CROSS-REFERENCE TO RELATED APPLICATIONS
Not Applicable
STATEMENT REGARDING FEDERALLY SPONSORED RESEARCH OR DEVELOPMENT
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REFERENCE TO SEQUENCE LISTING, A TABLE, OR A COMPUTER PROGRAM LISTING COMPACT DISK APPENDIX
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BACKGROUND OF THE INVENTION
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
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.
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.
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.
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'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'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.
As with other games requiring skill, training methods and devices as well as playing aids are prominent.
SUMMARY OF THE INVENTION
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.
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.
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.
We further disclose systems and methods comprising the disclosed reflective billiard balls, aiming device, and cue stick.
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.
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.
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
FIG. 1 shows the divergence of reflected light on a curved convex surface;
FIG. 2 shows a cue stick aligned with the horizontal axis of a cue ball;
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;
FIG. 4 shows a typical positioning of the cue ball, an object ball, and a pocket on a pool table;
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;
FIG. 6 shows the placement of the angular light beam and the object ball for a specific dimension of the object ball;
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;
FIG. 8 shows the placement of laser beams on a grid with the object ball removed, based on object ball diameter as a parameter;
FIG. 9 is a first implementation of a spotting device;
FIG. 10 is a second implementation of the spotting device;
FIGS. 11A through 11C show a first implementation of the spotting device in side, front, and top views;
FIGS. 12A through 12C show a second implementation of the spotting device in side, front, and top views; and
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
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Reference Numerals
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|
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120
convex curved surface
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125
light ray
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130
reflected light ray
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135
pool table
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140
angle of incidence
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145
angle of reflection
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146
playing surface
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148
horizontal axis
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149
vertical axis
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150
cue stick
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152
cue ball
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154
object ball
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156
ghost ball spot
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158
pocket
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160
vertical light beam
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162
angular light beam
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164
ball diameter
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166
vertical member
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168
anglular light source
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170
arm
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172
direct light beam
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180
spotting device
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182
spotting device second implementation
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184
spotting device third implementation
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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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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).
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.
Patent Application
20140243109
