US20120214625A1 - Tennis racket and method - Google Patents

Tennis racket and method Download PDF

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US20120214625A1
US20120214625A1 US13/352,853 US201213352853A US2012214625A1 US 20120214625 A1 US20120214625 A1 US 20120214625A1 US 201213352853 A US201213352853 A US 201213352853A US 2012214625 A1 US2012214625 A1 US 2012214625A1
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string
racket
portions
sports
cross
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Richard A. Brandt
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    • A—HUMAN NECESSITIES
    • A63—SPORTS; GAMES; AMUSEMENTS
    • A63B—APPARATUS FOR PHYSICAL TRAINING, GYMNASTICS, SWIMMING, CLIMBING, OR FENCING; BALL GAMES; TRAINING EQUIPMENT
    • A63B49/00—Stringed rackets, e.g. for tennis
    • A63B49/02—Frames
    • A—HUMAN NECESSITIES
    • A63—SPORTS; GAMES; AMUSEMENTS
    • A63B—APPARATUS FOR PHYSICAL TRAINING, GYMNASTICS, SWIMMING, CLIMBING, OR FENCING; BALL GAMES; TRAINING EQUIPMENT
    • A63B49/00—Stringed rackets, e.g. for tennis
    • A63B49/02—Frames
    • A63B49/022—String guides on frames, e.g. grommets
    • A—HUMAN NECESSITIES
    • A63—SPORTS; GAMES; AMUSEMENTS
    • A63B—APPARATUS FOR PHYSICAL TRAINING, GYMNASTICS, SWIMMING, CLIMBING, OR FENCING; BALL GAMES; TRAINING EQUIPMENT
    • A63B49/00—Stringed rackets, e.g. for tennis
    • A63B49/02—Frames
    • A63B49/025—Means on frames for clamping string ends
    • A—HUMAN NECESSITIES
    • A63—SPORTS; GAMES; AMUSEMENTS
    • A63B—APPARATUS FOR PHYSICAL TRAINING, GYMNASTICS, SWIMMING, CLIMBING, OR FENCING; BALL GAMES; TRAINING EQUIPMENT
    • A63B49/00—Stringed rackets, e.g. for tennis
    • A63B49/02—Frames
    • A63B49/028—Means for achieving greater mobility of the string bed
    • A—HUMAN NECESSITIES
    • A63—SPORTS; GAMES; AMUSEMENTS
    • A63B—APPARATUS FOR PHYSICAL TRAINING, GYMNASTICS, SWIMMING, CLIMBING, OR FENCING; BALL GAMES; TRAINING EQUIPMENT
    • A63B49/00—Stringed rackets, e.g. for tennis
    • A63B49/02—Frames
    • A63B49/10—Frames made of non-metallic materials, other than wood
    • A—HUMAN NECESSITIES
    • A63—SPORTS; GAMES; AMUSEMENTS
    • A63B—APPARATUS FOR PHYSICAL TRAINING, GYMNASTICS, SWIMMING, CLIMBING, OR FENCING; BALL GAMES; TRAINING EQUIPMENT
    • A63B51/00—Stringing tennis, badminton or like rackets; Strings therefor; Maintenance of racket strings
    • A—HUMAN NECESSITIES
    • A63—SPORTS; GAMES; AMUSEMENTS
    • A63B—APPARATUS FOR PHYSICAL TRAINING, GYMNASTICS, SWIMMING, CLIMBING, OR FENCING; BALL GAMES; TRAINING EQUIPMENT
    • A63B51/00—Stringing tennis, badminton or like rackets; Strings therefor; Maintenance of racket strings
    • A63B51/004—Stringing tennis, badminton or like rackets; Strings therefor; Maintenance of racket strings using strings with different tension on the same frame
    • A—HUMAN NECESSITIES
    • A63—SPORTS; GAMES; AMUSEMENTS
    • A63B—APPARATUS FOR PHYSICAL TRAINING, GYMNASTICS, SWIMMING, CLIMBING, OR FENCING; BALL GAMES; TRAINING EQUIPMENT
    • A63B51/00—Stringing tennis, badminton or like rackets; Strings therefor; Maintenance of racket strings
    • A63B51/02—Strings; String substitutes; Products applied on strings, e.g. for protection against humidity or wear
    • A—HUMAN NECESSITIES
    • A63—SPORTS; GAMES; AMUSEMENTS
    • A63B—APPARATUS FOR PHYSICAL TRAINING, GYMNASTICS, SWIMMING, CLIMBING, OR FENCING; BALL GAMES; TRAINING EQUIPMENT
    • A63B60/00—Details or accessories of golf clubs, bats, rackets or the like
    • A63B60/42—Devices for measuring, verifying, correcting or customising the inherent characteristics of golf clubs, bats, rackets or the like, e.g. measuring the maximum torque a batting shaft can withstand
    • A—HUMAN NECESSITIES
    • A63—SPORTS; GAMES; AMUSEMENTS
    • A63B—APPARATUS FOR PHYSICAL TRAINING, GYMNASTICS, SWIMMING, CLIMBING, OR FENCING; BALL GAMES; TRAINING EQUIPMENT
    • A63B49/00—Stringed rackets, e.g. for tennis
    • A63B49/02—Frames
    • A63B2049/0201—Frames with defined head dimensions
    • A—HUMAN NECESSITIES
    • A63—SPORTS; GAMES; AMUSEMENTS
