WO2006002293A2

WO2006002293A2 - Apparatus, method and computer program product for analysing flight of an object

Info

Publication number: WO2006002293A2
Application number: PCT/US2005/022184
Authority: WO
Inventors: David Benjamin Rankin; Douglas Winfield
Original assignee: Accu-Sport International, Inc.
Priority date: 2004-06-22
Filing date: 2005-06-22
Publication date: 2006-01-05
Also published as: US20060030430A1; WO2006002293A3

Abstract

A method, apparatus and computer program product are provided that determine a measure of launch efficiency of a ball that is more readily understandable by golfers as being indicative of the quality of a shot. A system, method and computer program product are also provided in which the initial sidespin of a ball is measured such that the resulting flight path of the ball may be simulated more accurately. An apparatus, method and computer program product are further provided to analyze human performance, such as a golf shot, as defined by an initial data set that is comprised of a plurality of data elements.

Description

APPARATUS, METHOD AND COMPUTER PROGRAM PRODUCT FOR ANALYZING FLIGHT OF AN OBJECT

BACKGROUND OF THE INVENTION A wide variety of human performance statistics are collected and analyzed. In golf, for example, various parameters that define a golf shot are collected and analyzed. These parameters generally include distance downrange (typically either carry or total) and distance offline to the left or right. One such instance in which a variety of parameters that define a golf shot are collected and analyzed is in club fitting, hi club fitting, a golfer takes a number of shots with each of several different clubs, such as several different drivers. Parameters including distance downrange and distance offline, are collected for each shot, such as by means of a launch monitor system, such as that described by U.S. Patent Application No. 10/360,196 filed February 7, 2003 entitled "Methods, Apparatus and Computer Program Products for Processing Images of a GoIfBaIl" (the contents of which are incorporated herein in their entirety), or a distance measuring system, such as the Accushot™ system that is commercially available from Accusport International, hie. of Winston-Salem, NC. A person trained for club fitting can then analyze the golf shots as defined by the various parameters and recommend that the golfer subsequently use a particular golf club or a set of golf clubs in order to best match the golf clubs to their golf swing, thereby hopefully improving the golfer's performance. Alternately, club manufacturers have developed computer software applications for receiving and analyzing the parameters that define the shots taken by a golfer in order to similarly recommend a golf club or a set of golf clubs to the golfer. Unlike many other applications that generate a data set that is effectively smooth and continuous, human performance statistics including those that define a golf shot may commonly have one or more outliers as a result of the human element. In golf, for example, the parameters defining a missed shot would generally be outliers. Since the outliers differ substantially from the majority of the data, the outliers cause the data set to no longer be effectively smooth and continuous. As such, although the outlier may not be fairly representative of the general level of performance in the same manner that an infrequent missed shot is not representative of the golfer's typical shot, the outlier may have a significant deleterious effect upon any analysis of the parameters. For example, a missed shot may be defined by parameters that, when considered in combination with similar parameters defining other shots, undesirably influence the analysis of the golfer's swing and potentially result in the golfer being fit with clubs that are less than ideal. In order to address the spread of or variations in the data, human performance statistics are often analyzed on the basis of averages and standard deviations. These statistical measures also take into account outliers and therefore are similarly, albeit to a lesser degree, influenced in an adverse manner by the outliers. An additional issue with club fitting involves the adverse effect of golfer fatigue. In this regard, if the golfer fatigues during the club fitting process, the golf shots taken later in the session may not be truly representative of the golfer's performance. Fatigue is particularly an issue when the golfer misses shots since the golfer must take a sufficient number of shots with each club, such as three or more shots, that are representative of the golfer's true ability in order to maintain any level of accuracy and credibility in the fitting process. In addition to club fitting, another important aspect in the golf equipment and teaching industry is to provide insights on how to improve (game analysis), hi the past, game analysis and club fitting have been based mainly on speed measurements of the club and ball; but these measurements are only a small part of the total picture. Launch monitors have been developed that measure the complete set of information about the club swing prior to impact and the launch conditions of the ball. One launch monitor utilizes cameras to take 2 pre-impact pictures of the club and 2 post-impact pictures of the ball. The club images are processed and calculation of the club speed, attack angle, in/out angle, and ball impact position are made. Also, the ball images are processed and calculations of ball speed, launch angle, dispersion angle, backspin and sidespin are made. As noted above, further details regarding launch monitors are provided by U.S. Patent Application No. 10/360,196 filed February 7, 2003 entitled "Methods, Apparatus and Computer Program Products for Processing Images of a GoIfBaIl". Unfortunately, these measurements can be difficult to interpret and easily misapplied especially when trying to help the golfer choose from a wide variety of equipment options. During a typical fitting scenario, the golfer uses various club/ball combinations. For a driver fitting, the typical goal is to find the combination of club and ball to hit the longest, straightest drive possible. Generally speaking, club speed is the most consistent swing parameter of the golfer and would be the most difficult parameter to change for a given club. In contrast, the golfer can more easily change his swing path and impact position to accomplish a more efficient launch. However, golfers may be unable to determine which changes in swing path and impact position provide a more efficient launch and, even if a golfer can detect an improvement, may be unable to quantify the improvement. While launch monitors assist with the analysis process, the aforementioned difficulty in interpreting and comparing the results may limit their usefulness in this scenario. In addition to their use in conjunction with club fitting and game analysis, launch monitors maybe employed in conjunction with simulators that are utilized in conjunction with a variety of sports activities. For example, golf simulators where a golfer hits into a net, against a screen or the like are popular, both for entertainment and for practice purposes. Golf simulators are generally constructed of a base, an overhead canopy, a hitting net and a screen, typically comprised of nylon or a similar material, into which the golfer can hit. Many conventional golf simulators employ a radar-based system to track the initial or launch conditions of the ball immediately following the golf club striking the ball, i.e., immediately following launch, since it is believed that camera-based systems would be too expensive and too cumbersome to operate. Other golf simulators may use a club sensor that tracks the direction, speed and angle of the club head at the time of impact with the ball and a ball sensor that measures the speed and path angles of the ball. The initial conditions that are measured may include the initial speed of the golf ball and the angle at which the golf ball is launched. Golf simulators include a computer for receiving the measurements of the initial conditions and for determining ball flight based upon these initial conditions and a predefined flight model that is premised upon the physics associated with ball flight. Finally, golf simulators include a projector, such as an LCD projector, and an associated screen or display. The projector is driven by the computer to present the flight of the ball on the screen, which may be positioned in front of the golfer. Unfortunately, conventional simulators employing a radar-based system or ball sensor fail to measure all of the parameters that are necessary to predict actual ball flight. For instance, a radar-based system can measure initial ball velocity, vertical launch angle and lateral launch