Pythagoras & PoolPerpendiculars

by BOB JEWETT

EVERY BOOKABOUT pool thatgets far enough intothe subject to discusscombinations or po-sition play says thatthe "kiss angle," orthe angle betweentwo colliding balls,is 90 degrees or aright angle. None of

them tells you why. The explanation takesonly a little physics plus your favorite the-orem from high school geometry — theone by Pythagoras. Simple extensions ofthe analysis show how the kiss anglechanges if throw or imperfect balls are in-cluded in the calculations.

Figure 1 diagrams a simple collision.The cue ball (or it might be an object ball)arrives along path C, sending the targetball along path A. The cue ball leavesalong path B. For the time being, we willassume that there is no throw, so path A isalong the line joining the centers of thetwo balls at the instant of the collision.

How do we know the angle between Aand B is 90 degrees?

The solution is found by applying basiclaws of physics: momentum and energyare neither created nor destroyed duringthe collision, although they are both trans-ferred from one ball to another.

The momentum of an object is a trickyconcept in physics because it has both asize and a direction. The amount of mo-mentum increases with the speed and theweight of the object. The direction of mo-mentum is simply the direction which theobject is moving. In Figure 1, the lengthsof the arrows represent the speeds of theballs, so the arrows show both the size anddirection of the momentum of each ball.

All the momentum before the collision iscarried by the cue ball. (The object ballhas no momentum since it is standing stilland has no speed.) This starting momen-tum is represented by arrow C. After thecollision, some momentum has been trans-ferred to the object ball (arrow A) and the

cue ball has kept some (arrow B). Thetotal momentum after the collision. A+ B,is the same amount of momentum as be-fore the balls contacted each other, C, soA+B=C.

This equation doesn't take into accountthe directions involved. In physics, this isdone by "vectors," which for our purposesmeans we need to add the A and B arrowsgraphically by putting them head to tailand keeping their original directions asshown in Figure 2. If you go in the A di-rection for the A length and then in the Bdirection for the B length, you get to thesame spot as going in the C direction forthe C length. You may want to check thatif you go in the order B, A you still get tothe same place.

The main point of the equation is that A,B and C form a triangle since the twopaths from the left end of C go to the samepoint at the right end of C.

The amount of energy in a moving objectincreases with the weight of the object,just like momentum. Unlike momentum,

energy increases as the square of the ob-ject's velocity. A physicist calculates anobject's energy with the following equa-tion: E = 'A x mass x velocity2. So the ini-tial energy is 'A x m x C2. After the colli-sion, the energy is shared by the two balls,('A x m x A2) + ('A x m x B2). Since energycan be neither created or destroyed, that isthe second law of thermodynamics, andassuming that no energy goes into heat orsound, the energy before and after the col-lision must be equal:

Using algebra, that equation can be reor-ganized as:

Since 'A and m (the mass of one ball) areon both sides of the equal sign, algebra al-lows us to drop them from the equation al-together:

To summarize what we know so far, the

28 Billiards Digest • February 1995

"velocity vectors" of the balls form a tri-angle . Due to conservation of energy, thethree sides of the triangle have the rela-tionship A2 + B2 = C2. This is just the re-quirement of the Pythagorean Theorem,which states that any right triangle has A2

+ B2 = C2 if the 90-degree angle is be-tween sides A and B. QED, as Mrs.Morgan use to say in geometry class.

Now that we have the basic result, it'stime to examine some of the variationsthat can arise with use of English. Sup-pose there is some throw in the shot, forexample if the cue ball has right (counter-clockwise) side-spin. There will be asmall change, arrow a, to the A direction,as shown in Figure 3, which results in A'.It's important to note that the direction ofa is perpendicular to A because that's thedirection of the rubbing of the side-spin.In order to conserve momentum, B mustchange by an equal and opposite amount,resulting in B'.

For this outside English, the angle be-tween A and B is widened by just thethrow angle between A and A'. Further-more, the cue ball speed is slightly in-creased, from B to B', which can be esti-mated as about 7% for maximum Englishand a cut shot of about 45 degrees.

Conversely, if left English were used, theangle between the cue and the object ballwould close up some and the cue ballwould leave the collision with slightlylower speed than before.

What happens if the balls are differentweights? The problem becomes muchmore difficult to analyze, but the basic re-sult is that for a heavy cue ball, the kissangle is less than 90 degrees, while for alight cue ball it will be wider.