    • A63B—APPARATUS FOR PHYSICAL TRAINING, GYMNASTICS, SWIMMING, CLIMBING, OR FENCING; BALL GAMES; TRAINING EQUIPMENT
    • A63B49/00—Stringed rackets, e.g. for tennis
    • A63B49/02—Frames
    • A63B2049/0212—Frames with defined weight
    • A—HUMAN NECESSITIES
    • A63—SPORTS; GAMES; AMUSEMENTS
    • A63B—APPARATUS FOR PHYSICAL TRAINING, GYMNASTICS, SWIMMING, CLIMBING, OR FENCING; BALL GAMES; TRAINING EQUIPMENT
    • A63B2209/00—Characteristics of used materials
    • A63B2209/02—Characteristics of used materials with reinforcing fibres, e.g. carbon, polyamide fibres
    • A—HUMAN NECESSITIES
    • A63—SPORTS; GAMES; AMUSEMENTS
    • A63B—APPARATUS FOR PHYSICAL TRAINING, GYMNASTICS, SWIMMING, CLIMBING, OR FENCING; BALL GAMES; TRAINING EQUIPMENT
    • A63B2220/00—Measuring of physical parameters relating to sporting activity
    • A63B2220/50—Force related parameters
    • A63B2220/51—Force
    • A63B2220/53—Force of an impact, e.g. blow or punch
    • A—HUMAN NECESSITIES
    • A63—SPORTS; GAMES; AMUSEMENTS
    • A63B—APPARATUS FOR PHYSICAL TRAINING, GYMNASTICS, SWIMMING, CLIMBING, OR FENCING; BALL GAMES; TRAINING EQUIPMENT
    • A63B2220/00—Measuring of physical parameters relating to sporting activity
    • A63B2220/80—Special sensors, transducers or devices therefor
    • A—HUMAN NECESSITIES
    • A63—SPORTS; GAMES; AMUSEMENTS
    • A63B—APPARATUS FOR PHYSICAL TRAINING, GYMNASTICS, SWIMMING, CLIMBING, OR FENCING; BALL GAMES; TRAINING EQUIPMENT
    • A63B60/00—Details or accessories of golf clubs, bats, rackets or the like
    • A63B60/002—Resonance frequency related characteristics
    • A—HUMAN NECESSITIES
    • A63—SPORTS; GAMES; AMUSEMENTS
    • A63B—APPARATUS FOR PHYSICAL TRAINING, GYMNASTICS, SWIMMING, CLIMBING, OR FENCING; BALL GAMES; TRAINING EQUIPMENT
    • A63B60/00—Details or accessories of golf clubs, bats, rackets or the like
    • A63B60/50—Details or accessories of golf clubs, bats, rackets or the like with through-holes
    • A—HUMAN NECESSITIES
    • A63—SPORTS; GAMES; AMUSEMENTS
    • A63B—APPARATUS FOR PHYSICAL TRAINING, GYMNASTICS, SWIMMING, CLIMBING, OR FENCING; BALL GAMES; TRAINING EQUIPMENT
    • A63B60/00—Details or accessories of golf clubs, bats, rackets or the like
    • A63B60/54—Details or accessories of golf clubs, bats, rackets or the like with means for damping vibrations
    • A—HUMAN NECESSITIES
    • A63—SPORTS; GAMES; AMUSEMENTS
    • A63B—APPARATUS FOR PHYSICAL TRAINING, GYMNASTICS, SWIMMING, CLIMBING, OR FENCING; BALL GAMES; TRAINING EQUIPMENT
    • A63B71/00—Games or sports accessories not covered in groups A63B1/00 - A63B69/00
    • A63B71/06—Indicating or scoring devices for games or players, or for other sports activities
    • A63B71/0619—Displays, user interfaces and indicating devices, specially adapted for sport equipment, e.g. display mounted on treadmills

Definitions

  • the present invention relates generally to a tennis racket and method of making and stringing a tennis racket.
  • the present invention provides a tennis racket and method of making a tennis racket the provides a structure by which the strings of a tennis racket may be provided with equal string lengths and with desired string vibration frequencies when striking a tennis ball to provide improved ball striking performance.
  • the tennis racket includes grommets to establish and maintain the desired string length and string vibration frequencies.
  • a layered structure is provided for the racket structure, preferably in the form of a carbon fiber material sandwich.
  • the racket head of one embodiment includes outwardly bowed sides configured to be drawn into a straight configuration when subject to string tension forces.
  • the string or strings used in the present racket may have varying densities to achieve the desired string vibration frequencies.
  • the present invention also provides a method for testing racket structures.
  • grommets at the string mounting openings of the racket.
  • the grommets are structural elements at the sides of racket faces through which the strings pass.
  • the present invention provides locking grommets for holding the strings and algorithms for setting the tensions using the grommets.
