Badminton racket

Abstract

To provide a badminton racket 2 by which a variation of trajectories of a shuttle can be suppressed in shots the hit points of which are closer to a top 24.SOLUTION: A badminton racket 2 has a shaft 4, a grip 10 in which a portion of the shaft 4 closer to a butt end 20 is inserted, and a frame 6 attached to a portion of the shaft 4 closer to a tip end 22. An out-of-plane primary natural frequency ωo1 (Hz) and an out-of-plane secondary natural frequency ωo2 (Hz) in the natural vibration of the badminton racket 2 under a free constraint condition satisfies a following equation (1): ωo2≥2.5×ωo1+37.0 (1). A favorable out-of-plane secondary natural frequency ωo2 is 179 Hz or more.SELECTED DRAWING: Figure 1

Description

Technical Field

[0001] The present invention relates to a racket used for badminton.

Background Art

[0002] 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 hits a shuttlecock with the racket. By hitting, the face collides with the shuttlecock. The impact due to the collision is transmitted from the strings through the frame to the shaft. By hitting, the frame and the shaft deform. An attempt regarding optimization of the deformation behavior at the time of collision is described in Japanese Patent Laid-Open No. 2001-70481.

Prior Art Documents

Patent Documents

[0003]

Patent Document 1

Summary of the Invention

Problems to be Solved by the Invention

[0004] In a badminton game, a player makes various types of shots. The player makes shots such as a smash, a lob, a drop, and a clear.

[0005] A lob is often hit from near the net within the player's court. A lob is a shot intended to carry the shuttlecock to the back of the opponent player's court. The trajectory of the shuttlecock in a lob is high. A player needs the skill to fly the shuttlecock at the intended height. A player who frequently uses a lob hopes for the stability of the trajectory (speed, height, etc.) of the shuttlecock.

[0006] Statistical studies have shown that the typical point of contact for a lob is towards the top of the shuttlecock. Even in shots other than lobs, the shuttlecock can be hit at a point closer to the top of the shuttlecock.

[0007] The object of the present invention is to provide a badminton racket that can suppress variations in the trajectory of the shuttlecock in shots where the point of contact is closer to the top of the shuttlecock. [Means for solving the problem]

[0008] The badminton racket according to the present invention is A shaft having a butt end and a tip end. The grip is inserted near the butt end of this shaft. and Frame attached to the shaft near the tip end The badminton racket has the following characteristics. The out-of-plane first natural frequency ωo1 (Hz) and out-of-plane second natural frequency ωo2 (Hz) in the natural vibration of this badminton racket under free constraint conditions satisfy the following equation (1). ωo2 ≧ 2.5 × ωo1 + 37.0 (1)

[0009] Preferably, the badminton racket satisfies the following equation (2). ωo2 ≧ 2.5 × ωo1 + 44.0 (2) Preferably, the badminton racket satisfies the following formula (3). ωo2 ≧ 2.5 × ωo1 + 54.0 (3)

[0010] Preferably, the frequency ωo2 is 179 Hz or higher. Preferably, the frequency ωo2 is 184 Hz or higher. [Effects of the Invention]

[0011] A player using the badminton racket according to the present invention can easily execute shots where the point of contact is closer to the top of the shuttlecock. This racket can contribute to winning games. [Brief explanation of the drawing]

[0012] [Figure 1] Figure 1 is a front view showing a badminton racket according to an embodiment of the present invention. [Figure 2] Figure 2 is a right side view showing the racket of Figure 1. [Figure 3] Figure 3 is an enlarged cross-sectional view showing a part of the shaft of the racket of Figure 1. [Figure 4] Figure 4 is an enlarged cross-sectional view taken along line IV-IV of Figure 3. [Figure 5] Figure 5 is a developed view showing a prepreg for the shaft of the racket of Figure 1. [Figure 6] Figure 6 is an explanatory view showing a method for measuring the frequency of the natural vibration of the racket of Figure 1. [Figure 7] Figure 7 is a graph showing the results obtained in the measurement of Figure ⑥. [Figure 8] Figure 8 is a graph showing the relationship between the out-of-plane primary natural frequency ωo1 and the out-of-plane secondary natural frequency ωo2 of the badminton racket of Figure 1. [Figure 9] Figure 9 is a developed view showing a prepreg for the shaft of the badminton racket according to Example 10 of the present invention. [Figure 10] Figure 10 is a developed view showing a prepreg for the shaft of the badminton racket according to Example 7 of the present invention.