angle, but not backspin and sidespin of the golf ball at the time of launch. Since backspin and sidespin are critical to accurately predicting ball flight, backspin and sidespin may be inferred and then utilized in the flight model. The inference of the initial spin characteristics of the golf ball may be relatively inaccurate such that the resulting image of the flight of the ball is similarly inaccurate. For example, conventional golf simulators seem to underestimate at least the initial sidespin of the ball such that the calculated flight path appears more heavily influenced by the launch angle than by the sidespin of the ball. This underestimation manifests itself in an image of the flight path being constructed that tends to extend in a direction governed by the lateral launch angle without any substantial curvature of the flight path that would be attributable to sidespin. For golf shots, such as drives and long irons, that have substantial carry, the difference between the actual and simulated flight paths may be significant, especially in instances in which the ball has substantial sidespin. By failing to accurately account for the sidespin, conventional simulators likewise fail to reliably simulate the golf shots, especially those with substantial carry. SUMMARY OF THE INVENTION A method, apparatus and computer program product are provided according to one aspect of the present invention that determines a measure of launch efficiency of a ball that is more readily understandable by and/or intuitive to golfers as being indicative of the quality of a golf shot. Thus, any improvement offered by a club swing, a club fitting session or accorded by a change in swing path and/or impact position, can be identified. Club fitting and game/swing analysis should therefore be facilitated by the method and apparatus of embodiments of the present invention. In one embodiment of the present invention, the method, apparatus and computer program product determine a calculated distance of travel of a ball based upon the measured launch conditions including, among other launch conditions, the measured club speed. A maximum distance of travel of the ball is then determined for a ball struck by a club having the measured club speed. In this regard, the maximum distance of travel of the ball can be determined for balls struck by a club having the measured club speed but having different launch angles and/or spin rate. Finally, the measure of launch efficiency is then determined based upon the calculated distance of travel and the maximum distance of travel, such as by forming the ratio of the calculated distance of travel to the maximum distance of travel. hi another aspect of the present invention, a method, apparatus and computer program product determine a calculated distance of travel of the ball based upon measured launch conditions of the ball and a maximum distance of travel of the ball upon being struck by a club having any combination of launch angle and spin rate. The measured launch conditions may include a measured club speed such that the determination of the maximum distance of travel for a ball is performed for a ball struck by a club having the measured club speed. According to this aspect of the present invention, a measure of launch efficiency is again determined based upon the calculated distance of travel and the maximum distance of travel. According to either aspect of the present invention, the measured launch conditions may include a measured ball speed such that the determination of the maximum distance of travel is for a ball having the measured ball speed. In other embodiments, the measured ball speed may be adjusted for any change in spin loft necessary to obtain an optimum ball spin and/or for a distance that the ball is offset from a "sweetspot" of the club. hi the apparatus embodiment, a computing device generally performs the foregoing functions. The resulting measure of launch efficiency can therefore be easily interpreted to see how close the user's shot is to the maximum for that club speed. Among other uses, club fitting and game analysis can benefit from this more intuitive measure of launch efficiency. According to another aspect of the present invention, an apparatus, method and computer program product are provided to permit human performance, such as a golf swing, to be analyzed based on data that is more truly representative without unnecessarily tiring the subject, hi one embodiment, an apparatus, method and computer program product of the present invention analyze human performance as defined by an initial data set that is comprised of a plurality of data elements. Initially, at least one data element that constitutes an outlier is removed from the initial data set to create a representative data set, such as by removing a predetermined number of the largest and smallest data elements from the initial data set. A measure of the deviation, such as the standard deviation, of the representative data set is then determined. The initial data set is then filtered based, at least partially, upon the measure of deviation of the representative data set to create a filtered data set. The human performance is then analyzed based at least partially upon the filtered data set. hi the apparatus embodiment, a processing element generally performs the foregoing functions. The human performance that is analyzed may be a golf shot. For example, embodiments of the present invention may be designed to analyze the downrange distance and/or the offline distance of a golf shot, hi one embodiment, the data elements that comprise the initial data set are captured, such as by means of a sensor. For example, the sensor may comprise a launch monitor that captures the initial conditions and/or club swing parameters that constitute the data elements of the initial data set. By removing the outliers prior to analyzing the human performance, the analysis can be performed more credibly and accurately. Additionally, because of the removal of the outliers, a golfer need not fatigue themselves by hitting an excessive number of shots to insure that a representative data set is obtained, but can instead be apprised by the apparatus and method of one embodiment of the present invention that the representative data set is sufficiently large after removing any outliers. According to yet another aspect of the present invention, a system, method and computer program product are provided in which the initial sidespin of a ball is measured such that the resulting flight path of the ball may be simulated more accurately. In this regard, a plurality of initial conditions of the ball, including sidespin, are measured, such as by a sensor including, for example, at least one camera that captures at least two images of the ball. The flight path of the ball is then determined, such as by means of a computing device, based upon the initial conditions including measurement of the ball spin. A representation of the resulting flight path is then created, again typically by means of the computing device. By measuring sidespin, however, the resulting flight path can be simulated by the system, method and computer program products of embodiments of the present invention in an accurate fashion. In one embodiment, the backspin on the ball may also be measured and utilized to determine the flight path of the ball in order to further improve the accuracy with which a representation of the flight path may be created. An image of the representation of the flight path may also be presented, such as by a display. Further, as the method, apparatus and computer program product are designed to facilitate simulation of the flight path of a golf ball, the actual flight path is limited, such as by means of a net or screen. Moreover, to enhance the simulation experience, a simulated environmental image based upon the resulting flight path may also be created and presented concurrent with the image of the resulting flight path. BRIEF DESCRIPTION OF THE DRAWINGS Having thus described the invention in general terms, reference will now be made to the accompanying drawings and views, which are not necessarily drawn to scale, and wherein: Figure 1 is a block diagram of an apparatus according to one embodiment of the present invention; Figure 2 is a schematic representation of a club head and ball upon impact; Figure 3 is a flow chart of operations according to one embodiment of the present invention; Figure 4 is a flow chart illustrating operations performed in accordance with one embodiment of the present invention Figure 5 is a image of the flight path of a ball created by a system, method and computer program product of one embodiment of the present invention; and Figure 6 is a block diagram of the operations performed in accordance with one embodiment of the present invention.

