US20010034279A1

Movatterモバイル変換

Info

Publication number: US20010034279A1
Application number: US09/766,165
Authority: US
Inventors: Thomas Veilleux; Matthew Lacroix; Ronald LaLiberty; Ken Brown; John Axe
Original assignee: Top Flite Golf Co
Current assignee: Russell Asset Management Inc
Priority date: 1999-10-14
Filing date: 2001-01-19
Publication date: 2001-10-25
Also published as: WO2002060542A1

Abstract

A sport ball having an internal device such as an internal pump has a critical ratio that insures that rebound characteristics or coefficient of restitution of the ball, such as a basketball, will be acceptable for use. The invention also includes the method for evaluating design and/or quality control of a sport ball by measuring the internal vibration and determining the critical ratio of the sport ball.

Description

RELATED APPLICATIONS

This application is a Continuation-in-Part of and claims the benefit of U.S. patent application Serial No. 09/594,980, filed Jun. 15, 2000. That application is a Continuation-in-Part of and claims the benefit of U.S. patent application Ser. No. 09/478,225, filed Jan. 6, 2000, and further claims the benefit of U.S. Provisional Application No. 60/159,311, filed Oct. 14, 1999.[0001]

The applicant also claims priority based on a provisional U.S. patent application Ser. No. 60/252,443, filed Nov. 21, 2000 entitled “Avoidance of Resonance in the Inflatable Sport Ball by Limiting the Critical Ratio.”[0002]

FIELD OF THE INVENTION

The present invention relates to sport or game balls, preferably inflatable sport balls, and more preferably, inflatable sport balls with a mechanism for inflating or adding pressure to the ball, or other internal device, inside the ball.[0003]

BACKGROUND OF THE INVENTION

The present invention relates to all inflatable sport balls including those that contain pump mechanisms for inflating or adding pressure to the balls, or which contain another internal device within the ball. The mechanism for inflating or adding pressure to the ball is preferably a pump. Examples of other internal devices, referred to herein as components, which may be self-contained in the sport balls include, but are not limited to, a storage container, a flashlight, a key holder, a watch, and the like. In some cases, such balls have an inherent asymmetric construction. Even if a counterweight is positioned at a directly opposite portion of the ball from the pump mechanism or other component, the ball assembly still is asymmetric when considered from other axes.[0004]

Conventional inflatable sport balls, such as basketball, footballs, soccer balls, volleyballs and playground balls, are inflated through a traditional inflation valve using a separate inflation needle that is inserted into a self-sealing inflation valve. A separate pump, such as a traditional bicycle pump, is connected to the inflation needle and the ball is inflated using the pump. The inflation needle is then withdrawn from the inflation valve that self-seals to maintain the pressure. This system works fine until the sport ball needs inflation or a pressure increase and a needle and/or pump are not readily available.[0005]

Internal vibration in a sport ball may adversely affect the performance of the sport ball. For example, a basketball with vibration problems may not dribble or bounce consistently, and a soccer ball may roll or travel inconsistently or away from the intended target when kicked or thrown. If the sport ball is a sport ball with a self contained inflation mechanism, such as a pump, or other internal device, there is an increased potential for vibration problems due to the added internal component. One of the worst internal vibration problems is a condition called resonance. Resonance, as used herein, is when the impact loading of an object, such as a ball, occurs in tune with the object's natural frequency of vibration. The natural frequency of the ball is the frequency that the ball oscillates at in the absence of external forces. There is a need for a method to measure this vibration and minimize it in the final product so that the consumer does not notice the vibration. Examples of sport balls which may be affected include, but are not limited to, any inflatable sport ball such as a basketball, volleyball, soccer ball, football, playground ball or other inflated ball.[0006]

SUMMARY OF THE INVENTION

An object of the invention is to provide a sport ball having an internal pump, wherein the ball exhibits the same degree of bounce consistency when dropped repeatedly with various orientations as a corresponding sport ball that does not include an internal pump.[0007]

Another object of the invention is to provide a method of measuring the bounce consistency of a sport ball.[0008]

The present invention is directed to a sport ball having an internal device, whereby the sport ball having the internal device conforms to the same specifications as a corresponding sport ball that does not contain an internal device. The invention achieves the above-noted objectives and provides a method for measuring the internal vibration and determining the critical ratio of a sport ball, thereby enabling the design of a sport ball with internal device, wherein the ball is suitable for use in competitive play.[0009]

