferently that two? It turns out that for just echoing off the back end, and in some sense the cue ball leaves. It also works to use two balls, the Laws of Conservation of doubling the speed of the cue ball. Like an freshly waxed balls or balls with a wet film Energy and Momentum forbid anything echo, the compression of the stick moves from your condensed breath. The result is except the stop shot from happening. If with the speed of sound. Unlike the echo, that for a hard shot, the flat spot is a quar- three balls are involved, there are many out- the speed in the stick is not the standard ter-inch or six millimeters in diameter. How comes that satisfy the two Laws, and which speed of sound — lightning a mile away much did the surface of each ball compress outcome we see can only be predicted if we will be heard in five seconds — but is the during such a collision? Simple geometry include the exact details of how the balls speed of sound in the wood of the stick. says about 0.3mm or one hundredth of an interact. The three balls must be all touch- By now it should be clear that ball-ball inch. That's about the thickness of three ing at the same time during the collision. collisions aren't as simple as they may sheets of typing paper. So, if the cue ball is expected to bounce seem on the surface. When the cue ball hits How long does this collision take? It can back, how come we never see it do so? an object ball, a sequence like the one for be measured just from the size of the flat (Draw doesn't count.) The answer seems to the stick-ball begins. This is shown in spot and the speed of the cue ball. It has be that enough energy is lost in the colli- Diagram 1, with the compression slightly also been measured directly by Wayland sion that the cue ball is fully stopped, but exaggerated. At the first instant of contact, Marlow in an experiment described in his doesn't get enough push-back from the the cue ball is still moving forward but the book, The Physics of Pocket Billiards. He springs to get negative motion. You might object ball hasn't started to move yet. measured the time the balls were in contact try the experiment yourself with an old set Something has to give, and what gives is by having them make an electrical connec- of balls, and then some right out of the box.

28 BD-AUGUST 2001 Bob Jewett

table. It turns out that industrial processes which transport beads or pellets of material have lots of ball-ball collisions going on, and Hertz' Law is needed to understand them. If you have access to the Web, enter "Hertz contact law sphere" in a good search engine, and you should get plenty of equa- tions. If you've waded through all of this rather technical stuff, you deserve a reward. Here's an old puzzle, slightly reworded. If you get the correct answer and are the entry chosen by our autocratic judge — me — you'll get a one-year subscription to this magazine. It's better to send e-mail to jew- [email protected], but real mail sent to BD in my attention is OK. In 1887, the bright, young Mr. Hertz was What happens to the middle ball is the of 10 can be predicted from the physics. walking down a street in Berlin when he useful part. It is going forward some, which Also, since the compression length is so heard an unfamiliar clicking sound coming is contrary to the usual teaching of "stop- small (less than 0.3mm), the shot is greatly from a tavern. Entering, he saw a teacher shot physics." To make a shot from this for changed if the two balls that are supposed and a pupil and three ivory billiard balls. the double-spot shot, as shown in Diagram to be frozen are even the thickness of a dol- Hertz had heard of this "billiards" but had 3, place the cue ball a little off line, and hit lar bill apart. never seen a table before. The teacher shot the front ball full. It will get some speed to The compound spring law that governs a simple carom — with the click that had the side, but will also have some speed for- spheres in collision is called Hertz' law, and attracted Hertz — and explained the 90- ward, due to the "three-ball effect." If you it was discovered by the same physicist degree initial carom angle. Hertz piped up, have the right small angle, you can make who discovered radio waves and whose "But the angle between the paths of the the front ball in the corner pocket. This name you see in "megahertz" and such balls must be less than 90 degrees." How kind of shot has been described here before terms. The details of the law are an active did he know? For extra credit, what was his as the "10-times-fuller" system. The factor area of research, and not just on the pool mistake?

BD-AUGUST 2001 29 Bob Jewett Sliding Friction How far will you slide?

