Abstract:
A reflective billiard ball with a highly reflective surface, regardless of tint, of sufficient reflective qualities to allow the user to align the cue stick accurately with the axis of reflective billiard ball. The ball comprises a spherical convex mirror, where the reflected image is smaller than actual size because the light waves are diverged by the spherical shape. Further disclosed is an aiming device, to aid the user in aiming a cue ball towards an object ball so that the cue ball pushes the object ball into a desired pocket. Furthermore disclosed is a cue stick with a highly reflective surface, regardless of tint, of sufficient reflective qualities to allow the user to align the cue stick accurately with the axis of the disclosed reflective billiard ball. The reflective attribute extends from the tip of the cue stick to the butt of the cue stick. Still further disclosed are systems and methods comprising the disclosed reflective billiard balls, aiming device, and cue stick

Description:
CROSS-REFERENCE TO RELATED APPLICATIONS 
       [0001]    Not Applicable 
       STATEMENT REGARDING FEDERALLY SPONSORED RESEARCH OR DEVELOPMENT 
       [0002]    Not Applicable 
       REFERENCE TO SEQUENCE LISTING, A TABLE, OR A COMPUTER PROGRAM LISTING COMPACT DISK APPENDIX 
       [0003]    Not Applicable 
       BACKGROUND OF THE INVENTION 
       [0004]    The present invention is in the technical field of reflective billiard balls and billiard games such as pool, as well as systems, methods, and apparatus making use thereof. 
       PRIOR ART 
       [0005]    Table games such as billiards and pool require the use of a cue ball and one or more object balls. A table comprises a flat, level playing surface, with one or more holes or pockets deployed at the edges of the table, open towards the inside where the cue ball and object balls rest. The table surface is covered with a cloth with a fine “nap” that enables the cue ball and object balls to slide, roll, and spin with relatively low friction. Traditionally and commonly, the table is rectangular, with pockets on the sides as well as at the corners. However some such tables are circular and other shapes, with pockets at various locations. Invariably, such games also require a cue stick, having a leather tip or other relatively pliable material. A basis for all such games is for the player to use the cue stick to strike the cue ball, so that the cue ball in turn strikes a targeted object ball in such a way that the targeted object ball travels across the table and into the desired pocket. The leather tip protects the cue ball and holds chalk to provide grip and control over the cue ball and yet transfers mechanical energy from cue the stick to cue ball that it strikes. For skillful players, the transfer of force from stick to cue ball and to object balls is efficient as to magnitude and direction. 
         [0006]    The physics and mathematics of aiming in billiards is well known. Various methods are available. Among them is ghost ball aiming. The player envisions where the cue ball would be at the moment of impact with the object ball to propel the object ball in the desired direction. The player perceives that a ball is there, which is not and is thus referred to as a ghost ball. The location of the ghost ball becomes a target: the position where the player aims to pass the cue ball through to in turn strike the object ball in the spot necessary to pocket the shot. At the moment of impact, when the cue ball contacts the object ball, a line drawn through the centers of both balls is the line along which the object ball will travel. So, the proper placement of the ghost ball will direct the object ball towards the desired pocket. 
         [0007]    Players know well the notion of “English” applied to the cue ball. English is essentially spin or slide that takes place when the cue ball is struck with force (magnitude and direction) with direction not aligned with an axis of the cue ball; a glancing blow, in effect, that imparts spin or slide on the cue ball. The resulting path of the cue ball can be curved, and yet skilled players may still direct the spinning or sliding cue ball to the ghost ball spot, and thus impart energy into the object ball. This is similar to the skillful use of a curved ball path used by bowlers to direct a bowling ball to a target spot. 
         [0008]    A very important playing technique is the stun shot, which allows the player to control and accurately predict the path of the cue ball after it makes contact with the object ball. Consider an object ball and a pocket where the player wants the object ball to enter. Consider a line through the object ball&#39;s center and directed towards that pocket. Consider now a line on the surface of the object ball, at the point where the cue ball would strike and thus tangent to the object ball surface at that point. Thus the tangent line is also perpendicular to the axis line. If the cue ball is hit so that it both (a) goes past the position of the ghost ball, and also (b) is sliding at the moment of impact (not rolling or spinning), then object ball will move forward along the axis line and move towards the pocket (if sufficient force is imparted). But also the cue ball will leave the ghost ball spot and move along the tangent line. If it&#39;s a straight-in shot, where the cue ball strikes the object ball in line with the pocket-directed axis then the cue ball will stop on the ghost ball spot. Top instructors consider the stun shot, because of the cue ball path control aspects, to be the most important shot in pool. 
         [0009]    As with other games requiring skill, training methods and devices as well as playing aids are prominent. 
       SUMMARY OF THE INVENTION 
       [0010]    We disclose a reflective with a highly reflective surface, regardless of tint, of sufficient reflective qualities to allow the user to align the cue stick accurately with the axis of reflective billiard ball. The ball comprises a spherical convex mirror, chrome-like, silver-like, or gold-like, for example, where the reflected image is smaller than actual size because the light waves are diverged by the spherical shape. Although all billiard balls have some level of reflectivity and reflectance, we disclose such reflective billiard balls that are effective at reflecting images to a player at a usual distance away from the reflective billiard ball. 
         [0011]    We further disclose an aiming device, to aid the user in aiming a cue ball towards an object ball so that the cue ball pushes the object ball into a desired pocket. 
         [0012]    We further disclose a cue stick with a highly reflective surface, regardless of tint, of sufficient reflective qualities to allow the user to align the cue stick accurately with the axis of the disclosed reflective billiard ball. The reflective attribute extends from the tip of the cue stick to the butt of the cue stick. 
         [0013]    We further disclose systems and methods comprising the disclosed reflective billiard balls, aiming device, and cue stick. 
         [0014]    As a sphere, the reflective billiard ball has a center which is also its center of gravity (or center of mass). As with any sphere, a point on the surface also represents a point on a radius that also includes the center. Force applied to the surface, as a vector, is transferred to the center of gravity of the reflective billiard ball according to laws of physics and mathematics. The key parameters are the magnitude and direction of the force, the angle at which the force hits the reflective billiard ball surface, dimensions of the reflective billiard ball, weight of the reflective billiard ball, and other parameters. 
         [0015]    The truest reflection of an object off of a spherical convex mirror takes place when the object is directly facing the points on the ball that produce the reflection: when the angles of incidence equal the angles of reflection for each point of the object are equal to zero, or nearly so (depending on how large the object is). When the surface is curved, light from the various points strike the curved surface at different angles of incidence because of the curve. A point whose light strikes at zero degrees angle of incidence is also aligned with a radius and thus also aligned with the center of gravity of the ball. That point on the curved surface is on a line, or plane, that is perpendicular to the ball surface. Thus, the reflection of that point is true, as the light is not diverged by the curve. 
         [0016]    The tip of the cue stick, with its relatively small ball-striking surface, has the larger, elongated cue stick body behind it. Slight deviation in the angle of the cue stick with respect to the reflective billiard ball produce noticeable reflection. But when the cue stick is aligned and co-linear with a radius of the reflective billiard ball, then the reflection off of the tip is true and alignment of the rest of the stick is apparent. 
     