Mode for Carrying Out the Invention

[0013] Hereinafter, the present invention will be described in detail based on preferred embodiments while appropriately referring to the drawings.

[0014] In FIGS. 1 and 2, a badminton racket 2 is shown. This racket 2 has a shaft 4, a frame 6, a neck 8, a cap 9, a grip 10, and strings 12. In FIGS. 1 and 2, arrow X represents the width direction, arrow Y represents the axial direction, and arrow Z represents the thickness direction.

[0015] The shaft 4 has a butt portion 14, a middle portion 16, and a tip portion 18. The shaft 4 further has a butt end 20 and a tip end 22. The shaft 4 is hollow. The shaft 4 is formed of a fiber-reinforced resin. This fiber-reinforced resin has a resin matrix and a number of reinforcing fibers. The shaft 4 includes a plurality of fiber-reinforced layers (to be described in detail later).

[0016] Examples of the base resin of the shaft 4 include thermosetting resins such as epoxy resin, bismaleimide resin, polyimide, and phenolic resin; and thermoplastic resins such as polyether ether ketone, polyether sulfone, polyether imide, polyphenylene sulfide, polyamide, and polypropylene. A resin particularly suitable for the shaft 4 is epoxy resin.

[0017] Examples of the reinforcing fibers of the shaft 4 include carbon fiber, metal fiber, glass fiber, and aramid fiber. A fiber particularly suitable for the shaft 4 is carbon fiber. A plurality of types of fibers may be used in combination.

[0018] The frame 6 is annular and hollow. The frame 6 is formed of a fiber-reinforced resin. The same base resin as that of the shaft 4 may be used for this fiber-reinforced resin. The same reinforcing fibers as those of the shaft 4 may be used for this fiber-reinforced resin. The frame 6 is firmly coupled to the tip end 22 of the shaft 4 via the neck 8. The frame 6 has a top 24 and a bottom 26.

[0019] The grip 10 has a hole 27 extending in the axial direction (Y direction). Near the butt end 20 of the shaft 4 is inserted into this hole 27. The inner peripheral surface of the hole 27 and the outer peripheral surface of the shaft 4 are joined with an adhesive.

[0020] The string 12 is stretched over the frame 6. The string 12 is in the width direction X orThe string is stretched along the axial direction Y. The portion of the string 12 extending along the width direction X is called the transverse thread 28. The portion of the string 12 extending along the axial direction Y is called the longitudinal thread 30. Multiple transverse threads 28 and multiple longitudinal threads 30 form a face 32. The face 32 generally aligns with the XY plane.

[0021] In Figure 1, reference numeral 34 represents the exposed portion of the shaft 4. The exposed portion 34 is exposed from both the neck 8 and the grip 10. In Figure 1, reference numeral L represents the length of this exposed portion 34. The length L is typically between 150 mm and 210 mm.

[0022] Figure 3 is an enlarged cross-sectional view showing a portion of the shaft 4 of racket 2 in Figure 1. Figure 4 is an enlarged cross-sectional view along line IV-IV in Figure 3. As mentioned above, this shaft 4 is hollow. As shown in Figure 4, the cross-sectional shape of this shaft 4 is circular. In other words, this shaft 4 is cylindrical.

