Abstract:
A device for calculating where a cue ball must cause an object billiard ball to strike the bumper of a billiards table in order to drive the object ball into a selected pocket of the billiards table of the type having two opposed end rails and two opposed side rails. The device includes a plotting board and a guide. The plotting board comprises a scaled playing table portion and at least one scaled mirror table portion having pocket positions formed thereon, wherein the mirror table adjoins at least one of the opposed end rails or opposed side rails and is a mirror image of the playing table portion. The plotter comprises a guide and an object ball arm, the object ball arm having a pocket guide end and an object end. When the guide is placed over a selected pocket position on the mirror table portion and the object ball end of the object ball arm is aligned with the object ball on the scaled playing table and the pocket guide end is aligned with the guide over the selected pocket position, the object ball arm will cross the scaled playing table at a point where the object ball must strike the bumper of the billiards table.

Description:
FIELD OF THE INVENTION 
   The present invention relates to the game of billiards, and, more particularly to a handheld device and method for calculating bank and kick shots using a mirror-image plotting technique. 
   BACKGROUND OF THE INVENTION 
   The game of billiards, of which the game of pool is one particular type of game, is a well known game of skill which has been played for hundreds of years in some form or fashion. The game is played by striking a cue ball with a cue stick, causing the cue ball to collide with another ball (the object ball) so as to drive the object ball into a selected pocket on the playing surface. Players accomplish this by employing one of two different shots utilizing the rails/cushions of the playing table. 
   When the cue ball is caused to strike the target ball directly, so that the target ball rebounds from a rail cushion into a selected pocket, the shot is referred to as a “bank” shot. If, however, the cue ball is caused to strike the rail first before subsequently striking the target ball, that is referred to as a “kick” shot. In either case, players of the game of billiards must develop an ability to understand and accurately judge angles so as to properly aim and execute each shot. 
   To achieve an acceptable level of proficiency in the game requires considerable practice. As this can be frustrating and unfruitful for beginners, and at times for even the more advanced players, numerous learning aids have been devised over the years to assist players in developing and enhancing their proficiency in the game. 
   Most of the learning aids that have been marketed, however, are complex and unwieldy. Many require that some type of gadget, mirror, or attachment be positioned on or around the actual playing table. As such, these devices are often prohibited from commercial playing tables. Further, since these aids must be used on a full-scale playing table, players who do not own their own tables are rarely able to use the devices for individual practice. 
   What is needed is a portable, handheld learning aid that overcomes the above problems and that can be used apart from an actual playing table, yet with considerable accuracy. 
   SUMMARY OF THE INVENTION 
   The present invention is directed to a portable, handheld device and method for calculating bank shots and kick shots on a conventional billiards, or pool, table. 
   One aspect of the present invention is directed to a device for calculating where a cue ball must cause an object billiard ball to strike the bumper of a billiards table in order to drive the object ball into a selected pocket of the billiards table. This is commonly known as a “bank” shot. The device includes a handheld plotting board and a plotter. The plotting board comprises a scaled playing table portion and a scaled mirror table portion. The scaled mirror table, which adjoins at least one of the opposed end rails or opposed side rails of the scaled playing table portion, has apertures that represent pocket positions on the scaled playing table portion, and hence, on the actual playing table. The plotter includes a guide and an object ball arm. When the guide is placed over a selected pocket position on the mirror table portion and the object ball arm is aligned with the object ball on the scaled playing table, the object ball arm will cross the scaled playing table rail/bumper at a point where the object ball must strike the bumper of the billiards table. 
   Optionally, a full-size rail ruler which corresponds to the scale on the scaled playing table portion may be provided for placement on the rail/bumper of the actual billiards table corresponding to the scale on the scaled playing table portion. This would assist a player in causing the object ball to strike the bumper at the calculated point on the billards table. 
   A second embodiment of the present invention is directed to a device for calculating where a cue ball must strike the bumper of a billiards table in order to rebound and strike an object ball, driving the object ball into a selected pocket of the billiards table. This is commonly known as a “kick” shot. This device also includes a plotting board and a plotter, similar to the board and plotter of the first embodiment. For this type of shot calculation, when the guide is placed over the selected pocket on the mirror table portion, the object ball arm is aligned with the object ball on the mirror table portion, and the cue ball arm is aligned with the cue ball on the playing table, the cue ball arm will cross the scaled playing table at the point where the cue ball must strike the bumper of the billiards table. 
