JP2014503337A - Tennis racket and method - Google Patents

Abstract

  A tennis racquet is provided having a rectangular ball striking face with rounded corners. The racket is formed from a carbon fiber sandwich with a lightweight material incorporated in between. Carbon fiber strips are attached to the outer edges of the upper and lower sheets of the two carbon fibers. A rectangular frame is formed having sides that are curved outwards so that they are drawn by gut tension into the form of straight sides. Various structures of locking grommets are provided to hold the gut at a predetermined tension. Test equipment and methods for testing tennis rackets are provided.

Description

(Cross-reference of related applications)
This application claims the benefit of US Provisional Patent Application No. 61 / 436,259, filed Jan. 26, 2011, which is incorporated herein by reference.

  The present invention relates generally to a tennis racket and a method for creating and stretching a tennis racket.

  In US Pat. No. 6,344,006 B1 and US Pat. No. 7,081,056 B2, R. Brandt says that the gut (string) length is equal in the vertical and horizontal directions, or more generally Taught the advantages of a tennis racket with equal gut frequencies. In this patent document, these ideas are further developed and improved, and a construction method for manufacturing and testing such a racket is presented.

  The present invention provides a tennis racket and provides a structure capable of providing a tennis racket gut with equal gut length and desirable gut frequency when hitting a tennis ball to improve hitting performance. A method for creating a tennis racket is provided. In a preferred embodiment, the tennis racket includes grommets that establish and maintain the desired gut length and gut frequency. In a further development, 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 an outwardly curved side configured to be pulled into a linear configuration when subjected to gut tension. In order to achieve the desired gut frequency, the gut (s) used in the racket of the present invention may have a varying density. The present invention also provides a method for testing a racket structure.

  More particularly, a number of possible structures and methods for achieving the desired gut length and frequency are achieved by using grommets in the racket gut mounting opening. Grommets are structural elements on the side of the racket striking face (face) through which the gut passes. The present invention provides locking grommets (rings, locking grommets) for holding guts and algorithms for setting tension using grommets. The present invention also helps to achieve the desired gut length and frequency, eg, made of Teflon or other low friction material, elastic material, or having an adjustable height Provides a type of grommet. A racket head configuration is provided that quantitatively establishes how far the sides of the racket striking surface before stretching are curved outward so that the gut lengths are equal after stretching.

  In a further development, the present invention provides a method of manufacturing a racket according to the principles of the present invention. In a preferred embodiment, the entire racquet body is fabricated from a carbon fiber sandwich. This structure provides superior strength and simplicity compared to other racket structures. The dimensions of the carbon fiber racket embodiment are determined to be optimal for the specific strength of the racket. The present invention also provides a method for testing the strength and performance of rackets constructed in accordance with the present invention, as well as other racket structures. The racket corner strength and grommet gut holder strength are tested. The performance of the racket is tested by laboratory measurements. Laboratory tests provide data supporting the performance advantages of the racket structure of the present invention over other structures.

  In general, the structure and procedure of a tennis racket according to the present invention applies to a rectangular tennis racket, but other shapes may be included within the scope of the present invention. Various embodiments of the present invention include the following. (1) The contour of the outward curvature that is derived to offset the inward curvature, and the determination of when an outward curvature is required for optimal performance. (2) Means for achieving equal gut frequencies in the horizontal and vertical directions by using different gut tensions and / or gut mass densities. (3) Using locking grommets that maintain different tensions for different guts, allowing guts to vibrate at equal frequencies without using equal lengths, and allowing individual guts to be adjusted or replaced. . (4) Derivation of algorithm for determining initial gut tension that provides equal gut frequency. (5) Specification of an embodiment of a rectangular racquet sandwich structure, where the strength per pound (0.454 kg) is about twice that of a conventional racquet fabricated from tubular elements. (6) The strength per pound (0.454 kg) is almost the same as that of the embodiment in which the face sides are sandwiched, and the corners are much stronger and the filling material is better. Specification of an embodiment of an excellent table structure with a rectangular racket that protects and makes construction easier than ever. (7) Use of a cantilever model to analytically estimate the stress on the racket corner. (8) Design and realization of devices that test the strength of the side beams and corners of the racket.

1 is a top view of a tennis racket head having a generally rectangular shape according to a preferred embodiment of the present invention. FIG. It is a graph which shows the bending of the racket element at the time of applying gut tension. FIG. 3 is a deflection graph according to FIG. 2 with the vertical axis emphasized to better show the amount of deflection. 1 is a top view of a tennis racket according to one embodiment of the present invention establishing the dimensions described herein. FIG. 5a-5j are schematic cross-sectional views showing multiple embodiments of gut grommets, as used in the preferred embodiment of the tennis racket of the present invention. FIG. 4 is a schematic diagram showing a beam supported at an end, to which a regularly spaced force is applied, in order to explain the force on the side of the stretched racket. It is the schematic which shows the bending of the beam of FIG. 6 when receiving a tension force. It is sectional drawing of the flame | frame which shows the tension force with respect to a hollow cylindrical tennis racket frame. 1 is a cross-sectional view of a tennis racket frame according to the principles of the present invention. It is a top view of the tennis racket by one Embodiment of this invention. It is the schematic of the tennis racket by another embodiment of this invention. It is the elements on larger scale of the corner | angular part of the rectangular tennis racket which show tension force. FIG. 2 is a schematic view of a beam being subjected to a force. It is sectional drawing of the edge | side of the tennis racket frame of preferable one Embodiment. It is the elements on larger scale of the corner | angular part of the rectangular tennis racket of preferable one Embodiment. 1 is a schematic diagram showing a sandwich of materials used to make a tennis racket according to a preferred embodiment. FIG. 1 is a schematic view of a tennis racket manufactured as described. FIG. FIG. 18a is a plan view of a tennis racket hitting surface according to a preferred embodiment, and FIG. 18b is a side view thereof. 19a is a plan view of a handle portion of a tennis racket according to a preferred embodiment, FIG. 19b is a side view thereof, and FIG. 19c is an end view thereof. It is the schematic of the force measuring device used with the method of this invention. 1 is a perspective view of a test apparatus as used in the method of the present invention. FIG. It is a close-up top view of a measuring device. It is the figure of the frame prototype manufactured in order to prove the concept. FIG. 24 is a perspective view of the frame prototype of FIG. 23 being tested. FIG. 5 is another diagram of a frame prototype being tested. 1 is a top perspective view of a racket constructed in accordance with the teachings of the present invention. FIG. It is a figure of the test equipment for testing the tennis racket of this invention.

  The present invention will be described with reference to the drawings. The first thing to consider is the gut frequency when hitting a tennis ball. General considerations for gut frequencies include:

(Gut frequency)
Since all guts interact with each other during a collision with a tennis ball, the calculation of the performance of a given tennis racket is a complex problem in a significant part. Such calculations are reported in U.S. Pat. No. 5,672,809 and U.S. Pat. No. 6,344,006, where a rectangular striking racket with equal gut length in each direction provides optimal performance. Was the main conclusion. The reason for this is as follows.
a) Guts of equal length (and tension and density) vibrate at the same frequency. Thus, they respond to the impacting balls all at once, resulting in the maximum repulsive force.
b) When a ball collides with two parallel guts of unequal length, the ball receives different forces from each gut and the rebound direction becomes unintended. This error is eliminated if all parallel guts have the same length.
c) When a ball collides with a gut away from the center of the gut, the ball receives unequal forces from each side of the pressed gut. The shorter the gut length, the greater this effect. In the case of a rectangular hitting racket, each gut has the same (maximum) length, so this source of error is minimized.
d) Given a racket weight, the moment of inertia about the longitudinal center axis of the rectangular striking racket is much greater than that of a conventional racket. Thus, the collision away from the axis causes the racket to rotate away from the colliding ball, but the amount of rotation is much less than in conventional rackets. Thus, the resulting angular error and speed reduction is greatly reduced.
e) Since the angular rotation of the rectangular racket is less than that of the conventional one, physical injury (generally called “tennis elbow”) of the player's arm due to eccentric hitting is reduced.

  The main benefit of equal gut lengths is obtained when the lengths are not exactly equal, but the gut frequencies are equal. The frequency of the gut with the fixed end is given by:

(Formula 1)
Where l is the gut length, T is the tension against the gut, and m is the linear mass density of the gut. In the case of a conventional racket, T and m are constant, but the gut length varies greatly, and therefore the frequency also varies greatly. In a rectangular hitting racket, the values of T, m, and l (in each direction) can all be constant, and therefore the frequency f can all be constant. This is the simplest possibility, and an innovative way to achieve this is described below. More general possibilities are considered below.

  The gut on the tennis racket is, of course, not free between the sides of the frame. Since the guts intersect each other many times along their length, the performance of a given racket is complex on a computer as described in US Pat. No. 6,344,006 B1. Must be determined by calculation. The patent shows that a racket with equal fundamental frequency guts (as calculated using Equation 1) provides optimal performance.

  When referring to a racket having a rectangular striking surface, it is understood that it is essential that the opposing surfaces of the striking surface to which the gut is attached are parallel. This leaves the freedom to round the corners of the striking face frame in a section beyond where the tension holes are located. Such rounded corners increase the strength of the racket and improve its appearance. Such a racket is shown in FIG.