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         [0017]      FIG. 1  shows the divergence of reflected light on a curved convex surface; 
           [0018]      FIG. 2  shows a cue stick aligned with the horizontal axis of a cue ball; 
           [0019]      FIG. 3  shows a cue stick off center with respect to the horizontal axis of the cue ball, to impart “English” on the cue ball; 
           [0020]      FIG. 4  shows a typical positioning of the cue ball, an object ball, and a pocket on a pool table; 
           [0021]      FIG. 5  shows the position of and angular light beam to mark a ghost ball spot by reflection off of the object ball, and a vertical light beam used for aligning a vertical axis of the object ball; 
           [0022]      FIG. 6  shows the placement of the angular light beam and the object ball for a specific dimension of the object ball; 
           [0023]      FIG. 7  shows the placement of the angualr light beam, the vertical light beam, and the object ball on a grid, based on object ball diameter as a parameter; 
           [0024]      FIG. 8  shows the placement of laser beams on a grid with the object ball removed, based on object ball diameter as a parameter; 
           [0025]      FIG. 9  is a first implementation of a spotting device; 
           [0026]      FIG. 10  is a second implementation of the spotting device; 
           [0027]      FIGS. 11A through 11C  show a first implementation of the spotting device in side, front, and top views; 
           [0028]      FIGS. 12A through 12C  show a second implementation of the spotting device in side, front, and top views; and 
           [0029]      FIGS. 13A through 13C  show a third implementation of the spotting device in side, first top view, and second top views. 
       