  • the present invention also provides a plurality of types of grommets, formed for example of Teflon or other low friction material, of elastic materials, or having an adjustable height, which help achieve the desired string lengths and frequencies.
  • a configuration of the racket head is provided that quantitatively establishes how far the sides of the racket face are bowed outward before stringing in order that the string lengths will become equal after stringing.
  • the present invention provides methods for manufacturing rackets according to the principles of the present invention.
  • the entire racket body is fabricated out of a carbon fiber sandwich. This construction provides superior strength and simplicity compared to other racket constructions.
  • the dimensions of the carbon fiber racket embodiment are determined so as to be optimized for racket strength to weight ratio.
  • the present invention also provides methods for testing the strength and performance of the rackets constructed according to the invention, as well as other racket constructions. The strength of the racket corners and the strength of the grommet string holders is tested.
  • the performance of the rackets is tested by laboratory measurements. The laboratory testing provides data that confirms the performance advantages of the present racket constructions over other constructions.
  • the tennis racket structures and procedures according to the present invention apply to rectangular-shaped tennis rackets, although other shapes may be encompassed within the scope of the invention.
  • Included in various embodiments of the present invention is (1) a derived outward bowing profile that compensates for inward bowing, and the determination of when outward bowing is necessary for optimal performance; (2) a means to achieve equal horizontal and vertical string frequencies by using different string tensions and/or string mass densities; (3) use of locking grommets that maintain different tensions on different strings, enabling strings to vibrate with equal frequency without equal length, and enabling the adjustment or replacement of individual strings; (4) a derivation of an algorithm for determining initial string tensions that provide equal string frequencies; (5) a specification of a sandwich-constructed embodiment of rectangular rackets that are approximately twice as strong per pound as conventional rackets fabricated from tubular elements; (6) a specification of a superior table-constructed embodiment of rectangular rackets that are nearly as strong per pound as the sandwich-constructed embodiment on the face sides
  • FIG. 1 is a top plan view of a tennis racket head having an overall rectangular shape according to a preferred embodiment of the present invention
  • FIG. 2 is a graph showing deflection of a racket element upon application of string tension forces
  • FIG. 3 is a graph of the deflection according to FIG. 2 but with the vertical axis exaggerated to better illustrated the quantity of deflection;
  • FIG. 4 is a top plan view of a tennis racket according to an embodiment of the present invention which establishes the dimensions described in the specification;
  • FIGS. 5 a - 5 j are schematic illustrations in cross section of a plurality of embodiments of string grommets as used in preferred embodiments of the present tennis racket;
  • FIG. 6 is a schematic diagram of a beam supported at its ends and along which is applied regularly spaced forces to demonstrate forces on a side of a strung racket;
  • FIG. 7 is a schematic illustration of deflection of the beam of FIG. 6 when subjected to the stringing forces
  • FIG. 8 is a cross section through a hollow cylindrical tennis racket frame showing stringing forces thereon;
  • FIG. 9 is a cross section through a tennis racket frame according to the principles of the present invention.
  • FIG. 10 is a plan view of a tennis racket according to one embodiment of the present invention.
  • FIG. 11 is a schematic representation of a tennis racket according to another embodiment of the invention.
  • FIG. 12 is an enlarged fragmentary view of a corner of a rectangular tennis racket showing string forces
  • FIG. 13 is a schematic illustration of a beam to which is applied a force
  • FIG. 14 is a cross sectional view through a side of a tennis racket frame in a preferred embodiment
  • FIG. 15 is an enlarged fragmentary view of a corner of a rectangular tennis racket of a preferred embodiment
  • FIG. 16 is a schematic representation of a sandwich of materials used in making a tennis racket according to a preferred embodiment
  • FIG. 17 is a schematic representation of a tennis racket manufactured as described.
  • FIGS. 18 a and 18 b are a plan view and side view, respectively, of a tennis racket face according to a preferred embodiment
  • FIGS. 19 a , 19 b and 19 c are a plan view, side view and end view of a handle portion of a tennis racket according to a preferred embodiment
  • FIG. 20 is a schematic representation of a force measuring apparatus used in the present method.
  • FIG. 21 is a perspective view of a testing apparatus as used in the present method.
  • FIG. 22 is a close up top view of the measuring apparatus
  • FIG. 23 is a diagram of a frame prototype manufactured to demonstrate a proof of concept
  • FIG. 24 is a perspective view of the frame prototype of FIG. 23 undergoing testing
  • FIG. 25 is another view of the frame prototype undergoing testing
  • FIG. 26 is a top perspective view of a racket constructed according to the teachings of the present invention.
  • FIG. 27 is a view of test equipment for testing the present tennis racket.
  • a first consideration is the vibration frequencies of the strings upon striking a tennis ball.
  • General considerations for the string frequencies include the following.
  • T is the tension on the string
  • m is the linear mass density of the string.
  • T and m are constant, but the string lengths vary considerably and therefore so do the vibration frequencies.
  • the values of T, m, and l (in each direction) can be all constant, and so the vibration frequencies f can be all constant. That is the simplest possibility, and innovative ways to accomplish this will be taught below. We will afterwards consider more general possibilities.
