Patent Publication Number: US-2016220874-A1

Title: Racquet configured with fewer cross strings than main strings

Description:
CROSS-REFERENCE TO RELATED APPLICATION 
     This application is a Continuation application of U.S. patent application Ser. No. 14/747,173 filed on Jun. 23, 2015, which is a continuation of U.S. patent application Ser. No. 13/894,588 filed on May 15, 2013 (now U.S. Pat. No. 9,089,743), which claims priority to U.S. Provisional Patent Application Ser. No. 61/675,029 titled RACQUET CONFIGURED WITH FEWER CROSS STRINGS THAN MAIN STRINGS, and filed on Jul. 24, 2012. 
    
    
     FIELD OF THE INVENTION 
     The present invention relates generally to a sports racquet. In particular, the present invention relates to racquet configured for use with a string bed having fewer cross string segments than main string segments. 
     BACKGROUND OF THE INVENTION 
     Sport racquets, such as tennis racquets, are well known and typically include a frame having a head portion coupled to a handle portion. The head portion supports a string bed having a plurality of main string segments alternately interwoven with a plurality of cross string segments. Many racquets also include a throat portion positioned between and connecting the handle portion to the head portion. The typical string bed of a sports racquet includes a central region, that provides the most responsiveness, the greatest power and the best “feel” to the player, upon impact with a ball, and a peripheral region. The central region, commonly referred to as the “sweet spot,” is typically defined as the area of the string bed that produces higher coefficient of restitution (“COR”) values. A higher COR generally directly corresponds to greater power and greater responsiveness. 
     The string bed and the configuration of the racquet can also play a role in the amount of spin that a player can impart to a ball during play. The ability to impart a spin (a top spin or a back spin) to a ball increases a player&#39;s ability to control the ball during play. For example, imparting a top spin onto a tennis ball can enable a player to swing faster, hit the tennis ball harder and still keep the tennis ball in play within the court. Imparting a top spin to a ball can enable a player to aim higher, swing faster, clear the net and keep the ball in play. Accordingly, characteristics such as spin rate and spin ratio (the ratio of the spin rate of a ball after impact to the spin rate of the ball before impact with the string bed) can be important factors in evaluating a racquet and/or a player&#39;s performance. Other characteristics can also be useful in determining the amount of spin a strung racquet can produce to a ball, such as main string deflection, main string snapback time and main string snapback velocity. 
     Prior art racquets have incorporated different design features in an effort to increase a racquet&#39;s ability to impart spin to a ball and/or increase a racquet&#39;s sweet spot. Some of the design features include increasing a racquet&#39;s head size, increasing the tension of the racquet strings, changing the material of the racquet and/or the racquet strings, and increasing the length of the main and/or cross strings of a racquet. However, such design changes can include drawbacks such as reduced reliability, premature string breakage, premature racquet failure, increased moment of inertia of a racquet and reduced maneuver-ability. 
     Thus, there is a continuing need for a racquet configured to enable more spin to be imparted onto a ball during play. There is also a continuing need for a racquet with an enlarged sweet spot that provides an increased “dwell time,” without negatively effecting the overall performance of the racquet. It would be advantageous to provide a racquet with an enlarged sweet spot, increased main string deflection, reduced main string snap time, increased main string snap back velocity, and an increased “dwell time” without increasing the polar moment of inertia of the racquet head and without negatively affecting the maneuverability of the racquet. There is also a need for a racquet configured to impart more spin to a ball that is not a radical departure in look and design from traditional sport racquet designs. 
     SUMMARY OF THE INVENTION 
     The present invention provides a tennis racquet configured for use with a string bed formed of a plurality of cross string segments interlaced with a plurality of main string segments. The racquet includes a frame extending along a longitudinal axis and including a head portion coupled to a handle portion. The head portion includes a hoop having inner and outer peripheral walls. The hoop defines a head size of the racquet. The head size is within the range of 93 square inches to 120 square inches, having a maximum longitudinal dimension, a, and having a maximum transverse dimension, b. The longitudinal dimension a is at least 1.2 times the transverse dimension b. The inner peripheral wall includes a plurality of cross-string holes and a plurality of main string holes. Each of the cross string holes is configured for receiving one end of one of the cross string segments, and each of the main string holes is configured for receiving one end of one of the main string segments. The number of main string holes is greater than the number of cross string holes such that the string bed configured for use with the racquet has a greater number of main string segments than cross string segments. 
     According to a principal aspect of a preferred form of the invention, a tennis racquet includes a frame extending along a longitudinal axis and including a head portion coupled to a handle portion, and a string bed coupled to the head portion of the racquet. The head portion includes a hoop having inner and outer peripheral walls. The hoop defines a head size having a maximum longitudinal dimension, a, and has a maximum transverse dimension, b. The longitudinal dimension a is at least 1.2 times the transverse dimension b. The inner peripheral wall includes a plurality of string holes. The string bed includes a plurality of cross string segments interlaced with a plurality of main string segments. Each of the cross string segments transversely extends from one of the string holes to another one of the string holes, and each of the main string segments substantially longitudinally extends from one of the string holes to another one of the string holes. The cross string segment closest to the handle portion and the end point of the maximum longitudinal dimension, a, closest to the handle portion define a second longitudinal dimension, c. The ratio of the maximum longitudinal dimension a to the second longitudinal dimension c is at least 6.5. The string bed has at least one more main string segment than cross string segment. 
     According to another principal aspect of a preferred form of the invention, a tennis racquet is capable of being tested under a tennis ball spin test. In the spin test, the racquet is securely mounted to a test fixture by four spaced apart mounts such that a plane defined by a string bed is positioned 30 degrees from horizontal. A tennis ball is projected from a ball projecting machine to the string bed at a speed within the range of 38 to 42 miles per hour from an angle that is 50 degrees from an axis normal to the plane of the string bed. The ball and the string bed are monitored under a high speed video system at 5000 frames per second. The racquet includes a frame and a quantity of polyester, monofilament racquet string. The frame extends along a longitudinal axis and includes a head portion coupled to a handle portion. The head portion includes a hoop having inner and outer peripheral walls. The hoop defines a head size having a maximum longitudinal dimension, a, and a maximum transverse dimension, b. The longitudinal dimension a is at least 1.2 times the transverse dimension b. The inner peripheral wall includes a plurality of string holes. The racquet string has a diameter within the range of 1.10 to 1.55 millimeters. The racquet string is coupled to the head portion to form the string bed. The string bed includes a plurality of cross string segments interlaced with a plurality of main string segments. Each of the cross string segments transversely extends from one of the string holes to another one of the string holes, and each of the main string segments substantially longitudinally extends from one of the string holes to another one of the string holes. The string bed has at least one more main string segment than cross string segment. When the racquet is tested under the tennis ball spin test, at least one of the main string segments contacting the tennis ball exhibits a snap back velocity of at least 1 meter per second. 
     According to another principal aspect of a preferred form of the invention, a tennis racquet is capable of being tested under a tennis string displacement test. In the displacement test, the racquet is securely mounted to a test fixture by four spaced apart mounts such that a plane defined by a string bed is positioned 90 degrees from horizontal (vertically). A tennis ball is projected from a ball projecting machine to the string bed at a speed 60 feet per second from an angle that is 45 degrees from an axis normal to the plane of the string bed. The ball and the string bed are monitored under a high speed video system at 5000 frames per second. The racquet includes a frame and a quantity of polyester, monofilament racquet string. The frame extends along a longitudinal axis and includes a head portion coupled to a handle portion. The head portion includes a hoop having inner and outer peripheral walls. The hoop defines a head size having a maximum longitudinal dimension, a, and a maximum transverse dimension, b. The longitudinal dimension a is at least 1.2 times the transverse dimension b. The inner peripheral wall includes a plurality of string holes. The racquet string has a diameter within the range of 1.10 to 1.55 millimeters. The racquet string is coupled to the head portion to form the string bed. The string bed includes a plurality of cross string segments interlaced with a plurality of main string segments. Each of the cross string segments transversely extends from one of the string holes to another one of the string holes, and each of the main string segments substantially longitudinally extends from one of the string holes to another one of the string holes, such that each of the string holes includes at least one of the cross string segment and the main string segment. The string bed has at least one more main string segment than cross string segment. When the racquet is tested under the tennis ball displacement test, at least one of the main string segments contacting the tennis ball exhibits a string deflection of at least 5 mm. 
     This invention will become more fully understood from the following detailed description, taken in conjunction with the accompanying drawings described herein below, and wherein like reference numerals refer to like parts. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         FIG. 1  is a front side perspective view of a racquet in accordance with a preferred embodiment of the present invention. 
         FIG. 2  is a front view of a head portion of a prior art racquet including a string bed. 
         FIG. 3  is a front view of a head portion of another prior art racquet including a string bed. 
         FIG. 4  is a front view of the head portion of the racquet of  FIG. 1  including a string bed. 
         FIG. 5  is a front view of the head portion of the racquet including a string bed in accordance with an alternative preferred embodiment of the present invention. 
         FIG. 6  is a front view of the head portion of the racquet including a string bed in accordance with another alternative preferred embodiment of the present invention. 
         FIG. 7  is a side view of a tennis ball spin test set-up. 
         FIG. 8  is a side view of a racquet displacement test set-up. 
         FIG. 9  is a two dimensional mapping of the coefficients of restitution on the string bed of a representative prior art racquet. 
         FIG. 10  is a two dimensional mapping of the coefficients of restitution on the string bed of a racquet substantially similar to the racquet of  FIG. 2 . 
         FIG. 11  is a two dimensional mapping of the coefficients of restitution on the string bed of a racquet substantially similar to the racquet of  FIG. 4 . 
         FIG. 12  is a graph of the average string deflection data of Table 3 for racquets strung with varying numbers of cross-strings. 
         FIG. 13  is a graph of the string deflection data of Table 4 for racquets strung with varying numbers of cross-strings and different racquet string diameters. 
         FIG. 14  is a graph of racquet string snapback velocity measurements of Table 6 for racquets strung with varying numbers of cross-strings. 
         FIG. 15  is a graph of racquet string snapback velocity measurements of Table 7 for racquets strung with varying numbers of cross-strings and different string diameters. 
         FIG. 16  is a graph of spin ratio data of Table 8 for racquets strung with varying numbers of cross-strings. 
     