What happens if the balls are a little in-elastic or "dead"? In that case, some en-ergy of motion is lost during the collisionas heat energy, not as much speed is trans-ferred to the object ball, and A is short-ened to A' as shown in Figure 4. Momen-tum is conserved even when energy ischanging "type," so B must change by anequal and opposite amount to B' and theangle closes up to less than 90 degrees.This effect is very noticeable with ivoryballs, which are not as springy as plastic.

This column has mostly dealt with the"why" rather than the "how" of the kissangle. The cue ball path is so severely re-stricted by the physics of the collision thatthere is little room for adjustment if theobject ball is to be driven to a precise tar-get. Of course, after the collision, the cueball can be maneuvered with draw and fol-low, but in that first instant Newton andPythagoras are in control.

Billiards Digest • February 1995 29

Friction: FriendAnd Foe

by BOB JEWETT

JULY, 1980. MIKE Sigel and Ronnie Allen.One pocket.

It was the sort of after-hours match every-one at the San Francisco Open had beenhoping to see. Or at least everyone inter-ested in clever tactics, precision safety playand a change from the smash-'em-shoot-by-the-numbers 9-ball tournament. It was anight made memorable by two pool leg-ends, head to head in a tough, expensivecontest of wit and moves and traps.

About two hours into the match, a third participant arrived: thefog. San Francisco Bay relieves hot, summer days by generatingcool fog at night. The damp descended on the table, destroyedstroke, and especially aggravated Allen, who lamented, "It'stough. You know what the ball's supposed to do but it just won'tdo it."

Friction was the problem, as Allen well knew, and studying it alittle may reduce your own frustration when friction attacks.

There are three types of friction found on pool tables: static,sliding and rolling. The first two are usually explained with a sit-uation like a box on a table. (This is not much like a pool ball, butstick with me.) When you push on the side of the box, you haveto get up to a certain force to start the box moving, but then asmaller force can keep it moving. The first is due to "static" fric-tion and the second is due to "sliding" friction.

Physicists have found that how hard you need to push sidewaysis some fraction of the weight of the box. For example, with a 10-pound box, you might need 6 pounds of push to start the boxmoving and 2 pounds to maintain motion. If you double theweight of the box (20 pounds), you also double the requiredforces (12 and 4 pounds). The ratios of push to weight, in thiscase 0.6 and 0.2, are constant.

These ratios are called the "coefficients" of friction. They de-pend on the two materials rubbing against each other. Rubber onconcrete has high coefficients which makes it necessary to pushvery hard to slide a rubber object across pavement. Rubber on icehas low coefficients and little force is needed to slide.

"Rolling" is a third kind of friction that is a little more obviouson a pool table. It describes how quickly a rolling balls slowsdown. A convenient way to think of rolling friction is that a ballslows down continuously as if it were rolling up a hill. Thesteeper a hill, the higher the percentage of its grade, the quicker aball rolling up it will slow down. A moderately fast cloth acts likea 1% grade. Obviously the metaphor is not perfect, because a ballstops on a pool table, while a ball rolling up a hill will startrolling back down after stopping. But a hill's grade still providesa useful terminology for the speed of cloth.

There is an easy way to measure the speeds of cloth and therebycompare the speeds of tables. Shoot a lag shot that barely doesn'ttouch the head rail (the one you start from). Measure the time be-tween the contact on the foot rail and when the ball stops moving.Timing needs to be accurate to a tenth of a second and the cueball must not quite touch the head rail. The time will usually be

24 Billiards Digest • April 1995

between six and eight seconds. Multiplythe time by itself and then by two. For ex-ample, if the time was seven seconds, theresult would be 7 x 7 x 2 = 98. This is thespeed of the cloth.

The speed of cloth is the reciprocal of, orone over, the slope. A table with a speed of100 would slow a rolling ball as if it weregoing up 1 % grade slope, a 50-speed tablewould perform like a 2% slope.

To summarize, a faster cloth will pro-duce a higher number. A slow cloth willproduce a lower number and balls will rollas if they were going up a steeper incline.

I've seen tables as slow as 60; the clothmust have been a rug. The fastest tableI've clocked was on an Accu-stats tape of athree-cushion match at Sang Lee's room inNew York. The cloth was a very fine, thinweave, and the table was heated as re-quired by international rules. The 10-sec-ond measured lag time gives a speed of180. (The arithmetic is a little different for10-foot tables, after you multiply the timeby itself, then multiply by 1.8). The lessonthere is that if you want the cloth to befast, keep it thin, clean and dry.