It is the various kinds of friction that new or the cue ball is waxed — try silicone With little friction, the force on the base of make cue sports interesting. Without spray if you want to do the experiment — the ball is less. This leads to less accelera- rolling friction, the balls wouldn't stop until the cue ball will take the wide course and tion at each instant the rubbing is going on, they had all found pockets. Without the will look as if it is moving in slow motion. so the curve happens more slowly. It also friction between tip and ball, which is aided If the cloth and balls are sticky, the result is means that the spin is not being rubbed off by chalk, we would have no control of spin the sharper, faster curve. Under sticky con- the ball as quickly, so the curve goes on for and position. Without the friction between ditions, the shot can be fixed just by shoot- a longer time. In some sense these two the balls, the dimension added effects balance, so that in by throw shots would disap- Diagram 1, the final angle that pear. Without ball-cushion the cue ball takes is the same friction, position play would regardless of how much fric- be severely restricted. tion there is. A sharper curve Another kind of friction that for a shorter time gives the is at work on every shot is same angle. sliding friction between the The effect is present on balls and the cloth. This was straight shots as well, but it is mentioned briefly in the two a little harder to see. The main recent columns about calcu- result is that with low friction, lating and plotting the speed the cue ball holds its draw for and spin of a ball as it much longer. Have some fun achieves normal rolling on the with a friend: On a table with cloth. The natural state of the old cloth, secretly grease up ball is normal rolling, because the cue ball. Put an object ball any sliding between the ball in the jaws of a foot pocket, and the cloth produces a force and challenge your friend to on the ball that will tend to shoot a stop shot from behind eliminate the sliding. the line. If he's got a pretty Sliding friction is harder to good stroke, and is calibrated measure than the other kinds. for the old, sticky cloth, he's Rolling friction — which likely to draw the cue ball causes the ball to roll to a stop clear back to the kitchen. — can be measured easily Normally, the considerable with a stopwatch. Friction draw at the start of the shot between the balls is shown by would be worn away over the the maximum throw angle. six diamonds of travel, but the You can get at least a feel for silicone reduces the rubbing friction on the cushion by the and holds the draw for longer. resulting angle for a cue ball with maxi- ing harder, but that can get you into mis- How can we measure sliding friction? mum spin going straight into the cushion. cues, jumped balls, and other problems. These shots give you a feel for whether a The friction between ball and cloth is Silicone spray has become a standard tool particular ball/cloth combination is more or dynamic; it always has time as part of its for fancy-shot artists who want to move less sticky than you're used to, but it's good measurement. An example shot of the from amazing to impossible shots. The to have an actual number to compare. effect is shown in Diagram 1. This stan- main effect is to get much wider, slower Physics books suggest measuring sliding dard fancy shot demonstrates how to make curves with less effort. An example is a shot friction between an object and a surface the cue ball curve without masse. The idea by Semih Sayginer in his closing exhibition below it by pulling the object sideways, and is to pocket the first object ball, and then at the Conlon WorldCup Tournament, July noting what fraction of its weight must be curve around the obstacle ball without hit- 18-23, in Las Vegas. The cue ball was at A, applied to keep it in steady motion. Balls ting the side cushion and pocket the hang- and the target was at about B. The actual tend to roll when pulled sideways, so that's er. Shoot slightly fuller than half-ball, shot was a carom shot, but it would also not convenient. You could glue three balls which will allow the draw to pull the cue work as a pool shot. The cue ball massed together, like a mini-rack, and pull that ball back enough. around the obstacle ball over five diamonds sideways, but you would need glue, spare Shown in the diagram are two curves for away and came back to the target. With an balls, and a string, pulley and weights to do the cue ball's path. They represent shooting unwaxed cue ball, the standard shot is to the pulling. the shot at the same speed, and with the make just a right-angle turn from C and Another way would be to videotape a same amount of draw but with different then go to the target at B. curve shot like the one in Diagram 1, plot amounts of sliding friction. If the cloth is Exactly how does "slipperiness" enter in? the result to scale along with the time of 14 BD-SEPTEMBER 2001 Bob Jewett

