JP7505405B2 - Badminton Racket - Google Patents

Description

The present invention relates to a racket used in badminton.

A badminton racket has a frame, strings, and a shaft. The frame has a top and a bottom. The strings form a face. A player uses the racket to hit a shuttlecock. The shot causes the face to collide with the shuttlecock. The impact of the collision is transmitted from the strings to the frame and then to the shaft. The shot causes the frame and shaft to deform. An attempt to optimize the deformation behavior during a collision is described in JP 2001-70481 A.

JP 2001-70481 A

In the game of badminton, players perform various types of shots. These shots include smashes, lobs, and driven clears. Statistical studies have shown that the typical impact point for a smash is closer to the bottom, and the typical impact point for a lob is closer to the top. On the other hand, the typical impact point for a driven clear is near the center.

Unlike a normal clear, a driven clear involves a cutting action. Therefore, in a driven clear, the shuttle rotates. This rotation slows down the shuttle. This slowdown throws the opponent off balance. From the perspective of winning the game, a driven clear is an important shot.

In a driven clear, the shuttle must fly high enough to be above the net. In a driven clear, the shuttle must also fly low enough to not exceed the opponent's court. The player must have the skill to fly the shuttle at the intended height. Players who frequently use driven clears want a stable shuttle trajectory.

The objective of the present invention is to provide a badminton racket that can reduce variation in the shuttlecock trajectory when hitting a shot that hits near the center and involves a cut.

The badminton racket according to the present invention comprises:
a shaft having a butt end and a tip end;
A grip into which the butt end of the shaft is inserted;
and a frame attached to the shaft near the tip end. This badminton racket satisfies the following formula (1) or (2).
y ≧ x + 5.0 (1)
y≦x-6.0 (2)
In these formulas (1) and (2), y is calculated by the following formula (3).
y = (ωi1 * ωi2) ^1/2 (3)
In these formulas (1) and (2), x is calculated by the following formula (4).
x = EI1 * 8.0 + EI3 * 0.46 + 78.0 (4)
In this formula (3), ωi1 represents the in-plane primary natural frequency (Hz) of the natural vibration of the badminton racket under free and restrained conditions, and ωi2 represents the in-plane secondary natural frequency (Hz) of the natural vibration of the badminton racket under free and restrained conditions. In formula (4), EI1 represents the cantilever stiffness (N/mm) of the badminton racket, and EI3 represents the lateral pressure stiffness (N/mm) of the badminton racket.

The badminton racket may satisfy the following formula (5).
y ≧ x + 14.0 (5)

The badminton racket may satisfy the following formula (6).
y≦x-14.0 (6)

A player using a badminton racket according to the present invention can easily perform shots with a cutting point near the center. This racket can contribute to winning the game.

FIG. 1 is a front view showing a badminton racket according to an embodiment of the present invention. FIG. 2 is a right side view of the racket of FIG. FIG. 3 is an enlarged cross-sectional view showing a portion of the shaft of the racket of FIG. FIG. 4 is an enlarged cross-sectional view taken along line IV-IV in FIG. FIG. 5 is a development view showing a prepreg for the shaft of the racket of FIG. FIG. 6 is an explanatory diagram showing a method for measuring the natural vibration frequency of the racket shown in FIG. FIG. 7 is a graph showing the results obtained in the measurement of FIG. FIG. 8(a) is a plan view showing a method for measuring the cantilever rigidity of the racket in FIG. 1, and FIG. 8(b) is a front view thereof. FIG. 9(a) is a perspective view showing an indenter used in the measurement method of FIG. 8, and FIG. 9(b) is an enlarged cross-sectional view thereof. FIG. 10(a) is a plan view showing a method for measuring the side pressure rigidity of the racket in FIG. 1, and FIG. 10(b) is a front view thereof. FIG. 11 is a graph showing the relationship between the value x and the value y for the badminton racket of FIG. FIG. 12 is a front view showing a badminton racket according to a fourth embodiment of the present invention. FIG. 13 is a front view showing a badminton racket according to a sixth embodiment of the present invention. FIG. 14 is a front view showing a badminton racket according to a tenth embodiment of the present invention.

The present invention will now be described in detail based on a preferred embodiment, with reference to the drawings as appropriate.

Figures 1 and 2 show a badminton racket 2. The racket 2 has a shaft 4, a frame 6, a neck 8, a cap 9, a grip 10, and strings 12. In Figures 1 and 2, the arrow X represents the width direction, the arrow Y represents the axial direction, and the arrow Z represents the thickness direction.

The shaft 4 has a butt section 14, a middle section 16, and a tip section 18. The shaft 4 further has a butt end 20 and a tip end 22. The shaft 4 is hollow. The shaft 4 is made of fiber-reinforced resin. This fiber-reinforced resin has a resin matrix and a large number of reinforcing fibers. The shaft 4 includes multiple fiber-reinforced layers (described in detail later).

Examples of the base resin for the shaft 4 include thermosetting resins such as epoxy resins, bismaleimide resins, polyimides, and phenolic resins; and thermoplastic resins such as polyetheretherketone, polyethersulfone, polyetherimide, polyphenylene sulfide, polyamide, and polypropylene. A resin that is particularly suitable for the shaft 4 is epoxy resin.

