Method and system for characterizing golf ball striking ability

Alternate characterizations of golf ball striking ability is provided, as well as methods for determining the alternate characterizations and systems for carrying out such determinations. Such methods may include performing one or more golf strikes to impart trajectories to one or more golf balls. Such methods may also include measuring each of the golf strikes to determine golf club head, golf ball speed, side spin angle, and offline angle, calculating a trajectory magnitude factor and a trajectory offline factor on the basis of the measurements, and reducing the trajectory magnitude factor by the trajectory offline factor.

BACKGROUND

Handicap numbers are used by golfers as measures of golfing ability. A handicap number is typically determined on the basis of a golfer's performance over a range of holes with respect to a predetermined par value associated with each hole. In calculating a handicap number, for example, the number of strokes a golfer must make to move a golf ball from a particular tee spot to the hole is first recorded for each hole of a golf course. The predetermined par value of the hole is then subtracted from this number. If the golfer must make more strokes to move the golf ball to the hole than the par number for that hole, the resulting number will be positive, whereas if the golfer requires fewer strokes than the par number, the resulting number will be negative. A handicap number is then calculated on the basis of the resulting numbers for the range of holes.

However, measures of golfing ability such as handicap numbers present certain problems. A first problem is that handicap numbers are calculated based upon specific performances against specific holes of specific golf courses under specific environmental conditions. Weather conditions and subtle differences between specific holes of various golf courses may make handicap numbers inherently difficult to compare. While handicap numbers may attempt to compensate for such difference by taking into account factors relating to the general difficulty of particular golf courses, for example, such handicap numbers may still not reflect differences in hole-to-hole difficulty.

Additionally, since handicap numbers are based upon the difference between an actual number of strokes required to move a ball to a hole and the par number associated with that hole, handicap numbers may be relatively coarsely-grained. That is, the difference in handicap number between two golfers may be relatively small, especially at higher ability levels.

Moreover, since handicap numbers may derive from data gathered and analyzed by individual golfers, the value of such numbers may be related to factors such as an individual golfer's diligence in gathering and accurately recording the required data, as well as the golfer's skill in deriving the proper handicap number on the basis of the data.

Furthermore, handicap numbers may only be of general assistance in selecting golf equipment suitable to improve a particular golfer's game. For example, it may generally be known that a particular piece of golf equipment such as a particular type of golf club or golf ball may improve the game of golfers at a particular ability level as measured by handicap, i.e., it may generally be known that a particular type of golf ball may improve the golf game of golfers of a certain handicap range. However, handicap numbers may not be useful in determining whether or how a particular piece of golf equipment may improve the golfing ability of a particular golfer.

Accordingly, there is a need for alternate characterizations of golf ball striking ability, as well as methods for determining the alternate characterizations, methods for selecting golf equipment on the basis of the alternate characterizations, and systems for carrying out such methods.

SUMMARY

In one aspect, a method for selecting a piece of golf equipment comprises steps of striking, measuring, establishing, determining, and selecting. In one step, the method includes striking (a) a first golf ball with a first golf club to impart a first trajectory to the first golf ball, and (b) a second golf ball with a second golf club to impart a second trajectory to the second golf ball. In another step, the method includes measuring one or more magnitude parameters and one or more offline parameters of the first trajectory and the second trajectory. In another step, the method includes establishing, for each of the first trajectory and the second trajectory, (a) a trajectory magnitude factor based upon the one or more magnitude parameters and (b) a trajectory offline factor based upon the one or more offline parameters. In another step, the method includes determining, for each of the first trajectory and the second trajectory, a striking ability rating based upon a difference between the trajectory magnitude factor and the trajectory offline factor. In another step, the method includes selecting (a) if the striking ability rating for the second trajectory is less than the striking ability rating for the first trajectory, a piece of golf equipment from a group consisting of the first golf ball and the first golf club, and (b) if the striking ability rating for the second trajectory is not less than the striking ability rating for the first trajectory, a piece of golf equipment from a group consisting of the second golf ball and the second golf club.