Here's an experiment that shows that

draw is the victim of friction. Get twostriped balls of average cleanliness. Washone of them and wax it with a hard wax.Using the undoctored ball as the cue ball,place the stripe equatorially, and shootwith draw and medium speed. Note howfar up the table the draw lasts by notingwhen the rotation of the stripe turns over.Now try the same with the waxed ball. It'snot unusual to get twice the original dis-tance before the draw evaporates.

That night in San Francisco at the Sigel-Allen match, the damp had the oppositeeffect of wax; it increased the friction be-tween ball and cloth, and the draw rubbedoff very quickly. This seems backward,since lots of water makes things slippery.However, small amounts of moisture canactually increase friction. Have you everlicked your finger to turn a slippery page?

The last kind of friction is one that allplayers seek out — friction between the tipand cue ball — static friction. If the tipslides on the cue ball, it's a miscue, so thegoal is to prevent any sliding at all. Chalkincreases the friction. Again, this seemssomewhat backwards since you also seepeople using chalk as a substitute for talc

to make their bridge hand slippery.Measuring the coefficient of static fric-

tion between the tip and ball turns out tobe fairly easy. Just note how far from thecenter you can hit the cue ball withoutmiscuing. As mentioned in Robert Byrne'sseries of articles on fundamentals, GeorgeOnoda has found this to be half the wayfrom the center to the edge of the cue ball.With a little geometry it can be shown thatthe coefficient of static friction is 0.58 fora chalked tip on a cue ball.

If you can't hit as far from center asOnoda, here are some suggestions:• Roughen your tip. I press coarse sand-paper into the tip.• Chalk thoroughly but do not leave cak-ing. The only way to make sure you havedone a good job is to look at your tip.• Get good chalk. Opinions and batchesvary. Find what works for you.• Clean the cue ball. Most dirt increasesmiscues.

This is necessarily a brief overview of avery complicated subject. To discuss thisfurther, drop me a note in care of this mag-azine or send me E-mail, via the Internetto jewett@hpl.hp.com

26 Billiards Digest • April 1995

Seeking Truth of Beliefsby BOB JEWETT

ARE YOU A billiardexperimenter? In asense, every timeyou play, you're test-ing theories. "If Iplay with reverse, Ican kill the cue ballon the rail." "With afirm hit, this bankshot will shortenenough to make."

"This shot goes if I just roll it softly." Oneach shot, you have some theory that youput to the test.

There are past and present "pool physi-cists" who have undertaken some fairly se-rious studies of rotating spheres on greencloth. Below are some of their results andsome suggestions for how to do your ownexperiments.

In 1941, Prof. Arthur Moore of theUniversity of Michigan was investigatingWillie Hoppe's stroke. His interest hadbeen sparked by a multi-flash photo spreadin Life Magazine of the carom legend'sshots. (Some of these are in Hoppe's book.Billiards As It Should Be Played.) As apreliminary study, Prof. Moore measuredhow efficiently the cue stick hits the ball.To do this, he had to measure the speed ofthe stick before and after the hit, and thespeed of the cue ball. This would tell himhow much of the stick's energy was trans-ferred to the ball. Both ball and stick weresuspended on thin wires like a swing fromthe ceiling, then the stick was pulled backa measured distance to a backstop and re-leased. By measuring the swings of theball and stick, and applying some simplephysics, the speeds could be calculated.

Moore's somewhat surprising result wasthat the ball swung up higher than the stickstarted. Its speed was 30% above the speedof the stick for the whole range of speedsused. A roughly 50% increase is expectedfor a tip that wastes no energy during con-tact, so Moore's measurements showed acollision with 81% efficiency.

In a very readable book, The Physics ofBall Sports, by C. B. Daish, some relatedresults are given. Using fast strobe lights,like those used to photograph Hoppe'sstroke, the duration of the hit on golf andtennis balls were measured while the

speed of the shot was varied. The remark-able result is that the time of contact de-creases on faster shots.

The most thorough experimental treat-ment of pool available in print is JackKoehler's Science of Pocket Billiards. Hisexperiments have demonstrated facets ofhow balls and sticks work that most play-ers would never guess. If you want to tryyour own experiments, this is a great bookto start from. My only complaint is that itgives almost no theoretical background forthe subjects studied.