   Another aspect of the present invention is directed to a method for determining where a cue ball must cause an object billiard ball to strike the bumper of a billiards table in order to drive the object ball into a selected pocket of the billiards table. On a template having a scaled playing table portion and at least one interconnected mirror table portion, the selected pocket is first plotted on the mirror table portion pocket. As those skilled in the mathematical arts will appreciate, this method may be drawn and practiced on graph paper, or the like. A line is next plotted between the selected pocket on the mirror table portion and the object billiard ball on the playing table portion. The line then crosses the end or side of the playing table portion at the point where the object ball must strike the bumper of the billiards table in order to rebound into the selected pocket. 
   These and other aspects of the present invention will become apparent to those skilled in the art after a reading of the following description of the preferred embodiments when considered in conjunction with the drawings. It should be understood that both the foregoing general description and the following detailed description are exemplary and explanatory only and are not restrictive of the invention as claimed. 

   
     BRIEF DESCRIPTION OF THE DRAWINGS 
       FIG. 1  is an exploded perspective view of the device of the present invention; 
       FIG. 2  is illustrative of an exemplary rail ruler for use in conjunction with the device of the present invention; 
       FIG. 3  is a diagram illustrating an exemplary coordinate convention for the present invention; 
       FIG. 4  is a schematic illustration for one type of end rail bank shot calculated with the device of the present invention; 
       FIG. 5  is a schematic illustration for a second type of end rail bank shot calculated with the device of the present invention; 
       FIG. 6  is a schematic illustration for one type of side rail bank shot calculated with the device of the present invention; 
       FIG. 7  is a schematic illustration for a second type of side rail bank shot calculated with the device of the present invention; 
       FIG. 8  is a schematic illustration for one type of kick shot calculated with the device of the present invention; and 
       FIG. 9  is a schematic illustration for a second type of kick shot calculated with the device of the present invention. 
   

   DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS 
   Referring to  FIG. 1 , the present invention is directed to a portable, handheld device for calculating bank shots and kick shots in the game of billiards. As used herein, “billiards” shall refer to any of several games played with hard balls that are driven with a cue on a cloth-covered table. Similarly, “pool” is a species of billiards, and refers to any of various games played on a pool (playing) table with one cue ball and 15 other balls that are driven into pockets. 
   One aspect of the present invention provides a device, shown generally as  100 , for calculating where a cue ball must cause an object ball to strike the bumper of a billiards table in order to drive the object ball into a selected pocket on the billiards table. As used herein, the “object”or target, ball refers to a ball other than the cue ball which a player desires to drive into a selected pocket. 
   The device  100  comprises a plotting board  120  and a plotter  160 . In one preferred embodiment, the plotting board  120  comprises a scaled playing table portion  130  and two scaled mirror table portions  140 ,  150 . As will be explained in greater detail below, mirror table portion  140  will be used when calculating/playing bank shots or kick shots using either of the long/side rails of the playing table. Similarly, mirror table portion  150  will be used when calculating/playing bank shots or kick shots using either of the short/end rails of the playing table. 
   The table portions  130 ,  140 ,  150  comprising the device  100  are integrally formed from a single sheet of plastic, plexiglass, etc. that is relatively thin such that it is easily handled and is portable. The plotting board may be translucent, transparent, or opaque; i.e., the surface finish or color of the plotting board  120  is not important to the functionality or utility of the invention. 
   As shown in  FIG. 1 , a grid  130   a ,  140   a , and  150   a  is etched, painted, or printed on each table portion so that each table portion is scaled with a 4×8 grid pattern with each area of the grid having an equal dimension. Additionally, scales  130   b ,  130   c  are etched, printed, or painted along two edges  131 ,  133  of the scaled playing table portion  130 . The scales break down each of the larger grids along sides  131 ,  133  into 8 equal increments. As will be apparent to those skilled in the art, the size of the grids or the lengths of the increments are not limited hereto so long as they yield a desired level of accuracy when the device  100  is used to calculate shots. 
   Generally circular indicia  135  indicate the pocket positions of the actual playing table on the scaled playing table  130 . On the mirror table portions  140 ,  150 , round apertures  145 ,  155  are formed therethrough the table portions  140 ,  150  corresponding to the pocket  135  positions on the playing table. As shown in  FIG. 1 , there are four apertures  155  formed in mirror table portion  150  and three apertures  145  formed in mirror table portion  140 , each representing the mirror image of a pocket position  135  on the scaled playing table portion  130 . 