[0023] In Figures 3 and 4, the arrow Di represents the inner diameter of shaft 4. A typical inner diameter Di is between 3 mm and 10 mm. In Figures 3 and 4, the arrow Do represents the outer diameter of shaft 4. A typical outer diameter Do is between 5 mm and 15 mm.

[0024] As mentioned above, shaft 4 is formed from fiber-reinforced resin. This shaft 4 can be manufactured by the sheet winding method. In this sheet winding method, multiple prepregs are wound onto a mandrel. Each prepreg has multiple fibers and a matrix resin. This matrix resin is not cured.

[0025] Figure 5 is an unfolded view showing the prepreg configuration for the shaft 4 of the racket 2 in Figure 1. This prepreg configuration has 9 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, and a ninth sheet S9. Multiple fiber reinforcement layers are formed from these prepregs by a method described later. Specifically, the first fiber reinforcement layer is formed from the first sheet S1, the second fiber reinforcement layer from the second sheet S2, the third fiber reinforcement layer from the third sheet S3, the fourth fiber reinforcement layer from the fourth sheet S4, the fifth fiber reinforcement layer from the fifth sheet S5, the sixth fiber reinforcement layer from the sixth sheet S6, the seventh fiber reinforcement layer from the seventh sheet S7, the eighth fiber reinforcement layer from the eighth sheet S8, and the ninth fiber reinforcement layer from the ninth sheet S9.

[0026] In Figure 5, the left-right direction corresponds to the axial direction of the shaft 4. The positions of the butt end 20 and tip end 22 are indicated by arrows in Figure 5. For the sake of clarity, the scale in Figure 5 is not accurate.

[0027] The first sheet S1 extends throughout the entire shaft 4. The shape of the first sheet S1 is generally rectangular. This first sheet S1 contains multiple parallel carbon fibers. The direction of extension of each carbon fiber is inclined with respect to the axial direction. The angle of the direction of extension of these carbon fibers with respect to the axial direction is between 30° and 60°. In this embodiment, this angle is 45°. The width of this first sheet S1 is 102 mm and the length is 340 mm.

[0028] The second sheet S2 is present throughout the entire shaft 4. The shape of the second sheet S2 is generally rectangular. This second sheet S2 contains multiple parallel carbon fibers. The direction of extension of each carbon fiber is inclined with respect to the axial direction. The angle of the direction of extension of these carbon fibers with respect to the axial direction is between -60° and -30°. In this embodiment, this angle is -45°. The width of this second sheet S2 is 102 mm and the length is 340 mm.

[0029] The orientation of the carbon fibers in the second sheet S2 is opposite to the orientation of the carbon fibers in the first sheet S1. Therefore, the orientation of the carbon fibers in the second fiber reinforcement layer is opposite to the orientation of the carbon fibers in the first fiber reinforcement layer. In this shaft 4, a bias structure is achieved by the first fiber reinforcement layer and the second fiber reinforcement layer. The first fiber reinforcement layer and the second fiber reinforcement layer contribute to the bending stiffness and torsional stiffness of the shaft 4. In particular, the first fiber reinforcement layer and the second fiber reinforcement layer contribute to the torsional stiffness of the shaft 4.

[0030] The third sheet S3 is located biased toward the tip end 22 side of the shaft 4. The shape of the third sheet S3 is generally trapezoidal. This third sheet S3 contains multiple parallel carbon fibers. The direction of extension of each carbon fiber is inclined with respect to the axial direction. The angle of the extension direction of these carbon fibers with respect to the axial direction is between 30° and 60°. In this embodiment, this angle is 45°. In this third sheet S3, the width is 36 mm, the length of the upper base is 185 mm, and the length of the lower base is 195 mm.

[0031] The fourth sheet S4 is located biased toward the tip end 22 side 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 trapezoidal. This fourth sheet S4 contains multiple parallel carbon fibers. The direction of extension of each carbon fiber is inclined with respect to the axial direction. The angle of the extension direction of these carbon fibers with respect to the axial direction is between -60° and -30°. In this embodiment, this angle is -45°. In this fourth sheet S4, the width is 36 mm, the length of the upper base is 185 mm, and the length of the lower base is 195 mm.