    
    
     DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS 
     Referring to  FIG. 1 , a sports racquet is indicated generally at  10 . The racquet  10  of  FIG. 1  is configured as a tennis racquet. The racquet  10  includes a frame  12  extending along a longitudinal axis  16  and including a head portion  18 , a handle portion  20 , and a throat portion  22  coupling the head and handle portions  18  and  20 . The frame  12  is a tubular structure formed of a lightweight, durable material, preferably a carbon-fiber composite material. 
     As used herein, the term “fiber composite material” or “composite material” refers to a plurality of fibers impregnated (or permeated throughout) with a resin. The fibers can be co-axially aligned in sheets, layers or plies, or braided or weaved in sheets or layers, and/or chopped and randomly dispersed in one or more layers. A single ply typically includes hundreds or thousands of fiber bundles that are initially arranged to extend coaxially and parallel with each other through the resin that is initially uncured. Each of the fiber bundles includes a plurality of fibers. The fibers are formed of a high tensile strength material such as carbon. Alternatively, the fibers can be formed of other materials such as, for example, glass, graphite, boron, basalt, carrot, Kevlar®, Spectra®, poly-para-phenylene-2,6-benzobisoxazole (PBO), hemp and combinations thereof. In one set of preferred embodiments, the resin is preferably a thermosetting resin such as epoxy or polyester resins. In other sets of preferred embodiments, the resin can be a thermoplastic resin. The composite material is typically wrapped about a mandrel and/or a comparable structure, and cured under heat and/or pressure. While curing, the resin is configured to flow and fully disperse and impregnate the matrix of fibers. In multiple layer or ply constructions, the fibers can be aligned in different directions with respect to the longitudinal axis  16 , and/or in braids or weaves from layer to layer. Alternatively, the frame  12  can be formed of other materials including metallic alloys, other composite materials, wood, or combinations thereof. 
     The head portion  18  is a tubular structure that includes inner and outer peripheral walls  24  and  26 . The head portion  18  can be broken down into regions, such as, a distal region  28 , first and second side regions  30  and  32 , and a proximal region  34 , which collectively define a hoop  36  having a string bed area  38  for receiving and supporting the string bed  14  (see  FIG. 4 ). In one preferred embodiment, the proximal region  34  includes a yoke  40 . The string bed area  38  is also referred to as the head size of the racquet  10 . In a preferred embodiment, the head size or string bed area  38  of the racquet  10  is within the range of 93 to 120 square inches. In a more preferred embodiment, the head size of the racquet  10  is within the range 98 to 115 square inches. In alternative preferred embodiments, other head sizes can also be used and are contemplated under the present invention. The string bed area  38  has a maximum longitudinal dimension, a, and a maximum transverse dimension, b. The hoop  36  can be any closed curved shape including, for example, a generally oval shape, a generally tear-drop shape, a generally pear shape, and combinations thereof. The shape of the hoop  36  is preferably non-circular. The maximum longitudinal dimension is preferably at least 1.2 times the maximum transverse dimension (a≧1.2*b). In a particularly preferred embodiment, the maximum longitudinal dimension is preferably at least 1.25 times the maximum transverse dimension (a≧1.25*b). 
     The yoke  40  is an elongate tubular structural member which extends from the first side region  30  to the second side region  32  of the head portion  18 . In one preferred embodiment, the yoke  40  is integrally formed with the frame  12  defining the proximal region  34 . In alternative preferred embodiments, the yoke  40  can be connected through use of adhesives, fasteners, bonding and combinations thereof. The yoke  40  is formed of a lightweight, durable material, preferably a carbon-fiber composite material. Alternatively, the yoke  40  can be formed of other materials, such as, for example, metallic alloys, other composite materials including basalt fibers, and combinations thereof. 
     In a preferred embodiment, the first and second side regions  30  and  32  downwardly extend from the head portion  18  to form first and second throat tubes  42  and  44  of the throat portion  22 . The first and second throat tubes  42  and  44  converge and further downwardly extend to form the handle portion  20 . The handle portion  20  includes a pallet (not shown), a grip  46  and a butt cap  48 . In alternative preferred embodiments, the handle portion  20  can be a tubular structure that does not include an extension of the first and second throat tubes. In this alternative preferred embodiment, the handle portion can be a tubular structure separate from either the throat portion or the head portion of the frame and attached to the throat portion through use of conventional fasteners, molding techniques, bonding techniques, adhesives or combinations thereof. 
     In another preferred embodiment, the head portion  18  is directly connected to one or both of the throat portion  22  and the yoke  40  through the use of conventional fasteners, adhesives, mechanical bonding, thermal bonding, or other combinations thereof. Alternatively, the head portion  18  can be separated from one or both of the throat portion and the yoke by a vibration and shock absorbing material, such as an elastomer. In yet another alternative preferred embodiment, the head portion  18  is integrally formed with one or both of the throat portion  22  and the yoke  40 . 
     Referring to  FIGS. 2 through 6 , the racquet  10  configured for supporting a string bed  14  is formed by a plurality of main string segments  50  alternately interwoven or interlaced with a plurality of cross string segments  52 . The string bed  14  is preferably generally uniform with constant spacing between the string segments  50  and  52 . Alternatively, the string bed  14  can have some spacing variability provided that the spacing of the main and cross string segments of the string bed is most dense at the center of the string bed  14  (or near the geometric center of the string bed or string bed area). The main and cross string segments  50  and  52  can be formed from one continuous piece of racquet string, or from two or more pieces of racquet string. The racquet string is formed of a high tensile strength, flexible material. In preferred embodiments, the racquet string can be formed of a polyester material, a nylon, a natural gut material and/or a synthetic gut material. The polyester materials used to make the racquet string can include polyether ether ketone (PEEK), polytetrafluoroethylene (PTFE), other polyester materials, and combinations thereof. The racquet string can be formed in a monofilament construction or in a multiple-filament construction. The racquet string can be formed of various different diameters (or gauges). Preferably, the diameter of the racquet string is within the range 1.10 to 1.55 mm. 