One preferred form of the invention is a sport ball comprising a self-contained inflation mechanism, wherein said sport ball comprising a self-contained inflation mechanism has substantially the same rebound characteristics as a corresponding sport ball that does not comprise a self-contained inflation mechanism. The self-contained inflation mechanism preferably is a pump.[0010]

The sport ball preferably is hollow, but also can contain a foam or other material. The ball can be a regulation or youth size basketball, soccer ball, football, volley ball or playground ball. The ball preferably comprises a cover formed from a material selected from the group consisting of leather, synthetic leather, composites, rubber materials, and combinations thereof.[0011]

Methods of characterizing the rebound characteristics of the ball include, but are not limited to, coefficient of restitution (COR), rebound height, rebound consistency, and critical ratio. A basketball comprising a self-contained inflation mechanism according to the invention preferably has a coefficient of restitution range of 0.750-0.813 when tested repeatedly at different ball orientations, combined with a difference between the maximum and minimum coefficient of restitution values of 0.051 or less. In another preferred form of the invention, the difference between the maximum and minimum coefficient of restitution values is 0.036 or less. When described by rebound height, a basketball of the invention has a rebound height of 50-57 inches when dropped on a wooden floor from a height of 72 inches. The difference between the maximum and minimum rebound heights when the ball is dropped repeatedly with different orientations is 5.5 inches or less and more preferably 4 inches or less. In another preferred form of the invention, the basketball has a rebound height of 50-54 inches when dropped on a wooden floor from a height of 72 inches.[0012]

In a preferred form of the invention, the sport ball having a self-contained inflation mechanism has a minimum critical ratio which is substantially the same as the critical ratio of a corresponding sport ball that does not comprise a self-contained inflation mechanism. The critical ratio is defined as the half period of component vibration divided by the duration of the ball's impact with the floor. Preferably, the critical ratio is 0.95 or greater.[0013]

Another form of the invention is a method of determining the critical ratio of an inflated sport ball, comprising the steps of:[0014]

a) determining the duration of the ball's impact with the floor,[0015]

b) determining the half period of component vibration, and calculating the critical ratio by dividing the half period of component vibration, (b), by the duration of the ball's impact with the floor (a).[0016]

BRIEF DESCRIPTION OF THE DRAWING

The invention will be better understood by reference to the accompanying drawings in which:[0017]

FIG. 1 shows a cross section of a portion of a sport ball with a self-contained piston and cylinder arrangement operable from outside the ball for adding air pressure to the ball.[0018]

FIG. 2 is a side view of the pump shown in FIG. 1.[0019]

FIG. 3 is an isometric view of the cap for the pump of FIG. 1 showing the configuration for locking and unlocking the pump piston.[0020]

FIG. 4 is a detailed cross-section view of a one-way valve assembly for use on the exit of the pump of FIG. 1.[0021]

FIG. 5 is a more detailed view of the duckbill valve in the FIG. 4 assembly.[0022]

FIG. 6 is a diagrammatic view showing the critical ratio versus maximum minus minimum rebound height for various basketball designs.[0023]

FIG. 7 is a graph of COR versus rebound height for a basketball according to the invention.[0024]

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

In a preferred embodiment, the sport ball is an inflated sport ball with a self contained inflation mechanism or other internal device. The interior of the sport ball may also be hollow or may contain a foamed material. The sport ball may be any sport ball, such as, but not limited to, a basketball, a football, a soccer ball, a volleyball, or a playground ball, and it is preferably a basketball with a self contained inflation mechanism or other internal device, more preferably a basketball with a self contained inflation mechanism such as a pump.[0025]

The invention will be better understood by first considering the structure of a typical ball incorporating one embodiment of an inflation pump. Referring first to FIG. 1 of the drawings, a portion of a[0026]

sport ball

10 is illustrated incorporating one embodiment of an inflation pump. Theball10 which is illustrated is a typical basketball construction comprising a carcass15 having arubber bladder12 for air retention, alayer14 composed of layers of nylon or polyester yarn windings wrapped around thebladder12 and anouter rubber layer16. For a laminated ball, an additionalouter layer18 of leather or a synthetic material comprises panels that are applied by adhesive and set by cold molding, or other process known in the art for adhering panels to the ball. The windings are preferably randomly oriented and two or three layers thick. The windings form a layer which cannot be expanded to any significant degree and which restricts the ball from expanding to any significant extent above its regulation size when inflated above its normal playing pressure. This layer for footballs, volleyballs and soccer balls is referred to as a lining layer and is usually composed of cotton or polyester cloth that is impregnated with a flexible binder resin such as vinyl or latex rubber.