  Specifically, FIG. 1 shows a tennis racket 20 having a striking surface or frame 22 composed of a substantially straight side 24 and a substantially straight end 26. The frame 22 has a rounded corner 28 and a neck 30 that extends to a handle (not shown in this view). The main gut 32 extends between the end portions 26 and intersects with a gut 34 extending between the sides 24.

(Constant tension)
The simplest way to get an equal gut frequency in each direction is to keep the values of l, T, and m all constant. First, assume a moment that begins with a completely rectangular striking surface before stretching and that the striking surface after stretching remains essentially rectangular. When tensioning the racket, the selected tension T is applied to each gut, but as the tension progresses, the tension applied to the previous gut changes slightly as a new gut is added at tension T. After all the guts have been attached, the gut tensions are balanced and the resulting tension T ′ for the gut is different from the applied tension T. A good gut craftsman will understand how to select the applied tension so that the resulting tension is desired.

  In conventional grommets with guts extending therethrough at the sides and ends of the racket, tension equalization is incomplete. Friction against the gut within each grommet and against the outer striking edge between the grommets prevents tension equalization. In addition, the force applied to the gut by impact with the ball at least temporarily redistributes the tension.

  These obstacles can be avoided by using grommets and side strips made of Teflon or with a Teflon coating. Teflon is very slippery and has the lowest coefficient of friction (about 0.05 for polished steel) among practical solids. By using it, it is ensured that tension equalization during tensioning and during ball collision can be obtained quickly and almost completely. Other materials having a low coefficient of friction may be used as well to equalize gut tension across the racket striking surface.

  Actually, when the racket striking surface before stretching is completely rectangular (except for the corner), the striking surface side is curved inward by the tension applied to the gut. This shortens all gut lengths, but the amount is more at the center of the side and less near the edge of the side. As a result, the racket gut lengths are not equal and the tension on the gut is reduced.

  To illustrate this effect, consider a beam of length 1 that is supported at each end and receives forces from n equally spaced guts of tension T. When E is the Young's modulus of the beam material and I is the area moment of the beam cross section, the beam deflection y (x) at a distance x from the beam origin is given by:

(Formula 2)

  This function is plotted in FIG. 2 using l = 13 inches (33.02 cm), T = 60 pounds (27.22 kg), n = 19 guts, and E and I standard values for carbon fiber tubes. ing. Curve 36 is plotted in the graph to illustrate the deflection of the beam along the length of the frame beam.

  Referring to FIG. 3, the plot of the deflection curve 36 is redrawn with an aspect ratio of 4: 1 for ease of viewing.

  Using the specified values for the relevant parameters, it can be seen that the beam representing the long side 24 in FIG. 1 of the racket striking surface is deflected at a maximum distance of about 0.5 inches (1.27 cm). This maximum deflection naturally occurs at the center of the beam (x = 6.5 inches (16.51 cm)), and the value of the deflection distance decreases continuously away from the center. Accordingly, the horizontal gut 34 at the center of the racket striking surface is reduced in length by approximately 1 inch (0.54 cm from each side 24 bend).

  The deflection of the sides 24 of the actual racket striking surface is more complex than this because the sides 24 are not rigidly supported beams and the force applied by the gut is not uniform. . These deflections are not given by simple analytical formulas such as Equation 2 above, but can be easily estimated by computer for any given racket geometry and material, and measured directly can do. The actual calculation of the side bend is that even after the gut tension is balanced to a constant value, the applied force is discrete and varies depending on the gut location, due to the geometry of the bent side It is complicated by the fact that. Therefore, the amount of side bending is determined by the gut tension, and the gut tension is determined by the amount of side bending. Therefore, the equations for obtaining a solution are highly coupled and nonlinear. Representative results are given below.

  As an example of these results, there are 19 gut holes, the first of which is 2 inches (5.08 cm) from the corner 28 and the rest at 0.5 inch (1.27 cm) intervals. Consider a parallel side of a rectangular carbon fiber racket striking face 22 that is 13 inches long (33.02 cm). Assuming the conventional values of the fiber Young's modulus and the cross-section of the striking surface, if the guts carry 60 pounds (27.22 kg) of tension each, the striking side is 0.21 inches at the maximum distance at the center of the beam. Curves inward (0.53 cm). However, if the racket is stretched by applying 60 pounds (27.22 kg) of tension to each gut, bending will reduce the resulting gut tension to only 51.7 pounds (23.45 kg). The maximum deflection distance of each side 24 is only 0.18 inch (0.46 cm). In order for the gut to support the desired 60 pounds (27.22 kg) tension, the applied tension must be 69.6 pounds (31.57 kg). These calculations are unique and are included within the scope of the present invention.

  Due to the bending of the racket side 24 described above, when starting with a rectangular racket striking face 22, a certain tension is brought about by the racket tension (after equalization, preferably Teflon (registered trademark) grommets and side straps) However, this is not the case with guts of equal length and as a result with guts of equal frequency. In order to achieve an equal length of gut, the present invention constructs the racket striking surface so that the striking side is curved outward by an appropriate (tension dependent) amount prior to stretching. As a result, after stretching, the sides become substantially rectangular due to the gut tension. Details of this structure are given below with respect to the preferred embodiment. These calculations are unique and are included within the scope of the present invention.

To determine the amount of induced inward curvature that is important enough to justify the use of outward curvature cancellation, Equation 1 is used to determine the change in gatt frequency change Δf. In relation to the change in length Δl, which gives:
Δf / f = −Δl / l (Formula 3)

Standard value l = 10 inches (25.4 cm), T = 60 pounds (27.22 kg), mg = 0.014 oz / inch (1.56 g / cm) (g = 32 ft / s ² (9.75 m / cm) Using s ² )), the typical frequency is f = 670 / s. A typical collision time is t0 = 0.004 s, so during the collision the gut vibrates about ft0 = 2.7 times and experiences a phase change of about 2πft0 = 17 rad. In order for a gut of different length Δl to interact with a colliding ball in a coherent manner, the phase change difference is less than π / 4, ie 2πΔft0 <π / 4, or Δf / f <1 / 8ft0≈ (If the phase change difference is more than π / 4, the adjacent gut moves in the opposite direction near the end of the collision time, resulting in reduced repulsive force on the ball). As a result, Δl <0.46 inch (1.17 cm) is given from Equation 3. This suggests that whenever the inward curvature at each side 24 exceeds Δl / 2≈0.23 inches (0.58 cm), an offset outward curvature should be used.

In addition to establishing equal gut length using outward curvature as described above, there is another way to achieve equal gut frequency when the striking face is curved inward.
The idea is to use a gut with a variable mass density m. If curvature reduces the length of one gut from l to l1 and the length of another gut from l to l2, these two guts will nevertheless have the density m1 of l1 and the g1 of l2 When the density m2 is selected at a ratio of m1 / m2 = l1 ² / l2 ² , it vibrates at the same frequency.

  It has been described above how a tennis racket having a rectangular striking surface has a gut of equal length and frequency in the horizontal and vertical directions. Furthermore, a more uniform behavior is obtained when the frequencies in the horizontal and vertical directions are the same. One way to accomplish this is to make the striking face square instead of simply rectangular. As a result, when the horizontal and vertical tensions are equal, the horizontal and vertical frequencies are also equal. However, most players prefer a rectangular hitting surface because they can get a wider hitting ball according to the current ITF (International Tennis Federation) rules that limit the size of the racket.

Another more practical way of achieving equal frequencies in the horizontal and vertical directions is the ratio Th / Tv = (lv / lh) ₂ , with the horizontal gut length lh and tension Th and the vertical direction The gut length lv and the tension Tv are selected. As a result, according to Equation 1, the horizontal and vertical frequencies are equal. For this configuration to be practical, the gut tension is typically in the range of 55 pounds to 65 pounds (24.95 kg to 29.48 kg) and

The difference between the horizontal and vertical gut lengths must be 10% or less. Suitable examples are lh = 11 inches (27.94 cm) and lv = 12 inches (30.48 cm).

(Variable tension)
This section teaches how to get a gut of the same frequency even when the gut tensions are not equal. The idea is to build a rectangular racket so that the tension of each gut can be set separately. This can be achieved by using a locking grommet that locks the attached gut in place. These grommets make it possible to pass the gut in one direction (outward from the striking surface) but not in the opposite (inner) direction. As a result, the (initial) tension of each gut can be set as desired, and the gut will not slip through the grommet, thus eliminating tension equalization for different guts.

  A method for constructing such a locking grommet is taught below. First, we explain how grommets can be used to achieve the goal of equal frequency. For this purpose, as shown in FIG. 4, a rectangular racket is shown with the striking face 22 on the left and the handle 38 on the right. An initial fixed distance between the upper and lower (long) sides 24 of the hitting surface 22 is set as w, and a distance between the left and right (short) sides or the end portions 26 of the hitting surface 22 is set as l. The distance from the left side of the hitting surface is x (0 <x <1). Assume that the stretching process starts with a vertical gut at the left end at a distance x = xl. This gut is attached to the lower side, pulled through the upper locking grommet with a selected tension tl, and then locked in place. This gut pulls down the upper side of the racket by a distance dl (x). Since the lower side is pulled up by the same distance, the length of the gut after locking is w-2dl (xl). When the second (adjacent) gut section is similarly attached at x = x2 with selective tension t2, the upper side of the racket is pulled down by a further distance d2 (x). This reduces the length of the first gut section to w-2dl (xl) -2d2 (xl), so that the tension of this gut section is reduced to tl = 2kd2 (xl), where k is The spring constant of the selected gut).