     The main and cross string segments  50  and  52  refer to the portions of the racquet string that make up the string bed  14 . The string bed  14  generally defines a string bed plane  54 . Each of the main and cross string segments  50  and  52  can be considered to have first and second ends or end regions. The racquet string can, but typically does not, terminate, end or cutoff in or at the ends or end regions. Rather, the ends or end regions of the main and cross string segments  50  and  52  are defined as the location where the main and cross string segments  50  and  52  extend through the string holes in the hoop  36 . Other than to accommodate the interlacing or interweaving of the main and cross string segments  50  and  52 , the main and cross string segments  50  and  52  preferably extend substantially along the string bed plane  54  as they extend across the string bed area  38 . Maintaining the main and cross string segments  50  and  52  substantially within the sting bed plane  54  throughout the string bed area  38  maximizes the playability of the entire string bed  14 , and provides the player with a greater ability to control the ball even on hits closer to the yoke. In other preferred embodiments a portion of the main and or cross strings can extend slight away from the string bed plane  54  near their ends or end regions. The inner and outer peripheral walls  24  and  26  of the hoop  36  preferably include string holes for receiving the racquet string. In a particularly preferred embodiment, the inner peripheral wall  24  is formed with a plurality of main string holes  56  and a plurality of cross string holes  58  for receiving the main and cross string segments  50  and  52 , respectively. The string holes  56  and  58  may be circular, oval, rectangular, or any generally curved shape. The string holes  56  and  58  can be sized to be just larger than the diameter of the racquet string, or the combination of the racquet string and the grommet, or a size that is larger to accommodate movement or deflection of the racquet string. The head portion  18  of the racquet  10  can also include one or more grommets or bumper guards for supporting and protecting the racquet string as it extends from one string hole to another. 
     Preferably, the main string holes  56  formed in the inner peripheral, wall  24  of the hoop  36  are positioned such that, when the racquet  10  is strung, each main string segment  50  extends in a direction that is substantially parallel to the longitudinal axis  16  of the racquet  10 . The terms substantially parallel or substantially longitudinally extending refers to a direction that is co-linear or parallel to the longitudinal axis  16  plus or minus 2 degrees. Similarly, the cross string holes  58  can be positioned in the inner peripheral wall  24  of the hoop  36  such that, when the racquet  10  is strung, each cross string segment  52  extends in a direction that substantially transverse (or orthogonal) to the longitudinal axis  16  (plus or minus 2 degrees). Accordingly, in a preferred embodiment, the string bed  14  includes a plurality of substantially longitudinally extending main string segments  50  and a plurality of substantially transversely extending cross string segments  52 . In other alternative embodiments, main string holes  56  in the inner peripheral wall  24  of the hoop  36  can be positioned such that one or more of the main string segments extend in a direction that is not substantially longitudinal. 
     In a preferred embodiment, the racquet  10  is configured such that each of the main and cross string holes  56  and  58  includes or receives a single end or end region of one of the main and cross string segments  50  and  52 , respectively, and no string hole are left without one of the main or cross string segments extending through it. In a particularly preferred embodiment, two main string holes  56  and two cross string holes  58  are formed in the inner peripheral wall  24  of the hoop  36  to accommodate one separate main string segment  50  and one separate cross-string segment  52 , respectively. Therefore, no string holes are left without a main or cross string segment extending through it. In other words, there is no doubling of the string segments through a single string hole, and there are no spare, extra or unused string holes. In another preferred embodiment, one or more of the string holes can be positioned to receive a main and a cross string segment  50  and  52 . In another preferred embodiment, two or more main string segments or two or more cross string segments can extend through a single string hole. 
     Referring to  FIGS. 2 and 3 , the head portions  18  of two prior art racquets is shown. In  FIG. 2 , the head portion  18  is formed such that the inner peripheral wall of the hoop  36  includes a sufficient number of string holes to provide for a string bed  14  having 16 main string segments  50  and 18 cross string segments  52 . The stringing pattern of the racquet of  FIG. 2  is referred to as a 16×18 stringing pattern. In  FIG. 3 , the head portion  18  is formed such that the inner peripheral wall of the hoop  36  includes a sufficient number of string holes to provide for a string bed  14  having 18 main string segments  50  and 20 cross string segments  52 . The stringing pattern of the racquet of  FIG. 2  is referred to as a 18×20 stringing pattern. Other stringing patterns are also conventionally used such as 14×16, 16×19, 16×20. etc. In conventional stringing patterns, such as the stringing patterns of  FIGS. 2 and 3 , the number of cross strings is always greater than the number of main strings. In some rare instances a stringing pattern may have an equal number of main and cross string segments. The conventional stringing patterns are necessitated by the non-circular shape of string bed areas and hoops of existing racquets and the strength and durability of the string and frame of the racquet. The non-circular shapes of the hoops of conventional racquets typically result in a maximum longitudinal dimension being greater than the maximum transverse dimension. As such, there is more room or space for cross strings than main strings. In order to distribute the stresses of racquet stringing throughout the head portion and the racquet so that the neither the head portion nor the racquet string fail, it is necessary to add additional transversely extending cross strings to a head portion than longitudinally extending main strings. Conventional racquet design teaches away from an even number of main and cross string segments, because such a design places excessive loads and stress on the racquet string and the head portion itself making such a racquet extremely difficult to string without racquet failure, or play without string failure. Accordingly, over the decades of racquet design, in non-circular head or hoop shapes, the number of cross strings segments is greater than the number of main string segments. 