   The plotter  160  of the present invention comprises a guide  162  and an object ball arm  164 . The guide  162  comprises a generally rectangular or square holder portion  162   a  and an integrally formed dowel  162   b  extending downwardly from the holder portion  162   a ; however, the shapes and relative dimensions of the plotter are not critical so long as their functionality is as described herein. As will be explained in greater detail below, the dowel  162   b  of the guide  162  is inserted into the selected mirrored pocket position on either mirror table portion  140  or mirror table portion  150 . The holder portion  162   a  is dimensioned with a slot  162   c  to slideably engage the object ball arm  164 . Accordingly, the slot  162   c  and the end  164   a  of the object ball arm are similarly dimensioned. The slot  162   c  permits the object ball arm  164  to slide within the slot  162   c  to accommodate the various shot calculations that a player may desire to complete. At the opposite end of the object ball arm  164  is a scaled circular indicia  164   a  representing the object ball. 
   In a second embodiment, the plotter  160  further comprises a cue ball arm  166  having an object ball end  166   a . The object ball end  166   a  of the cue ball arm  166  is pivotally connected to the object end  164   a  of the object ball arm  164  at pivot point  165 . A scaled circular indicia  165   a  at pivot point  165  represents the desired position of the cue ball at impact with the object ball in executing a calculated shot. A line  166   c  is etched, painted, or printed along the longitudinal center of the cue ball arm  166  to assist a player in aligning the center of the cue ball arm  166  with the actual cue ball position on the scaled playing table portion  130 . 
   Turning now to  FIG. 2 , the present invention may further include a scale  200  for placement on the actual billiards or pool table. The scale  200  corresponds to the scaled playing table portion  150  to assist a player in completing the actual shot during game play. The scale  200  may be provided in various lengths, e.g., 36 inches, 42 inches, and 48 inches. These lengths represent the distances between pocket positions on an end rail or side rail for billiards and pool tables of standard construction. Similar to the grid of the device  100 , the scale  200  is divided into eight equal increments  202 . 
   Having described the construction of the device  100  of the present invention, the use of the device  100  in calculating exemplary bank shots and kick shots will now be explained. To aid in understanding the numbering and coordinate system of the present invention, turn now to  FIG. 3  where a top view of the device  100  is shown. While one possible numbering or labeling of the coordinate system of the present invention is illustrated, any logical coordinate convention may be used. Referring to the scaled playing table portion  130 , the table  130  is divided into eight equal increments lengthwise and four equal increments widthwise. As viewed from the top, and for purposes of understanding the operation of the device and method of the present invention, a standard X-Y coordinate system will be used; i.e., the point labeled as ‘P’ on the playing table portion  130  is represented by the coordinates X 2  and Y 3 . Also shown on the scaled playing table portion are the six pocket positions, labeled A through F. It is also seen that from  FIG. 3  that mirror playing tables  140  and  150  are simply mirror images of the scaled playing table portion  130 . As constructed, the device  100  of the present invention permits the player to calculate bank and kick shots from the upper and right side rails. While the device could be enlarged to include mirror table portions interconnected to the bottom and left side rails, the device may also be turned 180 degrees for calculations involving shots off of those respective rails/bumpers. 
   While not exhaustive, the following examples are illustrative of bank shot and kick shot calculations using the device and method of the present invention: 
   EXAMPLE 1 
   End Rail Bank Shot 
   Turning now to  FIG. 4 , the first exemplary shot is an end rail bank shot to pocket ‘F’ on the scaled playing table portion  130 , shown as position  410 . The dowel  162   b  of the guide  162  is inserted into corresponding mirror pocket ‘F’, shown as position  420  on mirror table  150 . End  164   a  of the object ball arm is then inserted into the slot  162   c  of the guide  162 . The object ball arm  164  is then aligned with the object ball on the scaled playing table portion  130 , shown as position  430 . As shown in  FIG. 4 , the object ball position is approximately at coordinates X 2 , Y 6  ⅛. This represents the position of the object ball on the actual billiards table. Note that the center of the object ball arm  164  crosses the scale  150  on the end rail at approximately X 2  ⅜. This is the position that the actual object ball must strike in order to rebound into the corner pocket ‘F’, position  410 . As further shown, the cue ball arm  166  is pivotally connected to the object ball arm  164  at the pivot point  165  of the plotter  160  and aligned with the actual cue ball position of about X 1  ⅜, Y 2  ⅝ (position  450 ). As also shown in  FIG. 4 , the approximate point of impact of the cue ball with the object ball is formed on the cue ball arm end  16   a  as point  166   d . This assists the player in judging where the cue ball should impact the object ball so that the object ball rebounds into the desired pocket. 