Examples of reinforcing fibers for the shaft 4 include carbon fiber, metal fiber, glass fiber, and aramid fiber. A fiber that is particularly suitable for the shaft 4 is carbon fiber. Multiple types of fibers may be used in combination.

The frame 6 is annular and hollow. The frame 6 is made of fiber-reinforced resin. The fiber-reinforced resin may be made of the same base resin as the base resin of the shaft 4. The fiber-reinforced resin may be made of the same reinforcing fibers as the reinforcing fibers of the shaft 4. The frame 6 is firmly connected to the tip end 22 of the shaft 4 via the neck 8. The frame 6 has a top 24 and a bottom 26.

The grip 10 has a hole 27 extending in the axial direction (Y direction). The shaft 4 is inserted near the butt end 20 into this hole 27. The inner circumferential surface of the hole 27 and the outer circumferential surface of the shaft 4 are bonded with an adhesive.

The strings 12 are strung on the frame 6. The strings 12 are strung along the width direction X and the axial direction Y. The portions of the strings 12 that extend along the width direction X are referred to as cross threads 28. The portions of the strings 12 that extend along the axial direction Y are referred to as vertical threads 30. The multiple cross threads 28 and the multiple vertical threads 30 form a face 32. The face 32 is generally aligned along the XY plane. In FIG. 1, the arrow Lf represents the length of the face 32. The length Lf is measured along the Y direction.

In FIG. 1, the symbol FC represents the center of the face 32. The center FC is the midpoint of the face 32 in the X direction and the midpoint of the face 32 in the Y direction.

In FIG. 1, the reference symbol 34 indicates the exposed portion of the shaft 4. The exposed portion 34 is exposed from the neck 8 and from the grip 10. In FIG. 1, the reference symbol Ls indicates the length of the exposed portion 34. The length Ls is usually 150 mm or more and 210 mm or less.

Figure 3 is an enlarged cross-sectional view showing a portion of the shaft 4 of the racket 2 in Figure 1. Figure 4 is an enlarged cross-sectional view taken along line IV-IV in Figure 3. As mentioned above, the shaft 4 is hollow. As shown in Figure 4, the cross-sectional shape of the shaft 4 is a circle. In other words, the shaft 4 is cylindrical.

In Figures 3 and 4, the arrow Di represents the inner diameter of the shaft 4. A typical inner diameter Di is 3 mm or more and 10 mm or less. In Figures 3 and 4, the arrow Do represents the outer diameter of the shaft 4. A typical outer diameter Do is 5 mm or more and 15 mm or less.

As mentioned above, the shaft 4 is formed from fiber-reinforced resin. The shaft 4 can be manufactured by a sheet winding method. In this sheet winding method, multiple prepregs are wound around a mandrel. Each prepreg has multiple fibers and a matrix resin. The matrix resin is uncured.

Figure 5 is an exploded view showing a prepreg configuration for the shaft 4 of the racket 2 of Figure 1. This prepreg configuration has 11 prepregs (i.e., sheets). Specifically, this prepreg configuration has a first sheet S1, a second sheet S2, a third sheet S3, a fourth sheet S4, a fifth sheet S5, a sixth sheet S6, a seventh sheet S7, an eighth sheet S8, a ninth sheet S9, a tenth sheet S10, and an eleventh sheet S11. From these prepregs, a plurality of fiber-reinforced layers are formed by a method described below. Specifically, the first fiber-reinforced layer is formed from the first sheet S1, the second fiber-reinforced layer is formed from the second sheet S2, the third fiber-reinforced layer is formed from the third sheet S3, the fourth fiber-reinforced layer is formed from the fourth sheet S4, the fifth fiber-reinforced layer is formed from the fifth sheet S5, the sixth fiber-reinforced layer is formed from the sixth sheet S6, the seventh fiber-reinforced layer is formed from the seventh sheet S7, the eighth fiber-reinforced layer is formed from the eighth sheet S8, the ninth fiber-reinforced layer is formed from the ninth sheet S9, the tenth fiber-reinforced layer is formed from the tenth sheet S10, and the eleventh fiber-reinforced layer is formed from the eleventh sheet S11.

The left-right direction in FIG. 5 is the axial direction of the shaft 4. In FIG. 5, the positions of the butt end 20 and the tip end 22 are indicated by arrows. For ease of explanation, the scale in FIG. 5 is not accurate.

The first sheet S1 is present throughout the entire shaft 4. The shape of the first sheet S1 is generally rectangular. This first sheet S1 contains a plurality of carbon fibers arranged in parallel. The extension direction of each carbon fiber is inclined with respect to the axial direction. The angle of the extension direction of the carbon fibers with respect to the axial direction is 30° or more and 60° or less. In this embodiment, this angle is 45°. This first sheet S1 has a width of 60 mm and a length of 340 mm.

The second sheet S2 is present throughout the shaft 4. The shape of the second sheet S2 is generally rectangular. This second sheet S2 contains a plurality of carbon fibers arranged in parallel. The extension direction of each carbon fiber is inclined with respect to the axial direction. The angle of the extension direction of the carbon fibers with respect to the axial direction is -60° or more and -30° or less. In this embodiment, this angle is -45°. This second sheet S2 has a width of 60 mm and a length of 340 mm.