DETAILED DESCRIPTION OF THE INVENTION The present inventions now will be described more fully hereinafter with reference to the accompanying drawings, in which some, but not all embodiments of the invention are shown. Indeed, these inventions may be embodied in many different forms and should not be construed as limited to the embodiments set forth herein; rather, these embodiments are provided so that this disclosure will satisfy applicable legal requirements. Like numbers refer to like elements throughout.

1. Launch Efficiency An apparatus 10 for obtaining a measure of launch efficiency is shown in Figure 1. The apparatus includes a launch monitor as generally described by the above-referenced U.S. Patent Application No. 10/360,193. hi this regard, the apparatus typically includes a sensor 12 positioned, generally in front of or to the side of the golfer, to measure a plurality of initial conditions. See also step 20 of Figure 3. The initial conditions may include initial ball velocity, vertical launch angle, lateral launch angle, dispersion angle, back spin and sidespin, potentially among other parameters. The sensor can advantageously include a sensor, such as an image sensor and, more particularly, one or more camera(s), for capturing at least two images of the ball immediately after launch from which the foregoing initial conditions can be measured. Although the measure of launch efficiency may be based solely upon the initial conditions collected following the launch, the apparatus 10 of the illustrated embodiment also advantageously measures a number of parameters that define the club swing prior to impact, such as club speed, attack angle, in/out angle and ball impact position. See step 22 of Figure 3. As such, the sensor 12, such as a camera, can also capture images of the club swing prior to impact from which these parameters can be determined as will be apparent to one skilled in the art. Alternatively, the apparatus may include a separate club sensor for monitoring the club swing and determining these parameters as known to those skilled in the art. The resulting collection of initial conditions and club swing parameters may be collectively referenced as the launch conditions. The apparatus 10 of the illustrated embodiment also includes a computing device or computing device 14, such as a processor, a personal computer or the like that operates under control of a computer program stored in memory 16 as well as any other combination of hardware, such as an electronic circuitry, ASIC or the like, software or firmware, for thereafter determining the flight path of the ball at least partially based upon the initial conditions and, in some embodiments, club swing parameters. In this regard, the computing devicecomputing device can determine the flight path of the ball in accordance with a predefined flight model that relies upon the initial conditions and, in some embodiments, club swing parameters. The computing devicecomputing device can utilize any desired flight model including, for example, the flight model promulgated by the U.S. Golf Association (USGA) or by a similar flight model, such as those that dynamically vary the lift and drag coefficients based upon relative wind (the vector sum of the actual wind and the direction of travel of the ball), spin rate, ball speed and/or ball design. In order to define launch efficiency, the computing devicecomputing device 14 of the embodiment described below makes use of a robust set of measurements of the club speed and impact position as well as the launch conditions of the ball in conjunction with the application of the governing equations of motion for golf club/impact and golf ball trajectory. However, the computing devicecomputing device of other embodiments may utilize only a subset of these parameters, such as the initial conditions measured following launch. By way of background, the collision between the clubhead having a swing speed Vc and ball can be modeled using conservation of momentum of rigid bodies as shown in Figure 2. The normal impulse of the collision P_N acts in the direction normal to the colliding surfaces of the clubhead and ball while the tangential impulse PT acts in the direction tangent to the colliding surfaces. Angle θ is defined as the spin loft, which is the angle between the velocity vector and the normal vector at the impact point. The impact position on the clubhead with respect to its center of gravity can be related by d^ which is the component in the normal direction and dj which is the component in the tangential direction. The impact position on the ball with respect to its center of gravity is its radius R_B. Assuming that the club is not spinning prior to impact and neglecting smaller terms that involve the product of both d^ and dj, the normal momentum PN is shown by Wang et al, "Two Dimensional Rigid-Body Collision with Friction." Journal of Applied Mechanics 59, M pp. 635-42 (1992), to be:

where me is mass of the club, me is mass of the ball, Vc is the velocity of the club at the time of impact, Ic is the moment of inertia of the club in the plane containing PN and P_T, and e is the coefficient of restitution defined as the velocity of separation (e.g., the relative velocity of the club and ball after impact in the normal direction) divided by the velocity of approach of club to the ball in the normal direction (e.g., the velocity of the club immediately prior to impact in the normal direction). Assuming there is no relative velocity or sliding in the tangential direction when contact ceases and by making the same assumptions and simplification as that of equation 1, the tangential momentum P_τcan be expressed as shown Wang et al, as:

P_τ (2)

where IB is the moment of inertia of the ball. In reality, different ball types have different spin characteristics due to the different material properties and the different types of layered constructions. In the foregoing equations me, m_©, and R_B are typically measured in advance and Vc, e, dχ₅ I_B and θ axe determined by the apparatus 10 and, more typically, the computing devicecomputing device 14 as known to those skilled in the art. The foregoing expressions are not intended to model the velocity and spin characteristics of different ball types, but are intended to relate the spin change and velocity change of a given ball for different club swing speeds and spin lofts. The post-impact velocity V_B and spin CO_B on the ball can then be calculated by the computing devicecomputing device 14 as:

Once contact is broken between the club and the golf ball, the ball experiences four types of forces while in flight which are gravity, drag, lift, and skin friction. The gravitational force is equal to the mass of the ball times the gravitational constant g and acts in the negative vertical direction. The drag force is caused by air resistance and acts in the direction opposite to that of the velocity vector of the ball. The lift force is caused primarily by the spinning of the golf ball and acts in the direction normal to the cross product of the spin vector and the velocity vector. Skin friction acts to slow down the spinning of the ball by applying a torque over surface of the ball in the negative direction to that of the spin vector. The trajectory equations of motion are described by Mizuta, et al. "3- Dimensional Trajectory Analysis of Golf Balls," Science and GoIfIV, pp. 349-58, Routledge, London (2002) and Winfield, et al, Optimization of the Clubface Shape of a Golf Driver to Minimize Dispersion of Off Center Shots, Computers and Structures, 58-6, pp. 1217-24 (1996). The equations of motion of golf ball trajectory are second order differential equations and can be numerically solved by the computing device 14 as a function of time by, for example, a Runge-Kutta integration scheme, as known to those skilled in the art. At each time step, the values for the drag and lift coefficient are calculated for the ball speed and spin rate. The lift and drag coefficients of various balls are generally determined in advance for different ball speeds and spin rates, such as a result of measurements in a wind tunnel and the method described by Beasley, et al. Effects of Dimple Design on the Aerodynamic Performance of a GoIfBaIl, Science and GoIfIV, pp 328-340, Routledge, London (2002). The numerical integration procedure will generally be carried out by the computing device until the golf ball lands. See, for example, Werner, et al., How Golf Clubs Really Work and How to Optimize Their Design, Origin Inc., Jackson (2000) for a technique for calculating the landing position of the ball. Thus, the carry or flight distance can be determined. See step 24 of Figure 3. Once the golf ball lands, the ball interacts with the ground so as to bounce and roll. As known to those skilled in the art, the amount of roll can also be determined, and, in turn, the total distance based on the sum of the carry and the roll. According to embodiments of the present invention, the computing device 14 determines a measure of launch efficiency (LE) based on the calculated distance of the golf shot D_B based, in turn, upon the measured launch conditions as described above, and the maximum possible distance that a ball could travel D_max for the measured club speed. Although D_B and D_max will be described in terms of the distance of the initial carry, D_B and D_max may, instead, include roll so as to be total distances. In one embodiment, the computing device 14 determines the measure of launch efficiency by forming a ratio of DB to D_max as follows: LE = D_B/D_max (5) However, the measure of launch efficiency may be defined in other manners based on D_B and D_max, if so desired. See, generally, step 28 of Figure 3. In order to determine D_max, the computing device 14 repeatedly determines D_max using the launch conditions of the ball and the governing equations of motion for the golf club/ball impact and golf ball trajectory as known to those skilled in the art for a club having the same measured club speed, but for varied launch angles of the ball >_© and/or varied spin rates O>_B (including both the actual launch angle and spin rate of the shot as well as other, different combinations of launch angle and spin rate). In this regard, the club speed is maintained the same as the club speed may be the most difficult parameter to change for a given club, while the swing path and impact position and, in turn, the launch angle and spin rate may be more readily changed in an effort to improve a golfer's launch efficiency. Generally speaking, to achieve maximum distance the ball has to have a relatively high launch angle and low spin rate. The computing device then selects the maximum value from among those calculated with different combinations of launch angle and spin rate to be D_max. See step 26 of Figure 3. It should be noted that for a given club, swing speed, and swing path, the resulting ball speed from impact varies as a function of spin loft and impact position. Therefore, the computing device 14 can determine different values of launch efficiency depending on the speed of the ball that is used to find D_max. For example, three ball speeds can be used to calculate D_max which are: (1) the value of measured ball speed, (2) the value of measured ball speed adjusted for the change in spin loft needed obtain the optimum ball spin (i.e., the ball spin that provides the maximum distance), and (3) the value of measured ball speed adjusted for the change in spin loft needed obtain the optimum ball spin and adjusted for the distance dxthat the ball missed the "sweetspot" of the club (i.e., the impact position on the clubface that creates the maximum ball speed). The foregoing definitions of launch efficiency will be referred to as first order, second order, and third order depending on which ball speed is used to find D_max. First order launch efficiency does not require adjustments to the measured ball speed or measurements of club speed and impact position. Second order launch efficiency requires measurement of club speed at the time of impact, while third order launch efficiency requires measurements of both club speed at the time of impact and impact position. The adjustment in ball speed for second and third order launch efficiency is done by the computing device 14 by first calculating the spin loft θ and coefficient of restitution e for the measured impact. The spin loft for the measured impact is calculated by substituting the tangential momentum of Equation 2 into the ball spin expression of Equation 5 and solving for θ where

θ = asin (RBVCX (6)

Using this calculation of spin loft and the measured ball speed, the value for P_T can be calculated by the computing device 14 and substituted into Equation 3 where the coefficient of restitution e for the measured impact can be calculated as:

wherein V_B is the velocity of the ball generally immediately following impact by the club. Third order launch efficiency is calculated by the computing device 14 using the measured value of dr while second order launch efficiency is calculated by assuming that dx is 0, which will result in a lower calculated value of e. It should be noted in the case of assuming that dj is 0, the value of e does not represent the coefficient of restitution but relates a reduction in normal momentum due to mishits. After calculating the optimum launch conditions to obtain D_max (e.g., the launch angle and spin rate that are determined to generate the maximum distance), the value of spin loft θ using that value of optimum spin rate is calculated by again using Equation 6. This new value of spin loft can now be used by the computing device 14 to calculate a new value of tangential momentum Px. Using the value of e calculated from the measured impact, a new value of normal momentum P_N is calculated from Equation 1. This assumes that the coefficient of restitution does not significantly change for the measured impact and launch conditions versus the optimal impact and launch conditions. In Equation 1, the value of dx is assumed to be equal to zero in order to calculate the fastest ball speed for the collision. The new ball speed for the optimum launch is then calculated using Equation 3. Using this new ball speed, the value of D_max can be calculated using the new value of ball speed. This assumes that the optimum launch angle and spin rate does not significantly change for the change in ball speed. It should also be pointed out that moment of inertia measurements Ic in the direction perpendicular to the normal and tangential directions are needed to calculate third order launch efficiency. If the complete inertia description of the club is not known, Ic can be assumed to be the inertia in the vertical direction of the clubhead. Also, the inertia of the ball I_B is used for both second and third order launch efficiency. If measurements for I_B are not known, it can be calculated as known to those skilled in the art assuming the ball has a uniform mass distribution. If the sensor 12 fails to capture swing speed measurements of the club, the second order launch efficiency can still be approximated. For a change in ball spin on two launches at the same club speed, there is a change in both the tangential momentum and normal momentum transfer to the ball. An assumption can be made where the change in ball speed is simply due to the change in tangential momentum where ΔV_B « (m_BR_B)-¹I_BΔω_B (8)

The value ΔV_B is simply added to the measured ball speed and the launch efficiency is calculated. It should be pointed out that ball speed is proportional to the vector addition of normal and tangential momentum. By not having club speed measurement, it is impossible to calculate values for normal and tangential momentum, but the launch efficiency can still be calculated by using ball speed as a proxy as a result of its proportional relationship. The index of launch efficiency was applied and used to analyze the game of various golfers and to club fitting. A launch monitor was used to measure the club swing and ball launch conditions. A computing device employing the foregoing trajectory model was used to calculate the distance the ball would travel and the calculations of launch efficiency were made. As an example, two players were tested using two clubs and the average club speed, impact location, and launch condition values for a series of shots are shown in the Table 1. The calculated values of distance D_B which is the average down range distance for the measured launch conditions are also shown. The values for coefficient of restitution e of Equation 7 are shown where the subscripts 2 and 3 refer to the calculation being for second order, and third order launch efficiency, respectively. Similarly, values for first, second, and third order launch efficiency are shown where the subscript refers to the order of the launch efficiency while LE_2* is the second order launch efficiency using Equation 8. The values for the spin G>_B are the vector sum of the backspin and sidespin measurements. Table 1 Testing Results Player 1 Player 1 Player 2 Player 2 Club l Club 2 Club l Club 2