each location, and do a lot of arithmetic. A mum speed that still achieves smooth and 4 is 10 inches, we can calculate how simpler way is shown in Diagram 2. The rolling on the 3 ball. I also tried polishing much the 3 slowed in that distance due to idea is that if you shoot the three-ball 1-2-3 the 3 to reduce the friction, and the lower picking up follow from the cloth. This in combo at the 4 ball, the 3 ball will roll for- curve was the result. It shows only about turn gives the sliding friction on the ball. ward some distance after hitting the 4 ball, half the peak run-through of the regular The final result — details of the calculation and that distance will tell us how much fol- case, since the slippery 3 ball doesn't pick available on request — is that the cloth-ball low the 3 ball picked up on the way to the coefficient of friction is 0.25, so that the 4. If there is more sliding friction, the 3 force on the ball when it is sliding is 25% will pick up more follow and will roll far- of its weight. For the "slippery" case, the ther. coefficient of friction is reduced to 70% Suppose we vary the speed of this shot of this value or about 0.18. These values from very slow to fast. For the slowest agree well with the value that Coriolis shots, the 3 will just get to the 4 ball and measured over 160 years ago, of 0.20. will surely be rolling smoothly on the How can you use these ideas on the cloth. It will drive the 4 down the table table? The main thing is to realize that on and roll a little after it. These two dis- new cloth or with waxed balls, some tances will follow a simple rule that was things will change greatly. Many players covered here last December: the 4 will like to shoot "stun run-throughs" or stop roll seven times as far as the three. This shots that don't quite stop. The success of holds for full shots where the "cue ball" is such shots is critically dependent on how rolling smoothly on the cloth. As the shot up follow as effectively. much sliding friction there is. As the weath- gets faster, there will be a point when the 3 If we can figure out the speeds of the balls er gets humid, you will see the opposite of just gets to smooth rolling on the cloth as it for these cases, it is a simple matter of alge- the slippery condition; the ball-cloth fric- hits the 4. This should result in the maxi- bra to figure out the friction of the cloth. tion goes way up. In this situation, stop mum run-through of the 3, since for faster The whole calculation goes roughly like shots will turn into follow shots, and draw shots, it doesn't have enough time to pick this: A ball is measured to take eight sec- will be much harder to achieve. up full follow. In effect, we are shooting a onds to roll 98 inches. This lets us calculate stop shot with the 3. the speeds of the two balls, given their Bob Jewett is a Billiard Congress of The measured result is shown in Figure rolling distances; We can then calculate the America Advanced-level instructor, and a 1, where the follow distances of the two speed of the balls at impact, and the speed partner in the San Francisco Billiard balls are shown. For the regular case, there of the 3 ball when it is struck by the 2 ball. Academy, which has courses for beginners is a very clear peak which shows the maxi- Knowing that the distance between the 3 to instructors.

BD-SEPTEMBER 2001 15 Bob Jewett Playing Games Renew interest in your favorite game by trying a few others on for size.