Just this year, a group at the Universityof Wisconsin began some experiments. Intheir first trial, they measured the force onthe tip during a break shot by using an

electronic strain gauge. The peak forcewas about 450 pounds for a cue ball veloc-ity of 26 feet per second. Further experi-ments are planned using a video systemthat can shoot 1000 frames each second.

A very interesting experimental appara-tus has been built, again Michigan. TheClawson Cue Company has constructed"Iron Willie," a machine that can shootshots with precisely set speed, English,and elevation. Published results are sparseso far, but it appears Willie is being usedmostly to study the mysteries of squirt. Ihope to report more on this soon.

I'm sure you're eager to try some of yourown experiments by now. What do youneed to start? First is a hypothesis (or be-

30 Billiards Digest • June 1995

lief) to put to the test. "There is morethrow on soft combination shots thanmore forceful combination shots," is one.

Next you need a way to test this: Set upcombination shots and measure how muchthrow there is for different kinds of shots.

Now you may start worrying about thedetails of the experiment. Does the tableroll off? How fast is "soft?" How can youaccurately measure the angle of throw?Will spin on the cue ball change things?Will the angle of approach of the cue ballchange things? What if the two combina-tion balls aren't frozen? These representtoo many variables. Get rid of some, atleast for the first experiment; you can al-ways incorporate more and different fac-tors in later experiments.

Try this: Place the combo balls on thefoot string aimed straight up the table andfrozen together. Place a third object ballslightly separated and at an angle asshown in Figure 1. Shoot the cue ball intothe proxy cue ball. Call it a soft shot if theball just reaches the far rail, medium if itgoes another table length, and hard for an-other table length.

To get consistent results, you will needto be able to place the balls in the samepositions repeatedly. Get a large indexcard (3 by 5 inches is barely large enough)and a hole punch. Punch two holes for thefrozen combo balls, and a semi-circle ofholes, each whole 10 for the third objectball so it can contact the combo at variousangles. Tape the card to the table, roll theballs into the holes, and start your mea-surements. I find the use of a card like thismuch more precise than tapping the ballsinto position, and it is easier to set up theangles on paper.

When I did all of this, I got the resultsplotted in Figure 2. The amount of throwis on the vertical axis, and the cut angle ison the horizontal axis. For example, themaximum throw measured was six de-grees (A degree of throw is about half aball diameter in four diamonds of travel.)which happened for a 30-degree angle(half ball hit) and a soft shot.

The results are not completely as ex-pected. Note that up to a 20-degree hitangle, there is little change in throw forhard versus soft shots. As the angle con-tinues to increase, the soft shot keeps afairly constant five to six degrees of throw,but the throw on the hard shot graduallydrops down to a degree and a half.

The results suggest a further experiment.The three curves are nearly the samestraight line for cuts from zero to 20 de-grees. In theory, if the combination ballsare separated by a certain distance, the cut

Billiards Digest • June 1995 31

should exactly cancel the throw at allspeeds and for cut angles that aren't toolarge. Try the experiment for several sepa-rations from an eighth-inch to an inch.

Here's another experiment that will test acommon belief about banks. Prepare acard that will place three object balls in astraight line and separated from each otherslightly. Place the three as shown in Figure3. Shoot the cue ball softly straight intothe combo bank just hard enough tobounce the front ball a foot or two off thesecond rail. Place a "marker" ball wherethe ball hits on the second rail. With prac-

tice, you should be able to hit the markeralmost perfectly full. (It helps to have anassistant to adjust and replace the marker.)

Once you have the angle for a soft bankdown, predict where the ball will hit for amuch harder shot, then try the experiment.I think you'll be surprised; 1 was.

If you try these experiments — even theone already completed — I'd like to hearyour results. Please send them to me incare of this magazine or by E-mail to jew-ett@hpl.hp.com.Bob Jewett is an engineer at Hewlett-Packardand the 1974 ACU-1 men's billiard champion.

32 Billiards Digest • June 1995

Virtual PoolWOULD YOULIKE to have thestroke of MikeMassey for trickshots? To be able toplay daily againstsomeone who willrun 50 at straightpool more often thannot, and run over 100yourself? To be able

to predict exactly where the cue ball isgoing to end up on any shot? All this andmore is possible with a newcomputer simulation gamecalled Virtual Pool, available onCD-ROM.

