Billiards Tools and Methods

Abstract

A tool for assisting a billiards player to easily and accurately aim and direct the cue ball to strike a target ball an propel the target ball towards a target such as a pool table pocket. An aiming ring is placed on the billiards table adjacent to the target ball that allows the billiards player to automatically aim the cue ball and propel the target ball into a pocket or other desired location. A billiards goniometer tool is described to assist with bumper shots.

Claims

1. An aiming tool to assist a billiards player for directing a cue ball from a cue ball initial location on a billiards table to a cue ball final location where said cue ball is able to strike a target ball and propel the target ball toward a target comprising, A. an aiming ring vertically displaced from said cue ball final location, B. said target ball having a target ball vertical equator forming a target ball vertical equator plane, said target ball having a target ball horizontal central axis line directed toward said target and located within said target ball vertical equator plane; said target ball horizontal central axis line extending from a target ball contact point on a surface of said target ball to a target ball opposing pole located on said surface of said target ball nearest to said target, C. a marking line on said aiming tool, said marking line being parallel with said target ball horizontal central axis line, D. said aiming ring having an aiming ring center that is displaced along said marking line at a horizontal distance from said target ball contact point in a direction farther away from said target ball, said horizontal distance being equal to a radius of said cue ball, E. said aiming ring center providing a shooting line toward which a center of said cue ball is directed toward said aiming ring center for said cue ball to strike said target ball and propel said target ball toward said target.

2. The aiming tool of claim 1 wherein said aiming ring is vertically displaced below said cue ball final location.

3. The aiming tool of claim 1 wherein said aiming ring is formed from a flat planar material having a thickness ranging from 0.001-0.010 inches.

4. The aiming tool of claim 3 wherein said flat planar material is a metal, plastic, composite, or paper.

5. The aiming tool of claim 1 wherein said aiming ring is circular having an aiming ring diameter that is equal to a cue ball diameter.

6. The aiming tool of claim 1 further comprising a carpet region located below a portion of said target ball.

7. The aiming tool of claim 6 wherein a portion of said carpet region makes contact with said target ball.

8. The aiming tool of claim 1 wherein said aiming ring is vertically displaced above said cue ball final location.

9. The aiming tool of claim 8 wherein said aiming ring is held above said cue ball final location such that said cue ball can roll below said aiming ring without contacting said aiming ring.

10. The aiming tool of claim 1 further comprising a cover located above a portion of said target ball.

11. The aiming tool of claim 10 wherein said cover is attached to support members that hold a portion of said cover above said target ball.

12. The aiming tool of claim 10 wherein said cover holds said aiming ring above said cue ball final location.

13. An aiming tool to assist a billiards player for directing a cue ball from a cue ball initial location on a billiards table to a cue ball final location where said cue ball is able to contact a target ball and propel the target ball toward a target comprising, A. an aiming ring that is flat and circular, said aiming ring being vertically displaced from a cue ball final location, said aiming ring having an aiming ring diameter equal to a cue ball diameter, B. a marking line along at least a portion of a diameter of said aiming ring, said marking line being directed toward said target, C. an aiming ring contact point that is located along a perimeter of said of said aiming ring, said aiming ring contact point residing on said marking line or an extension of said marking line, said aiming ring contact point being displaced directly below a target ball contact point located within a target ball vertical equator, said target ball vertical equator forming a plane that passes through said target, D. whereby said aiming ring does not interfere with a travel direction of said cue ball in traveling from an initial position on a billiards table along a shooting line directing said cue ball across said cue ball diameter toward said aiming ring across said aiming ring diameter to contact said target ball and propel said target ball toward said target.

14. The aiming tool of claim 12 further comprising a flat horizontal carpet that extends horizontally below a portion of said target ball.

15. The aiming tool of claim 13 wherein said flat horizontal carpet makes contact with said target ball.

16. An aiming tool for directing a cue ball from a cue ball initial location on a billiards table to a cue ball final location on a billiards table to strike a target ball and propel said target ball towards a target, said aiming tool comprising, A. an aiming ring that is circular and extends in a horizontal plane, said aiming ring being vertically displaced from said cue ball final position, said aiming ring being located proximate to said target ball with an aiming ring center located a horizontal distance from a center of said target ball equal to a diameter of said cue ball, B. said aiming ring having a marking line directed toward said target, C. said aiming ring providing a shooting line for a center of said cue ball towards said aiming ring center, whereby contact of said cue ball in said cue ball final location with said target ball propels said target ball towards said target.

17. The aiming tool of claim 16 wherein said aiming ring is displaced below said cue ball final location.

18. The aiming tool of claim 16 further comprising a flat horizontal carpet, said flat horizontal carpet being located below a portion of said target ball.

19. The aiming tool of claim 18 whereby said flat horizontal carpet makes contact with a portion of said target ball.

20. The aiming tool of claim 16 whereby said aiming ring is displaced above said cue ball final location.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

[0010] FIG. 1 is a semi-perspective view from the top of a cue ball in a final location adject to a target ball and the cue ball in its initial location; the axes of the target ball and cue ball are directed towards a target.

[0011] FIG. 2A is a plan view from the top of planar aiming tool positioned below a cue ball in its final location and having an aiming ring central line directed toward a cue ball and directed toward a target.

[0012] FIG. 2B is a side view of the planar aiming tool with the cue ball in a final location on top of the aiming ring and making contact with the target ball.

[0013] FIG. 2C is a plan view from the top of planar aiming tool positioned below a final location for a cue ball and having an a cue ball in its initial location with a shooting line directed toward an aiming ring.

[0014] FIG. 2D is a plan view of a flat horizontal circular aiming ring having an aiming ring central line directed toward the target with the aiming ring contact point in contact with a target ball.