    
    
     DETAILED DESCRIPTION OF THE INVENTION 
       [0030]      
         [0000]    
       
         
               
             
               
               
               
             
           
               
                   
               
               
                 Reference Numerals 
               
               
                   
               
             
             
               
                   
               
             
          
           
               
                   
                 120 
                 convex curved surface 
               
               
                   
                 125 
                 light ray 
               
               
                   
                 130 
                 reflected light ray 
               
               
                   
                 135 
                 pool table 
               
               
                   
                 140 
                 angle of incidence 
               
               
                   
                 145 
                 angle of reflection 
               
               
                   
                 146 
                 playing surface 
               
               
                   
                 148 
                 horizontal axis 
               
               
                   
                 149 
                 vertical axis 
               
               
                   
                 150 
                 cue stick 
               
               
                   
                 152 
                 cue ball 
               
               
                   
                 154 
                 object ball 
               
               
                   
                 156 
                 ghost ball spot 
               
               
                   
                 158 
                 pocket 
               
               
                   
                 160 
                 vertical light beam 
               
               
                   
                 162 
                 angular light beam 
               
               
                   
                 164 
                 ball diameter 
               
               
                   
                 166 
                 vertical member 
               
               
                   
                 168 
                 anglular light source 
               
               
                   
                 170 
                 arm 
               
               
                   
                 172 
                 direct light beam 
               
               
                   
                 180 
                 spotting device 
               
               
                   
                 182 
                 spotting device second implementation 
               
               
                   
                 184 
                 spotting device third implementation 
               
               
                   
                   
               
             
          
         
       