[0032] The orientation of the carbon fibers in the fourth sheet S4 is opposite to the orientation of the carbon fibers in the third sheet S3. Therefore, the orientation of the carbon fibers in the fourth fiber reinforcement layer is opposite to the orientation of the carbon fibers in the third fiber reinforcement layer. In this shaft 4, a bias structure is achieved by the third and fourth fiber reinforcement layers. The third and fourth fiber reinforcement layers contribute to the bending and torsional rigidity of the middle section 16 and the tip section 18. In particular, the third and fourth fiber reinforcement layers contribute to the torsional rigidity of the middle section 16 and the tip section 18.

[0033] The fifth sheet S5 is located off-center towards the butt end 20 of the shaft 4. The shape of the fifth sheet S5 is roughly trapezoidal. This fifth sheet S5 contains multiple parallel carbon fibers. The direction of extension of each carbon fiber coincides with the axial direction. In other words, the angle of the extension direction of these carbon fibers with respect to the axial direction is substantially 0°. The width of this fifth sheet S5 is 72 mm, the length of the upper base is 145 mm, and the length of the lower base is 155 mm.

[0034] As mentioned above, the carbon fibers contained in the fifth sheet S5 are substantially oriented axially. Therefore, in the fifth fiber reinforcement layer, the carbon fibers are also substantially oriented axially. In this specification, a structure in which carbon fibers are substantially oriented axially is referred to as a "straight structure". The fifth fiber reinforcement layer has a straight structure. When the shaft 4 is bent, a large tension is exerted on these carbon fibers. This tension suppresses further bending of the shaft 4. In other words, these carbon fibers contribute to the bending stiffness of the shaft 4. The fifth fiber reinforcement layer, in particular, contributes to the bending stiffness of the butt section 14.

[0035] The sixth sheet S6 is located biased toward the tip end 22 side of the shaft 4. The shape of the sixth sheet S6 is generally trapezoidal. This sixth sheet S6 contains multiple parallel carbon fibers. The direction of extension of each carbon fiber is inclined with respect to the axial direction. The angle of the direction of extension of these carbon fibers with respect to the axial direction is between 30° and 60°. In this embodiment, this angle is 45°. In this sixth sheet S6, the width is 18 mm, the length of the upper base is 95 mm, and the length of the lower base is 105 mm.

[0036] The seventh sheet S7 is located biased toward the tip end 22 side of the shaft 4. In the axial direction, the position of the seventh sheet coincides with the position of the sixth sheet S6. The shape of the seventh sheet S7 is generally trapezoidal. This seventh sheet S7 contains multiple parallel carbon fibers. The direction of extension of each carbon fiber is inclined with respect to the axial direction. The angle of the extension direction of these carbon fibers with respect to the axial direction is between -60° and -30°. In this embodiment, this angle is -45°. In this seventh sheet S7, the width is 18 mm, the length of the upper base is 95 mm, and the length of the lower base is 105 mm.

[0037] The orientation of the carbon fibers in the seventh sheet S7 is opposite to the orientation of the carbon fibers in the sixth sheet S6. Therefore, the orientation of the carbon fibers in the seventh fiber reinforcement layer is opposite to the orientation of the carbon fibers in the sixth fiber reinforcement layer. In this shaft 4, a bias structure is achieved by the sixth fiber reinforcement layer and the seventh fiber reinforcement layer. The sixth fiber reinforcement layer and the seventh fiber reinforcement layer contribute to the bending stiffness and torsional stiffness of the butt section 14. In particular, the sixth fiber reinforcement layer and the seventh fiber reinforcement layer contribute to the torsional stiffness of the butt section 14.