  Proceeding in this manner by attaching N gut sections sequentially and locking the i th gut section at position xi with initial tension ti (i = 1, 2,..., N), the edge is finally Is bent inward by a total distance d (x) = Σdi (x), and the tension for the i-th gut section finally becomes Ti = ti−2kd (xi). After orthogonal guts are similarly attached, the gut reaches the final length wi and tension Ti, and their values depend on all selected initial tensions tl, ..., tN.

  The goal is to select the applied gut tension tl, ..., tN, so that

(Formula 4)
The final gut frequencies fi (fi = constants) are all made equal. For any given rectangular racket (geometry and material) and gut, the computer solves N equations (fi = constant) for N applied gut tensions tl, ..., tN it can. This is done for the preferred embodiment in the following section.

  There are further advantages to using the locking grommets of the present invention. For example, a locking grommet can be used to achieve the desired tension difference in different regions of the racket striking surface 22. The striking surface area close to the side is a region having low performance even in the case of a rectangular striking surface. This can be partially compensated by selecting the gut tension in these areas to be lower than the tension on the gut near the center of the striking surface. This provides a more uniform force across the racket striking surface.

  Another possible application of the locking grommet is to incorporate some elasticity into the grommet itself. This provides additional options for controlling gut length, tension, and frequency.

  Another important advantage of the locking grommet is the grommet's ability to offset the reduction in gut tension resulting from striking the racket. Each time the ball and the racket gut collide, the gut stretches and weakens, and the tension tends to decrease. This can be counteracted by simply pulling the gut through the locking grommet to shorten the gut section and increase its tension. Thus, the need to redo the tension is greatly reduced (a simple portable tension meter can be used in series with the pulled gut to distinguish it when the desired gut tension is achieved. ).

  Similarly, a broken gut of a stretched racket can be easily replaced with a separate individual gut without having to re-tension the whole. This saves the player time and money significantly and offsets the additional time required to stretch the racket.

  A number of locking grommet embodiments will now be described. These are shown in Figures 5a-5j. Each schematic view of the locking grommet shows a cross section of the beam 24 or 26 on the right side of the racquet striking face, so that the racquet striking face is on the left side of the segment. Each segment includes a single hole 40 through which a gut 32 or 34 passes, as shown as a right-pointing arrow. In this figure, the gut 32 or 34 is attached to the opposite (left) side of the striking surface and the desired tension is applied to the gut by pulling the gut to the right in the direction of the arrow through the hole 40 shown. Assuming that The drawing provides a way to lock the gut within the hole 40 of the beam with this selective tension using a locking grommet.

  In FIG. 5a, the hole 40 is conical and the gut 32 or 34 is locked in place by inserting the conical plug 42 shown in FIG. This simple locking grommet mechanism uses friction between the gut 32 or 34 and the plug 42 and hole 40 to restrain the gut. In FIG. 5 c, the conical hole 40 is threaded as indicated by the thick line 44, and the gut 32 or 34 passes through the central hole 48 of the compressible threaded conical screw 50. The screw 50 is of a material that, when tightened into the conical hole 40, shrinks to reduce the diameter of the central hole 48. The screw 50 includes means for tightening the screw into the hole 40, such as a slot for receiving a screwdriver or a molded recess. As the screw 50 is turned into the hole 40, it compresses the gut 32 or 34 and locks the gut in place. A conical threaded screw 50 is shown in cross-section in FIG. 5d, in a position where the central hole 48 is open to accept a gut. The outer surface 52 of the conical screw 50 is threaded corresponding to the thread 44 of the conical hole 40 of FIG. 5c. It will be appreciated that the two-part view of FIG. 5d shows two halves of a single conical screw.

  In the example of a further conical hole 40 of the locking grommet shown in FIG. 5e, the gut 32 or 34 is in the hole 40 on the left side (relative to the drawing) of the stop block 56 (shown as a black rectangle). Passes under the cylindrical rod 54. The stop block 56 is fixed in place in the conical hole 40 by being fixed in the hole wall 40, but other fixing means are also conceivable. Guts 32 and 34 can be pulled freely to the right as cylinder 54 rotates, but when the pulling force on the gut is released, cylinder 54 bites into conical hole 40 and holds the gut in place.

  The view of FIG. 5f includes a pair of elements 60 (shown as shaded bars angled toward each other) with holes 58 in the racket frame having a stepped configuration and attached to the steps in the holes 58. A locking grommet is shown. The elements 60 are pressed against each other by, for example, a spring mechanism, schematically indicated at 62, positioned between the racket body and each element 60 to contact the elements and press them against the gut. Two or more such elements 60 may be provided in the hole 58. The friction between the element 60 and the gut 32 or 34 prevents the gut from returning to the left side, but can easily pull the gut to the right side. Thus, the gut is locked in place with the desired tension by the locking grommet.

  The locking grommet in FIG. 5g shows that the clamping screw 64 is used to lock the gut 32 or 34 in place. The gut passes through the center hole 66 of the outer block 68 (shown in black) secured to the racket frame at the location of the hole 70. The screws 64 are screwed into cooperating threads in a block bore 72 that extends perpendicular to a hole 66 through which the gut extends. The screw 64 is turned into the bore 72 until it touches the gut 32 or 34 and presses the gut against the opposing wall of the center hole 66 to lock the gut in place. The outer block 68 is secured to the racket frame so that it does not loosen during use.

  Referring to FIG. 5 h, a similar threaded screw 64 is threadably received in a bore 72 in the portion 74 of the frame as defined by the recess 76. By tightening the screw 64 into the bore 72, the screw 64 presses the gut 32 or 34 against the inner wall of the hole 70 so as to secure the gut at the desired tension and position. The recess 76 and / or the screw 64 are configured such that the screw can be tightened or loosened by a user's finger or tool. Therefore, in this embodiment, the gut position is locked by the locking grommet incorporated in the frame itself.

  In FIG. 5i, an embodiment of a locking grommet that utilizes a compressible elastic element 78 through which the gut 32 or 34 passes as indicated by the dashed line is shown. The compressible element 78 is disposed within a conical sleeve or cone 82 formed in the racket frame. The compressible element is compressed by screwing a threaded nut 80 onto a threaded cone 82. A threaded cone 82 is disposed in the recess 84 of the frame. By rotating the nut 80 counterclockwise, the cone 82 compresses and presses the element 78 against the gut, resulting in holding the gut in place. In FIG. 5i, element 78 may release the gut and adjust the tension by turning threaded nut 80 clockwise to threaded threaded cone 82. When the nut 80 is rotated counterclockwise again, the elastic element 78 is compressed and pressed against the gut, holding the gut in place, thereby locking the gut with the desired tension.

  A similar concept is illustrated in FIG. 5j, in which element 78 is compressed by screwing threaded cone 86 onto threaded cylinder 88. FIG. By rotating the cone 86 counterclockwise, the cone 86 compresses and presses the element 78 against the gut so that the gut is held in place.

  As will be apparent to those skilled in the art, there are many other possible embodiments of locking grommets that may be used within the scope of the present invention that achieve the goal of maintaining individual gut tensions.

(Frame embodiment)
A general discussion of the frame structure is discussed herein. In the first part of this specification, the performance advantages of the rectangular tennis racket strike surface are outlined and detailed. This section describes the structure of such a racket. Conventional racket construction techniques are unsuitable for rectangular rackets unless the racket is too heavy for competition. The problem is that even if the right-angled corner is rounded, it is a region where a large stress is concentrated when it is stretched on the racket. In order for the racket to withstand these stresses, a relatively large amount of reinforcing material must be incorporated into the corners, making the racket heavy and unbalanced.

Two properties that determine the strength of the racket are the material and the geometry. The primary material used to process virtually all modern rackets is carbon fiber. The reason is that the carbon fiber has the maximum specific strength of any practical material. The bulk measure of material strength is its Young's modulus E. This coefficient is defined by the following equation as the ratio of stress (force applied per unit area, F / A) to strain (elongation or shrinkage per unit length δl / l).
F / A = Eδl / l (Formula 5)

The bulk indicator of the weight of the material is its density ρ, and the ratio of weight W to volume V is:
W = ρV (Formula 6)

  The following table lists E and ρ for aluminum, carbon fiber, and titanium.

  The Young's modulus values indicate that carbon fibers are stronger than aluminum and weaker than titanium, but are much less dense than these metals, and therefore have a much higher specific strength. For this reason, carbon fiber is an optimal material for a racket.

  To understand the role of geometry in racket strength, consider a supported uniform beam 90 of length L material as shown in FIG. The beam 90 is a simple model of the side 24 or 26 of the striking surface of the rectangular racket with a support 92 near each end. The gut attached to the side applies a substantially uniform force of size F = NT (T is the tension of each gut and N is the number of guts) over the upper surface of the beam 90. This force causes the beam 90 to deflect downward by a maximum distance D as shown in FIG.

