Systems and methods for determining optimum putting speed and angle

Abstract

Systems and methods for calculating a path of a golf ball on a putting surface and for calculating an ideal putt direction and speed to cause a golf ball in an initial location on a putting surface to, when putted, enter a hole in a putting surface as described are significantly more computationally efficient and rapid. The efficiency allows implementation of the systems and methods with lower-powered computing devices, including mobile computing devices such as smart phones and the like.

What is claimed and desired to be secured by Letters Patent is: 
     
         1 . A computer-implemented method for calculating an ideal putt direction and speed to cause a golf ball in an initial location on a putting surface to, when putted, enter a hole in the putting surface, the method comprising computing-device-performed steps of:
 calculating a first plurality of reverse paths leading from the hole;   determining which of the reverse paths passes closest to the initial location of the golf ball;   calculating an additional plurality of reverse paths leading from the hole, the additional plurality of reverse paths comprising reverse paths closer to the reverse path that passed closest to the initial location of the golf ball than other prior reverse paths;   repeating the steps of determining which of the reverse paths passes closest to the initial location of the golf ball and calculating an additional plurality of reverse paths leading from the hole until one of the additional plurality of reverse paths passes within a selected distance of the initial location of the golf ball; and   determining and outputting a putt speed and angle based on the reverse path that passes within the selected distance of the initial location of the golf ball.   
     
     
         2 . A computer-implemented method as recited in  claim 1 , wherein each reverse path is calculated using a final, at-the-hole, speed chosen to emulate having the golf ball pass over the hole as if the putting surface lacked the hole, and stop within a chosen distance range of the hole. 
     
     
         3 . A computer-implemented method as recited in  claim 2 , wherein the chosen distance range is selected from the group consisting of:
 between approximately 17 to approximately 19 inches;   between approximately 15 to approximately 21 inches;   between approximately 13 to approximately 23 inches;   between approximately 11 to approximately 25 inches;   between approximately 9 to approximately 27 inches;   between approximately 7 to approximately 29 inches;   between approximately 5 to approximately 31 inches;   between approximately 3 to approximately 33 inches; and   between approximately 1 to approximately 35 inches.   
     
     
         4 . A computer-implemented method as recited in  claim 1 , wherein calculating each reverse path leading from the hole comprises:
 selecting a final, at-the-hole, direction; and   selecting a final, at-the-hole, speed chosen to emulate having the golf ball pass over the hole in the final, at-the-hole, direction as if there was no hole in the putting surface, and stop within a chosen distance range of the hole.   
     
     
         5 . A computer-implemented method as recited in  claim 4 , wherein calculating each reverse path comprises:
 beginning from the hole as a first current location and with a first current velocity comprising the selected final, at-the-hole, direction and the selected final, at-the-hole, speed;   determining a sum of forces to which the golf ball, when rolling across the putting surface, is subject at the current location based on gravitational, normal, and frictional forces at the current location of the golf ball;   calculating a previous location and a previous velocity of the golf ball using the current location, the current velocity, and an opposite of the sum of forces at the current location;   repeating the steps of calculating the sum of forces to which the rolling golf ball is subject at the current location and calculating a previous location and a previous velocity while using the previous location and the previous velocity as the current location and the current velocity for each repetition until the reverse path has been calculated to a selected extent.   
     
     
         6 . A computer-implemented method as recited in  claim 5 , wherein determining the sum of forces to which the rolling golf ball is subject at the current location comprises referencing a force map of the putting surface. 
     
     
         7 . A computer-implemented method as recited in  claim 6 , further comprising generating the force map of the putting surface. 
     
     
         8 . A computer-implemented method as recited in  claim 5 , wherein determining the sum of forces to which the rolling golf ball is subject at the current location comprises:
 determining a slope of the putting surface at the current location; and   determining a coefficient of rolling friction of the putting surface for current conditions of the putting surface.   
     
     
         9 . A computer-implemented method as recited in  claim 4 , wherein calculating the first plurality of reverse paths comprises calculating three reverse paths comprising:
 a first reverse path having a first direction lying along a line extending between the initial location and the hole;   a second reverse path having a first direction at a selected angle from the first direction of the first reverse path; and   a third reverse path having a first direction at a selected angle from the first direction of the first reverse path that is opposite and equal to the angel of the second reverse path.   
     
     
         10 . A computer-implemented method as recited in  claim 9 , wherein the selected angle of the second reverse path is approximately ninety degrees. 
     
     
         11 . A computer-implemented method as recited in  claim 9 , wherein calculating an additional plurality of reverse paths comprises calculating two reverse paths, the two reverse paths comprising:
 a first new reverse path having a first new direction at a new angle from the first direction of a best reverse path of the prior calculation iteration, the new angle being approximately half the size of the selected angle from the prior calculation iteration; and   a second new reverse path having a second new direction at an angle from the best reverse path of the prior calculation iteration opposite and equal to the new angle of the first new reverse path.   
     
     
         12 . A computer-implemented method as recited in  claim 1 , wherein the step of determining and outputting a speed and angle based on the reverse path that passes within the selected distance of the initial location of the golf ball comprises an action selected from the group consisting of:
 determining and outputting a putt speed and angle based on a point of the reverse path that passes within the selected distance of the initial location of the golf ball that is most proximate the initial location of the golf ball; and   determining and outputting a putt speed and angle based on an interpolation between two points of the reverse path that passes within the selected distance of the initial location of the golf ball that are most proximate the initial location of the golf ball.   
     