     
         [0031]    As shown in  FIG. 1 , the light from an object in front of a convex curved surface  120  is reflected off of that surface in a way that distorts the view. As in the passenger side mirror of an automobile, the reflection appears smaller than the actual object the farther away the object is from the surface. The statement on such automobile mirrors is that “objects are closer than they appear.” This is because the light is spread out. It is well known that the angle of incidence  140  equals the angle of reflection  145 . For a flat surface the reflections are not spread out. For the convex curved surface  120 , each point where a light ray  125  hits, the respective angle of incidence  140  is determined relative to the curvature, thus spreading the reflection.  FIG. 1  shows the convex curved surface with a center. A radius from the center and through the point where the light ray  125  hits defines the incidence reference line for the angle of incidence  140  and the angle of reflection  145 . 
         [0032]      FIG. 2  shows a cue stick  150  aligned with the horizontal axis  148  of a reflective cue ball  152  and the reflection of light off of the tip of the cue stick  150 . The symmetry of the reflection is readily visible to the player. If the cue stick  150  were not aligned with the horizontal axis of the reflective cue ball  152 , the asymmetry of the reflected image of the cue stick  150 , reflected by the cue ball  152 , would be apparent in the reflection. 
         [0033]      FIG. 3  shows a view where the cue stick  150  is purposefully not aligned with the horizontal axis of the cue ball  152 . Such is typical placement for imparting “English” on the cue ball  152 , and various training cue balls are on the market. Such training cue balls have markings to identify points of the ball as targets for the cue stick  150  for particular effect. With use and practice with the reflective cue ball  152 , the player may adapt to select the desired points on the cue ball  152  by becoming familiar with the reflection patterns. And still, because the reflective cue ball  152  is in fact reflective, the player may align the cue stick  150  with a selected spot, and not sway or swerve the cue stick  150  inadvertently. 
         [0034]    In  FIG. 4  we see a typical shot in billiard and other cue games, on a pool table  135 . The cue ball  152  must strike an object ball  154  in such a way as to drive the object ball  154  into a pocket  158 . It is well known that if the cue ball  152  strikes the object ball  154  at a point on the surface that is opposite to the target pocket  158  and on the horizontal axis  148  of the cue ball  152  that is aligned with the target pocket  158 , then the object ball  154  (if struck with sufficient force) will enter the pocket  158 . A ghost ball spot  156  is a place on the playing surface  146  where the cue ball  152  must be in order to strike the object ball  154  so that it moves towards the pocket  158 . Given that the cue ball  152  and object ball  154  are of equal diameter, in order for the cue ball  152  to strike the object ball  154  at the desired location, two things must be true: (1) bottom point of the cue ball  152  must be one diameter away from the object ball  154 , on a vertical plane that includes the desired object ball  154  horizontal axis  148  that is aimed at the pocket  158 , and (2) the cue ball  152  must strike the object ball  154  at a point on the object ball  154  equator that is on the horizontal axis  148  that is aimed at the target pocket  158 . The bottom point of the cue ball  152 , one diameter away from the bottom point of the object ball  154  and on a plane that includes the object ball  154  horizontal axis  148  that points to the target pocket  158 , is the ghost ball spot  156 . 
         [0035]      FIG. 5  shows that an angular light beam  160  directed at the object ball  154  at a particular angle will reflect onto the ghost ball spot  156  on the playing surface  146 . Four considerations tell us the angle of the angular light beam  162  and where it must hit the object ball  152  in order to mark the ghost ball spot  156 :
       (1) angle of incidence  140  equals angle of refection  150 .   (2) at the equator of the object ball  154 , the point of incidence is on a the surface and on a vertical plane that is tangent to that point of incidence.   (3) at the equator of the object ball  154 , the angle of incidence  140  of reflected light to point of incidence on the object ball  154  is 45 degrees, given that height of the point of incidence on the equator is 1 radius high and the horizontal distance from the ghost ball spot to the vertical plane is 1 radius, thus making a 45-45-90 degree triangle. The combination of 45 degree angle of incidence  140  and 45 degree angle of reflection  145  create the 90 degree angle of that triangle.   (4) the horizontal axis  148  of the object ball  154  is aligned with the target pocket  158 .       
 