Incorporated into the carcass of the ball of the invention during the formation is the rubber pump boot or[0027]

housing

20 with a central opening and with aflange22 which is bonded to the bladder using a rubber adhesive. The boot is located between therubber bladder12 and the layer ofwindings14. An aluminum molded plug is inserted into the boot opening during the molding and winding process to maintain the proper shape central opening and to allow the bladder to be inflated during the manufacturing process. The central opening through theboot20 in configured with agroove24 to hold the flange26 on the upper end of thepump cylinder28. The cylinder can optionally be bonded to the boot using any suitable flexible adhesive (epoxy, urethane or other.) The pump boot or housing has agroove25 which contributes to the bounce consistency of the ball.

Located in the[0028]

pump cylinder

28 is thepump piston30 which is shown in FIGS. 1 and 2. The piston includes anannular groove32 at the bottom end, which contains thespring34 which forces the piston up in thecylinder28. Also, at the bottom end of thepiston30 is a circumferential O-ring groove36 containing an O-ring38. As seen in FIG. 1, this O-ring groove36 is dimensioned such that the O-ring38 can move up and down in thegroove36. The O-ring is forced into the position shown in FIG. 1 when the piston is pushed down. In this position, the O-ring seals between the cylinder wall and the upper flange40 of thegroove36. When thepiston30 is forced up by thespring34, the O-ring38 moves to the bottom of thegroove36 which opens up a by-pass around the O-ring through therecesses42 so that the air can enter thecylinder28 below thepiston30. Then, when the piston is pushed down, the O-ring moves back up to the top of the groove and seals to force the air out through thecylinder exit nozzle46.

At the upper end of the piston are the two[0029]

flanges

48 which cooperate with acylinder cap50 to hold the piston down in the cylinder and to release the piston for pumping. Thecylinder cap50 is fixed into the top of thecylinder28 and thepiston30 extends through the center of thecylinder cap50. Thecap50 is cemented into thecylinder28. FIG. 3 shows an isometric view of the bottom of thecylinder cap50 and illustrates theopen areas52 on opposite sides of the central opening through which the twoflanges48 on the piston can pass in the unlocked position. In the locked position, the piston is pushed down and rotated such that the twoflanges48 pass under theprojections54 and are rotated into the locking recesses56. Attached to the upper end of thepiston30 is a button or cap58 that is designed to essentially completely fill the hole in the carcass and to be flush with the surface of the ball. This button may be of any desired material such as cast urethane or rubber. Mounted on the upper surface of thecylinder cap50 is pad60 which is engaged by the button58 when the piston is pushed down against the spring force to lock or unlock the piston. The pad provides cushioning to the pump and should also be flexible to match the feel of the rest of the ball. Its surface should be textured to increase grip.

FIG. 1 of the drawings shows a[0030]

pump exit nozzle

46 but does not show the one-way valve that is attached to this exit. Shown in FIG. 4 is a one-way valve assembly62 of the duckbill-type to be mounted in theexit nozzle46. This assembly comprises aninlet end piece64, anoutlet end piece66 and anelastomeric duckbill valve68 captured between the two end pieces. The

end pieces

64 and66 are preferably plastic, such as a polycarbonate, and may be ultrasonically welded together.

Although any desired one-way valve can be used on the[0031]

exit nozzle

46 and although duckbill valves are a common type of one-way valves, a specific duckbill configuration is shown in FIG. 4 and in greater detail in FIG. 5. Theduckbill structure68 is formed of an elastomeric silicone material and is molded with acylindrical barrel70 having aflange72. Inside of thebarrel70 is theduckbill74 which has anupper inlet end76 molded around the inside circumference into thebarrel70. The walls orsides78 of theduckbill74 then taper down to form the straight-line lower end with the duckbill slit80. The duckbill functions in the conventional manner where inlet air pressure forces the duckbill slit open to admit air while the air pressure inside of the ball squeezes the duckbill slit closed to prevent the leakage of air. Such a duckbill structure is commercially available from Vemay laboratories, Inc. of Yellow Springs, Ohio.