     
         13 . A computer-implemented method for calculating a projected path of a golf ball on a putting surface to a hole in the putting surface, the method comprising computing-device-performed steps of:
 setting the hole as a current location;   selecting a current velocity comprising a selected final, at-the-hole, direction and a selected final, at-the-hole, speed;   determining the sum of forces to which the golf ball, when rolling, is subject at the current location based on gravitational, normal, and frictional forces at the current location of the golf ball;   calculating a previous location and a previous velocity of the golf ball using the current location, the current velocity, and an opposite of the sum of forces at the current location;   repeating the steps of calculating the sum of forces to which the rolling golf ball is subject at the current location and calculating a previous location and a previous velocity while using the previous location and the previous velocity as the current location and the current velocity for each repetition until the reverse path has been calculated to a selected extent.   
     
     
         14 . A computer-implemented method as recited in  claim 13 , wherein the final, at-the-hole, speed is chosen to emulate having the golf ball pass over the hole in the final, at-the-hole, direction as if there was no hole in the putting surface, and stop within a chosen distance range of the hole. 
     
     
         15 . A computer-implemented method for calculating an ideal putt direction and speed to cause a golf ball in an initial location on a putting surface to, when putted, enter a hole in the putting surface using the computer-implemented method of  claim 13 , the method for calculating an ideal putt direction and speed comprising computing-device-performed steps of:
 calculating a first plurality of reverse paths leading from the hole according to the computer-implemented method of  claim 13 ;   determining which of the reverse paths passes closest to the initial location of the golf ball;   calculating an additional plurality of reverse paths leading from the hole according to the computer-implemented method of  claim 13 , the additional plurality of reverse paths comprising reverse paths closer to the reverse path that passed closest to the initial location of the golf ball than other prior reverse paths;   repeating the steps of determining which of the reverse paths passes closest to the initial location of the golf ball and calculating an additional plurality of reverse paths leading from the hole until one of the additional plurality of reverse paths passes within a selected distance of the initial location of the golf ball; and   determining and outputting a speed and angle based on the reverse path that passes within the selected distance of the initial location of the golf ball.   
     
     
         16 . A computer-implemented method as recited in  claim 15 , wherein a precision of calculation of each reverse path increases as the calculated reverse paths pass more closely to the initial location of the golf ball. 
     
     
         17 . A computer-implemented method as recited in  claim 15 , wherein a step size between current positions and previous positions of each reverse path is decreased as the calculated reverse paths pass more closely to the initial location of the golf ball. 
     
     
         18 . A non-transitory computer-readable medium containing computer program code means to cause a computing device to execute a method for calculating a projected path of a golf ball on a putting surface to a hole in the putting surface, the method comprising steps of:
 setting the hole as a current location;   selecting a current velocity comprising a selected final, at-the-hole, direction and a selected final, at-the-hole, speed;   determining the sum of forces to which the golf ball, when rolling, is subject at the current location based on gravitational, normal, and frictional forces at the current location of the golf ball;   calculating a previous location and a previous velocity of the golf ball using the current location, the current velocity, and an opposite of the sum of forces at the current location;   repeating the steps of calculating the sum of forces to which the rolling golf ball is subject at the current location and calculating a previous location and a previous velocity while using the previous location and the previous velocity as the current location and the current velocity for each repetition until the reverse path has been calculated to a selected extent.   
     
     
         19 . A non-transitory computer-readable medium containing computer program code means to cause a computing device to execute a method for calculating an ideal putt direction and speed to cause a golf ball in an initial location on a putting surface to, when putted, enter a hole in the putting surface using the method of  claim 18 , the method for calculating an ideal putt direction and speed comprising steps of:
 calculating a first plurality of reverse paths leading from the hole according to the method of  claim 18 ;   determining which of the reverse paths passes closest to the initial location of the golf ball;   calculating an additional plurality of reverse paths leading from the, the additional plurality of reverse paths comprising reverse paths closer to the reverse path that passed closest to the initial location of the golf ball than other prior reverse paths;   repeating the steps of determining which of the reverse paths passes closest to the initial location of the golf ball and calculating an additional plurality of reverse paths leading from the hole until one of the additional plurality of reverse paths passes within a selected distance of the initial location of the golf ball; and   determining and outputting a speed and angle based on the reverse path that passes within the selected distance of the initial location of the golf ball.   
     
     
         20 . A system for improving putting comprising:
 a base station configured to calculate the position of the ball utilizing a device selected from the group consisting of a compass and a module configured to receive carrier wave signals from a satellite-based navigation system and to transmit phase measurements of the carrier wave signals;   a server system comprising a topographical data set and configured to calculate recommended swing parameters using a position of a ball, a known position of a hole, and the topographical data set; and   a digital ball marker comprising:   a housing containing an indication for orienting the ball marker with respect to a hole in a green, wherein the ball marker is placed on a surface of the green proximate to the position of the ball lying on the green, the orientation defining a line from the ball marker that intersects the hole;   a receiver configured to receive signals from the global navigation satellite system and to receive phase measurements of the carrier wave signals from the base station, wherein the ball marker calculates the position of the ball by using the received signals and the received phase measurements;   a communication module configured to transmit the position of the ball to the server system and to receive the recommended swing parameters for putting the ball into the hole; and   
       a display for displaying the recommended swing parameters.