The inclination direction of the carbon fibers in the second sheet S2 is opposite to the inclination direction of the carbon fibers in the first sheet S1. Therefore, the inclination direction of the carbon fibers in the second fiber reinforced layer is opposite to the inclination direction of the carbon fibers in the first fiber reinforced layer. In this shaft 4, a bias structure is achieved by the first fiber reinforced layer and the second fiber reinforced layer. The first fiber reinforced layer and the second fiber reinforced layer contribute to the bending rigidity and torsional rigidity of the shaft 4. The first fiber reinforced layer and the second fiber reinforced layer especially contribute to the torsional rigidity of the shaft 4.

The third sheet S3 is biased toward the middle portion 16 of the shaft 4. The shape of the third sheet S3 is generally a parallelogram. This third sheet S3 contains a plurality of carbon fibers arranged in parallel. The extension direction of each carbon fiber is inclined with respect to the axial direction. The angle of the extension direction of the carbon fibers with respect to the axial direction is 30° or more and 60° or less. In this embodiment, this angle is 45°. This third sheet S3 has a width of 19 mm and a length of 70 mm.

The fourth sheet S4 is biased toward the middle portion 16 of the shaft 4. In the axial direction, the position of the fourth sheet S4 coincides with the position of the third sheet S3. The shape of the fourth sheet S4 is generally a parallelogram. This fourth sheet S4 contains a plurality of carbon fibers arranged in parallel. The extension direction of each carbon fiber is inclined with respect to the axial direction. The extension direction of the carbon fibers forms an angle with respect to the axial direction of -60° or more and -30° or less. In this embodiment, this angle is -45°. This fourth sheet S4 has a width of 19 mm and a length of 70 mm.

The inclination direction of the carbon fibers in the fourth sheet S4 is opposite to the inclination direction of the carbon fibers in the third sheet S3. Therefore, the inclination direction of the carbon fibers in the fourth fiber reinforced layer is opposite to the inclination direction of the carbon fibers in the third fiber reinforced layer. In this shaft 4, a bias structure is achieved by the third fiber reinforced layer and the fourth fiber reinforced layer. The third fiber reinforced layer and the fourth fiber reinforced layer contribute to the bending rigidity and torsional rigidity of the middle section 16. The third fiber reinforced layer and the fourth fiber reinforced layer especially contribute to the torsional rigidity of the middle section 16.

The fifth sheet S5 is biased toward the tip end 22 of the shaft 4. The shape of the fifth sheet S5 is generally trapezoidal. This fifth sheet S5 contains a plurality of carbon fibers arranged in parallel. The extension direction of each carbon fiber coincides with the axial direction. In other words, the angle of the extension direction of the carbon fibers with respect to the axial direction is substantially 0°. This fifth sheet S5 has a width of 37 mm, a length of the upper base of 105 mm, and a length of the lower base of 115 mm.

As mentioned above, the carbon fibers contained in the fifth sheet S5 are substantially oriented in the axial direction. Therefore, in the fifth fiber-reinforced layer, the carbon fibers are also substantially oriented in the axial direction. In this specification, a structure in which the carbon fibers are substantially oriented in the axial direction is referred to as a "straight structure." The fifth fiber-reinforced layer has a straight structure. When the shaft 4 bends, a large tension is applied to these carbon fibers. This tension suppresses further bending of the shaft 4. In other words, these carbon fibers contribute to the bending rigidity of the shaft 4. The fifth fiber-reinforced layer particularly contributes to the bending rigidity of the tip portion 18.

The sixth sheet S6 is biased toward the butt end 20 of the shaft 4. The shape of the sixth sheet S6 is generally trapezoidal. This sixth sheet S6 includes a plurality of carbon fibers arranged in parallel. The extension direction of each carbon fiber coincides with the axial direction. In other words, the angle of the extension direction of the carbon fiber with respect to the axial direction is substantially 0°. This sixth sheet S6 has a width of 37 mm, a length of the upper base of 155 mm, and a length of the lower base of 165 mm.

As mentioned above, the carbon fibers contained in the sixth sheet S6 are substantially axially oriented. Therefore, in the sixth fiber-reinforced layer, the carbon fibers are also substantially axially oriented. The sixth fiber-reinforced layer has a straight structure. When the shaft 4 is bent, a large tension is applied to these carbon fibers. This tension suppresses further bending of the shaft 4. In other words, these carbon fibers contribute to the bending rigidity of the shaft 4. The sixth fiber-reinforced layer particularly contributes to the bending rigidity of the butt portion 14.

The seventh sheet S7 is biased toward the butt end 20 of the shaft 4. The shape of the seventh sheet S7 is generally trapezoidal. This seventh sheet S7 includes a plurality of carbon fibers arranged in parallel. The extension direction of each carbon fiber is inclined with respect to the axial direction. The angle of the extension direction of the carbon fibers with respect to the axial direction is 30° or more and 60° or less. In this embodiment, this angle is 45°. This seventh sheet S7 has a width of 46 mm, a length of the upper base of 235 mm, and a length of the lower base of 245 mm.