Your introduction to VirtualPool begins with an animatedvideo clip about the history ofcue sports. Paintings and dia-grams — the Billiard Archiveand Mike Shamos are in thecredits — illustrate the narrator'ssummary of billiard events fromthe elevation of lawn bowling totables up to the current boomand recent players.

The basic control of play ismuch like other simulators onthe market. You use the mouseto select the aiming angle and toplace the tip for various amountsof English. To shoot, you press a key to letthe program know you're ready, and thenmove the mouse back and then forward.The speed of motion determines the forceof the shot. To avoid broken mice on hardshots, there is a "speed amplify" buttonwhich is especially useful on break shots.

There are lots of different things the sim-ulator lets you do. You can practice alone,play against another player either on thesame machine or over the phone or net-work, or play against a computer-gener-ated foe. Of the latter, don't try your handagainst Deadeye Dan until you have youraiming perfected; in our last match, hebeat me 150-7 in straight pool.

Where Virtual Pool really shines is in thedisplay graphics. The table is presented ina three-dimensional perspective. The play-er's point of view can easily be pannedaround the table to check angles and clear-ances, and can be zoomed in to check

(Better than the real thing?)by BOB JEWETT

whether two balls are really touching. Asingle key returns you to an overhead shotto check the whole table. All of this worksvery quickly, so that the motion is smooth.

A very useful feature, and one that trans-forms the program from a mere game to alearning tool, is the shot prediction feature,called "tracking." With this turned on, theexpected paths of all the balls are shown,and are updated as quickly as you changeanything in the shot, such as the angle,speed or English. For example, at straightpool, you often need to break up clusters

during a run. You can see exactly howmuch draw, follow and English will beneeded to get the cue ball to break up acluster. Even better, you will see where theballs in the cluster will end up, and youmay conclude that there is no good way togo into the cluster along the path you hadplanned. This sort of prediction would notbe of much use if the results weren't trueto real life, and the programmers havedone a very accurate job.

Another feature is a brief instructionalclip taught by BCA Hall-of-Famer"Machine Gun" Lou Butera. He begins bysaying that he'll run a rack of straight poolin 90 seconds, but only takes 66. A galleryof trick shots is also available. Lou shootsthem in video clips and you can set themup and try them yourself in the simulator.

I have a few minor complaints. The "vir-tual" cloth is a little slow and slippery, per-haps just like many players will find on

their new home tables. You are never re-quired to raise the butt of the cue to avoidan obstacle, such as an object ball just onyour side of the cue ball. If you crank upthe speed, you can get more spin on theball than Mike Massey; that's a fantasy formost of us. Also, Deadeye Dan kicks ballsin better than any living human.

My major complaint about Virtual Poolis that although the game knows four dif-ferent types of pool games, and you can doothers in practice mode, snooker andcarom billiards are not included. I under-

stand that a snooker version is inthe works; I hope that carom isnot far behind.

The program comes with astartling guarantee. If your ac-tual pool game does not improveafter using Virtual Pool, you canget your money back. I won't begetting my money back, since Ihad a personal best at InternetEqual Offense after "virtually"running 150 a couple of times.(IEO is a pool competition heldover a computer network, butplayed by real people on real ta-bles.)

The hardware required is a PC,running Microsoft DOS orWindows 3.1, with at least a386SX 40MHz or higher proces-

sor (I used a computer with a 60 MHzPentium chip while evaluating the pro-gram), a SVGA card, a CD-ROM drive, atleast four megabytes of RAM and twomegabytes of free hard disk space. Asound card is needed if you want to listento the music, sound effects or narration.The price is under $50, which in my mindmakes this a must for any pool player whoalso has a PC.

Virtual Pool, is available for $49.95,from Interplay Productions, Inc.,17922 Fitch Ave., Irvine, CA 92714,(800) INTERPLAY. (A demo version ofis available on the Internet; connect to theURL http://www.interplay.com/. A versionfor Macintosh platform is planned.)

Bob Jewett (E-mail at jewett@netcom.com) is aformer ACU-I billiards champion and currentlytrains BCA Certified Instructors in San Francisco.

26 Billiards Digest • August 1995

Follow and Draw Systemsby BOB JEWETT

WHEN YOU ARElearning pool, afteryou have control ofthe object ball direc-tion, the next thingto master is the di-rection of the cueball after contact. Ina previous column, Icalled on the Pythag-orean theorem to ex-

plain why the initial path of the cue ball isat a right angle to the path of the objectball. This column offers some systems forplanning how follow and draw will bendthe cue ball's path.