[0038] The eighth sheet S8 is located off-center towards the butt end 20 of the shaft 4. The shape of the eighth sheet S8 is roughly trapezoidal. This eighth sheet S8 contains multiple parallel carbon fibers. The direction of extension of each carbon fiber coincides with the axial direction. In other words, the angle of the extension direction of these carbon fibers with respect to the axial direction is substantially 0°. The width of this eighth sheet S8 is 36 mm, the length of the upper base is 235 mm, and the length of the lower base is 245 mm.

[0039] As mentioned above, the carbon fibers in the eighth sheet S8 are substantially oriented axially. Therefore, in the eighth fiber reinforcement layer, the carbon fibers are also substantially oriented axially. The eighth fiber reinforcement layer has a straight structure. When the shaft 4 is bent, a large tension is exerted on 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 eighth fiber reinforcement layer contributes particularly to the bending rigidity of the butt section 14 and the middle section 16.

[0040] The ninth sheet S9 is present throughout the entire shaft 4. The shape of the ninth sheet S9 is generally rectangular. This ninth sheet S9 contains multiple parallel carbon fibers. The direction of extension of each carbon fiber coincides with the axial direction. In other words, the angle of the direction of extension of these carbon fibers with respect to the axial direction is substantially 0°. The width of this ninth sheet S9 is 30 mm and the length is 340 mm.

[0041] As mentioned above, the carbon fibers in the ninth sheet S9 are substantially oriented axially. Therefore, in the ninth fiber reinforcement layer, the carbon fibers are also substantially oriented axially. The ninth fiber reinforcement layer has a straight structure. When the shaft 4 is bent, a large tension is exerted on these carbon fibers. This tension suppresses further bending of the shaft 4. In other words, these carbon fibers contribute to the bending stiffness of the shaft 4.

[0042] In this shaft 4, the first fiber reinforcement layer, the second fiber reinforcement layer, and the ninth fiber reinforcement layer are present from the butt end 20 to the tip end 22. These fiber reinforcement layers can contribute to the durability of the shaft 4.

[0043] In the manufacture of this shaft 4, the sheets shown in Figure 5 are wound onto a mandrel in sequence. The first sheet S1 and the second sheet S2 may be stacked and wound onto the mandrel. The third sheet S3 and the fourth sheet S4 may be stacked and wound onto the mandrel. The sixth sheet S6 and the seventh sheet S7 may be stacked and wound onto the mandrel. Other sheets may be wound onto the mandrel along with these sheets. Examples of other sheets include those containing glass fibers.

[0044] Wrapping tape is then wrapped around these sheets. These mandrels, prepregs (sheets S1-S8), and wrapping tape are heated in an oven or the like. Heating causes the matrix resin to flow. Further heating causes this resin to harden, and a molded body is obtained. This molded body is then subjected to processes such as end face processing, polishing, and painting to complete the shaft 4.

[0045] The material of shaft 4 is fiber-reinforced resin. The material of shaft 4 may also be a resin composition that does not contain fibers. The material of shaft 4 may also be metal, wood, etc.

[0046] Figure 6 is an explanatory diagram illustrating the method for measuring the natural frequency of racket 2 shown in Figure 1. In this method, racket 2 is suspended by a string 36. This racket 2 does not have strings 12. In other words, a racket 2 without strings 12 is used for measuring the natural frequency. In Figure 6, the axial direction (Y direction) of the shaft 4 coincides with the vertical direction. In Figure 6, the frame 6 is located above the shaft 4.

[0047] As shown in Figure 6, an acceleration pickup 38 is attached to the racket 2. The position of the acceleration pickup 38 is at the tip of the grip 10. The orientation of this acceleration pickup 38 is in the Z direction. This acceleration pickup 38 has a mass of 3.5g. Next, point Ph on the shaft 4 opposite the acceleration pickup 38 is excited by an impact hammer (not shown). The input vibration measured by the force pickup of this impact hammer and the response vibration measured by the acceleration pickup 38 are sent via an amplifier to a frequency analyzer (Hewlett-Packard's "Dynamic Signal Analyzer"). Based on the transfer function obtained by this device, the frequency of the out-of-plane natural vibration is calculated. The direction of the out-of-plane natural vibration is mainly in the Z direction. In this method, the natural frequency is measured with no part of the racket 2 rigidly fixed. In other words, the natural frequency is measured under free constraint conditions.