The eighth sheet S8 is biased toward the butt end 20 of the shaft 4. In the axial direction, the position of the eighth sheet S8 coincides with the position of the seventh sheet S7. The shape of the eighth sheet S8 is generally trapezoidal. This eighth sheet S8 includes a plurality of carbon fibers arranged in parallel. The extension direction of each carbon fiber is inclined with respect to the axial direction. The angle of the extension direction of the carbon fibers with respect to the axial direction is -60° or more and -30° or less. In this embodiment, this angle is -45°. This eighth sheet S8 has a width of 46 mm, a length of the upper base of 235 mm, and a length of the lower base of 245 mm.

The inclination direction of the carbon fibers in the eighth sheet S8 is opposite to the inclination direction of the carbon fibers in the seventh sheet S7. Therefore, the inclination direction of the carbon fibers in the eighth fiber reinforced layer is opposite to the inclination direction of the carbon fibers in the seventh fiber reinforced layer. In this shaft 4, a bias structure is achieved by the seventh fiber reinforced layer and the eighth fiber reinforced layer. The seventh fiber reinforced layer and the eighth fiber reinforced layer contribute to the bending rigidity and torsional rigidity of the butt section 14. The seventh fiber reinforced layer and the eighth fiber reinforced layer especially contribute to the torsional rigidity of the butt section 14 and the middle section 16.

The ninth sheet S9 is biased toward the tip end 22 of the shaft 4. The shape of the ninth sheet S9 is generally trapezoidal. This ninth sheet S9 contains a plurality of carbon fibers arranged in parallel. The extension direction of each carbon fiber coincides with the axial direction. In other words, the angle of the extension direction of the carbon fiber with respect to the axial direction is substantially 0°. This ninth sheet S9 has a width of 92 mm, a length of the upper base of 95 mm, and a length of the lower base of 105 mm.

As mentioned above, the carbon fibers contained in the ninth sheet S9 are substantially axially oriented. Therefore, in the ninth fiber-reinforced layer, the carbon fibers are also substantially axially oriented. The ninth fiber-reinforced layer has a straight structure. When the shaft 4 bends, these carbon fibers are subjected to a large tension. This tension suppresses further bending of the shaft 4. In other words, these carbon fibers contribute to the bending rigidity of the shaft 4. The ninth fiber-reinforced layer particularly contributes to the bending rigidity of the tip portion 18.

The tenth sheet S10 is biased toward the butt end 20 of the shaft 4. The shape of the tenth sheet S10 is generally trapezoidal. This tenth sheet S10 contains a plurality of carbon fibers arranged in parallel. The extension direction of each carbon fiber coincides with the axial direction. In other words, the angle of the extension direction of the carbon fibers with respect to the axial direction is substantially 0°. This tenth sheet S10 has a width of 71 mm, a length of the upper base of 235 mm, and a length of the lower base of 245 mm.

As mentioned above, the carbon fibers contained in the tenth sheet S10 are substantially axially oriented. Therefore, in the tenth fiber-reinforced layer, the carbon fibers are also substantially axially oriented. The tenth fiber-reinforced layer has a straight structure. When the shaft 4 bends, these carbon fibers are subjected to a large tension. This tension suppresses further bending of the shaft 4. In other words, these carbon fibers contribute to the bending rigidity of the shaft 4. The tenth fiber-reinforced layer particularly contributes to the bending rigidity of the butt section 14 and the middle section 16.

The eleventh sheet S11 is biased toward the tip end 22 of the shaft 4. The shape of the eleventh sheet S11 is generally trapezoidal. This eleventh sheet S11 contains a plurality of carbon fibers arranged in parallel. The extension direction of each carbon fiber coincides with the axial direction. In other words, the angle of the extension direction of the carbon fiber with respect to the axial direction is substantially 0°. This eleventh sheet S11 has a width of 71 mm, a length of the upper base of 95 mm, and a length of the lower base of 105 mm.

As mentioned above, the carbon fibers contained in the eleventh sheet S11 are substantially axially oriented. Therefore, in the eleventh fiber-reinforced layer, the carbon fibers are also substantially axially oriented. The eleventh fiber-reinforced layer has a straight structure. When the shaft 4 bends, these carbon fibers are subjected to a large tension. This tension suppresses further bending of the shaft 4. In other words, these carbon fibers contribute to the bending rigidity of the shaft 4. The eleventh fiber-reinforced layer particularly contributes to the bending rigidity of the tip portion 18.

In this shaft 4, the first fiber-reinforced layer and the second fiber-reinforced layer are present from the butt end 20 to the tip end 22. These fiber-reinforced layers can contribute to the durability of the shaft 4.

In manufacturing this shaft 4, the sheets shown in FIG. 5 are wound around the mandrel in order. The first sheet S1 and the second sheet S2 may be stacked and wound around the mandrel. The third sheet S3 and the fourth sheet S4 may be stacked and wound around the mandrel. The sixth sheet S6 and the seventh sheet S7 may be stacked and wound around the mandrel. Other sheets may be wound around the mandrel together with these sheets. Examples of other sheets include those containing glass fiber.