Has your game reached a plateau? Do contains the rules of over 30 games and is Billiards. you feel like you're in a rut? What you may available for less than 10 bucks, shipping A game rarely seen in the U.S. but defi- need is a new game. included. Parts of the rules are online at the nitely worth learning is English billiards. It Pool halls are largely filled with players BCA Web site, or you can use a search is played with two cue balls and a red ball who know only one game. If they play 8- engine such as www.google.com to find like carom billiards, but a snooker table is ball, they will refuse to play 9-ball because other sites. used. Points are scored by pocketing any the shots are too hard and they don't understand the safety play. If 9-ball is their game, they won't shoot straight pool because they're confused by all the choices, and of course they don't understand the safety play. If they play pool, they'll never get close to those tables across the room that are 12 feet long or don't have any pockets. Such stick-in-the-muds never stretch their minds, never learn new tech- niques, and will be playing the same game in the same way in 20 years that they have for the last 10. I hope you aren't one of them. When I first started playing, I had an ideal situation to try different games. Pool, snooker and carom tables were all available at the comfortable rate of 40 cents per hour. There were fairly good players on all of those tables — at least they were a lot better than I was — Many games will be valuable for master- ball (three for the red, two for the oppo- and national- or world-class players could ing your favorite games because they make nent's cue ball, and three or two for your always be seen on a trip to "The City." you polish particular facets that may get cue ball depending on whether you hit red Among the games that I played during my neglected in the normal course of play. For or white first. You also get two points for first year or so were straight pool, 6-ball, 9- example, straight-rail billiards (on the making a "cannon," which is what the ball, 8-ball, cribbage, cut-throat, partners pocketless table, just make your cue ball hit British call a simple carom. It's possible to rotation (money ball), kiss pool, call-posi- both the other balls to score a point and score 10 points in one shot by pocketing all tion 14.1, and one-pocket on the pool table; continue shooting) will teach you how to three balls, but this is a bad idea, as your snooker, golf, pink ball, and English bil- hit the ball softly, because once all three opponent's cue ball stays off the table until liards on the snooker table; and straight rail, balls are close, soft shots will tend to keep his turn, and scoring with just two balls on 3-cushion and fancy shots on the carom bil- them together. Straight rail also teaches you a 12-foot table is quite a challenge. When liard table. Bank pool, bumper pool, bottle to control all three balls on each shot, red is pocketed (they say "potted"), it pool, cowboy, 21-ball rotation, equal which will do wonders for both your preci- comes back to the seven or black spot (they offense, Fargo, line-up, pea pool, and pin sion-banking game and your cue ball con- say "billiard spot"). Many turn-of-the-cen- billiards I played later as the opportunities trol. Allen Hopkins and Dallas West have tury British books go into detail about the came up. both recommended straight rail to improve strategy and such of English Billiards, and The first step to adopting a new game is to pool skills. you can often find these in on-line auctions. learn the rules. The easiest way is to play If you have trouble locating a carom The full rules for the game are online at against someone who knows them already, table, visit the United States Billiards www.wpbsa.com. or, if you're shy, to watch a game in Association Web site at www.uscarom.org A game similar to English billiards but progress. As important as the rules are the for a list of all known rooms in the U.S. that designed for the pool table is cowboy. The tactics and strategy. While watching an have tables. The best explanation of ball-to- game uses a shared cue ball and the 1, 3 and accomplished player, try to predict what he ball caroms is in Daly's Billiard Book, 5 balls. Points are scored by pocketing the will do. If a shot really puzzles you, ask which was first published over 80 years object balls (score: the number on the ball) about it — most players like to show off ago, but gives far better general cue-wield- or by caroming from one object ball to their knowledge. ing instruction than many modern books. another (score: one point for hitting two, Another good source of rules, especially An excellent modern book that covers a lot two points for hitting all three). The game if you're striking out on your own, is the of straight rail in a few pages is Robert is to 101, with some details. You must land Billiard Congress of America rule book. It Byrne's Wonderful World of Pool and exactly on 90 points, or the shot that takes

14 | BD-OCTOBER 2001 Bob Jewett

you over 90 is a foul. On a foul, all points shoot the 5 towards D and take the cue ball would like to see discussed, please drop me of that inning are lost, but there is no other towards the 3. The 5 should bank over to a line in care of this magazine. penalty. Points 91 through 100 must be join them, if your speed is correct. With all In the August issue, I proposed a puzzler scored by caroms only, and it's a foul to three object balls together, your run-out is involving Herr Hertz and billiard-ball kiss pocket a ball. Point 101 must be scored by assured. angles. A billiard instructor was telling a a called scratch off the 1 ball. The 1 spots The games you try should fit your skill student that the angle is a right angle or 90 on the head spot, the 3 on the foot spot, and level. Of course, if a game is fun, stay with degrees, and Hertz stated correctly that it is the 5 on the center spot. The full rules are it, but I'd recommend that beginners start less. The first question was: how did Hertz in the BCA rule book, and a good search with cowboy, cribbage and straight rail. If know that the kiss line is less than 90 engine will find several unofficial rules you've never run out a rack of 9-ball, why degrees? The big hint here was that Hertz sites on the Web. not play 6-ball instead? When I first played, was drawn into to the room by the clicking In Diagram 1 is an example position 6-ball was the rotation game of choice, of the balls and didn't even see the colli- from cowboy. Your score is 85. What while 9-ball was considered too hard for sion. That sound is energy being lost in the should you play? Fairly obvious is the 5 most players in the room. collision, and from George McBane's guest ball in the side which brings you to the Advanced players should try more chal- column last February you know that lost required first step of 90 points, but you lenging games such as snooker, 3-cushion, energy means the angle between the cue have to start planning for the carom shots bank pool and one-pocket. These will in ball and the object ball will be less than the that are required after 90. Play the cue ball turn help you work on pocketing accuracy, ideal 90 degrees. The second question off the end cushion to end at A, and you cue-ball control with spin, cushion reaction asked what Hertz' error was. The answer to should have an easy carom shot from the 1 and precise speed control. that is that he should not have corrected the ball to the 5 when it is spotted on the center Good books are readily available for most instructor in front of the student. Of the cor- spot (where the shaded ball is). But that games — does anyone know of a good one rect answers, Anthony DeAngelo had the shouldn't be the end of your planning. on bank pool? Byrne covers many "alterna- most complete response, so he'll be getting Since your last 10 points must be scored by tive" games in Wonderful World as well as a year's subscription to Billiards Digest. caroms, you want to gather the object balls his Advanced Technique book, and his together to make scoring easier. Play the 1 Standard book is the best available on 3- Bob Jewett is a Billiard Congress of ball to hit the cushion near B and to come cushion billiards. George Fels and Jack America Advanced-level instructor, and a to rest near C. If the 5 ball after the carom Koehler each have two or three books in partner in the San Francisco Billiard ends up near its starting location, and the print on strategies and techniques. Academy, which has courses for beginners cue ball is near the center spot, you can If you have a favorite "other" game you to instructors.