[0048] Figure 7 is a graph showing the results obtained from the measurement in Figure 6. In Figure 7, the horizontal axis represents frequency (Hz), and the vertical axis represents the acceleration magnitude (m / s²). 2 The value is / N). In Figure 7, the symbol P1 indicates the first-order peak. The frequency at this first-order peak P1 is the out-of-plane first-order natural frequency ωo1. In Figure 7, the symbol P2 indicates the second-order peak. The frequency at this second-order peak P2 is the out-of-plane second-order natural frequency ωo2.

[0049] Figure 8 is a graph showing the relationship between the out-of-plane primary natural frequency ωo1 and the out-of-plane secondary natural frequency ωo2 of badminton racket 2. In this graph, the symbol Pr represents the point of racket 2 shown in Figure 1-5.

[0050] The straight line indicated by the symbol L1 in Figure 8 can be represented by the following formula. ωo2 = 2.5 × ωo1 + 37.0 As shown in Figure 8, point Pr is located above the line L1. In other words, the coordinates (ωo1, ωo2) of racket 2 are given by the following equation (1). ωo2 ≧ 2.5 × ωo1 + 37.0 (1) According to the inventors' findings, racket 2, which satisfies equation (1), is suitable for lobbing. Players who use racket 2 to lob the shuttlecock can easily achieve the intended trajectory. With racket 2, there is little variation in the shuttlecock's trajectory during lobbing.

[0051] According to the inventors' findings, when the shuttlecock is struck with the part of the face 32 closer to the bottom 26, mainly out-of-plane second-mode vibrations are excited. According to the inventors' findings, when the shuttlecock is struck with the part of the face 32 closer to the top 24, mainly out-of-plane first-mode vibrations are excited. The typical point of contact in a lob is closer to the top 24. Therefore, in a lob, mainly out-of-plane first-mode vibrations are excited. However, even in a lob, the point of contact varies. In a racket 2 that satisfies the above formula (1), the out-of-plane first-mode natural frequency ωo1 is relatively small, and the out-of-plane second-mode natural frequency ωo2 is relatively large. According to the inventors' findings, in a lob using a racket 2 with a small out-of-plane first-mode natural frequency ωo1 and a large out-of-plane second-mode natural frequency ωo2, even if the point of contact varies, the variation in the initial velocity of the shuttlecock is small. The reason for this is that even if the shuttlecock is struck at a position deviating from the intended position, the rebound of the racket 2 is not extremely small. Because the initial velocity of the shuttlecock is small, the trajectory of the shuttlecock is also small. This racket 2 is suitable for players who frequently use lobs. This racket 2 is also suitable for players who prioritize lobs.

[0052] As mentioned above, the typical point of contact in a lob is closer to the top 24 of the racket face. The racket 2 according to the present invention is also suitable for shots other than lobs, where the shuttlecock is struck with the part of the racket face 32 closer to the top 24.

[0053] By changing the position, number, width, length, fiber angle, basis weight, and modulus of elasticity of the prepregs in shaft 4, a small frequency ωo1 and a large frequency ωo2 can be achieved. Specifically, (a) A fiber-reinforced layer having a straight structure is unevenly distributed in the butt portion 14. (b) The number of fiber-reinforced layers in the bat section 14 is set to be large. (c) A fiber-reinforced layer with a large basis weight is unevenly distributed in the bat portion 14. (d) A fiber-reinforced layer having fibers with a high modulus of elasticity is unevenly distributed in the butt portion 14. (e) Set the number of fiber-reinforced layers in the tip section 18 to a small number. (f) A fiber-reinforced layer with a small basis weight is unevenly distributed in the tip portion 18. (g) A fiber-reinforced layer having fibers with a low modulus of elasticity is unevenly distributed in the tip portion 18. Examples include the above. In this embodiment, as described above, the high rigidity of the butt portion 14 is achieved by the fifth fiber reinforcement layer obtained from the fifth sheet S5 and the eighth fiber reinforcement layer obtained from the eighth sheet S8. As a result, a small frequency ωo1 and a large frequency ωo2 are achieved.