  • FIG. 1 shows a tennis racket 20 having a face or frame 22 made up of substantially straight sides 24 and substantially straight ends 26 .
  • the frame 22 has rounded corners 28 and a neck 30 that extends to a handle (not shown in this view).
  • Main strings 32 extend between the ends 26 and cross strings 34 extend between the sides 24 .
  • Teflon or Teflon coated, grommets and side strips.
  • Teflon is extremely slippery, having the lowest coefficient of friction (about 0.05 against polished steel) among practical solids. Its use will insure that the tension equalization obtains quickly and nearly perfectly during stringing and during impacts with balls. Other materials having a low coefficient of friction may be used as well to provide equalization of string tension across the face of the racket.
  • the plot of the deflection curve 36 is redrawn with a 4 to 1 aspect ratio.
  • the beam representing the long side 24 , in FIG. 1 , of the racket face
  • the beam is seen to deflect a maximum distance of about 0.5 inch.
  • the horizontal string 34 at the center of the racket face therefore decreases in length by about 1 inch (0.5 inch from the bending of each side 24 ).
  • the phase change difference be less than ⁇ /4, i.e. 2 ⁇ ft 0 ⁇ /4, or ⁇ f/f ⁇ 1 ⁇ 8 ft 0 ⁇ 0.046.
  • This string is attached at the bottom side and pulled through the top locking grommet with a chosen tension t 1 , and then locked into place.
  • This string will pull the upper racket side down a distance d 1 ( x ).
  • the lower side will be pulled up the same distance, so that the length of the string after locking will be w ⁇ 2d 1 (x 1 ).
  • the goal is to choose the applied string tensions t 1 , . . . , tN such that the final string frequencies fi, according to the formula
  • the locking grommets can be used to implement desired tension differences at different areas of the racket face 22 .
  • the areas of the face near the sides are, even for rectangular faces, areas of lower performance. This can be partially made up for by choosing the string tensions in these areas to be less than the tension on the strings near the center of the face. This will provide more uniform power across the entire racket face.
  • Another possible application of the locking grommets is to incorporate some elasticity within the grommet itself. This will provide additional options for controlling the string lengths, tensions, and frequencies.
  • Another important advantage of the locking grommets is the ability the grommets provide to compensate for decreases in string tensions that result from hitting with the racket. Each impact between a ball and the racket strings tends to lengthen and weaken the strings and reduce their tensions. The simple pulling of a string through a locking grommet can compensate for this by shortening the string section and increasing its tension. The need for restringing will therefore be significantly reduced. (A simple hand-held tension gauge can be used in series with the pulled string to tell when the desired string tension is achieved.)
  • FIGS. 5 a - 5 j Each of the schematic illustrations of the locking grommets show a section through a right side beam 24 or 26 of a racket face, so that the racket face is to the left of the segment.
  • Each segment contains a single hole 40 through which a string 32 or 34 , depicted as a right-facing arrow, passes.
  • the string 32 or 34 is attached to the opposite (left) side of the face, and that the desired tension is applied to the string by pulling the string to the right through the depicted hole 40 in the direction of the arrow.
  • the illustrations provide methods of locking the string within the hole 40 in the beam at this chosen tension using the locking grommet.
  • the hole 40 is conical and the string 32 or 34 is locked in place by inserting a conical plug 42 , shown in FIG. 5 b , into the hole 40 .
  • This simple locking grommet mechanism uses the friction between the string 32 or 34 and the plug 42 and hole 40 to restrain the string.
  • the conical hole 40 is threaded as indicated by heavy lines 44 and the string 32 or 34 passes through a center hole 48 in a compressible threaded conical screw 50 .
  • the screw 50 is of a material that compresses when tightened into the conical hole 40 so as to decrease the diameter of the central hole 48 .
  • the screw 50 includes means for threadably tightening the screw into the hole 40 , such as a slot or shaped recess that receives a screwdriver, for example.
  • the conical threaded screw 50 is shown in cross section in FIG. 5 d with the central hole 48 in an open, string receiving position.
  • An outer surface 52 of the conical screw 50 is threaded with a threading corresponding to the threading 44 in the conical hole 40 of FIG. 5 c . It is understood that the two part illustration of FIG. 5 d shows the two halves of a single conical screw.
  • the string 32 or 34 passes under a cylindrical bar 54 that resides in the hole 40 to the left (with respect to the drawing) of a stopping block 56 (shown as a black rectangle).
  • the stopping block 56 is secured in place in the conical hole 40 by being anchored into the hole wall 40 although other anchoring means are also contemplated.
  • the string 32 and 34 can be freely pulled to the right as the cylinder 54 rotates, but when the pulling force on the string is released, the cylinder 54 is wedged into the conical hole 40 and holds the string in place.
  • FIG. 5 f depicts a locking grommet with a hole 58 in the racket frame having a stepped configuration and includes a pair of elements 60 (shown as shaded bars that are angled toward one another) mounted at the step in the hole 58 .
  • the elements 60 that are forced together by spring mechanisms shown schematically at 62 that for example are positioned between the racket body and each element 60 to bear against the elements and press them against the string. Two or more such elements 60 may be provided at the hole 58 .