         [0040]    Thus, the angular light beam  160  that strikes the highly reflective object ball  154  at the equator and at an angle of 45 degrees from the horizontal axis  148  will reflect the angular beam  162  to precisely show the ghost ball spot  156  on the playing surface  146 . 
         [0041]      FIG. 6  shows these relationships for a typical object ball  154  and cue ball  152  of 2.25 inches diameter. The horizontal distance away from the object ball  154  may be a variety of distances, provided that the angular light beam  162  strikes the object ball  154  at the equator, at an angle of incidence  140  of 45 degrees, and aligned with the target pocket  158 . 
         [0042]      FIG. 7  shows these relationships applied to an X-Y grid along with images of the object ball  154  and the ghost ball spot  156 , with generic diameters D and the object ball  152  bottom at coordinate (0,0). Here X is the horizontal axis, and thus the corresponds to the playing surface  146  on the pool table  135 . Y is the vertical axis. The ghost ball spot  156  is at coordinate (D,0). The angular light beam  162  strikes the object ball  154  at (D/2, D/2), at an angle of 45 degrees from the equator (y=D/2 for all values of x).  FIG. 7  shows a source for the angular light beam  162  at (2D, 2D) but it may be any place provided that the angular light beam  162  strikes the object ball  154  at the equator, at an angle of incidence  140  of 45 degrees, and aligned with the target pocket  158 . 
         [0043]      FIG. 8 . shows these relationships applied to an X-Y grid without the images of the object ball  154  and ghost ball, also with generic diameters D and the object ball bottom at coordinate (0,0). Here also X is the horizontal axis, and thus the corresponds to the playing surface  146  on the pool table  135 . Y is the vertical axis. The ghost ball spot  156  is at coordinate (D, 0 ). The angular light beam  162  strikes the object ball  154  at (D/2, D/2), at an angle of 45 degrees from the equator (y=D/2 for all values of x).  FIG. 7  shows the source for angular light beam  162  at (2D, 2D) but it may be any place provided that the angular light beam  162  strikes the object ball  154  at the equator, at an angle of incidence  140  of 45 degrees, and aligned with the target pocket  158 . 
         [0044]      FIG. 9  shows a side view of a first implementation of a spotting mechanism  180 . A vertical light beam  160  is directed towards the top of the object ball  154  so that the spotting mechanism  180  can be may be aligned both with the object ball  154  and with the target pocket  158 . The angular light beam  162  is directed to the object ball  154  equator, and causes a reflection off of the object ball  154  and onto the ghost ball spot  156 . As shown the object ball  154  would move, when struck buy the cue ball  152 , between support members of the spotting mechanism  180 . 
         [0045]      FIG. 10  shows a side view of a second implementation  182  of a spotting mechanism, where support members are spaced farther away from the object ball  154 . This allows more flexibility in the path of the cue ball  152 , on which “English” may have been applied. A skilled player may otherwise direct the path of the cue ball  152  for set up of the next shot, but still would have it hit the object ball  154  at the desired spot for the target pocket  158 . The vertical light beam is directed towards the top of the object ball  154  so that the mechanism may be aligned both with the object ball  152  and with the target pocket  158 . The angular light beam  162  is directed to the object ball  154  equator, and causes reflection off of the object ball and onto the ghost ball spot  156  on the playing surface  146 . 
         [0046]      FIGS. 11A through 11C  show the first implementation of the spotting mechanism  180  in side, front, and top views. The also show a direct light beam  172  that points directly to the ghost ball spot  156 . The three lights together, angular light beam  162 , vertical light beam  160 , and direct light beam  172 , allow the player to place the spotting mechanism  180  in alignment with the target pocket  158 . 
         [0047]      FIGS. 12A through 12C  show the second implementation  182  in side, front, and top views. The also show a direct light beam  172  that points directly to the ghost ball spot  156 . The three lights together, angular light beam  162 , vertical light beam  160 , and direct light beam  172 , allow the player to place the spotting mechanism  180  in alignment with the target pocket  158 . 
         [0048]      FIGS. 13A through 13C  show the third implementation  184  in side, first top view, and second top view. This implementation includes an articulated swivel arm  170  on which sources for the direct light beam  172  and angular light beam  162  reside. However, the source for direct light beam would remain centered over the object ball  154 , although it will rotate with the articulated swivel arm  170 . The source for the angular light beam  162  moves with the arm  170  and can be aimed at the target pocket  158 . Thus, a base of the implementation  184  may be placed as required to be out of the way of other balls on the playing surface  146 , while the articulated swivel arm  170  is placed as required to reveal the ghost ball spot  156  while centered above the object ball  154 . 
         [0049]    The advantages here include, without limitation:
       1. The reflective cue ball  152  may be used both in training and in regular play.   2. The reflective curved surface greatly indicates alignment variation of the cue stick  150  from alignment with the horizontal axis  148  of the cue ball  152 , thus allowing the player to see whether the alignment of cue stick  150 , cue ball  152 , ghost ball spot  156 , and target pocket  158  are as desired.   3. At times, deviation from the horizontal axis  148  is desirable in order to apply spin, or “English” to the shot. Such depends on the tip of the cue stick  150  striking the cue ball  152  at positions away from dead center along the horizontal axis  148 . Reflection of the cue stick  150  from the cue ball  152  allows the player to assess alignment of the cue stick  150  with respect to the cue ball  152  in order to create any desired spin.   4. The spotting device mechanism  180 , and implementations  182  and  184 , allow accurate ghost ball spot  156  position marking without getting in the way of the shot, and thus may be used in training and in actual game play (if players agree).       
 
         [0054]    While the foregoing written description of the invention enables one of ordinary skill to make and use what is considered presently to be the best mode thereof, those of ordinary skill will understand and appreciate the existence of variations, combinations, and equivalents of the specific embodiment, method, and examples herein. The invention should therefore not be limited by the above described embodiment, method, and examples, but by all embodiments and methods within the scope and spirit of the invention.