[0054] A low frequency ωo1 and a high frequency ωo2 may be achieved by changing the specifications of components other than the shaft 4. An example of a component other than the shaft 4 that can affect the frequency is the frame 6. By changing the position of the prepregs, the number of prepregs, the width of the prepregs, the length of the prepregs, the fiber angle, the fiber basis weight, the fiber modulus of elasticity, etc., in the frame 6, a low frequency ωo1 and a high frequency ωo2 can be achieved. As a specific means, (a) A fiber-reinforced layer having a straight structure is unevenly distributed near the bottom 26 of the frame 6. (b) The number of fiber-reinforced layers near the bottom 26 of frame 6 is set to be large. (c) A fiber-reinforced layer with a large basis weight is concentrated near the bottom 26 of the frame 6. (d) A fiber-reinforced layer having fibers with a high modulus of elasticity is unevenly distributed near the bottom 26 of the frame 6. (e) Set the number of fiber-reinforced layers near the top 24 of frame 6 to a small number. (f) A fiber-reinforced layer with a small basis weight is concentrated near the top 24 of frame 6. (g) A fiber-reinforced layer having fibers with a low modulus of elasticity is unevenly distributed near the top 24 of the frame 6. Examples include the following.

[0055] The straight line indicated by the sign L2 in Figure 8 can be represented by the following formula. ω₀² = 2.5 × ω₀¹ + 44.0 As shown in Figure 8, point Pr is located above the line L2. In other words, the coordinates (ωo1, ωo2) of racket 2 are given by the following equation (2). ωo2 ≧ 2.5 × ωo1 + 44.0 (2) According to the inventors' findings, racket 2, which satisfies equation (2), is suitable for lobbing. Players who use racket 2 to lob the shuttlecock can easily achieve the intended trajectory. With racket 2, there is little variation in the shuttlecock's trajectory during lobbing.

[0056] The straight line indicated by the symbol L3 in Figure 8 can be represented by the following formula. ω₀² = 2.5 × ω₀¹ + 54.0 As shown in Figure 8, point Pr is located above the line L3. In other words, the coordinates (ωo1, ωo2) of racket 2 are given by the following equation (3). ωo2 ≧ 2.5 × ωo1 + 54.0 (3) According to the inventors' findings, racket 2, which satisfies equation (3), is suitable for lobbing. Players who use racket 2 to lob the shuttlecock can easily achieve the intended trajectory. With racket 2, there is little variation in the shuttlecock's trajectory during lobbing.

[0057] The straight line indicated by the symbol L4 in Figure 8 can be represented by the following formula. ωo2 = 179 As shown in Figure 8, point Pr is located above the line L4. The frequency ωo2 of point Pr is 179 or greater. In other words, the coordinates (ωo1, ωo2) of this racket 2 are given by the following equation (4). ωo2 ≧ 179 (4) According to the inventors' findings, racket 2, which satisfies equation (4), is suitable for lobbing. When using racket 2 for lobbing, the shuttlecock flies at high speed.

[0058] The straight line indicated by the symbol L5 in Figure 8 can be represented by the following formula. ωo2 = 184 As shown in Figure 8, point Pr is located above the line L5. The frequency ωo2 of point Pr is 184 or greater. In other words, the coordinates (ωo1, ωo2) of this racket 2 are given by the following equation (5). ωo2 ≧ 184 (5) According to the inventors' findings, racket 2, which satisfies equation (5), is suitable for lobbing. When lobbing with racket 2, the shuttlecock flies at high speed. [Examples]

[0059] The effects of the present invention will be demonstrated below by the examples, but the present invention should not be interpreted restrictively based on the description of these examples.