  • the friction between the elements 60 and the string 32 or 34 prevents the string from moving back to the left, but the string can be easily pulled to the right. The string is therefore locked in position at the desired tension by the locking grommet.
  • the locking grommet of FIG. 5 g depicts the use of a tightening screw 64 to lock the string 32 or 34 into place.
  • the string passes through a central hole 66 in an external block 68 (as shown in black) that is affixed to the frame of the racket at the hole 70 .
  • the screw 64 is threaded into cooperating threads in a bore 72 in the block that extends transverly to the hole 66 through which the string extends.
  • the screw 64 is turned down into the bore 72 until it bears against the string 32 or 34 , forcing the string against an opposite will of the central hole 66 to lock the string in place.
  • the external block 68 is affixed to the frame of the racket so as to not come loose during use.
  • a similar threaded screw 64 is threadably received into a bore 72 in a portion 74 of the frame as defined by a recess 76 .
  • the screw 64 presses the string 32 or 34 against an inside wall of the hole 70 so as to secure the string at the desired tension and position.
  • the recess 76 and/or the screw 64 are configured to permit the screw to be tightened and loosened by a user's fingers or by a tool.
  • this embodiment locks the string position by a locking grommet built into the frame itself.
  • FIG. 5 i a locking grommet embodiment that makes use of a compressible elastic element 78 through which the string 32 or 34 passes as indicated by the broken line.
  • the compressible element 78 is disposed in a conical shaped sleeve or cone 82 formed in the racket frame.
  • the compressible element is compressed by screwing a threaded nut 80 onto the threaded cone 82 .
  • the threaded cone 82 is disposed in a recess 84 in the frame. Rotating the nut 80 to the left causes the cone 82 to compress the element 78 onto the string and thus hold it in place.
  • FIG. 5 i is shown a locking grommet embodiment that makes use of a compressible elastic element 78 through which the string 32 or 34 passes as indicated by the broken line.
  • the compressible element 78 is disposed in a conical shaped sleeve or cone 82 formed in the racket frame.
  • the compressible element is compressed by screwing a threaded nut 80
  • the element 78 may release the string for tension adjustment by screwing the threaded nut 80 to the right on the threaded cone 82 . Rotating the nut 80 to the left again locks the string at the desired tension by the compression of the elastic element 78 onto the string and to hold it in place.
  • FIG. 5 j A similar concept is shown in FIG. 5 j , wherein the element 78 is compressed by screwing a threaded cone 86 over a threaded cylinder 88 . Rotating the cone 86 to the left causes the cone 86 to compress the element 78 onto the string and thus hold it in place.
  • the two properties that determine a racket's strength are materials and geometry.
  • the main material used to fabricate essentially all contemporary rackets is carbon fiber.
  • the bulk measure of the strength of a material is its Young's modulus E. This modulus is defined as the ratio of stress (applied force per unit area, F/A) to strain (elongation or compression per unit length ⁇ 1/1) according to the equation:
  • the bulk measure of weight of a material is its density ⁇ , the ratio of weight W to volume V according to the equation:
  • the beam 90 is a simple model of a side 24 or 26 of the face of a rectangular racket with supports 92 near each end.
  • the beam 90 deflects or bends under the applied force.
  • the deflection distance D is determined by the applied force F, the beam length L, the material Young's Modulus E, and the area moment of inertia I of the beam cross-section according to the following equation:
  • I is defined by the geometry of a cross-sectional slice of the beam according to the equation:
  • the integration is over the area of the cross-section containing material, with y being the perpendicular distance between the neutral axis and the area element dA.
  • y is the vertical distance between the horizontal neutral axis (as indicated by a dashed line) and the area elements in the material between the circles (as indicated by a shaded area). In this case.
  • the vertical arrow 98 in the FIG. 8 represents the force exerted by the string tension.
  • the area of the cross-section of the uniform beam is defined by equation.
  • the goal of the racket construction is to achieve adequate strength, so that the deflection D is relatively small, without requiring a relatively large area A, so that the weight W is also relatively small.
  • the goal is therefore to choose the geometry of the cross-section such that I is as large as practically possible. According to its definition (Eq. 8), I becomes larger when the racket material is placed as far as possible from the neutral axis of the face side (beam).
  • tubular carbon fiber racket frame is strong because much of the material is far from the neutral axis, as indicated for the circular annulus of FIG. 8 .
  • this structure is, however, not strong enough to form a preferred light-weight rectangular racket face embodiment.
  • a much stronger frame can be constructed using carbon fiber sandwiches. Such a sandwich consists of two parallel relatively thin carbon fiber plates separated by a light filler material.
  • FIG. 9 The cross-section of a beam 100 made out of such a sandwich is illustrated in FIG. 9 .
  • the neutral axis 102 is indicated by the dashed line, and the vertical arrow 104 represents the force exerted by the string tension.
  • Comparison of FIGS. 8 and 9 shows that the material in the tubular structure has some material far from the neutral axis, but also some material close to the neutral axis.
  • the sandwich structure on the other hand, has all the material (apart from the light filler material) far from the neutral axis.