In another aspect, a method of characterizing golf ball striking ability includes steps of performing, measuring, determining, calculating, and reducing. In one step, the method includes performing a plurality of golf strikes, in each of which a golf club head strikes a golf ball to impart a trajectory to the golf ball. In another step, the method includes measuring each of the plurality of golf strikes to determine (a) a speed of the golf club head, (b) a speed of the golf ball, (c) a side spin angle of the golf ball, and (d) an offline angle of the trajectory of the golf ball for each of the plurality of golf strikes. In another step, the method includes determining (a) a composite golf club head speed, (b) a composite golf ball speed, (c) a composite side spin angle, and (d) a composite offline angle from the measurements of the plurality of golf strikes. In another step, the method includes calculating (a) a trajectory magnitude factor from a ratio of the golf club head speed to the golf ball speed and (b) a trajectory offline factor from a sum of the side spin angle and the offline angle. In another step, the method includes reducing the trajectory magnitude factor on the basis of an absolute value of the trajectory offline factor to determine a golf ball striking ability rating.

In another aspect, a method of characterizing a golf ball striking ability includes steps of performing, measuring, calculating, and reducing. In one step, the method includes performing a plurality of golf strikes in which each of a plurality of golf club heads strikes a golf ball to impart a trajectory to the golf ball. In another step, the method includes measuring, for each of the plurality of golf strikes, (a) a speed of the golf club head, (b) a speed of the golf ball, (c) a side spin angle of the golf ball, and (d) an offline angle of the trajectory of the golf ball for each of the plurality of golf strikes. In another step, the method includes calculating, for each of the plurality of golf strikes, (a) a trajectory magnitude factor from a ratio of the speed of the golf club head to the speed of the golf ball and (b) a trajectory offline factor from a sum of the side spin angle of the golf ball and the offline angle of the trajectory of the golf ball. In another step, the method includes reducing, for each of the plurality of golf strikes, the trajectory magnitude factor on the basis of an absolute value of the trajectory offline factor to determine a golf ball striking ability rating.

In another aspect, a golf ball striking ability characterization for use in a golf ball fitting system comprises at least a trajectory magnitude factor reduced by a trajectory offset factor. The trajectory magnitude factor includes a ratio of a speed of a golf club head to a speed of a golf ball. The trajectory offline factor includes a sum of (a) the side spin angle of the golf ball modified by a side spin scaling factor and (b) a trigonometric function of an offline angle of a trajectory of the golf ball. The speed of the golf club head, the speed of the golf ball, the side spin angle of the golf ball, and the offline angle of the trajectory of the golf ball are determined from measurements taken upon a plurality of golf strikes in which the golf club strikes the golf ball.

In another aspect, a system for evaluating golf ball striking ability for a computer comprises an automated measurement device, a database, a determining device, a calculating device, a reducing device, and an output device. The automated measurement device obtains measurements related to (a) a golf club head speed, (b) a golf ball speed, (c) a side spin angle, and (d) an offline angle. The database stores a plurality of golf strike parameter values. The determining device determines (a) the golf club head speed, (b) the golf ball speed, (c) the side spin angle, and (d) the offline angle from the measurements. The calculating device calculates (a) a trajectory magnitude factor from a ratio of the golf club head speed to the golf ball speed and (b) a trajectory offline factor from a sum of the side spin angle and the offline angle. The reducing device reduces the trajectory magnitude factor on the basis of an absolute value of the trajectory offline factor. The output device outputs the reduced trajectory magnitude factor.

DETAILED DESCRIPTION

A method for selecting a piece of golf equipment is provided. Also provided are a method of characterizing golf ball striking ability, a golf ball striking ability characterization for use in a golf ball fitting system, and a system for evaluating golf ball striking ability for a computer.

Golf ball striking ability can be characterized with respect to golf swings undertaken in a variety of different locations and under a variety of different conditions. For example,FIGS. 1-10depict golf swings undertaken during a game of golf on a golf course100.FIGS. 1-8depict various moments in a game of golf being played by a first golfer10and a second golfer50on a fairway110of golf course100. InFIG. 1, first golfer10is playing on a portion of fairway110close to green120. First golfer10is beginning to swing a first golf club12at a first golf ball14, aiming at a target spot150, which is a hole on green120. Since first golfer10is relatively far away from green120and target spot150, first golf club12is a golf club capable of hitting a golf ball relatively long distances, such as a driver (i.e., a wood), or a low-numbered iron, or a hybrid club. Second golfer50is observing first golfer10.

InFIG. 2, first golfer10has swung at and struck first golf ball14with first golf club12, sending first golf ball14toward target spot150along first trajectory20. First golf ball14lands and comes to rest at a first stopping spot18. As depicted inFIGS. 3-4, first golf ball14does not follow a target trajectory140from a first lie spot16to target spot150. Instead, first golf ball14follows first trajectory20to arrive at first stopping spot18.