A pump assembly of the type described and illustrated in FIGS.[0032]1-5 is preferably made primarily from plastics such as polycarbonate or high impact polystyrene, most preferably from polycarbonate. Although the assembly is small and light weight, perhaps only about 25 grams, it is desirable that a weight be added to the ball structure to counterbalance the weight of the pump mechanism.

Other forms of the invention may utilize different pump constructions and the precise sequence of manufacturing steps may vary in various forms of the invention. Those skilled in the art will recognize the substantial benefits including the economies of construction inherent in allowing the pumping mechanism to be designed to accommodate the environmental considerations inherent in normal use of the sports ball and not the much harsher conditions that are encountered during the manufacturing process.[0033]

In the context of basketball performance testing, rebound height is defined as the height the top of a basketball attains when dropped from 72 inches onto a wooden floor surface. (Although the description of the preferred embodiment is phrased in terms of a basketball, it will be understood that the invention has application to other sports balls, such as soccer balls, volleyballs, footballs and playground balls.) The rebound height can also be described in terms of a coefficient of restitution (COR). The mathematical relationship between rebound height and coefficient of restitution is described below in example 1. In a rebound test, the surface upon which the ball is dropped is designed to simulate a regulation basketball-playing surface, and it is a two inch thick wooden piece securely attached to a foundation. The rebound height can vary for a particular ball when it is dropped on different spots on the ball. A useful measure of rebound height variability is the difference between the maximum rebound height and the minimum rebound height. It is a desirable feature to have basketball rebound height as uniform as possible when the ball is dropped repetitively with different orientations. Player testing shows that basketballs with maximum minus minimum rebound height of five and one half inches or more are difficult to play with and control and are difficult to dribble. The basketballs with maximum minus minimum rebound height of five inches or less are acceptable for play and show no obvious dribbling problem. Basketballs with maximum minus minimum rebound height of four inches or less are preferred. Additionally, it has been found that a basketball generally must rebound to a height of between fifty and fifty-six inches overall to be acceptable, although individual preferred rebound height may vary from player to player.[0034]

The act of bouncing a basketball, or other sport ball, on a floor is a dynamic event with impact loading, elastic deformation and vibration. In a perfect impact, the kinetic energy of motion is entirely converted into elastic deformation of a ball. The elastic deformation is like loading a spring or diving board; it deforms, then it springs back. After motion stops (i.e., when the ball is at its maximum deformation), the energy stored in the deformation is released and all of the energy is converted into rebound velocity. The rebound velocity provides the ball enough energy to rise to the original drop height under perfect impact conditions.[0035]

In reality, impact is not perfect. When components of the basketball vibrate after impact, they rob some of kinetic energy of the impact. This acts to store some of the energy in the form of local vibrations that cannot be recovered and are not converted into rebound velocity. The end result is to reduce the rebound height. Typically, the location on the basketball with the minimum rebound height coincides with the maximum vibration of the component. In contrast, the location on the basketball with maximum rebound height corresponds to a minimum amount of component vibration. It is therefore required to map the surface of the basketball such that rebound height is known for all points on the ball. Typical mapping of the entire surface of the ball will require rebound testing on each panel of the ball at approximately five points per panel. The panel that where the pump is located will have additional points tested, generally at one-half to one inch increments along the panel. Additionally, the two ends of the ball are also tested. Each point is tested several times to find the maximum and minimum. The difference between maximum and minimum rebound height can then be determined.[0036]

A “quick test” may be utilized once a full mapping scheme for a particular product has been determined. This quick test utilizes the data previously acquired when mapping the entire surface of the sport ball, and then tests only those locations where the maximum and minimum points are expected. Although the quick test is not as accurate, it may be utilized for quick decisions regarding the vibration and rebound of a sport ball.[0037]

Two critical factors must be considered in the study of the impact of a ball on a floor. The first factor is the nature of the impact loading, and the second factor is the natural frequency of the ball. The natural frequency of the ball is affected by the vibration of the internal device or component (i.e., a self contained inflation mechanism or other internal device) in the ball or part of the ball. The natural frequency of the ball with an internal component is measured with the internal device or component installed in the ball. As used herein, the term natural frequency of the ball is the lowest vibration frequency of the ball with the internal device installed in the ball. The impact loading is the force acting on the ball to decelerate it to a stop on the floor, backboard, rim, etc. and cause the ball to bounce back. The quantities of interest are the force and time history. The natural frequency of the ball influences how fast and to what extent the ball will respond to the impact and how much of the impact energy will be stored in local ball vibrations. The period of vibration is the time required to complete one cycle of motion. The period of vibration is equal to one divided by the frequency of vibration.[0038]