  • a A ⁇ (r 2 2 ⁇ r 1 2 ) is the area of the carbon fiber material in the annulus cross-section.
  • I S I A 1 3 ⁇ d 2 + d ⁇ ⁇ h + h 2 r 2 2 + r 1 2 . ( Eq . ⁇ 14 )
  • a better method of construction is to fabricate the entire racket face 114 out of a single sandwich beam. Such an embodiment, with rounded corners 116 , is shown in FIG. 11 .
  • the corners 116 are stronger, but still not strong enough without using carbon fiber plates that are relatively thick and wide and therefore rather heavy.
  • FIG. 12 This is a front view of the racket face, with the parallel carbon fiber plates 106 shown as shaded elements, and the strings 118 are represented by the vertical arrows. The tensions in these strings 118 exert strong stresses on the corners 116 because the carbon fiber plates 106 are long and thin. We will estimate these stresses below.
  • the upper plate As a cantilever beam 120 rigidly attached to a solid support 122 at the left end. If a force F is applied on the top of the beam 120 at a distance L from the support, and the beam 120 has width w and thickness t, the resultant stress at the support is given by the equation
  • This value is large because t must be small in order to have an acceptable racket weight.
  • the rupture stress of carbon fiber is about
  • the cantilever model is, of course, a simplification, and it does not incorporate the strengthening effects of the rounded corners and parallel plates. Also, one can use stronger fiber and a larger width, more complicated geometry, and more optimal fiber lay-up patterns. We have, however, used realistic finite element computer calculations to evaluate the relevant stresses, and the results substantiate the conclusions drawn from the model, Given these large estimates of the corner stress, the difficulty described here is obviously serious.
  • FIG. 14 Such a table cross-section is illustrated in FIG. 14 .
  • This section has three carbon fiber outer plates 130 , 132 and 134 , instead of the two plates 106 shown in FIG. 9 .
  • the upper (table top) plate 134 is similar to the upper sandwich plate 106 , but the bottom sandwich plate 106 is replaced by two side (table leg) plates 130 and 132 .
  • the neutral axis 136 is indicated by the dashed line, and the vertical arrow 138 represents the force exerted by the string tension.
  • the volume 140 between the table legs 130 and 132 consists of light filler material as in the sandwich.
  • This table section will have a smaller area moment of inertia per pound than the sandwich section because it has more carbon fiber material placed closer to the neutral axis. It is therefore necessary for the table beam 134 to be heavier than the sandwich beam in order to have equal strength, but this small additional weight is more than made up for by the fact that the racket constructed from these table beams requires no corner or filler reinforcement. We will establish these facts below.
  • the dimensions given in FIG. 14 are d, the width of the upper (table top) carbon fiber plate 134 , b, the height of the side (leg) plates 130 and 132 , h, the width of the filler material 140 between the plates, and c, the thickness of the upper plate 134 .
  • the thickness of the side plates 130 and 132 is (b ⁇ h)/2 each.
  • the first term in (Eq. 19) is the contribution from the top and the second term is the contribution from the legs. Since c will always be much less than b, a good approximation is
  • the sandwich corner 116 is illustrated in FIG. 12 above.
  • the corresponding table corner 142 is illustrated in FIG. 15 .
  • the plate is thin (t ⁇ 0.1 inch) and wide (w ⁇ 0.75 inch), whereas for the table corner, the plate 134 is fat (t ⁇ 0.75 inch) and narrow (w ⁇ 0.1′′). This makes a large difference in the stress ⁇ max at the support.
  • the cantilever model does not take into account the strengthening effects of the rounded corners and parallel plates.
  • the range in calculated stresses for the sandwich corner is 1,700,000-2,400,000 psi for the sandwich corner, and 530,000-650,000 psi for the table corner. The size of these ranges arises from use of different dimensions, lay-up patterns, and epoxies. With any of these possibilities, the superiority of the table construction is apparent.
  • Rectangular rackets fabricated from the present carbon fiber table elements thus possess strong sides, strong corners, and protected filler material. That is why they are the preferred embodiment for a rectangular racket.
  • Such a sandwich 148 is illustrated in FIG. 16 . It consists of top and bottom carbon fiber plates 150 and 152 , separated by light filler material 154 .
  • the filler material 154 may be a fiber or non-fibrous material, an expanded foam material, or other materials made of natural or synthetic materials. These plates will become the side (table leg) plates 130 and 132 of the table in FIG. 14 .
  • the racket frame can be cut out of this sandwich 148 in a single piece 156 , as illustrated in FIG. 17 . Then one attaches a long thin carbon fiber strip, of thickness equal to the dimension c in FIG. 14 , and width equal to the thickness of the above sandwich (the dimension d in FIG. 14 ).
  • This strip can be attached to the outer perimeter of the racket face in FIG. 17 , using suitable epoxy. For added strength, this strip can have upper and lower lips, rendering it into a c-shape.
  • Such a strip can be fitted around the outer perimeter of the racket face and bonded with epoxy. The lips or extensions extend onto the top and bottom plates 150 and 152 , adding not only strength but a finished look.