  The deflection compresses the upper part of the beam and expands the lower part of the beam. Thus, there is a surface 94 through the beam 90 called the neutral axis, whose length remains unchanged after deflection. This plane is indicated by the dashed line 94 through the center of the beam in FIG.

  As shown in FIG. 7, 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 Young's modulus E of the material, and the area moment of inertia I of the beam cross section, according to the following equation:

(Formula 7)

I is defined by the geometry of the cross-sectional slice of the beam according to the following equation:
I = ∫dAy ² (Formula 8)

  This integral is for the cross-sectional area containing the material, and y is the vertical distance between the neutral axis and the area element dA.

  For example, if the cross section is a circular annulus 96 with an inner radius r1 and an outer radius r2 as shown in FIG. 8, y is the area element of the material between the horizontal neutral axis (indicated by the dashed line) and the circle The vertical distance between (indicated by the shaded area). in this case,

(Formula 9)

  A vertical arrow 98 in FIG. 8 represents the force applied by the gut tension.

The uniform beam cross-sectional area is defined by:
A = ∫dA (Formula 10)
The weight is defined by the following formula.
W = ρAL (Formula 11)

  Since the goal of the racket structure is to achieve adequate strength, the deflection D is relatively small, does not require a relatively large area A, and therefore the weight W is also relatively small. Thus, for a given material (given E and ρ) and fixed weight (fixed A and L), the goal is to select the cross-sectional geometry so that I is as large as practical. That is. According to its definition (Equation 8), I is larger when the racquet material is located as far as possible from the neutral axis of the striking face (beam).

This is why conventional rackets are constructed from tubular elements. Thin walled tubes are most of their material relatively far from the neutral axis. This is illustrated by the annular cross section of FIG. Such tubular beam, it is much stronger than the solid rod of equivalent weight of the same material, it is the case of tubes I (Equation 9), when the rod ^{I (I = πr 4/4} , This is because r is much larger than the radius of the rod).

  This structure works well with conventional elliptical rackets. However, this structure is not ideal for rectangular rackets. The large stress at the corner of the racket striking surface requires a relatively thick tube wall for stability. The following sections teach alternative structural designs that are more suitable and have additional advantages for the racket of the present invention. These designs achieve adequate strength without requiring unacceptable weight.

(Sandwich embodiment)
As shown for the circular annulus of FIG. 8, the tubular carbon fiber racquet frame is strong because most of the material is away from the neutral axis. However, as described above, this structure is not strong enough to form a preferred embodiment of a lightweight, rectangular racket striking surface. This section teaches how a much stronger frame can be constructed using a carbon fiber sandwich. Such a sandwich consists of two parallel relatively thin carbon fiber plates separated by a lightweight filler material.

  A cross section of a beam 100 made from such a sandwich is shown in FIG. The neutral axis 102 is indicated by a dashed line, and the vertical arrow 104 represents the force exerted by the gut tension. Comparing FIGS. 8 and 9, the material of the tubular structure shows that some material is away from the neutral axis, but some material is close to the neutral axis. On the other hand, in the sandwich structure, all materials (except the lightweight filling material) are separated from the neutral axis.

The dimensions given in FIG. 9 are the total height d, the height h of the filling material 108 between the plates 106, and the width b of the sandwich. The thickness of each carbon fiber plate 106 is (d−h) / 2. The area moment of inertia of the cross section of this sandwich is defined by
I _S = b (d ³ −h ³ ) / 12 = b (d−h) (d ² + dh + h ² ) / 12 = A _S (d ² + dh + h ² ) / 12 (Formula 12)
In the formula, AS = b (d−h) is the area of the carbon fiber material in the sandwich section.
This moment is shown to be about twice as large as that of an annular body having the same area.
I _A = π (r ₂ ⁴ −r ₁ ⁴ ) / 4 = π (r ₂ ² −r ₁ ² ) (r ₂ ² + r ₁ ² ) / 4 = A _A (r ₂ ² + r ₁ ² ) / 4 ( Formula 13)
In the formula, A _A = π (r ₂ ² −r ₁ ² ) is an area of the carbon fiber material in the annular cross section.

  If the cross-sections have equal areas (AS = AA), the beam has equal weight (Equation 11), so the ratio of these moments is defined by:

(Formula 14)

  When the fact that the carbon fiber material is thin is used, the outer circle diameter d2 is h≈d and r1≈r2 = d2 / 2.

(Formula 15)

  Thus, if the cross-sections are of similar height, d2≈d, so IS is about twice as large as IA, and thus the sandwich beam is shown to be about twice as strong as the annular beam. .

  As a result, constructing a rectangular racket frame from a sandwich beam instead of a tube increases the strength of the frame and reduces the weight required at the corners. However, its structure is not optimal. The problem is still the corner. A cross-sectional sandwich beam as shown in FIG. 9 can be combined to construct a racket 110 as shown in FIG. The corners 112 of the striking surface consist of sandwich beams that are in contact with each other and held together with a suitable epoxy resin. However, this simple structure is not strong enough to withstand the corner stresses caused by gut tension. Corner reinforcement is essential, thereby increasing the weight and top-heaviness of the racket.

  A better construction method is to machine the entire racket striking surface 114 from a single sandwich beam. Such an embodiment having rounded corners 116 is shown in FIG. The corners 116 are stronger, but the strength is still not sufficient unless a carbon fiber plate is used that is relatively thick and wide and therefore quite heavy.

  To understand why the corners must be strengthened, consider the corners 116 shown in FIG. This is a front view of the racket striking face, with the parallel carbon fiber plates 106 shown as shaded elements and the gut 118 represented by a vertical arrow. Since the carbon fiber plate 106 is long and thin, a strong stress is applied to the corner portion 116 by the tension of these guts 118. These stresses are estimated below.

  Referring to FIG. 13, to estimate the corner stress, the top plate is modeled as a cantilever beam 120 rigidly attached to a solid support 122 at the left end. If a force F is applied to the top of the beam 120 at a distance L from the support and the beam 120 has a width w and a thickness t, the resulting stress on the support is given by:

(Formula 16)

For 19 guts each having a tension of 60 pounds (27.22 kg), F = 19 × 60 pounds (27.22 kg) = 1140 pounds (517.1 kg). When the side length is 12 inches (30.48 cm), L is an average distance of 6 inches (15.24 cm). Let w = 0.75 inch (1.91 cm) be the standard value of the racket striking face width. If the racket weighs up to 14 ounces (396.9 g), the beam thickness can be at most t = about 0.1 inch (0.25 cm). Using these values, Equation 16 gives:
σ _max = 5,500,000 psi (37,921,164 kPa) (Equation 17)
This value is large because t must be small to make the racket weight acceptable.

The breaking stress of carbon fiber is approximately as follows:
σ _rupt = 820,000 psi (5,653,701 kPa) (Formula 18)

  Since the applied stress is much greater than the breaking stress, it can be concluded that this sandwich embodiment of a rectangular racket must be significantly strengthened in order not to break the corners. This is difficult to do without significantly increasing the weight of the racket.

  The cantilever model is, of course, a simplification and does not incorporate the effect of reinforcement with rounded corners and parallel plates. Also, stronger fibers, wider widths, more complex geometries, and more optimal fiber layup patterns can be used. However, when using realistic finite element computer calculations to assess the associated stresses, the results demonstrate the conclusions drawn from the model. Given these large estimates of corner stresses, the difficulties described here are clearly significant.

  There is another problem with the above-described embodiment. The tension of the gut attached to the upper plate 124 of FIG. 11 tends to pull the plate down, making it difficult for the brittle filler material 126 between the plates to withstand this force. In order to prevent being crushed by the force, a stronger and heavier filler must be used, which again adds unnecessary frame weight.

  The next section describes a preferred embodiment of the rectangular racket of the present invention that avoids all of the above difficulties. The result is a strong and lightweight racquet that has all of the performance benefits including those described in US Pat. No. 6,344,006 B1 and US Pat. No. 7,081,056 B1. .

(Preferred embodiment)
The material of the sandwich embodiment described above has about twice the strength per pound (0.454 kg) of the conventional tubular material, but this has two prominent features that negate most of this material strength. It was confirmed that there was a property. Unless relatively heavy reinforcements were added, the corners were fragile and the filler material was exposed to damaging compressive forces unless relatively heavy resistance materials were incorporated. This section teaches how to build a modified sandwich structure that solves these problems, has other advantages, and enables the processing of strong and lightweight rectangular racquets.

  The idea is to use a beam whose cross section has a “table” structure instead of the sandwich structure shown in FIG. A cross section of such a table is shown in FIG. This compartment has three carbon fiber outer plates 130, 132, and 134 instead of the two plates 106 shown in FIG. The upper (table surface) plate 134 is similar to the upper sandwich plate 106, but the lower sandwich plate 106 is replaced by two side (table leg) plates 130 and 132. The neutral axis 136 is indicated by a broken line, and the vertical arrow 138 represents the force exerted by the gut tension. The volume 140 between the table legs 130 and 132 is made of a lightweight filler material as in the sandwich. This table section has more carbon fiber material located closer to the neutral axis, resulting in a smaller area moment of inertia per pound (0.454 kg) than the sandwich section. Thus, in order to have equal strength, it is essential that the table beam 134 is heavier than the sandwich beam, but this slight additional weight can cause a racket constructed from these table beams to be reinforced by corners or fillers. Is more than compensated for the fact that The following will confirm these facts.