Vc (mph) 96.1 96.6 112.0 111.5 dτ (in) 0.23 0.41 0.50 0.10 V_B (mph) 145.2 144.5 163.9 166.1 λ_B (deg) 10.71 9.87 11.83 8.93 ω_B (rpm) 2445 2574 3159 3468 D_B (yrd) 244.2 240.8 283.6 280.9 e₂ 0.777 0.762 0.728 0.767 e₃ 0.787 0.795 0.775 0.769 LE₁ 0.941 0.933 0.953 0.934 LE₂ 0.929 0.920 0.936 0.913 LE_2* 0.922 0.911 0.931 0.901 LE₃ 0.923 0.901 0.909 0.912

Player 1 when swinging Club 1 had a slower swing speed than when swinging Club 2 but had a more efficient launch as shown by all three values of launch efficiency. This would be a clear indication that Club 1 would be a better fit to Player 1 than Club 2. Player 2 swinging Club 1 had a greater distance D_B and a higher value of dx as well as a higher ball launch angle and lower spin rate when compared that of Club 2. So from a distance perspective and launch condition perspective, Club 1 launched the ball more efficiently than Club 2. This determination is validated by LE₁ and LE₂. However, when considering the impact position by calculating LE₃, Club 2 launched the ball more efficiently than that of Club 1. The fact that the impact position for Club 2 is much nearer the "sweetspot" than that of Club 1 means that Club 2 would result in more consistent shots than that of Club 1. Therefore, Player 2 would benefit from using Club 2 and by further working on their launch conditions. By combining the effect of the change in launch spin and impact position in calculating the performance aspects of the club, the third order launch efficiency may provide more insight into choosing a club. However, if the measurements of club speed and impact position are not available, the calculations of first order launch efficiency and LE_2* are useful in relating the performance based on the ball launch condition. The values of LE_2* tend to be lower than that LE₂. This may be due to the fact that Equation 8 may overcorrect ball velocity based on change in spin. Overall, the values of launch efficiency determined by the method and apparatus of embodiments of the present invention are useful in comparing the performance of clubs. It also gives the player an idea of how much more distance they can gain by altering his launch condition and hitting the "sweetspot" of the club. Another useful calculation is the value of e which basically relates the efficiency of the impact between the ball and club. This value can help in comparing the spring-like effect between two drivers or in the resiliency of two balls assuming the player has similar swing speeds and impact position for the comparison.

2. Human Performance Analysis Turning now to another aspect of the present invention which will be primarily described in conjunction with golf and, more particularly, in conjunction with golf club fittings, the apparatus, method and computer program product of this aspect can be employed in conjunction with the analysis of other human performance statistics. In the context of club fitting, however, a golfer takes a number of shots with each of a plurality of clubs, hi order to analyze the golf shots so as to fit a golf club or set of golf clubs to the golfer's swing, a number of parameters that define each golf shot are collected. The apparatus 10 of one embodiment therefore includes a launch monitor as shown in Figure 1 and as described in above-referenced U.S. Patent Application No. 10/360,196 to collect the parameters. While various parameters may be collected and analyzed, the apparatus, method and computer program product will be described to define golf shots in terms of downrange distance and offline distance. As shown in Figure 1 and as described above, the apparatus of one embodiment includes a sensor 12 to measure a plurality of initial conditions including initial ball velocity, vertical launch angle, lateral launch angle, dispersion angle, backspin, and side spin. Although not necessary for the present invention, the sensor may also include a conventional club head sensor, if desired to collect club swing parameters. The apparatus 10 also includes a computing device 14 for thereafter determining the flight path of the ball at least partially based upon the initial conditions including the measurement of the sidespin as described above. In this regard, the computing device can determine the flight path of the ball in accordance with a predefined flight model that relies upon the initial conditions including sidespin for its modeling activities. The launch monitor and, in particular, the computing device can then determine additional parameters, such as downrange distance and offline distance based on the flight model and the measured data. While a launch monitor as described above is advantageous, the apparatus 10 can collect and/or determine the parameters that define the golf shots in other manners, such as by means of a distance determining system as noted above. The computing device 14 constructs an initial data set, as noted in step 50 of Figure 4, that includes data elements representing the parameters that define each golf shot. In the example in which downrange distance and offline distance are the parameters that define each golf shot, the initial data set could contain the downrange distance and offline distance for each golf shot. While the initial dataset will be described as including both the downrange distance and offline distance values, separate data sets can be established for the downrange distance and for the offline distance, if so desired. The computing device 14 then identifies outliers in the initial data set. See step 52. Outliers are generally defined as values that vary significantly from a majority of the other data elements, hi one embodiment, outliers are defined as a predetermined number of the largest and/or smallest values of a particular parameter that are included in the initial data set, without consideration for the variation of the outliers from the remainder of the data elements. In the foregoing example in which the predetennined number is 1, the largest and smallest values of downrange distance and the largest and smallest values of the offline distance are identified as outliers. The outliers may be placed in an outlier data set, while the data elements remaining from the initial data set following removal of the outliers constitute a representative data set. See step 54. The computing device may define the outliers in other fashions if desired. For example, an outlier may be defined to be any value that deviates from the average of the initial data set by more than x%. The computing device 14 then determines a measure of deviation, such as standard deviation, of the representative data set and, more generally, of each different parameter included within the representative data set. See block 56. hi the foregoing example, the computing device can determine the standard deviation of the downrange distance values in the representative data set and the standard deviation of the offline distance values in the representative data set. The computing device can also determine the mean of each different parameter included in the representative data set, such as the mean of the downrange distance values in the representative data set and the mean of the offline distance values in the representative dataset. See also step 56. The computing device 14 then filters the initial data set based at least partially upon the measure of deviation, such as standard deviation, of the representative data set to create a filtered data set. In this regard, for each different parameter in the initial dataset, e.g., downrange distance and offline distance, the upper limit of the filter may be determined by summing the mean and the standard deviation of the respective parameter. Conversely, the lower limit of the filter may be determined by subtracting the standard deviation from the mean of the respective parameter. See block 58. The data elements of the initial data set are then examined, such as by the computing device 14, to determine if the respective data element is between the upper and lower limits established for the respective parameter. If so, the data element is included in the filtered dataset while, if not, the data element is not included in the filtered dataset. See block 60. For example, each downrange distance value in the initial dataset may be evaluated to determine if the downrange distance value is between the upper and lower limits on downrange distance and, if so, the downrange distance value is included in the filtered dataset. Likewise, each offline distance value in the initial dataset is separately analyzed to determine if it is between the upper and lower limits on offline distance and, if so, the offline distance value is included in the filtered dataset. The human performance can then be analyzed based upon the filtered dataset. See step 62. In the foregoing example, the golfer's swing can be analyzed based on the value of downrange distance and offline distance included in the filtered data set. hi this regard, a trained fitter can review the filtered dataset and fit the golfer with appropriate golf club(s). Alternatively, the filtered dataset can be provided to a conventional club fitting software application, such as the applications developed by some club manufacturers, for identifying an appropriate golf club or set of golf clubs for the golfer. By removing outliers prior to determining the deviation, such as the standard deviation of the data, the deviation (and generally the mean as well) more accurately represent the subject's performance and therefore permit the human performance to be more accurately analyzed. Additionally, by determining the bounds of the data filter after removing the outliers, but then filtering the entire initial dataset, the apparatus 10 and method of the present invention continue to analyze all representative values including any values previously identified as being an outlier that falls between the upper and lower bounds of the filter, thereby ensuring that the apparatus and method of embodiments of the present invention are robust. The apparatus 10 and method of embodiments of the present invention are capable of being repeated following the collection of each additional data element, such as following each shot. As such, the method and apparatus and, more typically, the computing device 14 can monitor the size of the representative dataset and provide the subject with a signal, such as an image upon a display, once the representative dataset is large enough to be a reasonable statistical sample of the subject's true performance, e.g., once enough shots with a respective club have been taken. The computing device may determine that the representative dataset is large enough in various manners including a comparison to a predetermined threshold, such as three shots in the club hitting scenario, or by a determination that some statistical measure of the representative dataset, such as the mean or standard deviation, is no longer changing by more than a predefined amount from shot to shot. Thus, the computing device of this embodiment can signal the subject to proceed to the next stage, such as by switching clubs, once the representative dataset is determined to be large enough prior to the subject becoming significantly fatigued. Thus, Sithe method and apparatus of this embodiment facilitates data collection in such a manner that the data should not suffer from variations introduced by the fatigue of the subject.