In Shot 1, the plan is to pocket the 1 balland follow forward for the 2 ball. Theproblem is to determine whether the cueball can be taken to the left side of the 2for an easy shot (A) or if the much moredifficult position on the "short side" at B isneeded.

The system to use here we'll call the"triple-angle follow system." For nearlyfull shots like this, take the small angle ofthe object ball cut (/OBC), triple it, andthe total is how far out the cue ball is de-flected (3 x /OBC). In Shot 1, the initialcue ball path goes towards C on the endrail. This is half a diamond from thepocket. If the object ball is pocketed, thecue ball will go towards a point three timesthat distance to the right. For this simpleshot, that would be towards point A, one-and-a-half diamonds to the right of the ini-tial cue ball path.

You have to make sure of several thingsfor this system to work well for you. Thecut angle must be small. The cue ball mustbe rolling smoothly on the cloth, whichwill happen immediately if you hit aboutone tip above center. The cue ball and theobject ball must be the same weight andfairly clean. As with any system, practice!

How accurate is this system? A lot de-pends on your pocketing accuracy. If youmiss the center of the pocket by half a ball,the cue ball will land a ball and a half fromthe expected point. If the cue ball is heavy,like some tavern balls, it will drive throughstraighter, and you'll find a smaller num-ber, maybe 2.5 or 2, must be used insteadof 3 to get the direction precisely.

A second follow system isn't a system so

much as a guide post. This is the half-ballfollow angle, which has been discussed byRobert Byrne in his column and his Ad-vanced Techniques book. In Shot 2, thebest choice at the 9 ball is to play a carom,sending the cue ball off the 1 to the wait-ing 9.

Use this technique: Aim for a half ballhit on the 1 ball, with the cue stick di-rected at the left edge of the 1. Hit the cueball high and shoot only hard enough to besure to get to the 9. The most commonmistakes are shooting too hard and playingwith draw or center.

For your practice, set the 1 a ball's widthoff the rail and place the cue ball one-and-

a-half ball's width off, so you will be driv-ing the cue ball parallel to the long rail.Move the 1 ball forward and back until thecarom seems automatic. Note carefully theangle of deflection of the cue ball. In the-ory it will be close to 37 degrees, but thiswill change if the cue ball is not the sameweight as the object ball.

The real importance of this shot comesfrom the stability of the deflection angle.While the object ball can be hit betweenthree- and one-quarters full (about 15 to 45degrees of cut), the cue ball path willchange by only a few degrees. While theremay not always be a 9 ball waiting for youat the half-ball follow angle, there will

often be position or an easy safety.Suppose the needed angle is not quite 37

degrees. To make the cue ball go straighterthrough, hit either more or less ball; howmuch requires judgment gained frompractice. Try Shot 2 with the cue ballcloser to the rail than for the ideal angle.

There are two ways to make the cue ballgo wider. A little draw, or even center ballwill bring the cue ball out some, but this ishard to control. It is easier to hit the cueball harder so it slides some to the left be-fore taking a path parallel to the soft shot.Try Shot 2 with the 1 ball a diamond far-ther down the table.

Knowledge of the half-ball follow angleis essential for position play. Practice thisshot until the information is etched intoyour brain.

Minor adjustments in either directioncan be achieved by adding side spin to thefollow. Begin in the ideal position and seewhat left and right do.

There is a draw system that is a lot likethe follow system; in fact, it is based onnearly identical physics. Suppose youhave a situation like Shot 3. You want todraw the cue ball off the object ball to-wards point X. There are two equivalentaiming systems; see which is most accu-rate for you.

For the first system, take the "outsideangle" between the two starting lines ofthe shot. Divide it in two, and in twoagain. Drive the object ball along the line

Billiards Digest • October 1995 33

closest to the path that goes straight-ahead,and the cue ball will draw back towards X.

The second way to aim is to shoot to-wards point P on the object ball, which ismidway between the two major lines. Notethat this is not where you will hit the ob-ject ball; the contact point will be the sameas in the first method.

The second aiming system, also knownas the "bisector point" system, is at least80 years old; it is in Daly's Billiard Book,but is explained better in Willie Hoppe'sBilliards As It Should Be Played.

This draw system requires very livelydraw and is best if the cue ball is close tothe object ball. The cut angle must not betoo wide. If you can't pull the cue ballback as much as expected, you will needto adjust the system by shooting somewhatfuller.