This invention includes a novel method to quickly analyze a sport ball. This invention has particular application to a basketball, although the invention is not limited to such balls. The inventors have now found that the ratio of two critical impact parameters are directly related to the maximum minus minimum rebound height. The two critical impact parameters are the duration of the ball's impact with the floor and the half period of component vibration. The half period vibration for a basketball having a self-contained inflation device installed is equal to one half of the inverse of the natural frequency of the installed component. The critical ratio is most easily measured when the ball, with the component installed, is dropped on the spot that yields the minimum rebound height. As previously described herein, the minimum rebound height is found by mapping the surface of the ball. The “quick test” may be used once a surface is mapped for the same construction sport ball, but small changes to the component or the materials will require complete mapping to determine the proper locations that yield maximum and minimum rebound heights. As used herein, “critical ratio” refers to the half period of component vibration divided by the duration of the ball's impact with the floor. (Although this description is most relevant to a basketball and a pump, it will be understood that the invention has application to other sport balls and other components, preferably other sport balls with a pump.)[0039]

The duration of the ball's impact with the floor can be measured with high speed digital imaging. It will be understood that the duration refers to the duration of contact of the ball with the floor, and the duration of impact does not vary with drop location. The duration of impact should be measured at the location yielding the minimum rebound height. The ball's impact with the floor is first captured with the high speed digital imaging system. A frame sampling rate of about 9,000 to 13,500 frames per second is preferably recommended. Analysis of the set of images will indicate the number of image frames that the ball is in contact with the floor. The duration of the impact event is simply the total number of frames that the ball is in contact with the floor divided by the frame sampling rate.[0040]

The half period of vibration of a basketball or other sport ball can also be measured using high speed digital imaging. Analysis of the set of images allows the determination of the number of frames between the maximum and the minimum length of vibration for a basketball having a self-contained inflation device. The half period of vibration for a basketball having a self-contained inflation device is simply the total number of frames between maximum and minimum vibration divided by the frame sampling rate. If the minimum vibration is difficult to estimate, an alternate method may be used to determine the half period of component vibration. Using the alternate method, the number of frames between one maximum and the next maximum limit of vibration is determined. In this method, the half period of component vibration is the total number of frames between the two maximums divided by two, and then divided by the frame sampling rate. Alternatively, the half period of basketball vibration can also be determined by measuring the natural frequency directly with an accelerometer. As indicated above, the half period of vibration is equal to one half of the inverse of the frequency. Alternatively, dropping the ball onto a load cell and measuring the force over time may be used to measure the duration of the ball's impact.[0041]

FIG. 6 illustrates test data for a plurality of basketballs. For each basketball, the maximum minus the minimum rebound height was determined by mapping the surface of the basketball. Thereafter, the critical ratio for each of these basketballs was determined by testing. Each point or dot in the diagrammatic view of FIG. 6 represents the test results for a single basketball. These test results corroborate decisively a strong negative correlation. More particularly, FIG. 6 establishes that the maximum minus minimum height increases as the critical ratio decreases.[0042]

In other words, the parameter that best correlates to maximum minus minimum rebound height for any specific basketball is the half period of vibration for a basketball having a self-contained inflation device divided by the duration of the ball's impact with the floor. The quotient of these numbers is referred to herein as the critical ratio. When this critical ratio is less than 0.95 for a regulation basketball, the maximum minus minimum rebound height is generally greater than five and one half inches, and the ball is therefore likely to be unacceptable for play due to dribbling problems. When this critical ratio is greater than or equal to 0.95, the maximum minus minimum rebound height is generally less than or equal to five inches, and the ball is therefore suitable for play. This critical ratio can be used in the design and development phase, as well as during quality control, to determine if an inflated ball will have rebound problems. If necessary, design changes may be made to minimize the vibration before producing balls to be sold to customers.[0043]