These sheets are then wrapped in wrapping tape. The mandrel, prepregs (sheets S1-S9), and wrapping tape are then heated in an oven or similar. The heating causes the matrix resin to flow. Further heating causes the resin to undergo a hardening reaction, resulting in a molded body. This molded body is then processed, its end faces polished, painted, and so on, to complete the shaft 4.

The material of the shaft 4 is a fiber-reinforced resin. The material of the shaft 4 may be a resin composition that does not contain fibers. The material of the shaft 4 may be metal, wood, etc.

Figure 6 is an explanatory diagram showing a method for measuring the frequency of the natural vibration of the racket 2 in Figure 1. In this method, the racket 2 is suspended by a string 36. This racket 2 does not have a string 12. In other words, a racket 2 without a string 12 is used to measure the frequency of the natural vibration. In Figure 6, the axial direction (Y direction) of the shaft 4 coincides with the vertical direction. In Figure 6, the shaft 4 is located below the frame 6.

As shown in FIG. 6, an acceleration pickup 38 is attached to the racket 2. The acceleration pickup 38 is located at the tip of the grip 10. The acceleration pickup 38 is oriented in the X direction. The acceleration pickup 38 has a mass of 3.5 g. Next, a point Ph of the grip 10 facing the acceleration pickup 38 is excited by an impact hammer (not shown). The input vibration measured by the force pickup of the impact hammer and the response vibration measured by the acceleration pickup 38 are sent to a frequency analyzer (Hewlett-Packard's "Dynamic Signal Analyzer") via an amplifier. The frequency of the in-plane natural vibration is calculated based on the transfer function obtained by this device. The direction of the in-plane natural vibration is mainly the X direction. In this method, the natural frequency is measured without any part of the racket 2 being firmly fixed. In other words, the natural frequency is measured under free constraint conditions.

Fig. 7 is a graph showing the results obtained from the measurement of Fig. 6. In Fig. 7, the horizontal axis is frequency (Hz) and the vertical axis is the magnitude of acceleration (m/ ^s2 /N). In Fig. 7, the reference symbol P1 indicates a primary peak. The frequency at this primary peak P1 is the in-plane primary natural frequency ωi1. In Fig. 7, the reference symbol P2 indicates a secondary peak. The frequency at this secondary peak P2 is the in-plane secondary natural frequency ωi2.

Figure 8(a) is a plan view showing a method for measuring the cantilever stiffness EI1 of the racket 2 in Figure 1, and Figure 8(b) is a front view thereof. The left-right direction in Figures 8(a) and (b) is the horizontal direction. The up-down direction in Figure 8(b) is the vertical direction. A racket 2 without strings 12 is used to measure the cantilever stiffness EI1.

In this measurement method, the grip is sandwiched between a first block 42 and a second block 44. The shape of the first block 42 is a rectangular parallelepiped. The shape of the second block 44 is the same as that of the first block 42. Each of the first block 42 and the second block 44 is positioned so that its front end coincides with the boundary line between the cap 9 and the grip 10.

Figure 8 shows the indenter 46. The indenter 46 extends in the X direction. The indenter 46 is located between the frame 6 and the cap 9 in the Y direction. The distance of the indenter 46 from the tip of the cap 9 is 180 mm.

This indenter 46 is shown in Figure 9. Figure 9(b) shows a cross section perpendicular to the length of the indenter 46. The indenter 46 has an abutment surface 48. As shown in Figure 9(a), the abutment surface 48 extends in the length direction of the indenter 46. The shape of the abutment surface 48 in the cross section of Figure 9(b) is a circular arc. The radius R1 of this circular arc is 5 mm.

In FIG. 8B, the indenter 46 is located above the shaft 4 and is separated from the shaft 4. The indenter 46 gradually moves in the direction indicated by the arrow A. This movement causes the contact surface 48 to contact the shaft 4. After contact, the indenter 46 continues to move. Due to the movement, a bending load is applied to the shaft 4, causing the shaft 4 to bend. As the movement distance La (m) of the indenter 46 after the contact surface 48 contacts the shaft 4 increases, the bending load Fa (N) increases. The bending load Fa1 (N) when the movement distance La is 0.5 mm and the bending load Fa2 (N) when the movement distance La is 1.5 mm are measured. The cantilever stiffness EI1 (N/mm) is calculated based on the following formula.
EI1 = (Fa2 - Fa1) / (1.5 - 0.5)

Figure 10(a) is a plan view showing a method for measuring the side pressure stiffness EI3 of the racket 2 in Figure 1, and Figure 10(b) is a front view thereof. The left-right direction in Figures 10(a) and (b) is the horizontal direction. The up-down direction in Figure 10(b) is the vertical direction. A racket 2 without strings 12 is used to measure the side pressure stiffness EI3.