[0015] FIG. 2E is a side view of a flat circular aiming ring with the cue ball in a final location on top of the aiming ring with the cue ball making contact with the target ball.

[0016] FIG. 2F is a plan top view of the aiming ring having an aiming ring central line and an aiming ring central line extension.

[0017] FIG. 3A is a plan top view of a platform aiming tool having an aiming ring positioned above a cue ball final location; a cue ball is positioned at an initial location with a shooting line to direct the cue ball towards the cue ball final location.

[0018] FIG. 3B is a perspective side view of a platform aiming tool positioned above a target ball and above a cue ball in its final location; a platform aiming ring middle line is directed towards a target.

[0019] FIG. 3C is a perspective view of the platform aiming ring showing the sliding member towards which the cue ball can be directed to propel the target ball towards a target.

[0020] FIG. 4A is a semi-perspective top view of the cue ball in a final location adjacent to the target ball and showing the cue ball initial location and shooting line for the cue ball to attain the cue ball final location.

[0021] FIG. 4B is a planar top view of the cue ball in its final location and its initial location showing how to rotate the cue ball in its initial location such that the cue ball contact point can be viewed by the billiards player.

[0022] FIG. 5 shows a billiards ball against the bumper and the imaginary incident angle and reflection angle if the cue ball horizontal equator contacted the bumper and the bumper compression was infinitely small and the bumper was perfectly elastic.

[0023] FIG. 6 is a plan view of a billiards ball showing a ball contact height with the bumper that is 27% higher than the ball radius.

[0024] FIG. 7 shows an actual ball reflection path that is downstream from an imaginary ball reflection path due to the ball adjusted contact diameter being smaller than the ball horizontal equator.

[0025] FIG. 8 shows a top view of a billiards ball making contact with a bumper and causing the bumper to compress thereby resulting in the actual reflection path being further directed downstream from a situation without bumper compression or slippage between the ball and the bumper.

[0026] FIG. 9A is a plan top view of a billiards goniometer placed against a billiards ball located with its horizontal equator in vertical alignment with the bumper edge and the goniometer incident and reflection arms touching the billiards ball.

[0027] FIG. 9B is a plan top view of a billiards goniometer placed against a billiards ball located with its ball adjusted diameter in vertical alignment with the bumper edge and the goniometer incident and reflection arms touching the billiards ball; the goniometer has been moved outwards and a gap has formed between the billiards ball and the goniometer arms.

[0028] FIG. 9C is a plan top view of a billiards goniometer placed further outwards from the bumper edge to account for bumper compression as well as ball adjusted diameter; a larger gap has formed between the billiards ball and the goniometer arms than the gap due only to ball adjusted diameter.

[0029] FIG. 10A shows a billiards ball travelling along an incident guiding edge of an incident arm and reflecting off of a bumper to follow a reflection guiding edge of a reflection arm; the billiards goniometer has been moved outwards to account for ball adjusted diameter and bumper compression, but the incident angle is equal to the reflection angle.

[0030] FIG. 10B shows a billiards ball travelling along an incident guiding edge of an incident arm and reflecting off of a bumper to follow a reflection guiding edge of a reflection arm; the billiards goniometer has been moved outwards to account for ball adjusted diameter and bumper compression, and the reflection angle has been decreased to account for slippage between the billiards ball and the bumper and nonideal bumper compression.

DETAILED DESCRIPTION

[0031] FIG. 1 shows a target ball 2 with a vertically oriented target ball equator 5 (or circumference at the maximal diameter of the spherical ball) extending along a target ball perimeter or equator forming a vertically oriented target ball plane that contains a horizontal target ball axis line 10 extending through the center of the target ball 2 from the target ball contact point 15 to the target ball opposing pole 20 (located on the target ball surface 25 farther from the target ball contact point 15 and closer to the target 35). The target ball axis line 10 is directed parallel to and colinear with an alignment line 30 that is directed horizontally toward the target 35; the target 35 can be a corner of a billiards table or a pocket located in a corner of a billiards or pool table, for example. The vertical target ball plane formed by the target ball equator 5 passes through the target 35.

[0032] A cue ball 40 that can be struck by the players cue stick or a second billiard ball is located in a cue ball final location 45 (at impact with the target ball 2) such that a cue ball vertical equator (or cue ball circumference) that is touching the target ball vertical equator with the cue ball 40 in a cue ball final location 45 (i.e., cue ball final location 45 on the billiards table). The cue ball vertical equator contains a horizontal cue ball axis line that extends through the center of the cue ball 40 from the cue ball contact point 60 to the cue ball opposing pole 65; the cue ball axis line is also directed colinear with the target ball axis line 10 and the alignment line 30 in the cue ball final location 45.

[0033] The vertical cue ball equator 50 in the cue ball final location 45 is coplanar with the vertical target ball equator 5. This cue ball final location 45 relative to the target ball 2 with the cue ball contact point 60 touching the target ball contact point 15 and the horizontal target ball axis line 10 (extending through the center of the target ball 2) directed towards the target 35 and colinear with the alignment line 30 and colinear with the horizontal cue ball axis line 55 (extending through the center of the cue ball 40 defines the cue ball final location 45 where the cue ball 40 must end up as it strikes the target ball 2 in order for the target ball 2 to be propelled toward the target 35. This cue ball final location 45 exists no matter where on the billiards table the cue ball 40 is initially located as long as the shooting line 70 from the cue ball initial location 75 to cue ball final location 45 forms an obtuse shooting angle, theta 80 (i.e., greater than 90 degrees) with respect to the alignment line 30 which is the direction of travel for the target ball 2 after it is impacted by the cue ball 40.