  The dimensions given in FIG. 14 are the width d of the upper (table surface) carbon fiber plate 134, the height b of the side (leg) plates 130 and 132, the width h of the filler material 140 between the plates, and the upper plate 134. Thickness c. Each of the side plates 130 and 132 has a thickness of (b−h) / 2.

The total area of the carbon fiber compartments in FIG. 14 is A _T = 2ab + cd, and the area moment of inertia of this cross section is defined by the following equation.
^{_{I T = d (3b 2 c}} + 6bc 2 + 4c 3) / 12 + ab 3/6 ( 19)
The first term in (Equation 19) is the contribution from the top, and the second term is the contribution from the leg.
Since c is always much smaller than b, a good approximation is
^{_{I T ≒ db 2 c / 4}} + ab 3/6 ( Formula 20)

Next, the reason why this embodiment provides a racket that is strong and lightweight without the above-mentioned difficulties (fragile corners, exposed filler). First, consider the beam intensity quantified as the beam deflection distance (Equation 7). For the same force F, length L, and coefficient E, the greater the moment, the higher the beam intensity. As noted above, for a given cross-sectional area (and therefore a given beam weight), the table moment I _T (Equation 19) is less than the sandwich moment I _S (Equation 12). However, the dimensions a, b, c, d are such that I _T is at least 90% larger than I _S (thus, given Eq. 15 more than 80% larger than the annular moment I _A ). You can choose. As a result, if the cross-sectional area of the table beam is selected to be slightly larger than the sandwich beam, the two beams have the same intensity. The following provides examples of table beam dimensions that produce a strong and lightweight rectangular racket.

Next, it is shown that the corners of the rectangular racquet of the frame using the table section are much stronger than those of the frame using the sandwich section. The corners 116 of the sandwich are shown in FIG. 12 above. The corresponding corner 142 of the table is shown in FIG. First, the cantilever of FIG. 13 is used to model the plate, and the stress caused by the tension in the vertical gut is estimated. In the case of a sandwich corner 116, the plate is thin (t to 0.1 inch (0.25 cm)) and wide (w to 0.75 inch (1.91 cm)), but in the case of a table corner, Plate 134 is thick (t to 0.75 inches (1.91 cm)) and narrow (w to 0.1 inches (0.25 cm)). This increases the difference in stress σ _max in the support.

Sandwich values (F = 1040 pounds (471.7 kg), L = 6 inches (15.24 cm), t = 0.1 inches (0.25 cm), w = 0.75 inches (1.91 cm)) Substituting into the equation for the stress in the support (Equation 16), the stress becomes very large at 5,500,000 psi (37,921,164 kPa), which is the carbon fiber breaking stress of 820,000 psi (5,653,701 kPa). Much larger than). On the other hand, sandwich values (F = 1040 pounds (471.7 kg), L = 6 inches (15.24 cm), t = 0.75 inches (1.91 cm), w = 0.1 inches (0.25 cm)) Substituting into this equation, the stress becomes much smaller as
σ _max = 730000 psi (5,033,173 kPa) (Formula 21)

  This is significantly less than the breaking stress, confirming that the corners of the table are much stronger than the corners of the sandwich and are strong enough to withstand the stresses caused by gut tension.

  The cantilever model does not take into account the strengthening effect of rounded corners and parallel plates. Finite element analysis techniques were used to accurately calculate corner stresses for rackets with rounded corners machined from sandwich and table beams. The result is a stress value that is smaller than the estimated value described above. The calculated stress ranges are 1,700,000 to 2,400,000 psi (11,721,087 to 16,547,417 kPa) at the corners of the sandwich and 530,000 to 650,000 psi at the corners of the table. (3,654,221 to 4,481,592 kPa). These range sizes result from the use of different dimensions, layup patterns, and epoxy resins. With any of these possibilities, the superiority of the table structure is obvious.

  Thus, the use of table elements allows the construction of rectangular rackets with corners that are strong enough to withstand the applied forces without the need for any reinforcement. Thus, these elements eliminate the brittle corner problem associated with sandwich elements. Also, the filler crushing problem associated with sandwich elements is eliminated. From the cross-section of the table shown in FIG. 14, the upper carbon fiber plate 134 is placed on the side plates 130 and 132 so that the gut tension 138 applied thereto does not exert a significant force on the filling material 140. It is clear. Substantially all of the applied force is resisted by the side plates 130 and 132. The laboratory verification of this fact is reported in the next section.

  Thus, a rectangular racket fabricated from the carbon fiber table element of the present invention has strong sides, strong corners, and a protected filler material. These are therefore preferred embodiments of rectangular rackets. In addition, there is another major advantage to this processing. Building a racket from a single carbon fiber sandwich is particularly simple. Such a sandwich 148 is shown in FIG. This consists of upper and lower carbon fiber plates 150 and 152 separated by a lightweight filler material 154. Filler material 154 may be a fibrous or non-fibrous material, a foamed foam material, or other material made of natural or synthetic materials. These plates become the side (table leg) plates 130 and 132 of the table of FIG.

  The racket frame can be cut from this sandwich 148 in the form of a single piece 156, as shown in FIG. Next, a long and thin carbon fiber strip having a thickness equal to dimension c in FIG. 14 and a width equal to the thickness of the sandwich described above (dimension d in FIG. 14) is attached. This strip can be attached to the outer periphery of the racket striking surface of FIG. 17 using a suitable epoxy resin. For added strength, this strip can have a C-shape with upper and lower lips. Such a strip can be fitted around the outer circumference of the racket striking surface and bonded using epoxy resin. The lip or extension extends over the upper and lower plates 150 and 152 to add not only strength but also a sophisticated appearance. Finally, stretch holes can be drilled at appropriate locations around the perimeter 158 of the striking surface, grommets or grommet strips can be inserted into these holes, and the carbon fiber handle shaft 160 is made of a lightweight material. Can be supplemented and then secured with a strap. In this way, preparations are made to stretch the racket.

  The shape of the cutout in FIG. 17 can be generalized to include the improvements described above. The corners 162 can be rounded to improve the strength and appearance of the racket. The striking face side 164 can be curved outward so that a purely rectangular striking face is obtained after stretching. The side strip can be grooved or otherwise modified to accommodate grommets and guts. This simplicity of construction is a major advantage of the table structure of the present invention.

  The preferred rectangular racket embodiment described in this section is based on theoretical calculations. The next section provides details of specific examples of how to actually build and test these rackets. Give the dimensions, specify the material, show a picture of the construction example and present strength and performance data.

(Example and Test of Preferred Embodiment)
To process a rectangular racket that illustrates one preferred embodiment, start by selecting the desired features. Most modern rackets have 19 short guts and 16 long guts and will follow this choice. According to the performance calculation reported in US Pat. No. 6,344,006 B1 (Brandt), the 0.5 inch (1.27 cm) inter-gut distance is close to optimal and will be selected as well. To accommodate this gut pattern, an inner striking surface dimension of 9.5 inches × 12 inches (24.13 cm × 30.48 cm) is selected. The racket hitting surface shown in FIG. 1 shows this pattern. The gap between the first and last gut and the inside of the frame is 1 inch (2.54 cm) in the vertical direction and 1.5 inches (3.81 cm) in the horizontal direction.

  Most modern tennis rackets weigh 10-14 ounces (283.5-396.9 g), have a center of mass located in the throat area, and incorporate these constraints. Thus, the sides and corners of the racket are large enough to withstand the gut tension in the normal range of 55-65 pounds (24.95-29.48 kg) and weigh 14 ounces (396.9 g) Table dimensions b, h, d, and c (defined in FIG. 14) must be selected that are sufficiently small so as not to exceed the limits. Once these table dimensions are determined, the amount of inward bending of the striking face caused by the gut tension must be calculated or measured. If the maximum bend distance exceeds the 0.23 inch (0.58 cm) limit derived above (according to Equation 6), the racket must be constructed with an outward side bend to offset this. I must.

Commercially available carbon fiber products were selected for plates with table beams. Table legs 130 and 132 are machined from carbon fiber plates in a 45 ° layup pattern. The table top surface 134 is processed from a carbon fiber plate in a unidirectional layup pattern. The Young's modulus of this material is E = about 2 × 10 ⁷ psi (13789.51 MPa) and the density is ρ = 0.96 oz / in ³ (1.66 g / cm ³ ).

  By substituting these values and any selected values of the table dimensions b, h, d, and c into Equation 19, which is the moment equation, Equation 7 can be used to estimate the deflection of the racket side, 16 can be used to estimate the stress at the corner of the racket and the weight of the racket striking surface can be calculated. These results can then be supported by performing a finite element analysis. These calculations make it possible to select table dimensions that produce a sufficiently strong and lightweight racket.