     Referring to  FIGS. 3 through 5 , head portions  18  of three separate racquets built in accordance with three separate preferred embodiments of the present invention are provided. In  FIG. 4 , the inner peripheral wall  24  of the hoop  36  of the head portion  18  includes thirty-two (32) main string holes and thirty (30) cross string holes to receive sixteen (16) main string segments  50  and fifteen (15) cross string segments  52 , respectively, thereby forming a 16×15 stringing pattern. The pair of cross string holes  58  closest to the handle portion  20  of the racquet  10  define end points of a transverse line  60  extending from the first side region  30  to the second side region  32 . The point where the transverse line  60  crosses the longitudinal axis  16  and the end point of the maximum longitudinal dimension a closest to the handle portion  20  define a second longitudinal dimension c. The spacing of the cross string segments  52  in the string bed  14  is optimized such that the ratio of the maximum longitudinal dimension a to the second longitudinal dimension c is at least 6.5 (a/c≧6.5). In a particularly preferred embodiment, the spacing of the cross string segments  52  in the string bed  14  is optimized such that the ratio of the maximum longitudinal dimension a to the second longitudinal dimension c is at least 7.5 (a/c≧7.5). Although the 16×15 stringing pattern is illustrated, the present invention contemplates other “minus 1” stringing patterns, such as, 20×19, 18×17, 14×13, etc. 
     In  FIG. 5 , the inner peripheral wall  24  of the hoop  36  of the head portion  18  includes thirty-two (32) main string holes and twenty-eight (28) cross string holes to receive sixteen (16) main string segments  50  and fourteen (14) cross string segments  52 , respectively, thereby forming a 16×14 stringing pattern. As with the stringing pattern of  FIG. 4 , the spacing of the cross string segments  52  in the string bed  14  is optimized such that the ratio of the maximum longitudinal dimension a to the second longitudinal dimension c is at least 6.5 (a/c≧6.5). In a particularly preferred embodiment, the spacing of the cross string segments  52  in the string bed  14  is optimized such that the ratio of the maximum longitudinal dimension a to the second longitudinal dimension c is at least 7.5 (a/c≧7.5). Although the 16×14 stringing pattern is illustrated, the present invention contemplates other “minus 2” stringing patterns, such as, 20×18, 18×16, 14×12, etc. 
     In  FIG. 6 , the inner peripheral wall  24  of the hoop  36  of the head portion  18  includes thirty-two (32) main string holes and twenty-six (26) cross string holes to receive sixteen (16) main string segments  50  and thirteen ( 13 ) cross string segments  52 , respectively, thereby forming a 16×13 stringing pattern. As with the stringing pattern of  FIG. 4 , the spacing of the cross string segments  52  in the string bed  14  is optimized such that the ratio of the maximum longitudinal dimension a to the second longitudinal dimension c is at least 6.5 (a/c≧6.5). In a particularly preferred embodiment, the spacing of the cross string segments  52  in the string bed  14  is optimized such that the ratio of the maximum longitudinal dimension a to the second longitudinal dimension c is at least 7.5 (a/c≧7.5). Although the 16×13 stringing pattern is illustrated, the present invention contemplates other “minus 3” stringing patterns, such as, 20×17, 18×15, 14×11, etc. In still other preferred embodiments, minus-4, minus-5 and greater stringing patterns may be used. It has been found that by adjusting racquet characteristics, such as maintaining the string bed within the string bed plane across the entire string bed area, positioning the main and cross strings in substantially longitudinal and transverse directions, respectively, incorporating a non-circular head, and optimizing the string spacing, including optimizing the second longitudinal dimension, racquets can be produced with fewer cross strings than main strings without causing premature racquet or string failure. 
     Racquets built in accordance with the present invention can provide a number of significant advantages to users of the racquets. Racquets built in accordance with the present invention enable a player to impart more spin to the ball than otherwise available with conventional racquet designs. The ability to impart more spin to the ball enables a player to obtain increased spin rates and increased spin ratios. Characteristics such as, snap back velocity of main string segments impacting the ball, and main string deflection can be substantially increased through use of racquets built in accordance with the present invention. The specific configurations of the racquets of the present invention including the shape of the head size, the ratio of the longitudinal dimensions a to c, orientation of the string holes and optimized spacing of the string segments enables all of the above-described characteristics to improve. The increased snap back velocity, and increased string deflection enables the user to impart more spin to the ball thereby improving his or her ability to swing faster, and hit the ball harder while keeping the ball in bounds and to clear the net. Additionally, racquets built in accordance with the present invention can provide the racquet and player with a larger, more powerful sweet spot. 
     The advantages of the present invention were illustrated in a test performed by Wilson Sporting Goods Co. involving three racquet models during Jun. 20, 2012 through Jul. 6, 2012 at the Wilson Innovation Center Spin Lab in Schiller Park, Ill. The Wilson Innovation Center Spin Lab incorporates the use of the Trackman® Ball Tracking System by Trackman A/S of Vedbaek, Denmark. Two of the racquet models were representative prior art models and the third model was a Wilson® racquet model Steam 99S™ configured with a 16×15 stringing pattern and the other features of the present invention. The first test racquet is a racquet model, Babolat® Pure Drive™, produced by Babolat VS of Lyon, France, and serves as a representative prior art racquet. The second test racquet a Wilson® racquet, model Steam 99™ produced by Wilson Sporting Goods Co. of Chicago, Ill. All three racquets were strung with Luxilon® 4G™ polyester monofilament racquet string having a diameter of 1.25 mm at a tension of 60 lbs. All three racquets were painted black to remove all indicia of brand or model. 
     Twenty four players of varying ability took 5 to 7 hits with each of the three different racquets. The three racquets were rotated randomly after each hit. Each player was handed one of the three racquets. After each hit, the player randomly received another one of the three racquets, until 5 to 7 recorded hits were obtained from each player hitting each racquet. The data reduction methodology included the following requirements.
         1. A shot must have a recorded spin rate   2. The ball must go over the net   3. Shot length must be less than 88 feet   4. Shot must land +/−18 feet of centerline left and right   5. Must have a ball speed &gt;40 mph to eliminate some frame hits   6. A player must have at least three recordable shots for each of the three racquets       