[0034] FIGS. 2A, 2B, and 2C show an embodiment for a flat, planar aiming tool 85 to help the billiards player properly identify the angle and location of which to strike the cue ball 40 towards the target ball 2 in order to propel the target ball 2 towards the target 35. The planar aiming tool 85 of this embodiment is placed onto the surface of the billiards table such that a target ball carpet 90 of the planar aiming tool 85 can reside below a portion of the target ball 2 without affecting the position of the target ball 2. The planar aiming tool is flat and positioned horizontally on the billiards table. The target ball carpet 90 can make contact with the target ball 2 near the bottom of the target ball to help set the cue ball final location 45 relative to the target ball 2. The carpet curvature 105 can be aligned vertically with the target ball rounded surface 100.

[0035] A neck 110 can join the target ball carpet 90 with the cue ball aiming ring 115 that can be the same as the cue ball 40 to allow the billiards player to easily aim the cue ball towards the aiming ring. The neck can have a neck width 112 ranging from 5 mm to the diameter of the cue ball 40. The aiming ring contact point 120 is vertically aligned below the cue ball contact point 60 in the cue ball final location 45. The aiming ring contact point 120 is also near or proximate to the target ball contact point 15. The cue ball aiming ring 115 is vertically displaced below the cue ball final location 45 required to allow contact of the cue ball 40 with the target ball 2 and propel the target ball 2 to the target 35. The cue ball aiming ring 115 can be a flat circular thin disc (0.005 inches thick, range 0.001-0.020 inch) that can lie on the billiards table and allow a cue ball 40 to roll over it without affecting the direction of cue ball travel as it is about to make contact with the target ball 2. The cue ball aiming ring 115 can be smaller in diameter than the cue ball 40 and have an aiming ring center 117 towards which the billiards player directs the center of the cue ball. The aiming ring center 117 is displaced horizontally along the aiming ring central line 130 from the target ball contact point at a distance equal to the radius of the cue ball. The cue ball aiming ring center 117 is also displaced horizontally along the aiming ring central line 130 from the center of the target ball 2 by distance equal to the diameter of the cue ball 40 or diameter (i.e., extending through its spherical center) of the target ball 2.

[0036] The cue ball aiming ring 115 can have a beveled edge 125 to allow the cue ball 40 to roll over it without affecting the direction of travel due to the aiming ring. The cue ball aiming ring 115 can be a flat ring structure similar to a flat disc, for example; the neck 110 and aiming ring 115 and target ball carpet 90 can be formed from a thin plastic film, paper-type materials, metal, composite, or other material that lies flat on the billiards table a vertical distance below the final cue ball location. The edges of the planar aiming tool 85 can have beveled edges 125. The neck 110 is a narrowed region of the planar aiming tool 85 about ? inch in width (range ?-2.5 inches in width and can be equal or smaller than the billiard reflection angle 255) that joins the target ball carpet 90 to the cue ball aiming ring 115 and does not interfere with the direction of travel of the cue ball 40.

[0037] The planar aiming tool 85 is not required to have a neck 110 and a target ball carpet 90 and can comprise only the cue ball aiming ring 115. The aiming ring can be colored or lighted to provide a contrasting color relative to the target ball carpet 90 and relative to the color of the billiard table surface. The neck 110 and target ball carpet 90 can be formed of a flat material similar to material of the cue ball aiming ring 115.

[0038] The planar aiming tool 85 has an aiming ring central line 130 that can extend from the frontal point 95 of the cue ball aiming ring 115 (located vertically below the cue ball opposing pole 65 in the cue ball final location 45) to the aiming ring contact point 120 which is aligned vertically directly below the target ball contact point 15. The aiming ring central line 130 can be extended colinearly along the target ball carpet 90 forming a target ball carpet central line 140. The cue ball contact point 60 and target ball contact point 15 are touching each other in the cue ball final location 45 in order to propel the target ball 2 toward the target 35 as described in FIGS. 1 and 2B. The target ball contact point 15 makes direct contact or impact with the cue ball contact point 60 as the cue ball 40 rolls into contact with the target ball 2. The aiming ring central line 130 is directed towards that target 35 and is parallel with the alignment line 30; the aiming ring central line 130 resides directly below the desired cue ball axis line 55 (the cue ball axis line 55 is directed colinearly with the alignment line 30) in the final cue ball location for the cue ball 40 when it contacts the target ball 2 to propel the target ball 2 towards the target 35. The aiming ring can be formed with a smaller diameter than the cue ball diameter; the billiards player can direct the center of the cue ball 40 towards the aiming ring center 117 to propel the cue ball 40 towards the aiming ring center 117 to propel the target ball 2 toward the target 35.

[0039] In use, as shown in FIGS. 2B and 2C, the target ball carpet 90 can be slid below the target ball contact portion with the aiming ring contact point 120 being aligned vertically with the contact point of the target ball contact point 15 and the aiming ring central line 130 directed towards the target 35 and parallel with the alignment line 30 when viewed vertically from above. The target ball carpet 90 (in some embodiments) and the target ball carpet line 140 can be made to touch the bottom of the target ball 2 to help set the position of the aiming ring contact point 120 vertically aligned with the target ball contact point 15. The carpet ball length 142 can be equal to a radius of the target ball 2 to set the location of the aiming ring contact point 120 vertically below the target ball contact point 15. The cue ball aiming ring 115 is displaced vertically below the desired cue ball final location 45 toward which the cue ball 40 is to attain its cue ball final location 45 after being struck by the billiards player with the cue ball 40 in the cue ball initial location 75.