These calculations suggest that an appropriate selection of table dimensions for a 12 inch (30.48 cm) hitting edge is as follows.
b = 0.625 inch (1.59 cm)
h = 0.55 inch (1.40 cm)
d = 0.75 inch (1.91 cm)
c = 0.0625 inch (0.159 cm) (Formula 22)

Therefore, the thickness of the upper surface of the table is c = 0.0625 inch (0.159 cm), and the thickness of the table leg is (d−h) /2=0.1 inch (0.25 cm). Using these values, the area moment of inertia of the beam cross section is I _T = 0.0083 in ⁴ (0.3455 cm ⁴ ) and at 60 pounds (27.22 kg) tension, it is about 12 inches (30.48 cm). The maximum deflection is 0.155 inches (0.39 cm). In the case of a 9.5 inch (24.13 cm) hitting side, b can be reduced to 0.5 inch (1.27 cm).

  The 12 inch (30.48 cm) side of the racket striking surface is designed to withstand 1140 pounds (517.1 kg) of force resulting from 19 guts each attached with a tension of 60 pounds (27.22 kg) Yes. The racket throat and handle need not be of this strength. The forces on these elements occur during a short collision time (approximately 0.004 seconds) when the racket hits the ball. This force is at most about 250 pounds (113.4 kg) and lasts only for such a short time, so the throat dimensions can be much smaller than the dimensions of Equation 22.

  The racket is preferably stretched in a separate gut section for each of the main gut and cross gut. It is also recalled that a gut may be a single continuous gut or may be a plurality of gut segments.

  The remaining elements of the racket design are not critical to performance and can be selected to be consistent with current practice. The final racket design is shown in FIGS. 18a and 18b (for racket striking surface 166) and FIGS. 19a, 19b and 19c (for throat 168 and handle 170). In addition to the features specified above, these drawings incorporate several other properties. Since the entire frame is cut from a carbon fiber sandwich with a thickness d = 0.75 inches (1.91 cm), all of its elements (striking surface 166, throat 168, handle shaft 170) will have this thickness. The inner corners are rounded with a radius of 1 inch (2.54 cm) and the outer corners are rounded with a radius of 1.625 inches (4.13 cm). The throat side has a width b = 0.625 inch (1.59 cm). The throat tapers to 0.625 inches (1.59 cm) wide on the handle shaft. All other dimensions are specified in the drawing. A number of holes are shown in the drawing. They help to lighten the racket in areas that are strong enough to accommodate the holes. For example, a hole 174 is shown in the corner 176 where the throat 168 attaches (see FIG. 18a). Holes 178 and 180 are aligned along the center of handle 170 in the top view of FIG. 19a, and hole 182 is orthogonal to hole 180 as seen in the side view of FIG. 19b. The holes may be filled with a lightweight material or left in the racket frame as an opening. A handle shaping element 184 is provided on the handle portion 170 to provide a comfortable grip.

  18a and 18b show a virtual tennis ball 172 in a scale sense.

  The handle shaft 170 of the racket cut from the sandwich has a width of 0.625 inches (1.59 cm) and a height of 0.75 inches (1.91 cm). As shown in FIGS. 19a, 19b, and 19c, the handle is of the desired size (width 1.25 inches (3.17 cm), height 1.14 inches (2.9 cm)) and shape (octagon is standard) Lightweight material, such as balsa material, is attached to this shaft as a handle shaping element to expand to (used here).

  After the frame is cut from the carbon fiber sandwich and the side (table top) plate is attached around the perimeter, a gut hole is drilled as shown in FIG. 18b. Grommets, and preferably locking grommets as described above, or other types of locking grommets can be inserted into these holes and then stretched over the racket. Finally, the end cap 186 and strap can be attached to the handle.

  The gut tension is preferably set to be equal for each main gut and each cross gut. In a preferred embodiment, the gut tensions for both the main gut and the cross gut are equal to each other. The gut frequencies of the main gut are preferably equal and the gut frequencies of the cross gut are preferably equal to each other. In one embodiment, the frequency of both the main gut and the cross gut are equal. In some calculations, the variables ti and li refer to the tension and length of each main gut, respectively, and the variables sj and kj refer to the tension and length of each cross gut, respectively. The gut linear density is designated mj for the main gut density and m'j for the cross gut density.

  The dimensions presented in the above figures have been selected using theoretical calculations of strength and performance. It is advisable to support these calculations with laboratory strength measurements before proceeding with racket processing. A suitable strength test protocol was devised as taught below.

  In order to support that the table structure (FIG. 14) having the selected dimensions (Equation 22) is strong enough to hold the inserted grommet and withstand the forces of gut tension, the apparatus shown in FIG. Devised. The section of table beam 200 (shown in gray) is held in place by a pair of solid stops 202 (shown in black). The racket gut 204 is threaded through grommets 206 in the two holes of the beam 200 and attached to a load cell 208 (shown as a shaded element on the right). The load cell 208 is attached to a block 210 (shown in black) that can be retracted by rotating the inserted threaded bolt 212. By this retreat, the force F is applied to the gut, and the magnitude of the force is displayed on the display device 214 (shown as a shaded block in the lower center) wired to the load cell.

  When the display 214 reads the value F, the tension in each of the two guts 204 is F / 2. In order for the beam to withstand 60 pounds (27.22 kg) of gut tension, it must withstand 120 pounds (54.43 kg) of applied force. A table beam having the dimensions given by Equation 22 was tested in this manner and found to withstand applied forces in excess of 200 pounds (90.72 kg). This confirms the calculation of the beam intensity. Pictures of the test apparatus are shown in FIGS.

  Since it was experimentally confirmed that the test length of the table beam having the specified dimensions is the intensity predicted by the calculation of the present invention, the intensity of the racket corner of the present invention is similarly tested. Describes how to do this. The method devised to do this utilizes a small replica 212 on the sides and corners of the racket striking surface as shown in FIG. The central part 214 at the top of the replica 212 has the same cross-sectional dimension (Formula 22) as the table cross-section shown in FIG. The inner length of the replica is 4.5 inches (11.43 cm) and the outer length is 5.75 inches (14.61 cm) (the inner length of the racket striking surface shown in FIG. 18a is 12 inches (30.30 cm). 48 cm)). The curvature of the corners of the replica and the actual racket are the same.

  The force on the long side of the actual racket striking surface generated from 60 pounds (27.22 kg) of tension for each of the 19 guts is 1140 (517.1 kg) pounds. The equivalent force F on the replica 212, that is, the force that produces the same stress in the corners when applied to the center of the replica, is 1390 pounds (630.5 kg) (this force is greater than the effective lever arm Because it is shorter). To confirm that the replica can withstand this amount of force, the replica 212 was inserted into a hydraulic press in series with a load cell that measures the applied force. Photographs of this test apparatus are shown in FIGS. The applied force F was continuously increased until one of the upper corners of the replica began to break (to make one of the corners thicker than the other, ensuring that the other corner broke first) ) Such breakage was observed when the applied force reached 2250 pounds (1021 kg). This actual rectangular racquet is encountered because this force greatly exceeds 1390 pounds (630.5 kg) equivalent to the 1140 pound (517.1 kg) force applied by the gut to the actual racket of the present invention. It can be concluded that it has corners that are strong enough to withstand the stress. This confirms that the theoretical estimate of the present invention regarding the corner strength of the present invention is accurate and provides confidence that the construction of the racket will proceed.

A photograph of a racket product 230 constructed according to the above specifications is shown in FIG. Measured weight (W), center of mass (COM), and weight inertia about an axis that is 6 inches (15.24 cm) from the end of the handle and perpendicular to the racket handle and parallel to the racket striking surface The moment (MOI) is as follows.
W = 14 oz (396.9 g)
COM = 9.87 inches (25.07 cm)
MOI = 2400 oz.in ² (16.95 N · m) (Equation 3.18)

  The racket of the present invention may have a weight of less than 14 ounces (396.9 g) including guts. It is also possible to construct rackets according to the present invention having a weight of less than 12 ounces (340.2 g), or even less than 10 ounces (283.5 g).

  Similar prototypes with slightly different dimensions and weight and different CFs by impacting a tennis ball 234 fired from the barrel to the racket at various positions with respect to different impact speeds and racket strikes The performance of the racket 232 was measured. The racket striking surface 232 was firmly pressed against the solid surface 236 perpendicular to the barrel direction. The incident ball 234 collided with the racket 232 at a right angle without spin. The velocity of the incident and repelled ball was accurately measured using a light gate (the racquet does not move during these collisions. These data can be used for game conditions where the racquet is essentially a free object during the collision. Conversion will be described later). For comparison, the same type of measurement was performed on a conventional elliptical racket. A photo of the setup is shown in FIG.

  The quantity that characterizes the performance of the fixed racket at any point on the hitting surface is the speed ratio at that point, ie the ratio of rebound velocity to incident velocity. When comparing the ratio between a rectangular racket and an elliptical racket, the performance at the racket center can be adjusted by changing the gut tension, so the ratio at the racket center (the highest performance point for fixed rackets) and from the center It is important to compare the difference between the ratio at a given distance. It is also important to compare the differences at the same incident speed, since the ratio always decreases as the incident speed increases.

