US20060030431A1

US20060030431A1 - Apparatus, method and computer program product for obtaining a measure of launch efficiency

Info

Publication number: US20060030431A1
Application number: US11/158,824
Authority: US
Inventors: David Rankin; Douglas Winfield
Original assignee: AccuSport International Inc
Current assignee: AccuSport International Inc
Priority date: 2004-06-22
Filing date: 2005-06-22
Publication date: 2006-02-09

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. The method, apparatus and computer program product determine a calculated distance of travel of a ball based upon the measured launch conditions that may include the measured club speed. A maximum distance of travel of the ball is then determined. The maximum distance of travel may be determined for a ball struck by a club having the measured club speed and/or for a ball struck by a club having different launch angles and/or spin rate. 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.

Description

CROSS-REFERENCE TO RELATED APPLICATION(S)

The present application claims priority from U.S. Provisional Application No. 60/581,991, filed Jun. 22, 2004 and entitled Apparatus and Method for Obtaining a Measure of Launch Efficiency, the contents of which are incorporated herein by reference.

FIELD OF THE INVENTION

The present invention relates generally to techniques for obtaining a measure of the launch efficiency of an object, such as a golf ball.

BACKGROUND OF THE INVENTION

An important aspect in the golf equipment and teaching industry is to provide the golfer with equipment that best fits his game (club fitting) and to provide insights on how to improve (game analysis). In 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. Further details regarding launch monitors are provided by U.S. patent application Ser. No. 10/360,196 filed Feb. 7, 2003 entitled “Methods, Apparatus and Computer Program Products for Processing Images of a Golf Ball,” the contents of which are incorporated herein in their entirety. 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.

SUMMARY OF THE INVENTION

A method, apparatus and computer program product are therefore provided according to one embodiment 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.
In 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.
In the apparatus embodiment, a processing element 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.

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:
FIG. 1 is a block diagram of an apparatus according to one embodiment of the present invention;
FIG. 2 is a schematic representation of a club head and ball upon impact; and
FIG. 3 is a flow chart of operations according to 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.
An apparatus 10 for obtaining a measure of launch efficiency is shown in FIG. 1. The apparatus includes a launch monitor as generally described by the above-referenced U.S. patent application Ser. No. 10/360,193. In 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 FIG. 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 FIG. 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 processing element 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 processing element 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 processing element 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 processing element 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 processing element 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 V_Cand ball can be modeled using conservation of momentum of rigid bodies as shown in FIG. 2. The normal impulse of the collision P_Nacts in the direction normal to the colliding surfaces of the clubhead and ball while the tangential impulse P_Tacts 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_Nwhich is the component in the normal direction and d_Twhich 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_Nand d_T, the normal momentum P_Nis shown by Wang et al, “Two Dimensional Rigid-Body Collision with Friction.” Journal of Applied Mechanics 59, M pp. 635-42 (1992), to be: $\begin{matrix} P_{N} = (1 + e) V_{C} \cos {θ (\frac{1}{m_{C}} + \frac{1}{m_{B}} + \frac{d_{T}^{2}}{I_{C}})}^{- 1} & (1) \end{matrix}$
where m_Cis mass of the club, m_Bis mass of the ball, V_Cis the velocity of the club at the time of impact, I_Cis the moment of inertia of the club in the plane containing P_Nand 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_Tcan be expressed as shown Wang et al, as: $\begin{matrix} P_{T} = V_{C} \sin {θ (\frac{1}{m_{C}} + \frac{1}{m_{B}} + \frac{R_{B}^{2}}{I_{B}})}^{- 1} & (2) \end{matrix}$
where I_Bis 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 m_C, m_B, and R_Bare typically measured in advance and V_C, e, d_T, I_Band θ are determined by the apparatus 10 and, more typically, the processing element 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_Band spin ω_Bon the ball can then be calculated by the processing element 14 as:
V_B=m_B ⁻¹√{square root over (P_N ²+P_T ²)} and ω_B=I_B ⁻¹(R_BP_T) (3 and 4)
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 Golf IV, 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 processing element 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 Golf Ball, Science and Golf IV, pp 328-340, Routledge, London (2002).
The numerical integration procedure will generally be carried out by the processing element 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 FIG. 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 processing element 14 determines a measure of launch efficiency (LE) based on the calculated distance of the golf shot D_Bbased, in turn, upon the measured launch conditions as described above, and the maximum possible distance that a ball could travel D_maxfor the measured club speed. Although D_Band D_maxwill be described in terms of the distance of the initial carry, D_Band D_maxmay, instead, include roll so as to be total distances.
In one embodiment, the processing element 14 determines the measure of launch efficiency by forming a ratio of D_Bto D_maxas follows:
LE=D_B/D_max (5)
However, the measure of launch efficiency may be defined in other manners based on D_Band D_max, if so desired. See, generally, step 28 of FIG. 3.
In order to determine D_max, the processing element 14 repeatedly determines D_maxusing 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 λ_Band/or varied spin rates ω_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 processing element 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 FIG. 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 processing element 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_maxwhich 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 d_Tthat 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 processing element 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 $\begin{matrix} θ = a \sin [{(R_{B} V_{C})}^{- 1} ω_{B} I_{B} (\frac{1}{m_{C}} + \frac{1}{m_{B}} + \frac{R_{B}^{2}}{I_{B}})] & (6) \end{matrix}$
Using this calculation of spin loft and the measured ball speed, the value for P_Tcan be calculated by the processing element 14 and substituted into Equation 3 where the coefficient of restitution e for the measured impact can be calculated as: $\begin{matrix} e = {(V_{C} \cos θ)}^{- 1} (\frac{1}{m_{C}} + \frac{1}{m_{B}} + \frac{d_{T}^{2}}{I_{C}}) \sqrt{{(V_{B} m_{B})}^{2} - P_{T}^{2}} - 1 & (7) \end{matrix}$
wherein V_Bis the velocity of the ball generally immediately following impact by the club.
Third order launch efficiency is calculated by the processing element 14 using the measured value of d_Twhile second order launch efficiency is calculated by assuming that d_Tis 0, which will result in a lower calculated value of e. It should be noted in the case of assuming that d_Tis 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 processing element 14 to calculate a new value of tangential momentum P_T. Using the value of e calculated from the measured impact, a new value of normal momentum P_Nis 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 d_Tis 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_maxcan 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 I_Cin 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, I_Ccan be assumed to be the inertia in the vertical direction of the clubhead. Also, the inertia of the ball I_Bis used for both second and third order launch efficiency. If measurements for I_Bare 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_Bis 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 processing element 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_Bwhich 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 ω^Bare the vector sum of the backspin and sidespin measurements.

TABLE 1


Testing Results

Player 1	Player 1	Player 2	Player 2
Club 1	Club 2	Club 1	Club 2

V_C(mph)	96.1	96.6	112.0	111.5
d_T(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_Band a higher value of d_Tas 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 LE₁and 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.
According to one aspect of the present invention, the functions performed by the processing element 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, FIG. 3 is an example of a flow diagram of one embodiment of the methods and computer program products according to 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

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 processing element capable of:

8. An apparatus according to claim 7 wherein the measured launch conditions comprise a measured club speed, and wherein said processing element 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 processing element 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 processing element 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 processing element 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 processing element 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

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 processing element capable of:

20. An apparatus according to claim 19 wherein said processing element 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 processing element 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.