[0040] The billiards player can place the cue ball 40 any suitable cue ball initial location 75 on the billiards table that allows the cue ball 40 to be struck with the cue stick and propelled along a shooting line 70 from the cue ball initial location 75 directly towards the cue ball aiming ring 115 (across the planar aiming ring diameter 197) such that the entire cue ball 40 (across the cue ball diameter 192 rolls over the entire cue ball aiming ring 115 striking the target ball 2 propelling the target ball 2 toward the target 35. Such suitable locations include locations where the shooting angle, theta, 80 between the shooting line 70 and the alignment line 30 are obtuse angles, theta. The cue ball 40 struck with such a shooting line 70 will contact the target ball 2 at the target ball contact point 15 with the cue ball contact point 60 and propel the target ball 2 towards the target 35.

[0041] FIGS. 2D and 2E show an embodiment of the aiming tool 85 without a carpet region 90 and having instead only a flat circular aiming ring 115 that is placed onto a billiards table horizontal surface 147 near a target ball 2. The aiming ring diameter 149 in this embodiment is the same as the target ball diameter 153 and the cue ball diameter 192. In other embodiments the aiming ring diameter need not be the same as the target ball diameter 153 and the cue ball diameter 192. The aiming ring 115 has an aiming ring central line 130 that extends across the aiming ring diameter 149 through the aiming ring center 117. One end of the aiming ring central line 130 closest to the target ball forms an aiming ring contact point 120; the other end of the aiming ring central line 130 farthest from the target ball 2 forms an aiming ring frontal point 95. The target ball has a target ball axis line 10 extending throughout the target ball 2 and passing through a target ball center 152; the target ball axis line 10 is directed toward the target 35. The target ball axis line has one end located on the target ball surface 25 that is farthest from the target forming a target ball contact point 15.

[0042] The aiming ring 115 is placed onto the billiards table surface 147 such that the aiming ring contact point 120 is located directly below the target ball contact point 15, and the aiming ring central line 130 is directed toward the target 35. There is only one such location for the aiming ring 115 to be placed relative to the target ball 2 that meets the requirements for placing the aiming ring contact point 120 below the target ball contact point 15 and directing the aiming ring central line 130 toward the target 35. A vertical positioning tool 135 can be used to assist positioning the aiming ring contact point 120 below the target ball contact point 15. The vertical positioning tool can be formed from a thin polymeric material having a positioning line 139 a portion of which is colinear with the aiming ring central line 130. The vertical positioning tool corner 137 and the positioning line 139 forming a ninety degree bend upwards; the positioning line 139 extending vertically to the target ball contact point 15. The vertical positioning tool 135 can be placed on top of the aiming ring 115 with the vertical positioning tool corner 137 located at the aiming ring contact point 120. The target ball contact point will then be positioned vertically above the aiming ring contact point 120. The vertical positioning tool 135 can then be removed to allow the aiming ring 115 a clear path to direct the cue ball 40 to contact the target ball 2 and propel the target ball 2 towards the target 35.

[0043] With the aiming ring 115 in place on the billiards table surface 147, the billiards player can then aim and direct the cue ball 40 from the cue ball initial location 75 directly toward the aiming ring 115 such the cue ball 40 across the entire cue ball diameter 192 is directed toward the aiming ring 115 across the aiming ring diameter 149. The cue ball 40 is directed to a cue ball final location 45 that is positioned above the aiming ring 115. Cue ball 40 contact with the target ball 2 will propel the target ball 2 towards the target 35. Similarly, the billiards player can direct the cue ball center 72 towards the aiming ring center 117 to make proper contact of the cue ball 40 with the target ball 2 and propel the target ball 2 along alignment line 30 towards the target 35.

[0044] As shown in FIG. 2F the aiming ring central line 130 can have an aiming ring central line extension 145 that directed colinear with the aiming ring central line 130 and is intended to provide the billiards player with a better capability to ensure that the aiming ring central line 130 is directed accurately towards the target 35. The aiming ring central line extension is located on a line extension support 147 that extends in a planar manner from the aiming ring 115. The line extension support can be formed from the same materials as the aiming ring 115 and lays on the billiards table surface and extends several inches in length from the frontal point 95.

[0045] FIGS. 3A-3C show an embodiment for a platform aiming tool 150 to help the billiards player properly strike the cue ball 40 towards the target ball 2 to travel towards the target 35. The aiming tool can have a target ball cover 155 that is located above the target ball 2 by a fraction of an inch and can be formed from a thin clear plastic planar material or other thin material that is supported by legs 160 that hold the target ball cover 155 above the target ball 2 such that the cue ball 40 can roll below the platform aiming ring 180 without making contact with the platform aiming ring 180. The cover 155 has an alignment mark 165 that is aligned parallel with the alignment line 30 when viewed from above and hence is directed toward the target 35. The planar target ball cover 155 has a length and width that is about 10% larger in length and width (range 5-25% larger) than the target ball diameter 162 such that the target ball 2 is able to freely roll towards the target 35 when it is impacted by the cue ball 40. The target ball cover 155 has a rounded front 170 that matches the rounded shape of the outer surface and diameter of the target ball 2.

[0046] The target ball 2 cover attaches via a platform neck 175 to a platform aiming ring 180 at an aiming ring middle line 185; the aiming ring middle line 185 extends on the surface of the cue ball aiming ring 115 in the direction parallel with the alignment line 30 and is colinear with the alignment mark 165. The platform neck 175 is located between the target ball cover 155 and the platform aiming ring 180. The platform neck 175 is a narrow structure about 0.5 inches in width (range 0.1Diameter of the billiard ball) that attaches to and holds the platform aiming ring 180 such that the platform aiming ring 180 extends coplanar with the cover and the aiming ring middle line 185 is colinear with the alignment mark 165 on the cover and extends across the platform aiming ring diameter 187 which can be the same as the cue ball diameter 192 (or billiards ball diameter).