  The following table shows speed ratio data specific to the measurements of the present invention. The collision speed is given in the first column. For rectangular and elliptical rackets, compare the speed ratio at the center and a point 3.5 inches (8.89 cm) below the center. It can be seen that the ratio is reduced by 0.52% and 0.75% for the rectangular racket and 10.48% and 8.55% for the elliptical racket. It can be seen that the performance at the eccentric position of the rectangular racket is much better.

  In order to convert these data into data characterizing the performance of the racket in game conditions where the racket is essentially a free object during a collision, the speed ratio is replaced with a coefficient of restitution (COR). The COR between the tennis ball and the tennis racket is the ratio of the relative repulsion speed to the relative incidence speed. This amount, which is reduced to the speed ratio when the racket is fixed, determines the performance of the swinging racket. The rebound ball linear and angular velocities are the COR at the collision point, as well as the details of the racket stroke (linear velocity, angular velocity), the kinetics of the racket (weight, COM, MOI), and the nature of the incident ball (weight, linear velocity, Angular velocity).

  The following table shows the change in COR data obtained from the above speed ratio data for a 65.3 mph (105.1 km / h) impact. Rectangular and elliptical rackets are assumed to have equal weight, MOI, and COM. The advantage over the elliptical racket is further improved by the fact that the actual MOI of the rectangular racket is larger.

  For fixed frame rackets, the best performance is at the center of the striking surface. In the case of a free racket, the point of best performance shifts towards the handle because this direction is towards the racket COM. In the case of a rectangular racket, the effect is that a 0.75% decrease in performance 3.5 inches (8.89 cm) from the center replaces a 1.19% increase in performance. In the case of a rectangular racket, the effect is that an 8.55% reduction in performance 3.5 inches (8.89 cm) from the center replaces a 7.45% reduction in performance.

  The COR differences shown in the above table cause a significant difference in the trajectory of the tennis ball that has struck. The velocity and spin of the struck ball is determined by the ball and racket COR, along with all of the details of stroke, incident ball, and kinematics. For the standard values of these quantities, the difference in the velocity of the ball hit against the center of the rectangular racket and under 3.5 inches (8.89 cm) is only about 0.15 mph (0.24 km / h). Assuming standard values for the coefficient of friction and drag of the ball, the resulting difference in the trajectory of the bumped ball is generally less than 4 inches (10.16 cm). The corresponding difference in the case of an elliptical racket is 6.5 mph (10.46 km / h), and the resulting difference in the trajectory of the hit ball is over 12.5 feet (3.81 m). The advantages of rectangular rackets are obvious.

  While certain preferred embodiments of the concept of a rectangular racket have been presented, there are many other possible embodiments of the present invention, as will be appreciated by those skilled in the art.

  While other modifications and changes may be suggested by one of ordinary skill in the art, we believe that all changes and modifications are reasonably and appropriately included within the scope of the patents warranted to this specification. It is intended to be embodied as being within the scope of contribution to the field.

20 tennis racket 22 striking face 24 side 26 end 28 corner 30 neck 32 gut 34 gut 36 curve 38 handle 40 hole 42 plug 44 thread 48 center hole 50 conical screw 52 outer surface 54 cylinder 56 stop block 58 hole 60 element 62 Spring 64 Clamping screw 66 Center hole 68 External block 70 Hole 72 Bore 74 Portion 76 Recessed portion 78 Element 80 Nut 82 Conical 84 Recessed portion 86 Cone 88 Cylinder 90 Beam 92 Support body 94 Neutral shaft 96 Toroidal body 98 Force 100 Beam 102 Neutral shaft 104 Force 106 Plate 108 Filling material 110 Racket 112 Corner 114 Racket striking surface 116 Corner 118 Gut 120 Beam 122 Support 124 Upper plate 126 Filling material 130 Outer plate 132 Outer play G 134 Outer plate 136 Neutral shaft 138 Force 140 Filling material 142 Corner portion 148 Sandwich 150 Upper plate 152 Lower plate 154 Filling material 156 Racket frame 158 Around 160 Handle shaft 162 Corner portion 164 Strike surface 166 Racket striking surface 168 Throat 170 Handle shaft 172 Tennis Ball 174 Hole 176 Corner 178 Hole 180 Hole 182 Hole 184 Handle Shaping Element 186 End Cap 200 Beam 202 Stopper 204 Gut 206 Grommet 208 Load Cell 210 Block 212 Replica 214 Display Unit 230 Racket Product 232 Prototype Racket 234 Ball 236 Solid

Claims (55)

A sports racket,
A racquet body including a racquet head and a racquet handle, wherein the racquet head has a substantially rectangular hitting face shape, and includes a corner portion in which the substantially rectangular hitting face shape is rounded. A racket body defining a plurality of gut mounting positions in a predetermined arrangement on four opposing sides of the rectangular striking face shape, wherein the racket handle is fixed to the racket head;
At least one gut mounted at the gut mounting position, wherein the gut defines a plurality of main gut portions and a plurality of cross gut portions, each of the main gut portions being approximately equal in length and approximately equal. A sports racquet comprising: at least one gut that is tensioned and each of said cross gut portions is approximately equal length and approximately equal tension.   The sports racquet of claim 1, wherein the weight of the racquet body including the at least one gut is less than 14 ounces (396.9 g).   The sports racquet of claim 1, wherein the weight of the racquet body including the at least one gut is less than 12 ounces (340.2 g).   The sports racquet of claim 1, wherein the weight of the racquet body including the at least one gut is less than 10 ounces (283.5 g).   The sports racket according to claim 1, wherein the main gut portion and the cross gut portion have a gut tension that is substantially equal when stretched over the racket head.   The rectangular racket head is formed in a shape having a side curved outward so that a side of the racket head is pulled by the gut tension to become a substantially straight side when stretched. The sports racket according to 1. A sports racket,
A racket body including a racket head and a racket handle, wherein the racket head has a substantially rectangular hitting surface shape, and includes a corner portion in which the substantially rectangular hitting surface shape is rounded, and the packet head includes: A racket body defining a plurality of gut mounting positions in a predetermined arrangement on four opposing sides of the rectangular striking face shape, wherein the racket handle is fixed to the racket head;
At least one gut mounted at the plurality of gut mounting positions, wherein the gut defines a plurality of main gut portions and a plurality of cross gut portions, and each of the main gut portions has a main gut frequency. A sports racquet comprising: a main gut fundamental frequency each being substantially the same, and said cross gut portions each having at least one gut each having a cross gut fundamental frequency that is substantially the same. .   The sports racquet of claim 7, wherein the weight of the racquet body and gut is less than 14 ounces (396.9 g).   The sports racquet of claim 7, wherein the weight of the racquet body and gut is less than 12 ounces (340.2 g).   The sports racquet of claim 7, wherein the weight of the racquet body and gut is less than 10 ounces (283.5 g). The at least one gut has a substantially constant gut linear density;
and,

Where ti is the gut tension of the main gut portion, li is the gut length of the main gut portion, sj is the gut tension of the cross gut portion, and kj is the gut length of the cross gut portion. Item 8. A sports racket according to item 7. The at least one gut has a varying gut linear density;
and,

Where ti is the gut tension of the main gut portion, mi is the gut density of the main gut portion, li is the gut length of the main gut portion, sj is the gut tension of the cross gut portion, and m′j is The sports racket according to claim 7, wherein a gut density of the cross gut portion, kj is a gut length of the cross gut portion.
The sports racket according to claim 7, wherein   The sports racquet of claim 7, further comprising a lockable grommet attached to at least some of the gut attachment locations to hold the gut portion in place.   The sports racquet of claim 7, further comprising a lockable grommet that holds the gut portion in place at one end of each of the main gut portions and one end of each of the cross gut portions.   The sports racket according to claim 7, further comprising a lockable grommet that holds the gut in place at each end of each of the main guts and at each end of the cross guts.   The sports racquet of claim 14, wherein the lockable grommet holds the gut portion in the gut mounting position such that a predetermined tension on a predetermined one of the gut portions is maintained. The lockable grommets of the cross gut portions maintain tension against the cross gut portions, thereby

Where sj is the tension on the intersecting gut portion, kj is the length of the intersecting gut portion,
The lockable grommets of the main gut portion maintain tension against the main gut portion, thereby

The sports racket according to claim 17, wherein ti is a tension with respect to the main gut portion and li is a length of the main gut portion. The lockable grommets of the cross gut portions maintain tension against the cross gut portions, thereby

Where sj is the tension on the intersecting gut portion, m′j is the mass density of the intersecting gut portion, and kj is the length of the intersecting gut portion,
The lockable grommets of the main gut portion maintain tension against the main gut portion, thereby