In this measurement method, the frame 6 is placed on a stand 50. As shown in FIG. 10, the axial direction (Y direction) coincides with the horizontal direction, and the width direction (X direction) coincides with the vertical direction. FIG. 10 shows a cylindrical indenter 47. The indenter 47 is located directly above the maximum width point Pmax. This maximum width point Pmax is the point where the width of the frame 6 is maximum. In FIG. 10(b), the indenter 47 is located above the frame 6 and is separated from the frame 6. The indenter 47 gradually moves in the direction indicated by the arrow A. This movement causes the abutment surface 48 to abut against the frame 6. After the abutment, the indenter 47 continues to move. Due to the movement, a bending load is applied to the frame 6, and the frame 6 is bent. As the movement distance Lc (m) of the indenter 47 after the abutment surface 48 abuts against the frame 6 increases, the bending load Fc (N) increases. The bending load Fc1 (N) when the moving distance Lc is 0.5 mm and the bending load Fc2 (N) when the moving distance Lc is 2.5 mm are measured. The lateral pressure stiffness EI3 (N/mm) is calculated based on the following formula.
EI3 = (Fc2 - Fc1) / (2.5 - 0.5)

In the present invention, the value y is calculated by the following formula (3).
y = (ωi1 * ωi2) ^1/2 (3)
As described above, ωi1 represents the in-plane primary natural frequency (Hz) of the natural vibration of the racket 2, and ωi2 represents the in-plane secondary natural frequency (Hz) of the natural vibration of the racket 2.

In the present invention, the value x is calculated by the following formula (4).
x = EI1 * 8.0 + EI3 * 0.46 + 78.0 (4)
As described above, EI1 represents the cantilever stiffness (N/mm) of the racket 2, and EI3 represents the lateral pressure stiffness (N/mm) of the racket 2.

Figure 11 is a graph showing the relationship between the value x and the value y of the badminton racket 2. In this graph, the symbol Pr represents the point of the racket 2 shown in Figure 1-5.

The straight line indicated by the symbol L1 in FIG.
y = x + 5.0
In this graph, the racket 2 included in the zone above the straight line L1 satisfies the following formula (1).
y ≧ x + 5.0 (1)

According to the knowledge of the inventor, when the shuttle is hit on the part of the face 32 closer to the bottom 26, vibrations of the in-plane secondary mode are mainly excited. According to the knowledge of the inventor, when the shuttle is hit on the part of the face 32 closer to the top 24, vibrations of the in-plane primary mode are mainly excited. According to the knowledge of the inventor, when the shuttle is hit on the center FC of the face 32, vibrations of the in-plane primary mode and the in-plane secondary mode are mainly excited. The typical impact point in a driven clear is near the center FC. Therefore, in a driven clear, vibrations of the in-plane primary mode and the in-plane secondary mode are mainly excited.

The value x is an index that correlates with the hardness of the racket 2. The value y is an index that correlates with the repulsion performance of the racket 2. The values x and y are indexes that the present inventor found after intensive research. In a racket 2 that satisfies the above formula (1), the value y is relatively large with respect to the hardness. As described above, in a driven clear, vibrations of the in-plane primary mode and the in-plane secondary mode are excited. However, even in a driven clear, the impact point varies. According to the knowledge obtained by the present inventor, in a driven clear using a racket 2 that satisfies the above formula (1), even if the impact point varies, the variation in the initial speed of the shuttle is small. The reason for this is that even if the shuttle is hit at a position shifted from the intended position, the repulsion of the racket 2 is not extremely small. Since the variation in the initial speed of the shuttle is small, the variation in the trajectory of the shuttle is also small. This racket 2 is suitable for players who frequently use driven clears. This racket 2 is also suitable for players who place importance on driven clears.

As mentioned above, the typical impact point in a driven clear is near the center FC. The racket 2 that satisfies the above formula (1) is also suitable for shots other than a driven clear, in which the shuttlecock is hit near the center FC.

The above formula (1) can be achieved by changing the position of the prepreg, the number of prepregs, the width of the prepreg, the length of the prepreg, the angle of the fibers, the fiber basis weight, the elastic modulus of the fibers, etc. in the shaft 4.
(a) A fiber-reinforced layer having a straight structure is unevenly distributed in the tip portion 18.
(b) The number of fiber-reinforced layers in the tip portion 18 is set to be large.
(c) A fiber-reinforced layer having a large basis weight is unevenly distributed in the tip portion 18.
(d) A fiber reinforced layer having fibers with a large elastic modulus is unevenly distributed in the tip portion 18.
(e) The number of fiber reinforced layers in the pad portion 14 is set to be small.
(f) The fiber reinforced layer having a small basis weight is unevenly distributed in the pad portion 14.
(g) A fiber reinforced layer having fibers with a low elastic modulus is unevenly distributed in the pad portion 14.
In this embodiment, as described above, the high rigidity of the tip portion 18 is achieved by the fifth fiber reinforced layer obtained from the fifth sheet S5, the ninth fiber reinforced layer obtained from the ninth sheet S9, and the eleventh fiber reinforced layer obtained from the eleventh sheet S11. This achieves the above formula (1).