   When calculated in accordance therewith, the object ball should rebound from bumper position  440  into pocket ‘F’  410  as indicated by the dotted line  460 . 
   EXAMPLE 2 
   End Rail Bank Shot 
   Turning now to  FIG. 5 , another example of an end rail bank shot is shown, whereby the desired pocket position is pocket ‘B’ (position  510 ). The dowel  162   b  of the guide  162  is inserted into corresponding pocket ‘B’, shown as position  520  on mirror table  150 . End  164   a  of the object ball arm is then inserted into the slot  162   c  of the guide  162 . The object ball arm  164  is then aligned with the object ball on the scaled playing table portion  130 , shown as position  530 . As shown in  FIG. 5 , the object ball position is approximately at coordinates X 3  ⅜, Y 7  ¼. Again, this represents the position of the object ball on the actual billiards table. Again, note that the center of the object ball arm  164  crosses the scale  150  on the end rail at approximately X 2  ⅞, Y 8 . This is the rail position that the actual object ball must strike in order to rebound into the side pocket ‘B’, position  510 . The cue ball arm  166  is pivotally connected to the object ball arm  164  at the pivot point  165  of the plotter  160  and aligned with the actual cue ball position of about X 3  ¾, Y 6  ⅜ (position  550 ). As also shown in.  FIG. 5 , the approximate point of impact of the cue ball with the object ball is formed on the cue ball arm end  166   a  as point  166   d . When calculated in accordance therewith, the object ball should rebound from bumper position  540  into pocket B, position  510  as indicated by the dotted line  560 . 
   EXAMPLE 3 
   Side Rail Bank Shot 
   Turning now to  FIG. 6 , the first exemplary side rail shot is shown whereby the desired pocket position is pocket ‘C’ (position  610 ) on the scaled playing table portion  130 , is shown as position  610 . The dowel  162   b  of the guide  162  is inserted into corresponding pocket ‘C’, shown as position  620  on mirror table  140 . End  164   a  of the object ball arm is then inserted into the slot  162   c  of the guide  162 . The object ball arm  164  is then aligned with the object ball on the scaled playing table portion  130 , shown as position  630 . As shown in  FIG. 6 , the object ball position is approximately at coordinates X 3  ⅜, Y 4  ½. This represents the position of the object ball on the actual billiards table. Note that the center of the object ball arm  164  crosses the scale  150  on the side rail at approximately X 4  ⅞, Y 5  position  640 . This is the rail position that the actual object ball must strike in order to rebound into the corner pocket ‘C’, position  610 . As further shown, the cue ball arm  166  is pivotally connected to the object ball arm  164  at the pivot point  165  of the plotter  160  and aligned with the actual cue ball position of about X 2  ⅝, Y 2  ½ (position  650 ). As also shown in  FIG. 6 , the approximate point of impact of the cue ball with the object ball is formed on the cue ball arm end  166   a  as point  166   d . When calculated in accordance therewith, the object ball should rebound from bumper position  640  into pocket ‘C’  610  as indicated by the dotted line  660 . 
   EXAMPLE 4 
   Side Rail Bank Shot 
   Turning now to  FIG. 7 , another exemplary side rail bank shot is shown whereby the desired pocket position is pocket ‘A’ (position  710 ). The dowel  162   b  of the guide  162  is inserted into corresponding pocket ‘A’, shown as position  720  on mirror table  140 . End  164   a  of the object ball arm is then inserted into the slot  162   c  the guide  162 . The object ball arm  164  is then aligned with the object ball on the scaled playing table portion  130 , shown as position  730 . As shown in  FIG. 7 , the object ball position is approximately at coordinates X 3  ½, Y 6 , ¼. This represents the position of the object ball on the actual billiards table. Note that the center of the object ball arm  164  crosses the scale  150  on the side rail at approximately X 4 , Y 5{fraction (9/16)}, position  740 . This is the rail position that the actual object ball must strike in order to rebound into the corner pocket ‘A’, position  710 . As further shown, the cue ball arm  166  is pivotally connected to the object ball arm  164  at the pivot point  165  of the plotter  160  and aligned with the actual cue ball position of about X 2  ½, Y 7  ⅝ (position  750 ). As also shown in  FIG. 7 , the approximate point of impact of the cue ball with the object ball is formed on the cue ball arm end  166   a  as point  166   d . When calculated in accordance therewith, the object ball should rebound from bumper position  740  into pocket ‘A’  710  as indicated by the dotted line  760 . 