The sports racket according to claim 17, wherein ti is a tension with respect to the main gut portion, mi is a mass density of the main gut portion, and li is a length of the main gut portion. A sports racket,
A racket head including an open frame, the racket head defining an array of a plurality of gut holes on opposite sides of the open frame, the gut holes including a generally conical hole portion;
A handle fixed to the racket head;
At least one gut disposed through the gut hole and extending across the open frame to define a racket striking surface;
A plurality of lockable grommets disposed in each of the gut holes, the grommets including a generally conical grommet portion that is inserted into the generally conical hole portion; Lockable, wherein the lockable grommet engages and restrains the at least one gut under tension by frictional engagement between a conical hole portion and the generally conical grommet portion and the gut. Sports racket with a special grommet. A sports racket,
A racket head including an open frame, wherein the racket head defines an array of gut holes including generally conical hole portions on opposite sides of the open frame, wherein the generally conical hole portions are threaded. When,
A handle fixed to the racket head;
At least one gut disposed through the gut hole and extending across the open frame to define a racket striking surface;
A plurality of lockable grommets disposed in each of the gut holes, wherein the lockable grommets are threaded into the threaded generally conical hole portions. A substantially conical grommet portion, and the lockable engagement by a threaded engagement between the threaded generally conical hole portion and the threaded generally conical grommet portion and the gut. A sports racquet comprising a lockable grommet, wherein the grommet engages and restrains the at least one gut under tension. A sports racket,
A racquet head including an open frame, the racquet head defining an array of gut holes including generally conical hole portions on opposite sides of the open frame; and
A handle fixed to the racket head;
At least one gut disposed through the gut hole and extending across the open frame to define a racket striking surface;
A plurality of lockable grommets disposed in each of the gut holes, wherein the lockable grommets are substantially cylindrical rods disposed in the substantially conical hole portions. Each includes a lockable grommet that includes a stop block in each of the generally conical holes, and wherein the at least one gut is under tension by causing the generally cylindrical rod to bite into the generally conical holes. Lockable by holding in place and with the generally cylindrical rod pulling the at least one gut through the grommet to increase tension on the gut while preventing the gut from moving in the opposite direction Sports racket with a special grommet. A sports racket,
A racket head including an open frame, the racket head defining an array of gut holes on opposite sides of the open frame;
A handle fixed to the racket head;
At least one gut disposed through the gut hole and extending across the open frame to define a racket striking surface;
A plurality of lockable grommets disposed in each of the gut holes, wherein the lockable grommets include first and second locking portions and a biasing member; A biasing member biases the first and second locking portions toward each other to engage the at least one gut, holding the at least one gut under tension, and And a second locking member that allows the at least one gut to move through the locking portion in a direction that increases tension on the gut while preventing the gut from moving in the opposite direction. Sports racket with a special grommet. A sports racket,
A racket head including an open frame, the racket head defining an array of gut holes on opposite sides of the open frame;
A handle fixed to the racket head;
At least one gut disposed through the gut hole and extending across the open frame to define a racket striking surface;
A plurality of lockable grommets disposed in each of the gut holes, wherein the lockable grommets include a gut passage, a threaded bore opening on the gut passage, and the screw. A threaded member that is threadably engaged within a threaded bore, wherein the threaded member contacts the at least one gut within the gut path and causes the at least one gut to pass through the gut path. A sports racket comprising a lockable grommet that is secured within.   25. The sports racquet of claim 24, further comprising an outer block that defines the gut passage and the threaded bore, and wherein the threaded member is engaged therein.   25. The sports racquet of claim 24, further comprising a portion of the racquet head that defines the threaded bore and into which the threaded member is engaged. A sports racket,
A racket head including an open frame, the racket head defining an array of gut holes on opposite sides of the open frame;
A handle fixed to the racket head;
At least one gut disposed through the gut hole and extending across the open frame to define a racket striking surface;
A plurality of lockable grommets disposed in each of the gut holes, each of the lockable grommets including a compressible elastic gut gripping element that engages the gut; Each of the lockable grommets includes a threaded cone engaged with the gripping element to compress the gripping element and thereby secure the gut in place. A sports racquet comprising a lockable grommet including a threaded nut that is threadably engaged onto a cone of the same. A sports racket,
A racket head including an open frame, the racket head defining an array of gut holes on opposite sides of the open frame;
A handle fixed to the racket head;
At least one gut disposed through the gut hole and extending across the open frame to define a racket striking surface;
A plurality of lockable grommets disposed in each of the gut holes, each of the lockable grommets including a compressible elastic gut gripping element that engages the gut; The gut gripping element is held in a threaded nut, a threaded portion is provided in the gut hole, and the thread on the gut hole to hold the gut in the gut hole under tension. A sports racket comprising a lockable grommet with a threaded nut engaged thereto. A sports racket,
Racket frame,
A racket handle connected to the racket frame;
The racquet frame and the racquet handle are formed of a carbon fiber composite material and have a sandwich structure, the sandwich structure comprising first and second opposing carbon fiber sheets with a lightweight core material disposed therebetween. Including sports racket.   30. A sports racquet according to claim 29, wherein the racquet frame and the racquet handle are in the form of a single piece and are cut from a single sheet of sandwich material.   31. A sports racquet according to claim 30, wherein a striking face cross section of the sports racquet has a moment of inertia at least twice that of an annular cross section of the same area and similar dimensions.   30. The sports racquet of claim 29, further comprising a carbon fiber strip affixed to an outer peripheral surface of at least a portion of the sports racquet.   33. A sports racquet according to claim 32, wherein the carbon fiber strip is "C" shaped and has first and second portions respectively overlying the first and second outer layers of the sandwich structure.   The sports racquet of claim 32, further comprising a plurality of layers of Kevlar material applied to the carbon fiber strip.   The sports racquet according to claim 32, wherein the moment of inertia of the hitting surface section is at least 1.8 times the moment of inertia of the annular body having the same area.   33. A sports racquet according to claim 32, wherein the weight of the racquet is less than 14 ounces (396.9 g).   33. A sports racquet according to claim 32, wherein the weight of the racquet is less than 12 ounces (340.2 g).   33. A sports racquet according to claim 32, wherein the weight of the racquet is less than 10 ounces (283.5 g).   The racket frame has an inner striking length of 11 inches to 15 inches (27.94 cm to 38.1 cm), and the racket frame has an inner striking surface of 9 inches to 11 inches (22.86 cm to 27.94 cm). The racket frame has a striking face side width of 0.25 inch to 0.75 inch (0.64 cm to 1.91 cm), and the racket frame has a width of 0.5 inch to 1 inch (1. 33. A striking face depth of 27 cm to 2.54 cm) and the racket frame has a sandwich plate thickness of 0.025 inches to 0.15 inches (0.064 cm to 0.38 cm). The described sports racket.   40. The sports racquet of claim 39, wherein the stress induced at the side portion of the racquet frame by a gut tension of less than 70 pounds is less than 80% of the breaking force of the frame striking face material. The racket frame has a substantially rectangular hitting face shape, the substantially rectangular hitting face shape includes rounded corners, and a racket head is arranged in a predetermined arrangement on four opposite sides of the rectangular hitting face shape. Define multiple gut attachment positions,
A racket handle fixed to the racket head;
Mounted at the plurality of gut mounting positions so as to define a main gut portion having a main gut fundamental frequency and a cross gut portion having a cross gut fundamental frequency substantially equal to the main gut fundamental frequency, respectively. The sports racquet of claim 32, comprising at least one gut.   40. The sports racquet of claim 39, further comprising a lockable grommet mounted to hold at least one gut with the racquet frame.   43. The sports racquet of claim 42, wherein the lockable grommet maintains a predetermined gut tension against at least one gut stretched over the racket frame.   The lockable grommet maintains a predetermined tension on the at least one gut, and the predetermined tension is a tension such that the main gut portion of the at least one gut has a substantially equal fundamental frequency; 43. The sports racquet of claim 42, wherein the predetermined tension is a tension such that the intersecting gut portions of the at least one gut have substantially equal fundamental frequencies.   45. A sports racquet according to claim 44, wherein the fundamental frequency of the main gut portion is approximately equal to the fundamental frequency of the cross gut portion.   30. A sports racquet according to claim 29, wherein the weight of the sports racquet is less than 14 ounces (396.9 g).   30. A sports racquet according to claim 29, wherein the weight of the sports racquet is less than 12 ounces (340.2 g).   30. A sports racquet according to claim 29, wherein the weight of the sports racquet is less than 10 ounces (283.5 g). A method for providing a sports racket comprising:
Forming a racket frame such that the frame has a substantially rectangular shape;
Stretching the racket frame with at least one gut such that a main gut portion and a cross gut portion extend between opposite sides of the generally rectangular frame;
Applying tension to the main gut portions such that the main gut portions are each approximately equal length and approximately equal tension;
Tensioning the crossed gut portions such that the crossed gut portions are each approximately equal length and approximately equal tension.   The forming step includes forming the generally rectangular racket frame having outwardly curved sides, thereby tensioning the main gut portion and tensioning the cross gut portion; 50. The method of claim 49, wherein sufficient force is applied to the curved side to draw the curved side into a substantially linear side under gut tension. The stretching step applies initial tension to the main gut portion and the cross gut portion;
50. The method of claim 49, wherein the tensioning step applies a final tension to the main gut portion and the cross gut portion.   50. The method of claim 49, wherein applying the tension applies substantially the same tension to the main gut portion and the cross gut portion.   50. The method of claim 49, wherein the step of applying tension includes a sub-step of locking the gut portion to a lockable grommet to maintain tension on the gut portion.   54. The method of claim 53, wherein the locking substep includes locking the gut portion to the lockable grommet with a biting force.   The locking sub-step locks the gut portion to the lockable grommet by threadably engaging a first threaded member with a second threaded member; 54. The method of claim 53, comprising.