The formula (1) may be achieved by the specifications of a member other than the shaft 4. An example of a member other than the shaft 4 is the frame 6. The formula (1) can be achieved by changing the position of the prepreg, the number of prepregs, the width of the prepreg, the length of the prepreg, the angle of the fibers, the fiber basis weight, the elastic modulus of the fibers, and the like in the frame 6. Specific means include:
(a) A fiber-reinforced layer having a straight structure is unevenly distributed in the vicinity of the top 24 of the frame 6.
(b) The number of fiber reinforced layers near the top 24 of the frame 6 is set to be large.
(c) The fiber-reinforced layer having a large basis weight is unevenly distributed in the vicinity of the top 24 of the frame 6.
(d) A fiber-reinforced layer having fibers with a large elastic modulus is unevenly distributed in the vicinity of the top 24 of the frame 6.
(e) The number of fiber reinforced layers near the bottom 26 of the frame 6 is set to be small.
(f) The fiber-reinforced layer having a small basis weight is unevenly distributed in the vicinity of the bottom 26 of the frame 6.
(g) A fiber reinforced layer having fibers with a low elastic modulus is unevenly distributed in the vicinity of the bottom 26 of the frame 6.
etc. are exemplified.

The straight line indicated by the symbol L2 in FIG.
y = x - 6.0
In this graph, the racket 2 included in the zone below the straight line L2 satisfies the following formula (2).
y≦x-6.0 (2)

In the racket 2 that satisfies the above formula (2), the value y is relatively small with respect to the hardness. As mentioned above, in the driven clear, vibrations of the in-plane primary mode and the in-plane secondary mode are excited. However, even in the driven clear, the impact point varies. According to the knowledge obtained by the inventor, in the driven clear with the racket 2 that satisfies the above formula (2), even if the impact point varies, the variation in the initial speed of the shuttle is small. The reason for this is that the difference between the repulsion of the racket 2 when the shuttle is hit at the center FC and the repulsion of the racket 2 when the shuttle is hit at a position away from the center FC is small. Since the variation in the initial speed of the shuttle is small, the variation in the trajectory of the shuttle is also small. This racket 2 is suitable for players who frequently use driven clears. This racket 2 is also suitable for players who place importance on driven clears.

As mentioned above, the typical impact point in a driven clear is near the center FC. A racket 2 that satisfies the above formula (2) is also suitable for shots other than a driven clear, in which the shuttlecock is hit near the center FC and is accompanied by a cut.

The above formula (2) can be achieved by changing the position of the prepreg, the number of prepregs, the width of the prepreg, the length of the prepreg, the angle of the fibers, the fiber basis weight, the elastic modulus of the fibers, etc. in the shaft 4.
(a) A fiber-reinforced layer having a straight structure is unevenly distributed in the pad portion 14.
(b) The number of fiber-reinforced layers in the pad portion 14 is set to be large.
(c) The fiber-reinforced layer having a large basis weight is unevenly distributed in the pad portion 14 .
(d) A fiber reinforced layer having fibers with a large elastic modulus is unevenly distributed in the pad portion 14 .
(e) The number of fiber-reinforced layers in the tip portion 18 is set to be small.
(f) A fiber-reinforced layer having a small basis weight is unevenly distributed in the tip portion 18.
(g) A fiber reinforced layer having fibers with a low elastic modulus is unevenly distributed in the tip portion 18.
etc. are examples.

The formula (2) may be achieved by the specifications of a member other than the shaft 4. An example of a member other than the shaft 4 is the frame 6. The formula (2) can be achieved by changing the position of the prepreg, the number of prepregs, the width of the prepreg, the length of the prepreg, the angle of the fibers, the fiber basis weight, the elastic modulus of the fibers, and the like in the frame 6. Specific means include:
(a) A fiber-reinforced layer having a straight structure is unevenly distributed in the vicinity of the top 24 and the vicinity of the bottom 26 of the frame 6.
(b) The number of fiber-reinforced layers near the top 24 and near the bottom 26 of the frame 6 is set to be large.
(c) The fiber-reinforced layers having a large basis weight are unevenly distributed in the vicinity of the top 24 and the vicinity of the bottom 26 of the frame 6 .
(d) A fiber-reinforced layer having fibers with a large elastic modulus is unevenly distributed in the vicinity of the top 24 and the vicinity of the bottom 26 of the frame 6.
etc. are exemplified.

A racket 2 that satisfies either the above formula (1) or (2) can provide a stable trajectory during a driven clear. From the viewpoint of the shuttle flying at high speed during a driven clear, a racket 2 that satisfies the above formula (1) is preferred.

The straight line indicated by the symbol L5 in FIG.
y = x + 14.0
In this graph, the racket 2 included in the zone above the line L5 satisfies the following formula (5).
y ≧ x + 14.0 (5)
According to the findings of the inventor, the racket 2 that satisfies this formula (5) is suitable for driven clearing. A player who performs a driven clearing using this racket 2 can easily achieve the intended trajectory of the shuttlecock. With this racket 2, there is little variation in the trajectory of the shuttlecock in a driven clearing. The shuttlecock hit with this racket 2 flies at high speed.

The straight line indicated by the symbol L6 in FIG.
y = x - 14.0
In this graph, the racket 2 included in the zone below the line L6 satisfies the following formula (6).
y≦x-14.0 (6)
According to the findings of the inventors, the racket 2 that satisfies this formula (6) is suitable for driven clearing. A player who uses this racket 2 for driven clearing can easily achieve the intended trajectory of the shuttlecock. With this racket 2, the trajectory of the shuttlecock during driven clearing varies little.

The effects of the present invention will be explained below by way of examples, but the present invention should not be interpreted in a restrictive manner based on the description of these examples.