     
       
         
           
               
             
               
                 TABLE 1 
               
             
            
               
                   
               
               
                 TEST RESULTS 
               
               
                 1. Spin, Speed, Launch Statistics 
               
            
           
           
               
               
               
               
               
               
               
            
               
                   
                   
                   
                 Wilson 
                   
                 Puredrive 
                 Steam 99 
               
               
                   
                 Babolat 
                 Wilson 
                 Steam 
                   
                 vs Steam 
                 vs Steam 
               
               
                 24 players 
                 Puredrive 
                 Steam 99 
                 99S 
                   
                 99S 
                 99S 
               
               
                   
               
            
           
           
               
            
               
                 BALL SPEED (mph) 
               
            
           
           
               
               
               
               
               
               
               
            
               
                 AVG 
                 64.9 
                 66.3 
                 66.2 
                   
                 −1.3 
                 0.1 
               
               
                 STDEV 
                 7.2 
                 6.5 
                 7.0 
                   
                 3.1 
                 2.3 
               
               
                   
                   
                   
                   
                 95% 
                 ±1.30 
                 ±0.96 
               
               
                   
                   
                   
                   
                 Confidence 
               
               
                   
                   
                   
                   
                 Interval 
               
               
                   
                   
                   
                   
                   
                 SIGNIFICANT 
               
            
           
           
               
            
               
                 BALL SPIN (mph) 
               
            
           
           
               
               
               
               
               
               
               
            
               
                 AVG 
                 1360.2 
                 1394.9 
                 1501.7 
                   
                 −141.4 
                 −106.8 
               
               
                 STDEV 
                 402.8 
                 308.2 
                 305.6 
                   
                 274.9 
                 226.4 
               
               
                   
                   
                   
                   
                 95% 
                 ±134.56 
                 ±95.61 
               
               
                   
                   
                   
                   
                 Confidence 
               
               
                   
                   
                   
                   
                 Interval 
               
               
                   
                   
                   
                   
                   
                 SIGNIFICANT 
                 SIGNIFICANT 
               
            
           
           
               
            
               
                 LAUNCH ANGLE (deg) 
               
            
           
           
               
               
               
               
               
               
               
            
               
                 AVG 
                 9.6 
                 9.9 
                 10.4 
                   
                 −0.8 
                 −0.5 
               
               
                 STDEV 
                 2.2 
                 2.1 
                 2.6 
                   
                 1.0 
                 1.8 
               
               
                   
                   
                   
                   
                 95% 
                 ±0.41 
                 ±0.76 
               
               
                   
                   
                   
                   
                 Confidence 
               
               
                   
                   
                   
                   
                 Interval 
               
            
           
           
               
            
               
                 TRAJ HEIGHT (in) 
               
            
           
           
               
               
               
               
               
               
               
            
               
                 AVG 
                 79.9 
                 84.0 
                 89.1 
                   
                 −9.3 
                 −5.1 
               
               
                 STDEV 
                 13.2 
                 12.5 
                 16.4 
                   
                 7.9 
                 14.4 
               
               
                   
                   
                   
                   
                 95% 
                 ±3.35 
                 ±6.09 
               
               
                   
                   
                   
                   
                 Confidence 
               
               
                   
                   
                   
                   
                 Interval 
               
               
                   
                   
                   
                   
                   
                 SIGNIFICANT 
               
            
           
           
               
            
               
                 Landing ANGLE (deg) 
               
            
           
           
               
               
               
               
               
               
               
            
               
                 AVG 
                 22.4 
                 23.2 
                 24.3 
                   
                 −1.9 
                 −1.1 
               
               
                 STDEV 
                 3.6 
                 3.4 
                 4.4 
                   
                 1.9 
                 3.7 
               
               
                   
                   
                   
                   
                 95% 
                 ±0.8 
                 ±1.6 
               
               
                   
                   
                   
                   
                 Confidence 
               
               
                   
                   
                   
                   
                 Interval 
               
               
                   
                   
                   
                   
                   
                 SIGNIFICANT 
               
               
                   
               
            
           
         
       
     
     The results of the Player Test of the three racquets showed the racquet built in accordance with the present invention provided significantly improved ball speed, ball spin, launch angle, trajectory height and landing angle than the two prior art racquet models (see Table 1). The racquet built in accordance with the present invention improved the players&#39; ability to impart spin to the ball during the test and therefore enabled the players to increase the ball speed, the ball spin, and improve the balls trajectory and launch angle. The result is that players can hit the ball harder and faster and keep it in play and generate increased trajectory thereby allowing the ball to clear the net and stay in play. 
     Table 2 below provides a set of flight predictions developed by Wilson Sporting Goods Co. using a Wilson Trajectory Model for tennis balls. The calculated results of the Wilson Trajectory Model are consistent with measured Doppler radar results of impacted tennis balls. The Model shows the potential significant benefits that can be achieved from an increase in spin rate imparted to a tennis ball following impact with a racquet. 
     
       
         
           
               
               
               
               
               
               
             
               
                 TABLE 2 
               
               
                   
               
               
                   
                   
                   
                   
                 Avg Flight 
                 Avg Flight 
               
               
                 Launch 
                 Launch 
                   
                 Flight 
                 Distance 
                 Distance 
               
               
                 Ball 
                 Top 
                 Launch 
                 Distance 
                 Reduction 
                 Reduction 
               
               
                 Speed 
                 Spin 
                 Angle 
                 Travel 
                 per 100 rpm 
                 per 100 rpm 
               
               
                 (mph) 
                 (rpm) 
                 (deg) 
                 (feet) 
                 (feet) 
                 (INCHES) 
               
               
                   
               
             
            
               
                   
               
            
           
           
               
               
               
               
               
               
            
               
                 60 
                 1000 
                 10 
                 65.5 
                 0.52 
                 6.3 
               
               
                 60 
                 2000 
                 10 
                 59.2 
               
               
                 60 
                 3000 
                 10 
                 54.0 
               
               
                 60 
                 4000 
                 10 
                 49.8 
               
               
                 75 
                 1000 
                 10 
                 85.8 
                 0.75 
                 9.0 
               
               
                 75 
                 2000 
                 10 
                 76.7 
               
               
                 75 
                 3000 
                 10 
                 69.4 
               
               
                 75 
                 4000 
                 10 
                 63.4 
               
               
                 90 
                 1000 
                 10 
                 105.9 
                 0.97 
                 11.6 
               
               
                 90 
                 2000 
                 10 
                 94.0 
               
               
                 90 
                 3000 
                 10 
                 84.4 
               
               
                 90 
                 4000 
                 10 
                 76.7 
               
               
                   
               
            
           
         
       
     