Examples of the factors that affect the critical ratio include, but are not limited to, the stiffness modulus, flex modulus, bulk modulus, tension modulus and compression modulus values of each of the components of the ball, including the panels, carcass, bladder, windings, and boot; the inertia and mass of the pump or other internal component, the local stiffness of the component's support, the air pressure in the ball, and the quality of the bond between the component's housing (the “boot”) and the bladder and cover.[0044]

EXAMPLE 1

A regulation size synthetic leather basketball was made having a diameter of 9.43 inches (23.95 cm), a circumference of 29.5 inches (75 cm), a weight of about 600 grams. The ball contained an integral pump of the type shown in FIGS.[0045]1-5. The pump was configured to increase the pressure of the ball by at least 1 psi for every 200 pump strokes. The rebound of the ball when it was dropped from a height of 72″ (measured from the bottom of the ball) onto a wooden surface designed to simulate the floor of a basketball court was determined when the ball was dropped repeatedly with different orientations. The ball was found to have a rebound height in the range of 50-57 inches on all panels of the ball (measured from the top of the ball), with a difference between the maximum and minimum rebound heights of 5.5 inches or less. The lowest rebound height resulted when the portion of the ball surface that was located about 2 inches away from the pump was the part that contacted the wooden surface.

EXAMPLE 2

The procedure of Example 1 was repeated with a different basketball of the same type, and the basketball was found to have a rebound height in the range of 50-54 inches on all panels of the ball (measured from the top of the ball), with a difference between the maximum and minimum rebound heights of 4 inches or less.[0046]

EXAMPLE 3

The coefficient of restitution (COR) corresponding to various rebound heights for the balls described in Examples 1 and 2 was determined according to the following formula:[0047]

COR=V_H/V_I

wherein[0048]

V[0049]_Iis the downward velocity of the ball upon initial impact with the floor, and

V[0050]_His the velocity of the ball as it travels upward immediately after impact with the floor.

Velocity for an object traveling vertically can be defined by the equation[0051]

v²=2ax

Where v is velocity, a is acceleration due to gravity, x is the distance to the floor from the initial drop point.[0052] $More specifically, V_{1} = \sqrt{2 (32.2 ft . / s^{2}) (12 in / ft) (x in)}$ $And V_{H} = \sqrt{2 (32.2 ft / s^{2}) (12 in / ft) (h - d in)}$ $Stated another way, V_{H} / V_{I} = \frac{\sqrt{h - d}}{\sqrt{x}}$
Wherein, h is the rebound height, and d is the ball diameter.[0053]

Furthermore, delta COR was determined by subtracting the COR corresponding to the minimum rebound height of a particular ball from the COR corresponding to the maximum rebound height of the same ball. The calculated velocity, COR and delta COR results are shown below on Table 1. The data of Table 1 is plotted on FIG. 7, also shown below. Thus, a ball with a rebound of 50 inches has a COR of 0.7506, and a ball with a rebound of 54 inches has a COR of 0.7868. The ball of Example 1 was found to have a delta COR of 0.051. The ball of Example 2 was found to have a delta COR of 0.036. Thus, for both of these balls, the maximum and minimum COR values for any single measurement were in the overall range of 0.750-0.813.[0054]

TABLE 1


COR for Basketball Rebound Height
Test

	Height	Velocity	COR
	(in)	(in/sec)	(n/a)

Initial	72	235.88	—
Rebound	40	153.70	0.6516
	41	156.20	0.6622
	42	158.65	0.6726
	43	161.07	0.6828
	44	163.45	0.6929
	45	165.80	0.7029
	46	168.11	0.7127
	47	170.39	0.7224
	48	172.65	0.7319
	49	174.87	0.7413
	50	177.07	0.7506
	51	179.24	0.7598
	52	181.38	0.7689
	53	183.50	0.7779
	54	185.59	0.7868
	55	187.66	0.7956
	56	189.71	0.8042
	57	191.73	0.8128
	58	193.74	0.8213
	59	195.72	0.8297
	60	197.69	0.8381

	Min	Max	Delta COR
	(in)	(in)	(n/a)

Rebound	50	55	0.0449
Rebound	51	56	0.0444
Rebound	52	57	0.0439
Rebound	53	58	0.0434

The invention has been described with reference to the preferred embodiments. Modifications and alterations will occur to others upon reading and understanding the preceding detailed description. It is intended that the invention be construed as including all such alterations and modifications insofar as they come within the scope of the claims and the equivalents thereof.[0055]