BD-OCTOBER 2001 15 Bob Jewett Round-Robin Formats A simple alternative to double elimination.

Do you enjoy playing in double-elimi- you'll see that Player l's opponents in each because one of them has to win and will nation format tournaments? If you're like round are in numerical order. It may be that also have a 4-1 record. me, you find them torture. If you lose your it is better to have a different order. The The tournament director better still have first match, you have to win twice as many usual problem that comes up is that if two the paper he read from at the start of the matches as the guy who beat you in order to friends are matched up in a late round, they tournament that describes the tie-breaking finish in the same spot. How can that be may decide who should win to have the criteria. If Andy loses and Earl wins to tie fair? best chance to take first place. Suppose him with a 4-1 record, there are two com- Round-robin is an alternative for- mon ways to decide first place. One mat that solves many of the prob- is by a playoff, but often there is no lems with "DE." It was the most time for that. Alternatively, a two- popular championship format for way tie can be decided by the match many years, and was only displaced that the two players played. Since when tournaments started having Andy beat Earl earlier, he would get much larger fields. Even with a first and Earl would get second. large field, it is possible to have a Other ways to decide ties include modified round-robin that lets most total points scored, points allowed, of the players play more games, and and inning average. The actual is fairer in the selection of who method is not as important as hav- advances. ing it written down and posted. In the basic round-robin tourna- Include all the criteria in order, such ment, everyone plays everyone else as head-to-head; most points scored; once. This is a standard arrange- fewest points allowed; one-game ment for most league play. A main playoff. Also, the rule for forfeits is problem is to construct a schedule. important to set ahead of time. If a There are programs and pamphlets for this, Andy and Bill are buddies, and when they player abandons the tournament — that is, but it is very easy to do by hand. For exam- play each other, Andy has a 4-0 record and he fails to play his last several matches — ple, suppose we have eight players, or Bill is 2-2. There is a temptation for Bill not it is reasonable to simply erase his entire teams, numbered 1 through 8. Write these to shoot his best so that Andy can advance record. If someone misses one match, down in two rows like this: to 5-0 and have a lock on a major prize. To assign an F for his score for zero points. 1345 avoid this problem, you can invoke the Remember the brother-in-law rule? In the 2876 "brother-in-law" rule: matches between tournament shown, the angles are a little Pair these by columns to find the first- friends/cousins/road partners will be in the different. Because Andy is guaranteed first round matches: 1-2, 3-8, 4-7, 5-6. Ideally, early rounds. To accomplish this, simply before the final round is played, he can lose all these matches happen at the same time. rearrange the order of the rounds, or assign to Bill without cost. On the other hand, Now here's the tricky part. Keeping the " 1 " the names to the initial numbers to put all another win for Bill will tie him for third in its place, rotate all the rest counterclock- of the buddy-buddy matches in the first place with the loser of the Earl-Fiona wise: round or two. match, and that might be worth a little more 1456 The results are usually shown on a special prize money. 3287 round-robin chart. Figure 1 shows the par- In a league situation where one team trav- The numbers on the top row moved to the tial results of a six-player tournament. The els and one plays at home, you also have to left and the numbers on the bottom row players' names are entered on the left side assign home/away for each match. Usually moved to the right, giving the second-round and across the top (perhaps abbreviated). this can't be done perfectly, so that every matches: 1-3, 2-4, 5-8, 6-7. Continue this The entries in the grid show the match team gets an equal number of home and until you have seven rounds. Since each scores for the play so far in this race-to-four away games, and there are never more than player plays everyone else, the number of event. For example, Andy has four wins on two homes or aways in a row for any team. rounds in a round-robin will always be one his row from his matches, marked as Ws If the league plays a "double round-robin," less than the number of players. across. To find out the scores of his oppo- so that each match-up occurs twice, a sim- This method of "construction by rotation" nents in those matches, just read down the ple rule is to play at home in the second works for any even number of players. If "A" column to see, for example, that Carl half if you played that team away in the you have an odd number of players, just won three games against Andy. first half. insert an extra player named "Bye" and There are three matches left, Andy-Bill, In some situations, it is best to arrange the you're back to the even case. Bye's oppo- Carl-Dave and Earl-Fiona. At this point in rounds so that the best matches are saved nent gets to sit out that round. There will be the tournament, the spectators will be figur- for the final rounds. It helps if the relative as many rounds as there are real players in ing out all the possibilities. If Andy wins, strengths of the players are known at the this case. he has first place for sure, but if he loses start, and the players are entered into the If you work through the above example, he'll be tied with either Earl or Fiona, chart in order of ability. A schedule con- Bob Jewett