     Accordingly, for every increase in spin rate of 100 rpm imparted to a tennis ball as top spin, a corresponding reduction in distance traveled until impacting the court on a typical groundstroke of 6 to 12 inches is found depending upon the speed of the groundstroke. 
     Referring to  FIG. 7 , Wilson Sporting Goods Co. also conducted a tennis ball spin test using a spin test assembly  70 . Under the tennis ball spin test, the racquet  10  was securely mounted to a test fixture  72  by four spaced apart mounts  74  such that a plane defined by a string bed  76  is positioned 30 degrees from horizontal, a tennis ball  78  is projected from a ball projecting machine  80  to the string bed  14  at a speed within the range of 38 to 42 miles per hour from an angle that is 50 degrees from an axis normal to the plane of the string bed, and the ball and the string bed are monitored under a high speed video system  82  at 5000 frames per second. The ball projecting machine  80  is configured to impart a spin on the ball as it exits the ball projecting machine. One example of such a machine is an ATEC® Casey® Pro 3G™ pitching machine produced by Athletic Training Equipment Company of Sparks, Nev. The high speed video is positioned at one or more locations to allow for optimal recording of tennis ball spin and/or string segment movement (deflection). The high speed video system is shown in one position in  FIG. 7 . In other preferred configurations, the video system can be positioned at an alternative position. The results of the Wilson tennis ball spin test found significant improvement in spin rate and spin ratio of tennis balls following impact with a racquet built in accordance with the present invention over other existing racquet configurations. 
     Referring to  FIG. 8 , Wilson Sporting Goods Co. also conducted a tennis ball displacement test using a displacement test assembly  100 . Under the tennis ball spin test, the racquet  10  was securely mounted to a test fixture  102  by four spaced apart mounts  104  such that a plane defined by a string bed  106  is positioned 90 degrees from horizontal (or vertically), a tennis ball  108  is projected from a ball projecting machine  110  to the string bed  14  at a speed of approximately 60 feet per second from an angle that is 45 degrees from an axis normal to the plane of the string bed, and the ball and the string bed are monitored under the high speed video system  82  at 5000 frames per second. The ball projecting machine  110  is preferably an air cannon. The high speed video is positioned at one or more locations to allow for optimal recording of tennis ball spin and/or string segment movement (deflection). The high speed video system is shown in one position in  FIG. 8 . In other preferred configurations, the video system can be positioned in one or more alternative positions. The results of the Wilson tennis displacement spin test found significant improvement in string deflection of a main string impacted by the tennis ball, and snapback time and velocity of main strings impacted by a ball. 
     The Wilson Tennis Ball Spin Test and the Wilson Displacement Test were conducted on four racquet models. Three of the racquet models were representative prior art models and the fourth model was a Wilson® racquet model Steam 99™ having a head size of 99 square inches, and configured with a 16×15 stringing pattern and the other features of the present invention. The first test racquet is a racquet model, Babolat® Pure Drive™, produced by Babolat VS of Lyon, France, and serves as a representative prior art racquet. The second test racquet is a racquet model, Babolat® Aero Pro Drive™, produced by Babolat VS of Lyon, France, and serves as a representative prior art racquet. The third test racquet a Wilson® racquet, model Steam 100™ having a head size of 100 square inches and produced by Wilson Sporting Goods Co. of Chicago, Ill. All four racquets were strung with Luxilon® 4G™ polyester monofilament racquet string having a diameter of 1.25 mm at a tension of 60 lbs. 
     In the Wilson Tennis Ball Spin Test, the inbound angular speeds of the projected tennis balls were approximately 1400 rpm. The rebound speeds were 20 to 30 miles per hour. The bounce angle was 80 to 90 degrees from horizontal (vertical or close to vertical). 
     The high speed camera  82  can be placed perpendicular to the path of the ball  78 , 3 feet from the racquet fixture  72 , or can be positioned at other locations (such as pointed at the side of the racquet frame) to provide desired images for measurement. The camera  82  is focused on the point of contact (center of the string bed  14 ). Video is recorded at 5000 frames per second to record as many ball locations as possible without sacrificing video quality. 
     Wilson® US Open® tennis balls with a quadrant logo are used in this test to aid in tracking with the high speed video analysis software TEMA. The quadrant option provides a location on the balls&#39; quadrant icon and allowing the spin rate to be tracked throughout the path of motion of the ball. This data was transferred to an excel template that averages speeds and spin rates for the portions of the video that show the most consistency. Six videos were recorded for each racquet/string/pattern tested. 
     The Wilson Tennis Ball Spin Test and Wilson Displacement Tests were also conducted on a series of Wilson® Six One® racquets having the same frame and hoop geometry and size (105 sq. inches), and varying string patterns. Each racquet was configured with 16 main string segments and a different number of cross string segments. The racquets incorporated a planar string bed across the stringing area, substantially longitudinally and substantially transervely extending main and cross string segments, respectively, and optimized cross string spacing for those racquets with reduded quantities of cross string segments. The following results for String Deflection (Tables 3 &amp; 4 and  FIGS. 12 and 13 ), Snap Back Time (Table 5), Snap Back Velocity (Tables 6 &amp; 7 and  FIGS. 14 and 15 ), and Spin Rate (Table 8 and  FIG. 16 ) were obtained from testing the series of Wilson® Six One® racquets under the Wilson Tennis Ball Spin Test. 
     
       
         
           
               
               
               
             
               
                 TABLE 3 
               
               
                   
               
               
                 String 
                 String 
                 String 
               
               
                 Diameter (mm) 
                 Pattern 
                 Deflection (mm) 
               
               
                   
               
             
            
               
                   
               
            
           
           
               
               
               
            
               
                 1.25 
                 16 × 11 
                 23.54 
               
               
                   
                 16 × 12 
                 23.60 
               
               
                   
                 16 × 14 
                 18.50 
               
               
                   
                 16 × 15 
                 16.50 
               
               
                   
                 16 × 18 
                 6.04 
               
               
                   
                 16 × 20 
                 8.00 
               
               
                 1.38 
                 16 × 14 
                 20.36 
               
               
                   
                 16 × 15 
                 19.95 
               
               
                   
                 16 × 20 
                 6.35 
               
               
                 1.45 
                 16 × 14 
                 11.17 
               
               
                   
                 16 × 15 
                 15.00 
               
               
                   
                 16 × 20 
                 2.72 
               
               
                 1.50 
                 16 × 14 
                 10.24 
               
               
                   
                 16 × 15 
                 10.00 
               
               
                   
                 16 × 20 
                 4.09 
               
               
                 1.55 
                 16 × 14 
                 10.40 
               
               
                   
                 16 × 15 
                 10.13 
               
               
                   
                 16 × 20 
                 3.00 
               
               
                   
               
            
           
         
       
     
     
       
         
           
               
             
               
                 TABLE 4 
               
             
            
               
                   
               
               
                 String Deflection: 
               
            
           
           
               
               
            
               
                   
                 Average String 
               
               
                   
                 Deflection (mm) 
               
               
                   
                   
               
            
           
           
               
               
               
            
               
                   
                 1.25 
                   
               
               
                   
                 16 × 14 
                 18.50 
               
               
                   
                 16 × 15 
                 16.50 
               
               
                   
                 16 × 20 
                 8.00 
               
               
                   
                 1.38 
               
               
                   
                 16 × 14 
                 20.36 
               
               
                   
                 16 × 15 
                 19.95 
               
               
                   
                 16 × 20 
                 6.35 
               
               
                   
                 1.45 
               
               
                   
                 16 × 14 
                 11.17 
               
               
                   
                 16 × 15 
                 15.00 
               
               
                   
                 16 × 20 
                 2.72 
               
               
                   
                 1.50 
               
               
                   
                 16 × 14 
                 10.24 
               
               
                   
                 16 × 15 
                 10.00 
               
               
                   
                 16 × 20 
                 4.09 
               
               
                   
                 1.55 
               
               
                   
                 16 × 14 
                 10.40 
               
               
                   
                 16 × 15 
                 10.13 
               
               
                   
                 16 × 20 
                 3.00 
               
               
                   
                   
               
            
           
         
       
     
     
       
         
           
               
               
               
             
               
                 TABLE 5 
               
               
                   
               
               
                 String 
                 String 
                 Snapback 
               
               
                 Diameter (mm) 
                 Pattern 
                 Time (s) 
               
               
                   
               
             
            
               
                 1.25 
                 16 × 11 
                 0.00738 
               
               
                   
                 16 × 12 
                 0.00900 
               
               
                   
                 16 × 14 
                 0.00800 
               
               
                   