3. Simulation with Sidespin According to yet another aspect of the present invention, a system 10 for simulating a flight path of a ball is provided. While the system and method will be primarily described in conjunction with golf simulation in which a golfer hits into a screen, a net or other means for limiting the flight path of the ball, the system and method may be employed in conjunction with the simulation of a number of other sports activities including the simulation of the flight path of a ball thrown by a pitcher or a ball hit by a batter in the baseball or softball context. hi the context of golf simulation, however, a golfer takes a shot, typically into a hitting net as described above. As shown again by Figure 1, the system 10 of embodiments of the present invention includes a sensor 12 to measure a plurality of initial conditions including initial ball velocity, vertical launch angle, lateral launch angle and sidespin, as well as back spin in some embodiments. See, for example, step 30 of Figure 6. Although, not necessary for the present invention, the sensor may also include a conventional club head sensor, if desired to capture club swing parameters. The system 10 also includes a computing device 14 for determining the flight path of the ball at least partially based upon the initial conditions including the measurement of the sidespin. See step 32 of Figure 6. In this regard, the computing device can determine the flight path of the ball in accordance with a predefined flight model that relies upon the initial conditions including sidespin for its modeling activities. The computing device 14 then creates a representation of the resulting flight path. See step 34 of Figure 6. In a simulation environment, the representation is generally an image of the resulting flight path along with accompanying statistics such as carry, roll, total distance and lateral distance, i.e., distance to the left or right. However, the computing device may merely represent the resulting flight path by means of the foregoing or other parameters that are displayed for the golfer and/or stored for subsequent analysis. In order to present the representation of the flight path that has been created by the computing device to the user, the system 10 may also include a display 18, such as a display screen or a projector, such as an LCD projector, that is driven by the computing device 14. As shown in Figure 5, the display can present an image of the flight path along with some accompanying statistics. See step 36 of Figure 6. Notably, the system and method of embodiments of the present invention measure sidespin and then determine that flight path based upon the measured sidespin such that the resulting flight path more realistically exhibits a hook or slice, thereby enhancing the user's simulation experience. As shown in Figure 5, the ball started to the right, but then moved right to left attributable, at least in part, to side spin. While a conventional simulator would likely have shown this same shot to have stayed to the right, the system and method of embodiments of the present invention more accurately reflect the effect of sidespin upon the flight path which curves back to the left in Figure 5. In addition to presenting an image of the flight path, the system 10 is advantageously also capable of presenting a simulated environmental image, such as an image of a portion of a golf course with the flight path superimposed thereupon. In this regard, the memory 16 may store data representative of images one or more golf courses or, at least, one or more holes of a golf course. Prior to the golfer taking a shot that will be simulated by the system of this embodiment of the present invention, the computing device 14 may drive the display 18 based upon data retrieved from the memory to present an image of that portion of the golf course from which the simulated golf shot is considered to have been taken, such as a tee box, a position on the fairway, etc. The golfer can then take a shot that is monitored by the sensor 12. Based upon the initial conditions captured by the sensor, the computing device can create a representation of the flight path of the golf shot and can then direct the display to present an image of the flight path of the golf shot. To enhance the simulation environment, the computing device can also retrieve data from the memory that represents that portion of the golf course over which the simulated golf shot traveled and can further drive the display to depict an image of that portion of the golf course over which the simulated golf shot carried. See step 38 of Figure 6. Li this regard, the computing device determines the portion of the golf course to be displayed based upon the flight path that has been created The resulting display can thereafter be driven by the computing device to depict the resting position of the golf ball from which the next simulated shot will be taken.