FIG. 4depicts first golf ball14in flight from first lie spot16to first stopping spot18. While in flight, first golf ball14has a back-spin about a first spin axis22. The back-spin was imparted to first golf ball14by first golf club12. First spin axis22is not horizontal, though. Instead, first spin axis22is at a first side spin angle23with respect to a horizontal axis. That is, first golf club12imparted a non-level back-spin to first golf ball14.

If first side spin angle23was zero, and absent any wind, the golf swing may have been a push (since first golfer10is golfing right-handed; else, if first golfer10were golfing left-handed, the golf swing may have been a pull). However, since first side spin angle23is non-zero and positive (i.e., tilting slightly to the right), the golf swing may be a fade (or, if first golfer10were golfing left-handed, a draw). If first side spin angle23were great enough, the golf swing may have been a slice (or, if from a left-handed swing, a hook). Non-zero side-spin angles such as those associated with fades or slices (or with draws or hooks) may alter a trajectory of a golf ball in flight.

Notably, as depicted inFIG. 3, first trajectory20is not a straight line from first lie spot16to target spot150. Instead, first trajectory20curves as first golf ball14flies toward target spot150. More particularly, first trajectory20curves to the right. Some portion of this curvature is a result of a wind blowing from left to right. However, another portion of this curvature is a result of non-zero and positive first side spin angle23imparted to first golf ball14when struck by first golf club12.

As depicted, first trajectory20has a first offline angle21relative to target trajectory140, and the magnitude of first offline angle21changes during the flight of first golf ball14. Near an initial portion of first trajectory20, first offline angle21has some non-zero value. Thereafter, between the initial portion of first trajectory20and a final portion of first trajectory20, first offline angle21relative to target trajectory140increases, in part due to the blowing wind and in part due to the spinning of first golf ball14about first spin axis22at non-zero first side spin angle23. First offline angle21increases throughout first trajectory20until it is the same as a first actual angle25associated with a first actual distance24at a final portion of first trajectory20.

Proceeding, inFIG. 5, second golfer50is playing on the same portion of fairway110. Second golfer50is beginning to swing a second golf club52at a second golf ball54, which lies at roughly the same spot as first golf ball14inFIG. 1. Second golfer50is aiming at the same target spot150on green120. From this distance, second golfer50has also chosen second golf club52to be a golf club capable of achieving relatively long distances, such as a driver, a low-numbered iron, or a hybrid club. First golfer10is, in turn, observing second golfer50.

InFIG. 6, second golfer50has swung second golf club52and has struck second golf ball54, imparting a second trajectory60to second golf ball54. Second golf ball54has followed second trajectory60in its flight and has come to rest at a second stopping spot58. As depicted inFIGS. 7-8, second golf ball54does not follow target trajectory140from a second lie spot56(which lies at roughly the same spot as first lie spot16) to target spot150. Second golf ball54has instead followed second trajectory60to arrive at second stopping spot58.

FIG. 8depicts second golf ball54in flight from second lie spot56to second stopping spot58. Second golf ball54has a back-spin about a second spin axis62, which was imparted to second golf ball54by second golf ball52. As with first spin axis22, second spin axis62is not horizontal, but is rather at a second side spin angle63with respect to a horizontal axis. Like first side spin angle23, second side spin angle63is non-zero. However, second side spin angle63is non-zero relative to the horizontal axis in a direction opposite the direction of non-zero first side spin angle23.

If second side spin angle63was zero, and absent any wind, the golf swing may have been a pull (since second golfer50, like first golfer10, is golfing right-handed; else, if second golfer50were golfing left-handed, the golf swing may have been a push). However, since second side spin angle63is non-zero and negative (i.e., tilting slightly to the left), the golf swing may be a draw (or, if first golfer10were golfing left-handed, a fade), and if second side spin angle63were great enough, the golf swing may have been a hook (or, if from a left-handed swing, a slice). Accordingly, while non-zero and positive side spin angles may alter the trajectory of a golf ball in flight to cause a golf ball to curve to the right, non-zero and negative side spin angles may alter the trajectory of a golf ball in flight to cause the golf ball to curve to the left.

As depicted inFIG. 7, second trajectory60is not a straight line from second lie spot56to target spot150. Second trajectory60instead curves as second golf ball54flies toward target spot150, and more particularly curves to the right. However, although non-zero and negative second side spin angle63imparted to second golf ball64when struck by second golf club62operates to alter the trajectory of second golf ball64to curve to the left, a wind blowing from left to right proves to be a more dominant factory in altering second trajectory60. As a result, second trajectory60curves to the right as did first trajectory20.