[0047] The platform aiming ring 180 can be formed from a thin plastic or metal (preferably formed from a clear plastic) can make direct contact with the rounded front 170 of the target ball cover 155 and lies directly above the cue ball final location 45. The platform aiming ring 180 can be a thin planar material that is held in a horizontal configuration. A contact spot 190 found at one end of the platform aiming ring middle line 185 is vertically displaced above the cue ball contact point 60 and above the target ball contact point 15; the two contact points are touching each other in the cue ball final location 45 below one end of the aiming ring middle line 185. The platform aiming ring 180 is a circular disc or ring having a diameter that can be equal to the cue ball diameter 192 as shown in FIG. 3B. The platform aiming ring 180 is vertically displaced above the cue ball final location 45. The platform aiming ring 180 is held at a location directly above the location that the billiard player aims the cue ball from an cue ball initial location 75 anywhere on the billiard table where the shooting line 70 forms an obtuse shooting angle, theta 80, with the alignment line 30.

[0048] The platform aiming ring 180 can have a diameter less (or more) than the cue ball diameter 192. The platform aiming ring 180 has an aiming ring center 117 that is displaced along the aiming ring middle line 185 at a horizontal distance from the contact spot 190 equal to the radius of the cue ball 40. The billiards player can direct the cue ball 40 along a shooting line from the center of the cue ball 40 to the aiming ring center 117 to properly propel the target ball 2 towards the target 35. It is noted that the platform aiming ring center 117 is displaced along the aiming ring middle line 185 at a horizontal distance from the center of the target ball that is equal to the diameter of the cue ball 40.

[0049] The aiming ring can have a variety of added members to assist the player in viewing the platform aiming ring 180 during striking of the cue ball 40. For example, the aiming ring can be lit using battery operated lights 195 including laser lights 195. The platform aiming ring 180 can have a sliding member 200 attached to assist the player in viewing the aiming ring; the sliding member 200 can be slid along the perimeter of the platform aiming ring 180 and placed in a direction towards the cue ball initial position, for example. The aiming ring can be fitted as shown in FIG. 3C with low powered, battery operated, laser lights 195 that are directed downwards, for example, towards the billiards table at each end of a sliding member 200 to define two lines towards which the player must strike and direct the cue ball 40 toward the entire aiming ring in between to provide accurate contact and impact with the target ball 2 to propel the target ball 2 towards the target 35.

[0050] If the player strikes the cue ball 40 directly towards the aiming ring such that the cue ball 40 rolls directly beneath the entire aiming ring, the cue ball contact point 60 will make proper contact with the target ball contact point 15 propelling the target ball 2 towards the target 35 as discussed earlier in FIGS. 1-3B. It is noted that the planar aiming tool 85 can be comprised of only the platform aiming ring 180 with the aiming ring being held by legs or support members 160 to hold the aiming ring above the billiards table at a height that is greater than a cue ball height 207. The legs 160 are spaced apart far enough to allow easy entry of a cue ball 40 between the legs 160 and strike the target ball 2 at the target ball contact point 15 as described earlier.

[0051] FIGS. 4A and 4B show another embodiment for a tool to assist the billiards player in determining the proper angle to aim the cue ball 40 relative to a target ball 2 to propel the target ball 2 towards a desired target 35. This embodiment places a vertically oriented target ball equator 5 on the target ball 2 (i.e., the circumference of the cue ball 40 at its largest diameter and directed vertically relative to the playing surface 328 of the billiards table) in line and coplanar with a vertically oriented cue ball cue ball equator 50 at the cue ball final location 45 shown in FIG. 4A. The horizontal target ball axis line 10 is located within a plane of the vertically oriented target ball equator 5 and passes through the center of the target ball 2 from the target ball contact point 15 to the target ball opposing pole 20 and is aligned parallel and colinear with an alignment line 30; the alignment line 30 being a horizontal line that is directed from the target ball opposing pole 20 towards the target 35 with the target ball axis line 10 colinear with the alignment line 30. The cue ball horizontal axis line is also aligned colinearly with the alignment line 30, passing through the center of the cue ball 40, and hence is directed towards the target 35 in the cue ball final location 45. The cue ball contact point 60 is placed into contact with the target ball contact point 15 and the horizontal cue ball axis line 55 is coplanar with the horizontal target ball axis line 10. The target ball axis line 10 and the cue ball axis line 55 are colinear with each other and the alignment line 30 and are directed towards the target 35.

[0052] This final cue ball location with the cue ball contact point 60 making contact with the target ball contact point 15 on the target ball surface 25 on the target ball equator 5 is required to propel the target ball 2 towards the target 35 from any cue ball initial location 45 to any suitable location on the billiards table or pool table; such suitable location having the shooting line 205 making an obtuse shooting angle, theta 80, with respect to the alignment line 30. The shooting line 70 is directed from the cue ball contact point 60 in its initial position to the target ball contact point 15; it is the direction that the billiards player must direct the cue ball 40 in order to propel the target ball 2 towards the target 35. A center point shooting line 70 direction can also be noted to be parallel with the shooting line 70 and thereby extends from a center of the cue ball 40 in its initial position to the center of the cue ball 40 in its final position; the center point shooting line direction 205 being the direction that a billiards player strikes a surface of the cue ball 40 along a cue ball central axis that would not generate spin on the ball as it is struck by the pool cue at its initial cue ball location and rolls the cue ball 15 to a final cue ball location 45.