4. Computer Program Product According to one aspect of the present invention, the functions performed by the computing device 14 are performed under control of a computer program product. The computer program product of embodiments of the present invention includes a computer-readable storage medium, such as memory 16, and computer- readable program code portions, such as a series of computer instructions, embodied in the computer-readable storage medium. In this regard, Figures 3, 4 and 6 are examples of a flow diagram of the methods and computer program products according to the various embodiments of the present invention. It will be understood that each block or step of the flowchart, and combinations of blocks in the flowchart, can be implemented by computer program instructions. These computer program instructions may be loaded onto a computer or other programmable apparatus 14 to produce a machine, such that the instructions which execute on the computer or other programmable apparatus create means for implementing the functions specified in the flowchart's block(s) or step(s). These computer program instructions may also be stored in a computer-readable memory 16 that can direct a computer or other programmable apparatus to function in a particular manner, such that the instructions stored in the computer-readable memory produce an article of manufacture including instruction means which implement the function specified in the flowchart's block(s) or step(s). The computer program instructions may also be loaded onto a computer or other programmable apparatus to cause a series of operational steps to be performed on the computer or other programmable apparatus to produce a computer implemented process such that the instructions which execute on the computer or other programmable apparatus provide steps for implementing the functions specified in the flowcharts' block(s) or step(s). Accordingly, blocks or steps of the flowcharts support combinations of means for performing the specified functions, combinations of steps for performing the specified functions and program instruction means for performing the specified functions. It will also be understood that each block or step of the flowcharts, and combinations of blocks or steps in the flowcharts, can be implemented by special purpose hardware-based computer systems which perform the specified functions or steps, or combinations of special purpose hardware and computer instructions. Many modifications and other embodiments of the inventions set forth herein will come to mind to one skilled in the art to which these inventions pertain having the benefit of the teachings presented in the foregoing descriptions and the associated drawings. Therefore, it is to be understood that the inventions are not to be limited to the specific embodiments disclosed and that modifications and other embodiments are intended to be included within the scope of the appended claims. Although specific terms are employed herein, they are used in a generic and descriptive sense only and not for purposes of limitation.

Claims

THAT WHICH IS CLAIMED: 1. A method of obtaining a measure of launch efficiency of a ball, the method comprising: determining a calculated distance of travel of the ball based upon measured launch conditions of the ball; determining a maximum distance of travel of the ball upon being struck by a club having any combination of launch angle and spin rate; and determining the measure of launch efficiency based upon the calculated distance of travel and the maximum distance of travel.

2. A method according to Claim 1 wherein the measured launch conditions comprise a measured club speed, and wherein determining the maximum distance of travel comprises determining the maximum distance of travel for a ball struck by a club having the measured club speed.

3. A method according to Claim 1 wherein the measured launch conditions comprise a measured ball speed, and wherein determining the maximum distance of travel comprises determining the maximum distance of travel of a ball having the measured ball speed.

4. A method according to Claim 1 wherein the measured launch conditions comprise a measured ball speed, and wherein determining the maximum distance of travel comprises determining the maximum distance of travel of a ball having a ball speed based upon the measured ball speed as adjusted for any change in spin loft necessary to obtain an optimum ball spin.

5. A method according to Claim 1 wherein the measured launch conditions comprise a measured ball speed, and wherein determining the maximum distance of travel comprises determining the maximum distance of travel of a ball having a ball speed based upon the measured ball speed as adjusted for any change in spin loft necessary to obtain an optimum ball spin and as further adjusted for a distance that the ball is offset from a predefined impact position on the club.

6. A method according to Claim 1 wherein determining the measure of launch efficiency comprises forming a ratio of the calculated distance of travel and the maximum distance of travel.

7. An apparatus for obtaining a measure of launch efficiency of a ball, the apparatus comprising: a computing device capable of: determining a calculated distance of travel of the ball based upon measured launch conditions of the ball; determining a maximum distance of travel of the ball upon being struck by a club having any combination of launch angle and spin rate; and determining the measure of launch efficiency based upon the calculated distance of travel and the maximum distance of travel.

8. An apparatus according to Claim 7 wherein the measured launch conditions comprise a measured club speed, and wherein said computing device is capable of determining the maximum distance of travel by determining the maximum distance of travel for a ball struck by a club having the measured club speed.

9. An apparatus according to Claim 7 wherein the measured launch conditions comprise a measured ball speed, and wherein said computing device is capable of determining the maximum distance of travel by determining the maximum distance of travel of a ball having the measured ball speed.

10. An apparatus according to Claim 7 wherein the measured launch conditions comprise a measured ball speed, and wherein said computing device is capable of determining the maximum distance of travel by determining the maximum distance of travel of a ball having a ball speed based upon the measured ball speed as adjusted for any change in spin loft necessary to obtain an optimum ball spin.

11. An apparatus according to Claim 7 wherein the measured launch conditions comprise a measured ball speed, and wherein said computing device is capable of determining the maximum distance of travel by determining the maximum distance of travel of a ball having a ball speed based upon the measured ball speed as adjusted for any change in spin loft necessary to obtain an optimum ball spin and as further adjusted for a distance that the ball is offset from a predefined impact position on the club.

12. An apparatus according to Claim 7 wherein said computing device is capable of determining the measure of launch efficiency by forming a ratio of the calculated distance of travel and the maximum distance of travel.

13. A computer program product for obtaining a measure of launch efficiency of a ball, the computer program product comprising at least one computer-readable storage medium having computer-readable program code portions stored therein, the computer-readable program code portions comprising: a first executable portion capable of determining a calculated distance of travel of the ball based upon measured launch conditions of the ball; a second executable portion capable of determining a maximum distance of travel of the ball upon being struck by a club having any combination of launch angle and spin rate; and a third executable portion capable of determining the measure of launch efficiency based upon the calculated distance of travel and the maximum distance of travel.

14. A computer program product according to Claim 13 wherein the measured launch conditions comprise a measured club speed, and wherein said second executable portion is further capable of determining the maximum distance of travel for a ball struck by a club having the measured club speed.

15. A computer program product according to Claim 13 wherein said third executable portion is further capable of determining the measure of launch efficiency by forming a ratio of the calculated distance of travel and the maximum distance of travel.

16. A method of obtaining a measure of launch efficiency of a ball, the method comprising: determining a calculated distance of travel of the ball based upon measured launch conditions of the ball including a measured club speed; determining a maximum distance of travel of the ball upon being struck by a club having the measured club speed; and determining the measure of launch efficiency based upon the calculated distance of travel and the maximum distance of travel.

17. A method according to Claim 16 wherein determining the maximum distance of travel comprises varying at least one of a launch angle of the ball and a spin rate of the ball for a ball struck by a club having the measured club speed.

18. A method according to Claim 16 wherein determining the measure of launch efficiency comprises forming a ratio of the calculated distance of travel and the maximum distance of travel.

19. An apparatus of obtaining a measure of launch efficiency of a ball, the apparatus comprising: a computing device capable of: determining a calculated distance of travel of the ball based upon measured launch conditions of the ball including a measured club speed; determining a maximum distance of travel of the ball upon being struck by a club having the measured club speed; and determining the measure of launch efficiency based upon the calculated distance of travel and the maximum distance of travel.

20. An apparatus according to Claim 19 wherein said computing device is capable of determining the maximum distance of travel by varying at least one of a launch angle of the ball and a spin rate of the ball for a ball struck by a club having the measured club speed.