Accordingly, relative to target trajectory140, second trajectory60has a second offline angle61the magnitude of which changes during the flight of second golf ball54. Second offline angle61has some non-zero value toward an initial portion of second trajectory60. Between the initial portion of second trajectory60and a final portion of second trajectory60, second offline angle61decreases, as a blowing wind overpowers the spinning of second golf ball54about second spin axis62at non-zero second side spin angle63. Ultimately, second offline angle61is the same as a second actual angle65associated with a second actual distance64.

FIG. 9depicts first trajectory20superimposed with second trajectory60, whileFIG. 10depicts an early portion of trajectories20and60depicted inFIG. 9. Although first side spin angle23is positive and second side spin angle63is negative, blowing winds cause both first trajectory20and second trajectory60to curve to the right. In particular, as depicted inFIG. 10, an early portion of first trajectory20is at first offline angle21with respect to target trajectory140, while first actual distance24is at first actual angle25with respect to trajectory140, with first offline angle21being less than first actual angle25. In contrast, while an early portion of second trajectory60is at second offline angle61with respect to target trajectory140, second actual distance64is at second actual angle65with respect to trajectory140, with second offline angle61being greater than second actual angle65.

WhileFIGS. 1-10depict golf swings undertaken on golf course100, golf swings may be undertaken at other locations and under other conditions. For example,FIG. 11depicts substantially the same golf swings ofFIGS. 1-10, but undertaken on an outdoor driving range200. Being outside, driving range200is subject to winds that may be blowing. As depicted inFIG. 11, a wind is blowing similar to the wind blowing inFIGS. 1-10, and as a result first stopping spot18and second stopping spot58are positioned with respect to first lie spot16, second lie spot56, and target spot150in a manner similar to that depicted inFIGS. 1-10.

In contrast, golf swings may be undertaken under conditions substantially free of blowing winds, such as in controlled environments. For example, as depicted inFIG. 12, substantially the same golf swings as depicted inFIGS. 1-10are undertaken in a first enclosed structure300which extends at least as far as driving range200, or the portion of fairway110depicted inFIGS. 1-10. First enclosed structure300may be an indoor driving range, or a large building such as a warehouse or hangar, or any substantially enclosed indoor area or area otherwise sheltered from the elements. As depicted inFIG. 12, first trajectory20and second trajectory60are not impacted by winds.

However, in contrast with the depiction inFIGS. 1-11, first side spin angle23and second spin angle of first trajectory20and second trajectory60as depicted inFIG. 12are substantially zero. As a result, in the absence of winds and non-zero side spin angles, first trajectory20is to the right of target trajectory140, and first offline angle21of first trajectory20and first actual angle25of first actual distance24are substantially the same. Similarly, second trajectory60is to the left of target trajectory140, and second offline angle61of second trajectory60and second actual angle65of second actual distance64are substantially the same.

Accordingly, golf swings that may be used to characterize golf ball striking ability may be undertaken in locations that are physically long enough to encompass an entire trajectory of a struck golf ball, including outdoor locations such as golf course100and driving range200, as well as indoor locations such as first enclosed structure300. Alternatively, golf swings that may be used to characterize golf ball striking ability may be undertaken in locations that are not physically long enough to encompass an entire trajectory of a struck golf ball.

For example, as depicted inFIG. 13, such golf swings may be undertaken in a second enclosed structure400which is dimensioned to encompass initial portions of trajectories of struck golf balls. Smaller enclosed locations may be advantageous for use in characterizing golf ball striking ability, as they may permit more tightly controlled data-gathering conditions and may facilitate quicker data generation and therefore collection. As depicted, first trajectory20begins on a mat405and extends to a barrier420, which may be a material functioning as a net, or a screen, or both. Similarly, second trajectory60begins on mat405and also extends to barrier420. A measurement device460, which may include a launch monitor, acquires data associated with various golf swing parameters. Golf swing parameter measurements may then be inputted into a processing system470to determine a golf ball striking ability rating or otherwise characterize a golf ball striking ability.