If a league plays a double players into four flights of four with one round robin, the second player advancing to a final round of four half can be set up by Seed- players. That would leave six rounds on the ings from the standings final day. after the first half, to make At the recent Conlon Worldcup 3- the final weeks of play the Cushion tournament in Las Vegas, the most important. problem was how to accommodate 132 The main problem with entries on eight tables in three days to round-robins is the very select 12 qualifiers to advance to the main large number of matches tournament with the seeded players. One for a large number of way would have been to have a single-elim- entries. Local pool tourna- ination tournament, but it would be brutal ments commonly draw 50 for the many foreign players to travel such players or more, and even if a long way for possibly only one match. To you had 25 tables to play guarantee at least two matches for every- on, 49 rounds would be one, the first round was set up as 48 round- more than most could robins in groups of three. Some groups had stand. The standard way to only two players, so they played each other handle this is to play twice. The single winner from each group structed to "save the best for last" is shown "round-robins in flights." The players are then went on to two rounds of single-elim- in Figure 2. The entries in the grid are the divided up into smaller groups, and each ination, so no one played more than four rounds in which each match takes place. group plays its own mini-round-robin. For matches in the preliminaries. For example, the top-ranked player (1st) 48 players, eight groups of six would work. Round-robins are especially well suited plays the worst player (8th) in the first Two players could advance from each to determine the best player among eight or round. Notice that the nominal "number group, giving 16 in the next round. At that so. They also work well for a league format one" has progressively more difficult point, everyone would have played five with a long schedule. Even for fairly large, matches in each round, until he plays the matches, so to save time you could switch short tournaments, their advantage of giv- nominal number two in the seventh round. to a single-elimination format, and there ing everyone a reasonable amount of play Also note that all the matches among the would be only four more rounds. With makes them worth trying. A free on-line top four players will take place in the final plenty of time, perhaps in a two-day tour- schedule planner is available at the Web site three rounds (5-6-7). nament, you could instead divide the 16 http://www.playpool.com. Bob Jewett Elimination Formats More formatting alternatives for running your own tournament.