  • stringing holes can be drilled in appropriate places around the face perimeter 158 , grommets, or grommet strips, can be inserted into these holes, and the carbon fiber handle stem 160 can be supplemented with a light material and then strapped. The racket would then be ready for stringing.
  • the shape of the cutout in FIG. 17 can be generalized to include the improvements discussed previously.
  • the corners 162 can be rounded, to improve the racket strength and appearance.
  • the face sides 164 can be bowed outward so that a purely rectangular face will obtain after stringing.
  • the side strips can be grooved or otherwise altered to accommodate grommets and strings. This ease of construction is a major advantage of the present table construction.
  • the table legs 130 and 132 are fabricated out of carbon fiber plates with a 45° lay-up pattern.
  • the tabletops 134 are fabricated out of carbon fiber plates with a unidirectional lay-up pattern.
  • I T 0.0083 in 4
  • the maximum deflection of a 12 inches side is 0.155 inch.
  • b can be reduced to 0.5 inch.
  • the 12 inches side of the racket face has been designed to withstand the 1140 pounds of force arising from the 19 attached strings at 60 lbs. tension each.
  • the throat and handle of the racket need not be this strong.
  • the forces on these elements arise during the brief impact times (about 0.004 sec), during which the racket strikes a ball. This force is at most about 250 lbs, and lasts for such a short time that the throat dimensions can be significantly less than those in Eq. 22.
  • the racket is preferably strung with separate string sections for each of the main strings and cross strings. It is also contemplated that the string may be a single continuous string or may be of several string segments.
  • FIGS. 18 a and 18 b for the racket face 166
  • FIGS. 19 a , 19 b and 19 c for the throat 168 and handle 170 .
  • the throat tapers into a handle stem 0.625 inch wide. All of the other dimensions are specified in the drawings. A number of holes are depicted in the drawings. These serve to lighten the racket in areas where there is sufficient strength to accommodate them. For example, holes 174 are shown at the corners 176 where the throat 168 attaches (see FIG. 18 a ). Holes 178 and 180 are aligned along the center of the handle 170 in the top view of FIG. 19 a and holes 182 are transverse to the holes 180 as seen in the side view of FIG. 19 b . The holes may be filled with a light weight material or left as openings in the racket frame. Handle shaping elements 184 are provided on the handle portion 170 to provide a comfortable grip.
  • FIGS. 18 a and 18 b show a tennis ball 172 in phantom for a sense of scale.
  • the racket handle stem 170 cut out of the sandwich, has width 0.625 inch and height 0.75 inch.
  • Light material such as balsa wood, is attached to this stem, as shown in FIGS. 19 a , 19 b and 19 c as the handle shaping elements to enlarge the handle into the desired size (width 1.25 inches and height 1.14 inches), and shape (an octagonal shape is standard and is used here).
  • the string tensions are preferably set so be equal for each main string and each cross string.
  • the string tensions on both the main strings and cross strings are equal to one another.
  • the string vibration frequencies of the main strings are preferably equal and the string vibration frequencies of the cross strings are preferably equal to one another.
  • the vibration frequencies of both the main strings and the cross strings are equal.
  • the variables ti and li refer to the tension and length, respectively, of each main string
  • the variables sj and kj refer to the tension and length, respectively, of each cross string.
  • the linear density of the strings are designated mj for the density of the main strings and m′j for the densities of the cross strings.
  • FIG. 20 To confirm that the table construction ( FIG. 14 ), with the chosen dimensions (Eq. 22), is strong enough to hold the inserted grommets and withstand the force from the string tensions, we have devised the apparatus illustrated in FIG. 20 .
  • a section of the table beam 200 (shown in grey) is held in place by a pair of solid stops 202 (shown in black).
  • a racket string 204 is threaded through grommets 206 in two holes in the beam 200 , and attached to a load cell 208 (shown as a shaded element to the right).
  • the load cell 208 is attached to a block 210 (shown in black) that can be moved backward by rotating an inserted threaded bolt 212 . This backward movement exerts a force F on the strings, and the magnitude of the force is indicated on a display unit 214 (shown as a shaded block in the lower center) wired to the load cell.
  • the method we have devised to do this utilizes a small replica 212 of a racket face side and corners, as illustrated in FIG. 23 .
  • the central part 214 of the upper part of the replica 212 has the same cross-section dimensions (Eq. 22) as the table cross-section shown in FIG. 14 .
  • the inside replica length is 4.5 inch, and the outside length is 5.75 inch. (The inside length of the racket face drawn in FIG. 18 a is 12 inches.)
  • the corner curvatures of the replica and the real racket are the same.
  • the force on the long side of the real racket face arising from 60 lbs. of tension on each of 19 strings is 1140 lbs.
  • the equivalent force F on the replica 212 the force that produces the same stress at the corners, when applied to the center of the replica, is 1390 lbs. (This force is greater because the effective lever arm is less.)
  • Photographs of this testing apparatus are given in FIGS. 24 and 25 . We continually increased the applied force F until one of the upper corners in the replica began to rupture.
  • FIG. 26 A photograph of a produced racket 230 , constructed according to the above specifications, is shown in FIG. 26 .