As with trajectories20and60depicted inFIG. 12, first trajectory20ofFIG. 13is to the right of target trajectory140, and second trajectory60is to the left of target trajectory140. However, although the initial portion of trajectories20and60are substantially similar to the initial portion of trajectories20and60ofFIG. 12, first golf ball14may have a non-zero first side spin angle23and second golf ball54may likewise have a non-zero second side spin angle63, such as the non-zero and side spin angles23and63depicted inFIGS. 1-10. Although side spin angles23and63may be non-zero, trajectories20and60may be interrupted by barrier420before any non-zero side spin angles can substantially influence trajectories20and60. That is, in relatively smaller enclosed locations such as second enclosed location400, there may not be enough room for non-zero side spin angles23and63to influence trajectories20and60before barrier420cuts trajectories20and60short.

Accordingly, a golf ball striking ability may be characterized by striking and imparting trajectories to one or more golf balls and measuring various golf swing parameters associated with those strikes. Some golf swing parameters may be associated with the magnitude of a trajectory, such as a distance, a speed, a momentum, or a kinetic energy associated with a golf club head or a golf ball. Other golf swing parameters may be associated with the direction of the trajectory, or an offline (i.e., error) portion of the trajectory relative to a desired or target trajectory, such as an angle associated with the distance, an offline angle relative to a target trajectory, or a side spin angle. On the basis of these measurements, a trajectory magnitude factor and a trajectory offline factor may be established or calculated. The golf ball striking ability characterization may then be obtained by reducing the trajectory magnitude factor on the basis of the trajectory offline factor, such as by subtracting the trajectory offline factor from the trajectory magnitude factor, or by multiplying the trajectory magnitude factor by the trajectory offline factor (for trajectory offline factors that are structured to range from 0 to 1).

For example, in locations that are physically long enough to encompass an entire trajectory of a struck golf ball such as golf course100, driving range200, and first enclosed structure300, one or more golf balls may be struck and the actual distance resulting from each strike may be measured, similar to first actual distance24and second actual distance64as depicted inFIGS. 1-10. The actual angle associated with each actual distance may also be measured, similar to first actual angle25and second actual angle65as depicted inFIGS. 1-10. The trajectory magnitude factor may then be associated with the measured actual distance as reduced by the measured offline factor.

In locations that are not physically long enough to encompass an entire trajectory of a struck golf ball, such as second enclosed structure400, actual distances and actual angles achieved by a golf ball strike are not available to be measured. However, other parameters may be available regardless of whether or not the location is physically long enough to encompass an entire trajectory of a struck golf ball. For example, in second enclosed structure400, measurement device460may measure a golf club head speed and a golf ball speed, and may also measure an offline angle and a side spin angle. These measurements may then be used to establish or calculate a trajectory magnitude factor and a trajectory offline factor.

The trajectory magnitude factor may include the ratio of the golf club head speed to the golf ball speed, which may be referred to as the “smash factor” of a golf swing. This ratio may be normalized with respect to a known or reference trajectory magnitude, such as by dividing the ratio by the known or reference trajectory magnitude (i.e., a reference “smash factor”). The ratio may also be modified by a trajectory magnitude scaling factor, such as by multiplying the ratio by the trajectory magnitude scaling factor. In some embodiments, the ratio may be both normalized with respect to the reference trajectory magnitude and modified by the trajectory magnitude scaling factor. For example, the reference trajectory magnitude may be a trajectory magnitude associated with a certain level of striking ability, such as a “smash factor” that is characteristic of PGA Tour golfers, such as an average “smash factor” of PGA Tour golfers. Additionally, the trajectory magnitude scaling factor may be a number high enough to yield whole numbers that are distinct, while at the same time being low enough to yield whole numbers that are small enough to be manageable, such as a number between 10 and 1000, with 100 being a particularly suitable number.

The trajectory offline factor may include the sum of the side spin angle and the offline angle. In this sum, either of the side spin angle or the offline angle may be modified by a scaling factor, and either of the side spin angle or the offline angle may be modified by a trigonometric function. In some embodiments, the side spin angle may be multiplied by a side spin scaling factor, and the offline angle may be modified by a trigonometric function. For example, the side spin scaling factor may be a number between 0.001 and 0.01, with 0.007 being a particularly suitable number. Additionally, the offline angle may be modified by the sin trigonometric function to become the sine of the offline angle.

Subsequently, the trajectory offline factor may be modified by a trajectory offline scaling factor, which may be a number between 10 and 1000, with 100 being a particularly suitable number. Moreover, instead of reducing the trajectory magnitude factor on the basis of the trajectory offline factor by subtracting the trajectory offline factor from the trajectory magnitude factor, an absolute value of the trajectory offline factor may be subtracted from the trajectory magnitude factor.