[0053] The billiards player can maintain the cue ball axis line 55 extending from the cue ball contact point 60 to the cue ball opposing pole 65 in a parallel direction and orientation from a final position on the billiards table to any initial position on the billiards table with the cue ball horizontal axis line 55 directed parallel to the alignment line 30. The cue ball vertical equator 50 can also be viewed from above as being a parallel with the cue ball axis line 55. The player can move the cue ball 40 to any such suitable location on the billiards table while maintaining the cue ball axis line 55 parallel with the target ball axis line 10. The player can then strike the cue ball 40 at the cue ball initial location 75 such that the cue ball contact point 60 impacts the target ball contact point 15; such a strike will ensure that the target ball 2 is propelled toward the target 35. The billiards player simply must aim the cue ball contact point 60 towards the target ball contact point 15 to successfully propel the targe ball towards the target 35.

[0054] Maintaining the cue ball axis line 55 parallel to the target ball axis line 10 while moving the cue ball 40 to a suitable cue ball initial location 75 on the billiards table can be accomplished by making the target ball contact point 15 and target ball opposing pole 20 along with the cue ball contact point 60 and cue ball opposing pole 65 out of a ferrous or magnetic material or material that can cause a compass to record the direction of the target ball axis line 10 and provide this information via an electromagnetic sensing device, a magnetic sensing device, or other electronic device along with a computer chip to the player to place the cue ball axis line 55 or vertical cue ball equator 50 as viewed from a top view in a direction that is parallel to the target ball axis line 10 or vertical target ball equator 5 as viewed from above. The target ball contact point 15 and target ball opposing pole 20 can also be visually colored or marked; the target ball vertical equator can also be colored or visibly marked. Similar markings can be place onto the cue ball 40 to visualize the cue ball contact point 60, cue ball opposing pole 65, and cue ball vertical equator 50.

[0055] As shown in FIG. 4B, to enhance the visibility of the cue ball equator line 210 or cue ball contact point 60 by the billiards player when striking the cue ball 40, the cue ball axis line 55 can be rotated relative to a cue ball central vertical axle 222 a specified angle. Following rotation of the cue ball 40 in its initial position, the horizontal cue ball axis line 55 is no longer parallel with the target ball axis line 10 but allows the billiards player to view a newly adjusted cue ball contact point 215 that can be aligned with the target ball contact point 15 to direct the cue ball 40 by the billiards player such that the target ball 2 is properly propelled toward the target 35. The adjusted cue ball contact point 215 is colinear with the initial cue ball contact point 60 (prior to rotating the cue ball 40) and with the target ball contact point 15.

[0056] An acute shooting angle, beta 220, can be described between the shooting line 70 and the alignment line 30, where beta equals 180 degrees minus the obtuse shooting angle, theta 80. The horizontal cue ball axis line 55 can be rotated along a cue ball central vertical axle by a ball rotation angle, alpha 225, where alpha equals 180 degrees minus (2?beta) to place the cue ball contact point 60 at one end of the horizontal cue ball axis line 55 in full view of the billiards player on a cue ball surface nearest the billiards player. The cue ball 40 is rotated in a rotational direction from the alignment line 30 towards the shooting line 70 by an angle alpha to move the cue ball contact point 60 to a cue ball rotated contact point 215 location that is in view of the billiards player, thus allowing the billiards player to view the shooting line 70 from the adjusted cue ball contact point 215 to the target ball contact point 15. The billiards player then strikes the cue ball 40 such that the rotated target ball contact point 15 is directed to contact the target ball contact point 15 and the target ball 2 is propelled toward the target 35.

[0057] A ferrous material or a magnetic material can be placed at the target ball contact point 15 and also at the target ball opposing pole 20 such that the ferrous or magnetic material is located at each end of the target ball equator line. The target ball contact point 15 can be distinguished from the target ball contact opposing pole via difference in magnetic material type and amount at each site, for example. Similarly, a ferrous material or magnetic material can be place at the cue ball contact point 60 and cue ball opposing pole 65. An electromagnetic sensor or compass can sense the direction of the target ball contact point 15 and target ball opposing pole 20 such that the target ball axis line 10 is directed parallel to the alignment line 30. In a similar manner to the target ball 2, a cue ball 40 can have ferrous material or magnetic material placed at a cue ball contact point 60 and at a cue ball opposing pole 65. The cue ball 40 can be placed on the billiards table at a cue ball initial location 75 with the cue ball contact point 60 and cue ball opposing pole 65 form a cue ball axis line 55 that is directed parallel with the target ball axis line 10 using the same electromagnetic sensor or compass used to identify the direction of the target ball axis line 10. A shooting line 70 is then determined via the same electromagnetic sensor or compass to identify a shooting direction from the cue ball contact point 60 to the target ball contact point 15. An obtuse shooting angle, theta 80, is noted from the cue ball contact point 60 to the target ball contact point 15 and directed via the alignment line 30 towards the target 35. An acute shooting angle, beta 220, is defined where beta=180 degrees minus theta.

[0058] The cue ball 40 can then be rotated directly toward the billiards player along a cue ball central vertical axle 222 by an angle, alpha, 225 placing the where alpha=180 degrees minus (2?beta). This rotation of the cue ball 40 places the cue ball contact point 60 in direct view of the billiards player and maintains the shooting line 70 direction the same as prior to rotating the cue ball 40. The electromagnetic sensor or compass can determine the amount of cue ball rotation to 180 degrees minus (2?beta) via calculation based on a computer chip. The electromagnetic sensor or compass can also detect and indicate that the shooting line 70 direction is the same before and after rotating the cue ball 40.

[0059] The compass or electromagnetic sensor is able to sense and identify the direction of the cue ball contact point 60 to the target ball contact point 15. The shooting line 70 can alternately be identified by a compass or via an electromagnetic sensor by placing a ferrous wire or marking onto the billiards table in line with the shooting line 70. The billiards player can direct the cue ball 40 along the shooting line 70.