  • the racket of the present invention may have a weight with string of less than 14 oz. It is also possible to construct a racket according to the present invention with a weight of less than 12 oz., or even less than 10 oz.
  • the quantity that characterizes the performance of a fixed racket at any point on the face is the velocity ratio at that point, the ratio of the rebound speed to the incident speed.
  • the following table exhibits velocity ratio data that is typical of our measurements.
  • the impact speeds are given in the first column.
  • the velocity ratios are compared at the center and at the point 3.5′′ below the center. The ratio is seen to decrease by 0.52% and 0.75% for the rectangular racket, and by 10.48% and 8.55% for the oval racket.
  • the off-center performance of the rectangular racket is seen to be far better.
  • the rebound ball linear and angular velocities are completely determined by the COR at the impact point, along with the details of the racket stroke (linear velocity, angular velocity), the racket kinematics (weight, COM, MOIs), and the incident ball properties (weight, linear velocity, and angular velocity).
  • the best performance is at the center of the faces.
  • the point of best performance is shifted towards the handle because that is the direction towards the COM of the racket.
  • the effect of this is to replace the 0.75% decrease in performance by a 1.19% improvement in performance 3.5′′ down from the center.
  • the effect of this is to replace the 8.55% decrease in performance by a 7.45% decrease in performance 3.5′′ down from the center.
  • the COR differences exhibited in the above table give rise to significant differences in the trajectory of a struck tennis ball.
  • the velocity and spin of a hit ball is determined by the ball-racket COR together with all the details of the stroke, the incident ball, and the kinematics.
  • the difference in the hit ball speed at the center of the rectangular racket and 3.5 inches down is only about 0.15 mph.
  • the resultant difference in the hit ball trajectory is less than 4 inches overall.
  • the corresponding difference for the oval racket is 6.5 mph, and the resultant difference in the hit ball trajectory is more than 12.5 feet.
  • the superiority of the rectangular racket is clear
US13/352,853 2011-01-26 2012-01-18 Tennis racket and method Abandoned US20120214625A1 (en)

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US20140038754A1 (en) * 2011-04-20 2014-02-06 Lacoste Next-Generation Wooden Racket
US9132322B1 (en) * 2014-05-22 2015-09-15 Kenneth R. Coley Tennis racket
US20150335960A1 (en) * 2011-08-24 2015-11-26 Ojoee Industries, Inc. Tennis racket having an optimized striking area
US20220016503A1 (en) * 2020-07-17 2022-01-20 Head Technology Gmbh Characterization of a ball game racket frame

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Publication number Priority date Publication date Assignee Title
CN107050784A (zh) * 2017-05-12 2017-08-18 邬惠林 圆角长方形三边圆弧化羽毛球拍

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US4566695A (en) * 1983-03-17 1986-01-28 Melby Phillip J Game racket having adjustable string mounts
US6074315A (en) * 1998-02-19 2000-06-13 Linda C. Yimoyines Racquet with visually differentiated grommets and method of stringing thereof
US6179735B1 (en) * 1997-02-24 2001-01-30 Mcmahon Marshal Apparatus and method for maintaining differential tensions in the strings of a sporting racket
US6344006B1 (en) * 2000-11-17 2002-02-05 Richard A. Brandt Sports racket having a uniform string structure

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US6506134B2 (en) * 1997-06-25 2003-01-14 Fabio Paolo Bertolotti Interlocking string network for sports rackets
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US1526734A (en) * 1923-04-04 1925-02-17 Frederick B Andrews Tennis racket
US4566695A (en) * 1983-03-17 1986-01-28 Melby Phillip J Game racket having adjustable string mounts
US6179735B1 (en) * 1997-02-24 2001-01-30 Mcmahon Marshal Apparatus and method for maintaining differential tensions in the strings of a sporting racket
US6074315A (en) * 1998-02-19 2000-06-13 Linda C. Yimoyines Racquet with visually differentiated grommets and method of stringing thereof
US6344006B1 (en) * 2000-11-17 2002-02-05 Richard A. Brandt Sports racket having a uniform string structure

Cited By (5)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US20140038754A1 (en) * 2011-04-20 2014-02-06 Lacoste Next-Generation Wooden Racket
US20150335960A1 (en) * 2011-08-24 2015-11-26 Ojoee Industries, Inc. Tennis racket having an optimized striking area
US9132322B1 (en) * 2014-05-22 2015-09-15 Kenneth R. Coley Tennis racket
US20220016503A1 (en) * 2020-07-17 2022-01-20 Head Technology Gmbh Characterization of a ball game racket frame
US11857855B2 (en) * 2020-07-17 2024-01-02 Head Technology Gmbh Characterization of a ball game racket frame

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JP2014503337A (ja) 2014-02-13
EP2667951A4 (en) 2014-10-22
RU2013138629A (ru) 2015-03-10
MX2013008630A (es) 2014-02-27
BR112013018946A2 (pt) 2018-06-26
WO2012102924A1 (en) 2012-08-02
CN103619423A (zh) 2014-03-05
AU2012209400A1 (en) 2013-08-15
CA2825530A1 (en) 2012-08-02
EP2667951A1 (en) 2013-12-04

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