                 16 × 15 
                 0.00800 
               
               
                   
                 16 × 18 
                 0.00410 
               
               
                   
                 16 × 20 
                 0.00800 
               
               
                 1.38 
                 16 × 14 
                 0.00800 
               
               
                   
                 16 × 15 
                 0.00800 
               
               
                   
                 16 × 20 
                 0.00800 
               
               
                 1.45 
                 16 × 14 
                 0.00997 
               
               
                   
                 16 × 15 
                 0.01000 
               
               
                   
                 16 × 20 
                 0.00801 
               
               
                 1.50 
                 16 × 14 
                 0.01000 
               
               
                   
                 16 × 15 
                 0.01000 
               
               
                   
                 16 × 20 
                 0.01399 
               
               
                 1.55 
                 16 × 14 
                 0.01000 
               
               
                   
                 16 × 15 
                 0.01000 
               
               
                   
                 16 × 20 
                 0.01402 
               
               
                   
               
            
           
         
       
     
     
       
         
           
               
               
               
             
               
                 TABLE 6 
               
               
                   
               
               
                 String 
                 String 
                 Snap Back 
               
               
                 Diameter (mm) 
                 Pattern 
                 Velocity (m/s) 
               
               
                   
               
             
            
               
                   
               
            
           
           
               
               
               
            
               
                 1.25 
                  8 × 10 
                 2.79 
               
               
                   
                  8 × 20 
                 1.787 
               
               
                   
                 10 × 20 
                 1.261 
               
               
                   
                 16 × 10 
                 2.675 
               
               
                   
                 16 × 11 
                 3.19 
               
               
                   
                 16 × 12 
                 2.62 
               
               
                   
                 16 × 14 
                 2.31 
               
               
                   
                 16 × 15 
                 2.06 
               
               
                   
                 16 × 18 
                 1.47 
               
               
                   
                 16 × 20 
                 1.00 
               
               
                 1.38 
                 16 × 14 
                 2.55 
               
               
                   
                 16 × 15 
                 2.49 
               
               
                   
                 16 × 20 
                 0.79 
               
               
                 1.45 
                 16 × 14 
                 1.12 
               
               
                   
                 16 × 15 
                 1.50 
               
               
                   
                 16 × 20 
                 0.34 
               
               
                 1.50 
                 16 × 14 
                 1.02 
               
               
                   
                 16 × 15 
                 1.00 
               
               
                   
                 16 × 20 
                 0.29 
               
               
                 1.55 
                 16 × 14 
                 1.04 
               
               
                   
                 16 × 15 
                 1.01 
               
               
                   
                 16 × 20 
                 0.21 
               
               
                   
               
            
           
         
       
     
     
       
         
           
               
             
               
                 TABLE 7 
               
             
            
               
                   
               
               
                 Snapback Velocity: 
               
            
           
           
               
               
            
               
                   
                 String Snap Back 
               
               
                   
                 Velocity (m/s) 
               
               
                   
                   
               
            
           
           
               
               
               
            
               
                   
                 1.25 
                   
               
               
                   
                 16 × 14 
                 2.31 
               
               
                   
                 16 × 15 
                 2.06 
               
               
                   
                 16 × 20 
                 1.00 
               
               
                   
                 1.38 
               
               
                   
                 16 × 14 
                 2.55 
               
               
                   
                 16 × 15 
                 2.49 
               
               
                   
                 16 × 20 
                 0.79 
               
               
                   
                 1.45 
               
               
                   
                 16 × 14 
                 1.12 
               
               
                   
                 16 × 15 
                 1.50 
               
               
                   
                 16 × 20 
                 0.34 
               
               
                   
                 1.50 
               
               
                   
                 16 × 14 
                 1.02 
               
               
                   
                 16 × 15 
                 1.00 
               
               
                   
                 16 × 20 
                 0.29 
               
               
                   
                 1.55 
               
               
                   
                 16 × 14 
                 1.04 
               
               
                   
                 16 × 15 
                 1.01 
               
               
                   
                 16 × 20 
                 0.21 
               
               
                   
                   
               
            
           
         
       
     
     
       
         
           
               
               
               
             
               
                 TABLE 8 
               
               
                   
               
               
                 String 
                 String 
                 Spin 
               
               
                 Diameter (mm) 
                 Pattern 
                 Ratio 
               
               
                   
               
             
            
               
                 1.25 
                 16 × 14 
                 1.81 
               
               
                   
                 16 × 15 
                 1.71 
               
               
                   
                 16 × 18 
                 1.66 
               
               
                   
                 16 × 20 
               
               
                 1.38 
                 16 × 14 
                 1.81 
               
               
                   
                 16 × 15 
                 1.73 
               
               
                   
                 16 × 18 
                 1.62 
               
               
                   
                 16 × 20 
                 1.64 
               
               
                 1.45 
                 16 × 14 
                 1.96 
               
               
                   
                 16 × 15 
                 1.70 
               
               
                   
                 16 × 18 
                 1.64 
               
               
                   
                 16 × 20 
                 1.63 
               
               
                 1.50 
                 16 × 14 
               
               
                   
                 16 × 15 
                 1.84 
               
               
                   
                 16 × 18 
                 1.76 
               
               
                   
                 16 × 20 
                 1.75 
               
               
                   
               
            
           
         
       
     