[0060] In another embodiment a tool is described that allows the billiards player to more accurately use the bumper 235 of the billiards table. As shown in FIG. 5, under non-real or imaginary conditions a billiard ball would approach a bumper 235 at an incident angle 240 and strike the bumper 235 at a billiards ball horizontal equator 250 tangent point 245 located along the billiards ball horizontal equator 250 and be reflected from that equator tangent point 245 at a reflection angle 255 equal to the incident angle 240. As shown in FIG. 6, the bumper height 260 or rail height for most billiard tables is 63.5% of the billiards ball diameter 262; the bumper 235 height is 127% of the height of the ball radius 265 of the billiard ball. The result is that the bumper 235 makes contact with the ball at a diameter adjusted contact point 270 with a ball contact height 272 that is 27% higher than the ball radius 265 at a location on the ball with a ball adjusted contact diameter that is 96.5% of the ball diameter 262 of the ball at the ball horizontal ball equator 250.

[0061] FIG. 7 shows a top view of a billiard ball approaching a bumper 235 at an incident angle 240 and an imaginary contact point 285 that would occur if the bumper 235 made contact with the billiards ball horizontal equator 250. Instead, under real conditions, the billiard ball continues along its shooting line 70 until the ball adjusted contact diameter 275 makes contact with the bumper 235 at its diameter adjusted contact point 270 located downstream 290 of the imaginary contact point 285. After contact of the ball with the bumper 235 the ball is reflected along an actual ball reflection path 295 with a reflection angle 255 that can be approximately equal to the incident angle 240. The ball is not reflected along the ball imaginary reflection path 300.

[0062] FIG. 8 further shows a top view of a billiard ball 230 approaching a bumper 235 at an incident angle 240 and the ball adjusted contact diameter making contact with the bumper 235 and causing the bumper 235 to compress by a bumper compression distance 305. The ball horizontal equator 250 does not make contact with the bumper 235 at the imaginary contact point 285 defined by the horizontal equator 250. The result is that the ball adjusted contact diameter 275 contacts the bumper 235 and compresses the bumper 235 such that the bumper 235 compression adjusted contact point 310 is located further downstream 290 from the diameter adjusted contact point 270 described in FIG. 7 resulting in a ball further-actual reflection path 315 due to ball adjusted diameter and bumper 235 compression. This bumper 235 compression can have an inelastic componency that results in the reflection angle 255 being smaller than the incident angle 240 (i.e., reflection angle 255 is less perpendicular to the bumper 235) when a greater bumper compression distance 305 is created due to a larger billiard ball velocity (under the condition of assuming no ball spin). Billiard ball spin in a horizontal circumferential direction will affect the reflected angle such that spin (like the spin on a car tire) in a downstream 290 direction will cause the reflected angle to be reduced, and visa-versa.

[0063] FIG. 9A shows a (billiards goniometer 320) tool to assist the billiard player to more effectively use the bumper 235 to strike a billiard ball with an incident angle 240 with respect to the bumper 235 and know the diameter adjusted contact point 270 and the bumper 235 compression adjusted contact point 310 and measure the reflection angle 255 and reflection path (295, 315 in FIG. 7 and FIG. 8) relative to the incident angle 240. A billiard goniometer 320 is shown in FIG. 9 that can be placed onto a billiard table edge 325 of the top surface surrounding the playing surface 328 of a billiard table such that the goniometer edge member 330 is parallel with the bumper 235 and parallel with the billiard table edge 325. The incident arm of the billiard goniometer 320 has incident and reflection gears 340 or sprocket that engages the incident arm and the reflection arm 345. When the incident arm is moved or pivoted to provide an incident angle 240 with respect to the bumper 235, the reflection arm 345 can move a similar amount to maintain the reflection angle 255 equal to the incident angle 240. Both the incident arm and the reflected arm pivots are rotationally attached to the goniometer edge member 330. Several alternate mechanisms are anticipated that control the angle of the incident arm 335 relative to the reflected arm. Such mechanisms include feed and take-up spools with string or fiber connected to the incident arm 335 and reflected arm. The use of more than two gears 340 to coordinate the movement of the incident arm 335 with the reflected arm is also anticipated.

[0064] As shown in FIG. 9A, the billiard goniometer 320 is placed onto the edge of the billiard table such that a billiard ball touches the incident guiding edge 350 of the incident arm 335 and the reflection guiding edge 355 of the reflection arm 345 for a specific incident angle 240 that the billiards player wishes to explore and learn the actual reflection path (295 and 315 in FIGS. 7 and 8, respectively). The ball horizontal equator 250 is aligned such that it is in alignment (as shown in FIG. 9A as viewed from the top; the ball horizontal equator 250 is just touching the bumper edge 365. Numerical markings 360 on the incident arm 335 and the reflection arm 345 are used to identify the location of the goniometer edge member 330 relative to the bumper edge 365 and define a bumper-goniometer guiding edge distance 370. As shown in FIG. 9A, the bumper 235 edge corresponds with numerical marking zero on the guiding edge of the incident arm 335 and reflection arm 345, for example.