   EXAMPLE 5 
   Side Rail Kick Shot 
   Turning now to  FIG. 8 , a first exemplary side rail kick shot is shown whereby the desired pocket position is corner pocket ‘C’ (position  810 ) on the scaled playing table portion  130 . The dowel  162   b  of the guide  162  is inserted into corresponding pocket ‘C’, shown as position  820  on mirror table  140 . End  164   a  of the object ball arm is then inserted into the slot  162   c  of the guide  162 . The object ball arm  164  is then aligned on mirror table portion  140 , shown as position  830 , with a mirror image of the object ball(position  830 ′) as it appears on the scaled playing table portion  130 . As shown in  FIG. 8 , the object ball position is approximately at coordinates X 2  ½, Y 6  ½ on both the scaled playing table portion and on the mirror table portion  140 . This represents the position of the object ball on the actual billiards table. Next, the cue ball arm is pivotally connected to the object arm  164  at the pivot point  165  of the plotter  160  and aligned with the actual cue ball position of about X 3  {fraction (3/18)}, Y 4  ⅝ (position  850 ). For a kick shot, note that the center of the cue ball arm  166  crosses the scale  150  on the side rail at approximately X 4 , Y 5  {fraction (3/16)}, position  840 . This is the rail position that the cue ball must strike the side rail in order to rebound, striking and driving the object ball into the corner pocket ‘C’, position  810 . As also shown in  FIG. 8 , the approximate point of impact of the cue ball with the object ball is formed on the cue ball arm end  166   a  as point  166   d , which mirrors the required impact on the playing table portion  130  (position  166   d ′). When calculated in accordance therewith, the cue ball should rebound from the bumper position  840  into the object ball and the object ball should rebound from the cue ball and into pocket ‘C’ (position  810 ) as indicated by the dotted line  860 . 
   EXAMPLE 6 
   End Rail Kick Shot 
   Turning now to  FIG. 9 , an exemplary end rail kick shot is shown whereby the desired pocket position is corner pocket ‘A’ (position  910 ) on the scaled playing table portion  130 . The dowel  162   b  of the guide  162  is inserted into corresponding pocket ‘A’, shown as position  920  on mirror table  150 . End  164   a  of the object ball arm is then inserted into the slot  162   c  of the guide  162 . The object ball arm  164  is then aligned on mirror table portion  150 , shown as position  930 , with a mirror image of the object ball (position  930 ′) as it appears on the scaled playing table portion  130 . As shown in  FIG. 9 , the object ball position is approximately at coordinates X 1 , Y 1  on both the scaled playing table portion and on the mirror table portion  150 . This represents the position of the object ball on the actual billiards table. Next, the cue ball arm  166  is pivotally connected to the object arm  164  at the pivot point  165  of the plotter  160  and aligned with the actual cue ball position of about X 3 , Y 1  ⅜ (position  950 ). For a kick shot, note that the center of the cue ball arm  166  crosses the scale  150  on the end rail at approximately X 2  ⅛, Y 8  (position  940 ). This is the rail position that cue ball must strike the end rail in order to rebound, striking and driving the object ball into the corner pocket ‘A’, position  910 . As also shown in  FIG. 9 , the approximate point of impact of the cue ball with the object ball is formed on the cue ball arm end  166   a  as point  166   d , which mirrors the required impact on the playing table portion  130  (position  166   d ′). When calculated in accordance therewith, the cue ball should rebound from the bumper position  940  into the object ball and the object ball should rebound from the cue ball and into pocket ‘A’  910  as indicated by the dotted line  960 . 
   Although the present invention has been described with exemplary constructions, it is to be understood that modifications and variations may be utilized without departing from the spirit and scope of the invention, as those skilled in the art will readily understand. Such modifications and variations are considered to be within the purview and scope of the appended claims and their equivalents.