In some embodiments, the trajectory magnitude factor and the trajectory offline factor may be established or calculated on the basis of composite values for the golf club head speed, the golf ball speed, the side spin angle, and the offline angle. For example, as depicted inFIG. 14, a plurality of golf ball strikes may produce a plurality of trajectories20a,20b,20c, and20d. Each of trajectories20a-20dmay be measured as having a golf club head speed, a golf ball speed, a side spin angle, and an offline angle relative to target trajectory140, each of which may differ from the other corresponding measurements associated with the remaining trajectories20a-20d. Composite values for such measurements across a plurality of trajectories may be arithmetic or geometric means, medians, modes, or other statistically derived values. For example, composite values could be average values of a particular measurement for a plurality of trajectories. (In calculating these composite values, various outliers may be disregarded.)

Alternatively, the trajectory magnitude factor and the trajectory offline factor may be established or calculated on the basis of individual golf strikes, each being measured as having a golf club head speed, a golf ball speed, a side spin angle, and an offline angle. A golf ball striking ability may then be characterized on the basis of the trajectory magnitude factor and the trajectory offline factor associated with each golf strike. Subsequently, a composite golf ball striking ability may be characterized, such as an arithmetic or geometric mean, a median, a mode, or another statistically derived value.

In some embodiments, a characterization of golf ball striking ability may be a golf ball striking ability rating. A golf ball striking ability rating (BSTAR) may comprise at least a trajectory magnitude factor (TFM) and a trajectory offline factor (TFO). The trajectory magnitude factory may be reduced by the trajectory offline factor, such as by subtracting the absolute value of the trajectory offline factor from the trajectory magnitude factor (TFM-ABS[TFO]). The trajectory magnitude factor may include a ratio of a speed of a golf club head to a speed of a golf ball, which may be a “smash factor” as described above (SF, or vclub-head/vgolf-ball), and may be both normalized with respect to a reference trajectory magnitude, which may be a reference “smash factor” as described above (SFref, or vclub-head-ref/vgolf-ball-ref) and modified by a trajectory magnitude scaling factor (CM). The trajectory offline factor may include a sum of a side spin angle (Aside-spin) modified by side spin scaling factor (Cside-spin) and a trigonometric function of an offline angle of a trajectory of the golf ball (ftrig[Aoffline]), and the sum may be modified by a trajectory offline scaling factor (CO). In determining the golf ball striking ability rating, any of the golf club head speed, the golf ball speed, the side spin angle, or the offline angle may be a single measured value or a composite value based upon a plurality of measured values.

That is, a golf ball striking ability rating may be represented as:
BSTAR=TFM−ABS(TFO)

Where the trajectory magnitude factor and trajectory offline factor may be represented as:
TFM=(CM)*(SF/SFref)
TFO=(CO)*([Cside-spin*Aside-spin]+[ftrig(Aoffline)])

In some exemplary embodiments, the values above may fall within exemplary ranges of numbers and may be particularly suitable numbers. The trajectory magnitude scaling factor (CM) may be a number between 10 and 1000, with 100 being a particularly suitable number. The trajectory offline scaling factor (CO) may be a number between 10 and 1000, with 100 being a particularly suitable number. The side spin scaling factor (Cside-spin) may be a number between 0.001 and 0.01, with 0.007 being a particularly suitable number. Additionally, the trigonometric function of the offline angle (ftrig) may be the sine trigonometric function.

Accordingly, an exemplary golf ball striking ability rating may be represented as:
BSTAR=TFM−ABS(TFO)

Where an exemplary trajectory magnitude factor and an exemplary trajectory offline factor may be represented as:
TFM=(100)*(SF/SFref)
TFO=(100)*([0.007*Aside-spin]+[sin(Aoffline)])

Related methods of characterizing golf ball striking ability may include (a) a step in which one or more golf strikes is performed, (b) a step in which each of the one or more strikes is measured to determine a golf club head speed, a golf ball speed, a side spin angle, and an offline angle, and (c) a step in which either single values or composite values for each of the golf club head speed, the golf ball speed, the side spin angle, or the offline angle is used in calculating a trajectory magnitude factor and a trajectory offline factor. The characterization of golf ball striking ability may then be the trajectory magnitude factor reduced by the trajectory offline factor.