[Example 1]
A shaft having the prepreg configuration shown in FIG. 5 was manufactured. Each prepreg contained carbon fiber. The tensile modulus of the carbon fiber in the fifth sheet S5, the ninth sheet S9, and the eleventh sheet S11 was 39 tf/ ^mm2 . The tensile modulus of the carbon fiber in the remaining sheets was 16 tf/ ^mm2 . A frame, a neck, a cap, and a grip used in a commercially available badminton racket having standard hardness and mass were attached to this shaft to manufacture a badminton racket. The in-plane primary natural frequency ωi1 of this racket was 64 Hz, the in-plane secondary natural frequency ωi2 was 253 Hz, the cantilever stiffness EI1 was 1.4 N/mm, and the lateral pressure stiffness EI3 was 24.5 N/mm. The coordinates of this racket are indicated by the symbol Pr in FIG. 11.

[Examples 2-21 and Comparative Examples 1-11]
Badminton rackets of Examples 2-21 and Comparative Examples 1-11 were obtained in the same manner as in Example 1, except that the prepreg configuration was as shown in Table 1-8. The width of the prepreg for the shaft of these rackets is shown in Table 1-8 below. The in-plane primary natural frequency ωi1, the in-plane secondary natural frequency ωi2, the cantilever stiffness EI1, and the lateral pressure stiffness EI3 of these rackets are shown in Table 1-8 below. The values x and y of these rackets are shown in FIG.

[Experiment 1]
A player who prefers a soft badminton racket was asked to evaluate the stability and resilience using the following method.

[Stability]
A shuttle was launched from a launching machine. A player was made to perform a driven clear of the shuttle, and the trajectory of the shuttle was photographed. The image was analyzed to measure the height of the shuttle as it passed over the net. Twenty measurements were taken, and the standard deviation of the height was calculated. Based on this standard deviation, the rackets were rated. The grading criteria are as follows. The results are shown in Tables 1 and 2 below.
A: Standard deviation is less than 0.18 m. B: Standard deviation is 0.18 m or more and less than 0.25 m. C: Standard deviation is 0.25 m or more.

[Resilience]
In the evaluation of stability described above, the speed of the shuttlecock passing over the net was measured. 20 measurements were taken and the average speed was calculated. Based on this average value, the rackets were rated. The grading criteria are as follows. The results are shown in Tables 1 and 2 below.
A: Average speed is 13.0 m/s or more. B: Average speed is 12.5 m/s or more but less than 13.0 m/s. C: Average speed is less than 12.5 m/s.

[Experiment 2]
Players who prefer badminton rackets with standard hardness were asked to evaluate the stability and resilience in the same manner as in Experiment 1. The results are shown in Tables 3 and 4 below.

[Experiment 3]
Players who prefer hard badminton rackets were asked to evaluate the stability and resilience in the same manner as in Experiment 1. The results are shown in Tables 5 and 6 below.

[Experiment 4]
Players who prefer very hard badminton rackets were asked to evaluate the stability and resilience in the same manner as in Experiment 1. The results are shown in Tables 7 and 8 below.

As is clear from Table 1-8, the shuttlecock trajectory during driven clearing is stable with the badminton rackets of each embodiment. From these evaluation results, the superiority of the present invention is clear.

The badminton racket of the present invention is suitable for players who use a style that makes heavy use of driven clears. This racket is also suitable for players who use a style that makes heavy use of other shots that involve cutting and have a striking point near the center.

2: Badminton racket 4: Shaft 6: Frame 8: Neck 10: Grip 12: String 14: Butt section 16: Middle section 18: Tip section 20: Butt end 22: Tip end 24: Top 26: Bottom 28: Horizontal threads 30: Vertical threads 32: Face 34: Exposed section 38: Acceleration pickup 40: First bar 42: Contact surface 44: Second bar 46: Indenter 48: Contact surface 50: Base S1: First sheet S2: Second sheet S3: Third sheet S4: Fourth sheet S5: Fifth sheet S6: Sixth sheet S7: Seventh sheet S8: Eighth sheet S9: Ninth sheet

Claims (3)

a shaft having a butt end and a tip end;
a grip into which the shaft is inserted near the butt end;
and a frame attached to the shaft proximate the tip end,
A badminton racket that satisfies the following formula (1) or (2).
y ≧ x + 5.0 (1)
y≦x-6.0 (2)
(In the above formulas (1) and (2), y is calculated by the following formula (3).
y = (ωi1 * ωi2) ^1/2 (3)
In the above formulas (1) and (2), x is calculated by the following formula (4).
x = EI1 * 8.0 + EI3 * 0.46 + 78.0 (4)
In the above formula (3), ωi1 represents the in-plane primary natural frequency (Hz) in the natural vibration of the badminton racket, and ωi2 represents the in-plane secondary natural frequency (Hz) in the natural vibration of the badminton racket. In the above formula (4), EI1 represents the cantilever stiffness (N/mm) of the badminton racket, and EI3 represents the lateral pressure stiffness (N/mm) of the badminton racket. 2. The badminton racket according to claim 1, which satisfies the following formula (5).
y ≧ x + 14.0 (5) 2. The badminton racket according to claim 1, which satisfies the following formula (6).
y≦x-14.0 (6)

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