21. An apparatus according to Claim 16 wherein said computing device is capable of determining the measure of launch efficiency by forming a ratio of the calculated distance of travel and the maximum distance of travel.

22. A method of automatically analyzing human performance as defined by an initial data set comprised of a plurality of data elements, the method comprising: removing at least one data element that constitutes an outlier from the initial data set to create a representative date set; determining a measure of deviation of the representative data set; filtering the initial data set based at least partially upon the measure of deviation of the representative data set to create a filtered data set; and analyzing the human performance based at least partially upon the filtered data set.

23. A method according to Claim 22 wherein analyzing the human performance comprises analyzing a golf shot.

24. A method according to Claim 23 wherein analyzing the golf shot comprises analyzing a downrange distance of the golf shot.

25. A method according to Claim 23 wherein analyzing the golf shot comprises analyzing an offline distance of the golf shot.

26. A method according to Claim 22 further comprising capturing the plurality of data elements that comprise the initial data set.

27. A method according to Claim 26 wherein capturing the plurality of data elements comprises capturing the plurality of data elements from among initial conditions and club swing parameters associated with a golf shot.

28. A method according to Claim 22 wherein removing at least one outlier comprises removing a predetermined number of the largest and smallest data elements from the initial data set to create the representative data set.

29. A method according to Claim 22 wherein determining the measure of deviation comprises determining a measure of standard deviation of the representative data set.

30. An apparatus for analyzing human performance as defined by an initial data set comprised of a plurality of data elements, the apparatus comprising: a computing device capable of: removing at least one data element that constitutes an outlier from the initial data set to create a representative date set; determining a measure of deviation of the representative data set; filtering the initial data set based at least partially upon the measure of deviation of the representative data set to create a filtered data set; and analyzing the human performance based at least partially upon the filtered data set.

31. An apparatus according to Claim 30 wherein said computing device is capable of analyzing a golf shot.

32. An apparatus according to Claim 31 wherein said computing device is capable of analyzing a downrange distance of the golf shot.

33. An apparatus according to Claim 31 wherein said computing device is capable of analyzing an offline distance of the golf shot.

34. An apparatus according to Claim 30 further comprising a sensor for capturing the plurality of data elements that comprise the initial data set.

35. An apparatus according to Claim 34 wherein said sensor comprises a launch monitor for capturing the plurality of data elements from among initial conditions and club swing parameters associated with a golf shot.

36. An apparatus according to Claim 30 wherein said computing device is capable of removing at least one outlier by removing a predetermined number of the largest and smallest data elements from the initial data set to create the representative data set.

37. An apparatus according to Claim 30 wherein said computing device is capable of determining the measure of deviation by determining a measure of standard deviation of the representative data set.

38. A computer program product for analyzing human performance as defined by an initial data set comprised of a plurality of data elements, the computer program product comprising at least one computer-readable storage medium having computer-readable program code portions stored therein, the computer-readable program code portions comprising: a first executable portion capable of removing at least one data element that constitutes an outlier from the initial data set to create a representative date set; a second executable portion capable of determining a measure of deviation of the representative data set; a third executable portion capable of filtering the initial data set based at least partially upon the measure of deviation of the representative data set to create a filtered data set; and a fourth executable portion capable of analyzing the human performance based at least partially upon the filtered data set.

39. A computer program product according to Claim 38 wherein said fourth executable portion is further capable of analyzing a golf shot.

40. A computer program product according to Claim 39 wherein said fourth executable portion is further capable of analyzing a downrange distance of the golf shot.

41. A computer program product according to Claim 39 wherein said fourth executable portion is further capable of analyzing an offline distance of the golf shot.

42. A method for simulating a flight path of a ball comprising: measuring a plurality of initial conditions of the ball including sidespin of the ball; determining the flight path of the ball at least partially based upon the initial conditions including measurement of the sidespin; and creating a representation of the resulting flight path.

43. A method according to Claim 42 wherein measuring the plurality of initial conditions comprises measuring backspin of the ball, and wherein determining the flight path of the ball comprises determining the flight path of the ball based upon measurement of the backspin.

44. A method according to Claim 42 further comprising presenting an image of the resulting flight path.

45. A method according to Claim 42 further comprising: creating a simulated environmental image based upon the resulting flight path; and presenting the simulated environmental image concurrent with the image of the resulting flight path.

46. A method according to Claim 42 wherein measuring the plurality of initial conditions comprises capturing at least two images of the ball.

47. A method according to Claim 42 further comprising limiting the flight path of the ball.

48. A system for simulating a flight path of a ball comprising: a sensor for measuring a plurality of initial conditions of the ball including sidespin of the ball; and a computing device for determining the flight path of the ball at least partially based upon the initial conditions including measurement of the sidespin, said computing device also creating a representation of the resulting flight path.

49. A system according to Claim 48 wherein said sensor comprises at least one camera for capturing at least two images of the ball.

50. A system according to Claim 48 wherein said sensor also measures backspin of the ball, and wherein said computing device is capable of determining the flight path of the ball based upon measurement of the backspin.

51. A system according to Claim 48 further comprising a display, responsive to said computing device, for presenting an image of the resulting flight path.

52. A system according to Claim 51 further comprising a memory for storing data representative of simulated environmental images, wherein said computing device is also capable of creating a simulated environmental image based upon the resulting flight path, and wherein said display is also capable of presenting the simulated environmental image concurrent with the image of the resulting flight path.

53. A system according to Claim 48 further comprising at least one of a screen or a net into which the ball is hit.

54. A computer program product for simulating a flight path of a ball, the computer program product comprising at least one computer-readable storage medium having computer-readable program code portions stored therein, the computer-readable program code portions comprising: a first executable portion capable of receiving measurements of a plurality of initial conditions of the ball including sidespin of the ball; a second executable portion capable of determining the flight path of the ball at least partially based upon the initial conditions including measurement of the sidespin; and a third executable portion capable of creating a representation of the resulting flight path.

55. A computer program product according to Claim 54 wherein said first executable portion is further capable of receiving a measurement of backspin of the ball, and wherein said second executable portion is further capable of determining the flight path of the ball based upon measurement of the backspin.

56. A computer program product according to Claim 54 further comprising a fourth executable portion capable of driving a display to present an image of the resulting flight path.

57. A computer program product according to Claim 56 further comprising: a fifth executable portion capable of creating a simulated environmental image based upon the resulting flight path; and a sixth executable portion capable of driving a display to present the simulated environmental image concurrent with the image of the resulting flight path.