There is a draw half-ball shot that is sim-ilar to the follow half-ball shot. In Dia-gram 4, a half-ball shot with draw pocketsthe object ball and bends the cue ball backas it goes up the table. For a typicalamount of draw, the final path is at a rightangle to the initial line of the cue stick. Ofall the systems mentioned, this one is the

most difficult to control, but it does pro-vide a reference point.

For example, if you have a fuller-than-half-ball shot, you'll know you can bringthe cue ball back behind the right-anglepath.

These systems all require either full fol-low or full draw. Of course, you can obtainany angle in between by using spin be-

tween these two extremes, but there is nogood system for these gray areas. Learn torely on your feel and use the systems toknow where the boundaries are.

Bob Jewett (E-mail at jewett@netcom.com) is aformer ACU-I billiards champion and currentlytrains BCA Certified Instructors in San Francisco.

A Basic Skill Testby BOB JEWETT

IN MY DECEM-BER 1992 column Idescribed a way tosharpen your skillscalled "progressivepractice." Since then,a set of drills basedon those ideas hasbeen developed bymy fellow instructorsat the San Francisco

Billiard Academy, Eric Harada and JosephMejia, and me. It is easy to use these drillsto measure your present skill level andkeep track of your improvement.

In Diagram 1, the goal is to pocket theobject ball with a stop shot that leaves thecue ball within nine inches of the "phan-tom" cue ball (the cue ball at the instant itcontacts the object ball). Start with the cueball by the diamond marked 2; this will bean easy shot for most players. If you makethe required shot, move the cue ball fartheraway, and try again. If you miss a shot,move the cue ball closer. So that you don'thave to remember the last location of thecue ball, mark it with a coin on the rail.

The goal is to work your way up to ashigh a number as possible. Remember toreduce the distance when you miss; that'sthe penalty for missing. When you are firsttrying the shot, you may want to move thecue ball one diamond at a time, but afterone or two misses, use a half-diamond ad-justment after each shot.

After you have shot 10 or 15 shots forthe first diagram, note your distance, andgo on to Diagram 2. This is a follow shot,with the goal of leaving the cue ball in theshaded area while pocketing the objectball. As before, if you meet the goals on ashot, move the coin and the cue ball back,but on this drill you also move the objectball back so that it remains one diamondfrom the cue ball. After a rack of shots,note your distance.

Diagram 3 is a draw shot. The object ballstays put again, and the cue ball is movedto change the difficulty. The goal, besidespocketing the object ball, is to draw thecue ball back at least as far as your startingpoint. For this drill, the coin on the rail isespecially important since it gives you atarget for your draw.

Diagram 4 is a cut shot. The object ballis always placed a diamond from the cor-ner pocket and a ball off the rail. The cue

26 Billiards Digest • December 1995

ball marches up the table always one dia-mond off the rail.

Once you have completed all four dia-grams, add up the distances and multiplyby two to find your total score. The factorof two comes from the fact that we havedeveloped five increasingly difficult sets ofdrills, and this is the second set. If you in-clude these shots as part of a regular prac-tice routine, you can note your progress.

If you have a score of 40 or more, thisset of drills is too easy for you. If youcan't get over 15, you need an easier set.The point of these drills is to make theshots challenging but not impossible foryour present level of play, whatever it is.With a score over 60, you may want to tryturning pro; to score 60, you will be shoot-ing most of your shots from the end rail.

Note whether your score on one diagramis considerably lower than the rest. If so,invest practice time there. For most play-ers, scores are fairly even across the dia-grams; if there is a low one, it is usuallythe draw shot.

Move the coin after each shot! Other-wise, you won't get a true indication ofyour average ability on the drill. If you

want a more accurate measure, takesmaller steps in each direction — a quar-ter-diamond rather than a half or full dia-mond.

It is OK to move the balls slightly in andout from the rail on the first three dia-grams. The important factor is the lengthof the shot, and you are free to make theangle as auspicious as you want. The fol-

low shot is impossible if you don't choosethe right angle for the cue ball.

A full set of 20 progressive practice dia-grams is included in the new BCA Instruc-tor's Manual, which is available to anyBCA member.Bob Jewett (E-mail at jewett@netcom.com) is aformer ACU-I billiards champion and currentlytrains BCA Certified Instructors in San Francisco.