Last month, I tried to convince you to special pattern that is important for both see them in the finals again. If we didn't try a round-robin format for your next tour- seeding players and placing byes. The seed them, and they were paired by chance nament. Round-robin is the fairest way to numbers are placed starting from the 1 on in the first round, there would be a good determine the best among a group. For best the right side. Moving to the left, the 1 runs chance that the best player would be quick- results, especially if the players are divided up the top of the chart. In the "finals" ly gone from the tournament. into preliminary flights, the relative round, the number 2 is added next to the 1 Of course, you don't always know how strengths of the players strong the players are, should be known so and then a random that the top players can draw for spots must be seeded into different suffice. There are also groups. It has the middle-strength play- advantages of more ers who will argue for play for most entrants random draw even if and a chance to recover the strengths are more from a single loss, but or less known, because it requires more tables they would rather have and time than are often the possibility of all the available. champions in one part When time and tables of the chart and them- are short, an elimina- selves in some other tion tournament of part. Random draws some kind is better. often produce very The standard in the unbalanced charts. U.S. has been double- This numbering elimination tourna- scheme also can be ments, but there are used to place byes. several alternatives. When placing byes, the This column will go idea is to spread them over single-elimination as evenly as possible formats of various through the chart. I types. remember a $100,000 The basic idea is simple: win and you and it runs down to the left. In the semi- pool tournament in the 1980s in which the play again, lose and you go home. Figure 1 finals, a 4 is added next to the one and it byes were drawn for position just like the shows an eight-player chart that illustrates also runs to the left. In the quarterfinals, or players, and they happened to clump several important points. The first is that as round of 8, an 8 is added next to the one, together on the bottom of the chart. In that you move from where the players start on and if we had more rounds, they too would tournament, Mr. Bye played his brother, the left side to the right, the number of run down to the left. The rule is that in each and one of them did get through to the sec- players left is reduced by half in each round, the number next to the 1 is the num- ond round. His opponent, who had played round, in the progression 8-4-2-1. The math ber of players in that round. their cousin, Mr. Bye, in the first round, whizzes will recognize these as the powers One spot is left in the semifinals is next to was very happy to see him there. of the number 2, which have become much the 2, and the obvious choice is 3, since 4 Suppose we have a tournament and six more popular with the rise of computers had already been placed next to the 1. This players show up. We need to fill the eight- and their binary number system. If you hints at the other rule for this numbering player chart, so two byes have to be added. need more room, the next added round to scheme: in every round, the numbers in Just place them in the highest spots (7 and the left would have 16 spots, then 32, 64, each match add up to the same total. Thus 8) in Figure 1, and have the players draw 128, and so on. 1+4=5 and 2+3=5. Check to see that in the cards numbered 1 through 6 for their spots. If you have a number of players that isn't quarterfinals, all the matches add up to 9. The numbering scheme guarantees that a power of two, you add enough "byes" to This total number is always one more than byes will be spread out. exactly fill the chart. If you happen to play the number of players in the round. Homework exercise: extend the chart one Mr. Bye in the first round, you can be pret- How does seeding work? The purpose of round to the left for 16 players, and place ty sure of a win — he rarely makes it to the seeding is to prevent the best players from five byes. second round. playing each other in the early rounds. Sometimes you have to both place byes In the example tournament, 1 beats 8 in Suppose we have the defending champion and seeded players. For this, you have to the first round, and continues winning and the defending runner-up in the tourna- decide whether the seeded players should through the finals, where 1 beats 2. ment. If we place them in the number 1 and get a free ride in the first round. If so, just The numbers in the diagram have a very 2 spots on the chart, we have a chance to use the chart as is — the high numbers Bob Jewett

number of spots to participate in a top-flight event and guar- plus one, and run- antee that all the top players will be in the ning up. In Figure later rounds, this format is a good choice. 1, this would be You can think of it as two separate tourna- 4+1=5 and 6 for ments: a qualification event between 16 two byes. players with four advancing, and the main In some single- event with eight players, including four elimination tourna- seeds. ments, a much A major advantage of single-elimination stronger form of events is the small number of rounds need- seeding is used. ed to determine a champion. With 256 play- The seeded players ers and an unlimited number of tables, you don't even show up need only eight rounds (256, 128, 64, 32, for the first several 16, 8, 4, 2) to determine a winner. The rounds; they join number of matches is also small, with only the tournament 255. (Rule: the number of matches is one already in progress. less than the number of real players.) For This is illustrated scheduling, you also have to factor in the in Figure 2. The number of tables available, since you usu- tournament begins ally won't have 128 tables available. With with 16 weaker 16 tables, you need 8 rounds of play just to players who play get through the group-of-256. After that, two rounds of things get easier, as you have only half as elimination to pro- many players in each succeeding round. duce four players Software is available on the Internet to help for the quarterfi- with planning and charting. where the byes go are guaranteed to be next nals. Those are joined by four seeded play- Next time, I'll go into some other tourna- to the 1, 2, 3, etc. If you decide that the ers to bring the player count up to eight. ment formats. If you have Byrne's seeded players should not get byes — after Is this a fair format? Of course not. Is it a Advanced Technique in Pool and all, they already have seeded spots — put good format? Maybe. If you want to pro- Billiards, turn to page 77 for some addi- the byes in the spots starting from half the vide both an opportunity for weaker players tional ideas.