Systems for characterizing golf ball striking ability may include a number of components. Such systems may include at least one automated measurement device for obtaining measurements related to golf club head speed, golf ball speed, side spin angle, and offline angle, such as a launch monitor, a device including a launch monitor, or a device effectively acting as a launch monitor, such as a camera. A database for storing a plurality of golf strike parameter values may also be included. Such systems may also include a determining device for determining values for golf club head speed, golf ball speed, side spin angle, and offline angle on the basis of measurements taken by the automated measurement device. A calculating device for calculating a trajectory magnitude factor and a trajectory offline factor on the basis of the determined values may also be included, as may a reducing device for reducing the trajectory magnitude factor on the basis of the trajectory offline factor. Such systems may also include an output device for outputting the reduced trajectory magnitude factor.

In addition, two or more of these devices may share physical resources with each other. For example, in some embodiments, the device for determining values based on measurements may be physically implemented with and share resources with the measurement device for obtaining measurements. Alternatively, the device for determining values may be physically separate from and receive inputs from the measurement device. As a further example, in some embodiments the device for determining values may be physically implemented with and share resources with, for example, the calculating device, the reducing device, or both.

As measurements of golf skill, golf ball striking ability ratings such as those described above may have a number of advantages over other measurements of golf skill, such as handicap numbers. With handicap numbers, for example, a golfer's performance relative to individual par values of various holes necessarily relates to all the variables that may possibly impact the golfer's game, including variables related to skill, but also including temporary environmental variables (such as weather) and variables relating to the specific physical environments (i.e., golf courses, or holes of golf courses) over which the golfer's performance relative to par is measured. Accordingly, since two handicap values may reflect data taken under two sets of different conditions, comparison of the two values may be rough or otherwise imprecise. In contrast, data gathered in the course of determining a golf ball striking ability rating may advantageously be controlled at a very fine level, beginning with variables such as golf balls and golf clubs used and proceeding down to the temperature and humidity of the space used to gather the data.

Additionally, par is a relatively coarsely-grained value, i.e., a relatively low number. Accordingly, performance against par is relatively coarsely-grained as well. Golf ball striking ability ratings, on the other hand, may advantageously be determined very precisely, by adjusting various scaling factors as well as by gathering data over statistically significant sets of golf swings and golf ball strikes under substantially similar and controlled conditions.

Moreover, since performance relative to par may be self-determined and self-reported, handicap may be susceptible to incompleteness or inaccuracy, depending upon the skill and diligence of those gathering and tallying the performance data. In contrast, golf ball striking ability ratings may advantageously be well-controlled and may be obtained subject to data objectively gathered and processed.

Furthermore, when the ratio of the golf club head speed to the golf ball speed (i.e., a “smash factor” as described above) is normalized, such as by dividing it by a known or reference trajectory magnitude (i.e., a reference “smash factor” as described above, such as a “smash factor” that is characteristic of PGA Tour golfers), golf club head speed may be diminished as a contributor to the golf ball striking ability rating. As a result, a golfer's golf ball striking ability rating may advantageously be an improved measure of the extent or degree to which the golfer is maximizing their potential striking ability. That is, the golf ball striking ability rating may aid in evaluating whether the golfer is hitting as well as the golfer can, or in evaluating how well the golfer is striking the ball independent of head speed.

Once determined, golf ball striking ability ratings may be used in various contexts. Golf ball striking ability ratings may be used to directly compare the performance of two golfers. For example, a player ability rating may include a driver distance, such as an actual distance, divided by a golf club head speed, which may be multiplied by a golf ball striking ability rating.

Characterizations of golf ball striking ability and methods of characterizing golf ball striking ability may also be useful in methods of selecting various pieces of golf equipment that may be suitable for a particular golfer. For example, golf ball striking ability ratings for a particular golfer may be separately determined against a first trajectory imparted to a first golf ball by a first golf club, and a second trajectory imparted to a second golf ball by a second golf club. Thereafter, if the striking ability rating determined for the second trajectory is less than the striking ability rating determined for the first trajectory, one of either the first golf ball or the first golf club may be selected for the golfer. Alternatively, if the striking ability rating for the second trajectory is not less than (i.e., is greater than or equal to) the striking ability rating for the first trajectory, one of either the second golf ball or the second golf club may be selected for the golfer.

In some embodiments, one of the pieces of golf equipment associated with the first trajectory and the second trajectory may be the same. For example, the first golf club and the second golf club may be the same (meaning that they may be identically the same piece of equipment, or may be different copies of the same or substantially the same make and model of equipment). In such embodiments, the comparison of the striking ability rating for the first trajectory and the striking ability rating for the second trajectory may determine the selection of either the first golf ball or the second golf ball. Alternatively, if the first golf ball and the second golf ball are the same, the comparison of the striking ability rating for the first trajectory and the striking ability rating for the second trajectory may determine the selection of either the first golf club or the second golf club.