     The test results summarized in Tables 3-8 demonstrate the significant beneficial performance characteristics that result from racquets produced in accordance with the present invention. Tables 3 and 4 (and  FIGS. 12 and 13 ) illustrate that the racquets configured in accordance with the present invention having fewer cross string segments exhibited greater main string segment deflection than racquets having a greater number of cross string segments. Main string deflection is a measure of the movement of the main string upon impact with a tennis ball. The greater the deflection the greater the ability of the string to impart spin to the ball. The test data showed that with racquet string having a string diameter within the range of 1.25 to 1.55 mm, the string deflection of a main string segment contacting a tennis ball in the Wilson Spin Test is at least 5 mm. Further, the string deflection can be at least 10 mm, and can extend over 20 mm. 
     The terms snap back time and snap back velocity refer to the time and velocity of the main string segment as it returns from its maximum deflection point to its original position prior to impact. Snap back time and velocity are inversely proportional. As snap back time decrease, snap back velocity increases. Snap back time and velocity can be used to measure a string bed&#39;s and racquet&#39;s ability to impart spin to a tennis ball. Tables 5 through 7 (and  FIGS. 14 and 15 ) illustrate that the racquets built in accordance with the preferred invention having a reduced number of cross string segments exhibited generally decreased snap back time, and significantly increased snap back velocities. The increased snap back velocity increases the likelihood that the main string segment will snap back at least partially while the tennis ball remains in contact with the string bed upon impact. The higher the snap back velocity, the greater the spin that can be imparted to the ball by the snapping back or returning of the main string segment to its original position. The test data showed that with racquet string having a string diameter within the range of 1.45 to 1.55 mm, at least one of the main string segments contacting the tennis ball exhibits a snap back velocity of at least 1 meter per second. Further, the test data showed that with racquet string having a string diameter within the range of 1.25 to 1.38 millimeters, at least one of the main string segments contacting the tennis ball exhibits a snap back velocity of at least 2 meter per second. 
     Table 8 (and  FIG. 16 ) illustrates that the racquets built in accordance with the preferred invention can provide an increased spin ratio. Spin rate is a measure the spin of a tennis ball. Spin ratio is the ratio of the spin rate of a tennis ball after impact with the tennis racquet to the spin rate of the tennis ball prior to impact with the tennis racquet. The higher the spin ratio, the greater the spin that was imparted to the ball. The test data showed that with racquet string having a string diameter within the range of 1.25 to 1.55 mm, the ratio of the outbound spin rate to the inbound spin rate is at least 1.67. Further, the test data showed that with racquet string having a string diameter of approximately 1.5 millimeters, the ratio of the outbound spin rate to the inbound spin rate is at least 1.8. 
     Referring to  FIGS. 9-11 , the enlarged sweet spot obtained through incorporation of the present invention into a racquet is demonstrated.  FIGS. 9-11  show the results of coefficient of restitution (“COR”) tests performed on three separate racquets. Each of the three racquets have similar head and hoops shapes and sizes. All three racquets have a hoop or head size of approximately 99 square inches. The head or hoop shapes of the three racquets are conventional, traditional generally ovoidal head shapes. 
       FIGS. 9-11  illustrate mappings of the areas of various COR values for a racquet of the present invention and for two representative prior art racquets. The COR is the ratio of the rebound velocity of a ball, such as, for example, a tennis ball, to the incoming velocity of the ball. The COR values of  FIGS. 9-11  were measured by using an incoming velocity of 90 feet per second, +/−5 feet per second. Each mapping reflects the COR values resulting from the impacts of the ball with the string bed at numerous, distributed locations about the string bed. The racquet is supported in the test apparatus only at the handle. In particular, the test apparatus secures the proximal end of the handle (approximately the proximal 6 inches of the handle). The attachment of the test apparatus to the racquet restricts the proximal end of the handle from moving or twisting along the x, y or z axes. Each racquet of  FIGS. 9-11  utilized a 16 gauge string, strung at a tension of 55 lbs tension. The racquets were measured in a strung condition generally at the center of the string bed. 
       FIG. 9  illustrates the areas of COR for a racquet having substantially the same frame as the racquet of  FIG. 10 , but the features of the present invention. The racquet of  FIG. 9  is a racquet model, Babolat® Pure Drive™, produced by Babolat VS of Lyon, France, and serves as a representative prior art racquet. The racquet of  FIG. 8  has a stringing pattern of 16×19. The numerical values of the COR areas for the racquet mapped in  FIG. 9  are provided in Table 9. The maximum COR reading for the racquet of  FIG. 9  was 0.40 with an area of 0.40 COR of 7.29 square inches. 
       FIG. 10  illustrates the areas of COR for another representative prior art racquet. The racquet is a Wilson® racquet, model Steam 99™ produced by Wilson Sporting Goods Co. of Chicago, Ill. The racquet has generally the same shape, head size, and weight as the racquet of  FIG. 11  and similar shape, head size and weight as the racquet of  FIG. 9 . The racquet of  FIG. 9  has a stringing pattern of 16×18. The numerical values of the COR areas for the racquet mapped in  FIG. 94  are provided in Table 9. The maximum COR reading for the racquet of  FIG. 10  was 0.40 with an area of 0.40 COR of 7.58 square inches. 
       FIG. 11  illustrates the enlarged areas of COR for a racquet built in accordance with a preferred embodiment of the present invention. The racquet of  FIG. 11  a 16×15 stringing pattern and other features of the present invention. The numerical values of the COR areas for the racquet mapped in  FIG. 11  are also provided in Table 9. The maximum COR reading for the racquet of  FIG. 11  was 0.45 with an area of 0.40 COR of 9.903 square inches. 
     In  FIGS. 9-11 , the curved line labeled 0.40 represents the border of the area on the strings where the COR was 0.40 or greater. The curved line indicated as 0.35 represents the border of the area on the strings where the COR was 0.35 or greater. Similarly, the other curved lines in  FIGS. 9-11  represent borders for the areas on the strings for various values of COR. In  FIG. 11  alone, the curved line labeled 0.45 is illustrated indicating the border of the area on the strings where the COR was 0.45 or greater. The “sweet spot” of the racquet is generally defined as the area of the string bed having one of the three following COR values: 0.25 or greater, 0.30 or greater, or 0.35 or greater. The numbers on the horizontal and vertical axes of  FIGS. 9-11  represent the distance from the center of the strung surface. For example, the center of the strung surface is indicated as 0.00. Two inches to the right of center of the strung surface is indicated as 2.00, 2 inches to the left of the center is indicated as −2.00, etc. 
     Table 9 below summarizes the COR data provided on  FIGS. 9-11 . 
     
       
         
           
               
             
               
                 TABLE 9 
               
             
            
               
                   
               
               
                 COMPARISON OF COR AREAS FOR RACQUETS OF PRESENT 
               
               
                 INVENTION WITH TWO PRIOR ART RACQUETS 
               
            
           
           
               
               
               
               
               
            
               
                   
                   
                 WILSON 
                 WILSON 
                   
               
               
                   
                   
                 STEAM 
                 STEAM 
               
               
                   
                 BABOLAT 
                 WITH 16 × 18 
                 WITH 16 × 15 
               
               
                   
                 PURE DRIVE 
                 STRINGING 
                 STRINGING 
                 % 
               
               
                   
                 RACQUET 
                 PATTERN 
                 PATTERN 
                 DIF- 
               
               
                 COR 
                 OF FIG. 9 
                 OF FIG. 10 
                 OF FIG. 11 
                 FERENCE 
               
               
                   
               
            
           
           
               
               
               
               
               
            
               
                 0.45 
                 0.00 
                 0.00 
                 0.02 
                 None/ 
               
               
                   
                   
                   
                   
                 Present 
               
               
                 0.40 
                 7.29 
                 7.58 
                 9.903 
                 36% &amp; 31% 
               
               
                 0.30 
                 23.04 
                 24.02 
                 27.93 
                 21% &amp; 16% 
               
               
                 0.25 
                 32.25 
                 33.18 
                 38.19 
                 18% &amp; 15% 
               
               
                   
               
            
           
         
       
     
     A comparison of  FIGS. 9-11  and the data of Table 9 indicates that the racquet made in accordance with the invention has a significantly greater “sweet spot” than either of the prior art racquets of  FIGS. 9 and 10 . The racquet of  FIG. 11  of the present invention has greater area within most of the border lines for various CORS, and achieves a higher level of COR (0.45). In the 0.40 COR area, the improvement in the sweet spot area is dramatic with increases over 31% 
     The incorporation of the present invention significantly improves the racquet&#39;s performance by increasing the ability of a player to impart spin to a ball and by increasing the size of the sweet spot of the racquet. The present invention provides a racquet with an enlarged sweet spot, increased main string deflection, reduced snap back time, increased main string snap velocity, and an increased “dwell time” without increasing the polar moment of inertia of the racquet head and without negatively affecting the maneuverability of the racquet. 
     While the preferred embodiments of the present invention have been described and illustrated, numerous departures therefrom can be contemplated by persons skilled in the art. Therefore, the present invention is not limited to the foregoing description but only by the scope and spirit of the appended claims.