[0065] As shown in FIG. 9B, the goniometer edge member 330 is then moved outwards 380 (relative to the table playing surface 328) by one or more numerical markings 360 on each of the incident arm 335 and reflection arm 345 (while keeping the goniometer angle the same as in FIG. 9A) in order to account for the ball adjusted contact diameter as discussed in FIG. 7. The ball adjusted contact diameter 275 is then placed into direct contact with the bumper edge 365 (as shown in FIG. 9B). For a billiard ball having a diameter of 2.25 inches, the ball adjusted contact diameter is 2.17 inches (i.e., 2.25?0.965), the diameter of a horizontal circle that is tangent with the bumper edge 365. As shown in FIG. 9B the incident guiding edge 350 and the reflection guiding edge 355 of the incident arm 335 and reflection arm 345 are no longer in contact with the billiard ball and a gap 375 is formed between the billiards ball 230 and both the incident arm 335 and reflection arm 345. and the ball adjusted contact diameter is in contact with the bumper edge 365. As shown in FIG. 9B the goniometer edge member 330 has been moved outwards 380 by a distance of the bumper 235goniometer guide edge distance as defined by the numerical markings 360 from the bumper 235 edge to the initial bumper 235 numerical marking at zero. The numerical markings 360 on the incident arm 335 and reflection arm 345 are repositioned at number 1, for example, to account for the ball adjusted contact diameter.

[0066] As shown in FIG. 9C, the billiard goniometer edge member 330 is further moved outwards 380 (without moving the incident or reflected arms) by one or more numerical markings 360 to account for compression of the bumper 235 while maintaining the goniometer incident arm 335 and reflection arm 345 constant. The amount of goniometer edge member 330 movement outwards 380 can be about twice the amount associated with the ball adjusted diameter. This provides a larger gap between the incident arm 335 and the reflection arm 345 with the billiard ball 230. The bumper 235 can compress a small amount, about 0.5-3 mm, upon impact of the billiard ball with the bumper 235 depending upon the force placed upon the billiards ball 230 and the angle of the billiards ball incident angle 240 as it strikes the bumper 235. As shown in FIG. 9C the goniometer edge member 330 has moved outwards 380 to a larger bumper-goniometer guiding edge distance 370 (from the bumper edge 365 at numerical marking, 2, to the initial numerical markings 360 at zero) and the numerical markings on each of the arms are positioned at 2, for example.

[0067] It is noted that the bumper 235 compression and slippage between the billiards ball 230 and the bumper 235 also causes the reflected angle to decrease relative to the incident angle 240. A lower incident angle 240 causes a greater reduction in the reflected angle. The reflection arm 345 of the goniometer 320 can be disengaged from the incident arm 335 to allow a reduction of the reflection angle 255 relative to the incident angle 240. Striking the billiards ball 230 to follow along the incident arm 335 of the goniometer 320 will then reflect off of the bumper 235 and follow the lower angle of the reflection arm 345 of the goniometer 320. The user then can view the effect of the ball adjusted contact diameter, the bumper 235 compression, and ball slippage resulting in a gap 375 between the billiard ball and the reflection arm 345 as the billiard ball is in contact with the bumper 235, and view the reduced angle of the reflected angle and reflected ball path relative to the incident angle 240.

[0068] In use, the billiards goniometer 320 is shown in FIGS. 10A and 10B. The billiard ball is positioned at an ball initial position 385 along the incident guiding edge 350 of the billiards goniometer 320 at a distance of a foot or more, for example, (per the desire of the billiard player for practicing a bumper 235 shot) from the bumper 235 and at an incident angle 240 with respect to the bumper 235. The billiards goniometer 320 is placed outwards 380 (per FIG. 10A) relative to the actual billiards bumper 235; the billiards goniometer 320 guiding edge distance accounts for the bumper 235 compression and for ball adjusted contact diameter and is set at a numerical marking higher than zero, i.e., at numerical marking 2, for example. A gap 375 is viewed between the reflection arm 345 and the billiards ball 230.

[0069] The billiards player can then place the billiards ball 230 against the guiding edge of the incident arm 335. The billiards player can then strike the billiards ball 230 and propel the billiards ball 230 along the incident guiding edge 350 of the incident arm 335 into the bumper 235 where it contacts and compresses the bumper 235 and reflects along a reflection angle 255 as it follows the reflection guiding edge of the reflection arm 345. The gap 375 that was established due to moving outwards 380 of the goniometer edge member 330 to account for bumper 235 compression allows the billiard ball to follow the reflection path along the reflection arm 345 of the billiard goniometer 320.

[0070] The billiards player can adjust the incident and reflection angle 255 of the billiards goniometer 320 to direct the billiards ball 230 accurately off the bumper 235 towards a target 35. As the incident angle 240 relative to the bumper 235 is greater, the bumper-goniometer guiding edge distance 370 as described by the numerical markings 360 can be increased as shown in FIG. 10B since the guiding edge of the incident arm 335 and reflection arm 345 makes contact with the outer horizontal equator 250 of the billiards ball 230 as it travels on its incident path and reflected path. Hence, although the incident angle 240 is equal to the reflected angle, the cue ball 40 is displaced downstream 290 by a gap 375 distance due to bumper 235 compression and also ball adjusted contact diameter. It is further noted that the reflected angle can be less than the incident angle 240 due to slippage of the billiards ball 230 relative to the bumper 235 and due to asymmetric compression of the bumper 235. The reflection arm 345 can be adjusted to allow for a reduced reflection angle 255 relative to the incident angle 240. The present billiards goniometer 320 can thus provide for the billiards ball 230 to follow the incident arm with precise contact into the bumper 235 and follow the reflection arm 345 with precise contact out of the bumper 235. The spin placed onto the billiards ball 230 also has a great effect on the reflection angle 255 of the billiards ball 230 coming of the bumper 235. The reflection of the billiards ball 230 off of the bumper 235 as described in this invention applies to a billiards ball 230 that is struck with little or no horizontal circumferential spin.

[0071] Common reference numerals used throughout the specification and drawings for various embodiments describe structural elements that have the same description. Structural elements found in one embodiment can be applied to other embodiments and understood to be included within the present invention. Any of the embodiments presented can contain any of the features found in any other of the embodiments found in the present invention.