Golf ball striking ability ratings could also be used as inputs in simulated golf games.FIG. 15depicts first golfer10in second enclosed structure400. First golfer10is beginning to swing a golf club at a golf ball. Here, first golfer10is aiming at an image430projected on barrier420, which is being used both as a net and as a screen. Image430is a simulated depiction of target spot150on fairway110of golf course100. Measurement device460is positioned to measure swings made by first golfer10and transmit measurement information to processing system470, which may use both information about the swings as well as a golf ball striking ability rating for first golfer10to simulate a result.

For example, first golfer10may swing and strike the golf ball, hitting it toward barrier420and imparting a trajectory to it. Measurement device460may measure parameters associated with the trajectory, such as angles of the trajectory, and may determine a simulated stopping spot on the basis of the golf ball striking ability rating for first golfer10in combination with those parameter measurements. Image430may then be modified to reflect the determined simulated stopping point, and first golfer10may proceed with further swings. In this manner, a simulated game of golf may be played on golf course100, or any other golf course, by one or more golfers.

Furthermore, image430may alternatively be any of a variety of simulated depictions of target spots in locations other than golf courses. For example, as depicted inFIG. 16, first golfer10is beginning to swing a golf club at a golf ball, but image430depicts a non-golf course environment.

Golf ball striking ability ratings may also be determined for a golfer corresponding with each club of a range of clubs, such as each club across a range of golf clubs available in a golf bag. That is, one or more golf strikes may be performed in which each of a plurality of golf clubs strikes a golf ball to impart a trajectory to the ball. Subsequently, a golf ball striking ability rating may be determined for each of the plurality of golf clubs, which may be based upon a single golf strike, or may be a composite based upon a plurality of golf strikes.

Alternatively, a range of golf clubs may be separated into sub-ranges, and golf ball striking ability ratings may be determined for a golfer corresponding with each sub-range of the range of golf clubs. For example, a range of golf clubs in a bag of golf clubs may be separated into sub-ranges, such as woods, long irons, and short irons, and one or more golf strikes may be performed in which each club of the range of clubs strikes a golf ball to impart a trajectory to the ball. Subsequently, a golf ball striking ability rating may be determined for each of the sub-ranges of the range of golf clubs, which may be a composite based upon a plurality of the golf strikes for the golf clubs within a particular sub-range.

Once a golf ball striking ability rating has been determined, it may be compared with a scale of categories or grades to associate the rating with a category or grade. A golfer may then use the associated category or grade to select equipment suitable for improving the golfer's performance. There may be as few as two or three categories or grades, or as many as five or ten. The categories or grades may fall within a total range of golf ball striking abilities between 50 and 125, for example, and boundaries between the categories or ranges may be evenly distributed throughout the total range. In exemplary embodiments including five categories or grades, a first boundary may be a number between 80 and 100, a second boundary may be a number between 70 and 90, a third boundary may be a number between 60 and 80, and a fourth boundary may be a number between 50 and 70.

For example, a first boundary may be 90, a second boundary may be 80, a third boundary may be 70, and a fourth boundary may be 60. In turn, a scale of categories or grades may include a first range of golf ball striking ability ratings above 90, a second range from 90 to 80, a third range from 80 to 70, a fourth range from 70 to 60, and a fifth range below 60. A golfer for whom at least one golf ball striking ability rating has been determined for one club within a range of clubs, or for a sub-range of clubs within a range of clubs, may then select a piece of equipment (such as a club or a ball) designated by category or grade as being suitable to improve the performance of the golfer with that club or sub-range of clubs.

More particularly, the golfer may select a piece of equipment having a property, such as a property of forgiveness, that is likely to be suited to improving the game of the golfer. A golfer having a higher golf ball striking ability rating may be able to improve performance through use of equipment that is less forgiving, such as a golf club or a golf ball designed for the benefit of golfers having a greater degree of swing control. However, such equipment may not improve performance of all golfers. Performance may even decrease for golfers with lesser degrees of swing control who are accordingly unable to take advantage of the less forgiving equipment. Golf ball striking ability ratings may advantageously be used to help golfers select those golf clubs and those golf balls most likely to benefit them, given the category or grading of their golf ball striking ability rating or ratings.