[0060] [Example 1] A shaft with the prepreg configuration shown in Figure 5 was fabricated. Each prepreg contained carbon fiber. The tensile modulus of this carbon fiber was 35 tf / mm². 2 This was the shaft. A badminton racket was then constructed by attaching a frame, neck, cap, and grip, which are standard components of commercially available badminton rackets with typical stiffness and mass, to this shaft. The out-of-plane primary natural frequency ωo1 of this racket was 54 Hz, and the out-of-plane secondary natural frequency ωo2 was 189 Hz. The coordinates of this racket are indicated by the symbol Pr in Figure 8.

[0061] [Examples 2-11 and Comparative Examples 1-8] Badminton rackets for Example 2-11 and Comparative Example 1-8 were obtained in the same manner as in Example 1, except that the prepreg configuration was as shown in Table 1-4. The width of the prepreg for the shafts of these rackets is shown in Table 1-4 below. The out-of-plane primary natural frequency ωo1 and out-of-plane secondary natural frequency ωo2 of these rackets are shown in Table 1-4 and Figure 8 below.

[0062] [Stability] A shuttlecock was launched using a launching machine. A player was instructed to lob the shuttlecock, and its trajectory was photographed. The images were analyzed to measure the height of the shuttlecock as it passed over the net. Twenty measurements were taken, and the standard deviation of the heights was calculated. Based on this standard deviation, the rackets were ranked. The ranking criteria are as follows. The results are shown in Table 1-4 below. A: Standard deviation is less than 0.14m B: Standard deviation is 0.14m or greater and less than 0.20m C: Standard deviation is 0.20m or greater

[0063] [Rebound] In evaluating the stability mentioned above, the speed of the shuttlecock passing over the net was measured. Twenty measurements were taken, and the average speed was calculated. Based on this average, the rackets were ranked. The ranking criteria are as follows. The results are shown in Table 1-4 below. A: Average speed of 19.0 m / s or more B: Average speed is between 18.0 m / s and 19.0 m / s. C: Average speed is less than 18.0 m / s

[0064] [Table 1]

[0065] [Table 2]

[0066] [Table 3]

[0067] [Table 4]

[0068] As is clear from Table 1-4, the badminton racket of each embodiment provides a stable trajectory for lobs. This evaluation result clearly demonstrates the superiority of the present invention. [Industrial applicability]

[0069] The badminton racket according to the present invention is suitable for players who frequently use lobs. This racket is also suitable for players who frequently use other shots where the point of contact is closer to the top of the shuttlecock. [Explanation of Symbols]

[0070] 2. Badminton racket 4. Shaft 6...frames 8... neck 10. Grip 12...string 14. Bad Section 16. Middle Section 18...Tip section 20...Bad Ending 22... Tip end 24...Top 26...Bottom 28... Horizontal threads 30... Vertical threads 32...face 34...Exposed part 38. Acceleration pickup S1...First seat S2...Second seat S3...Third seat S4...Fourth seat S5...Fifth Sheet S6...Sixth seat S7...Seventh Seat S8... Eighth seat S9... Ninth Seat

Claims

1. A shaft having a butt end and a tip end. The grip into which the vicinity of the butt end of the above shaft is inserted, and A frame attached to the shaft near the tip end mentioned above. It is equipped with, A badminton racket in which, without strings and under free constraints, the out-of-plane primary natural frequency ωo1 (Hz) and the out-of-plane secondary natural frequency ωo2 (Hz) satisfy the following equation (2). ωo2 ≧ 2.5 × ωo1 + 44.0 (2)

2. A badminton racket according to claim 1 that satisfies the following formula (3). ωo2 ≧ 2.5 × ωo1 + 54.0 (3)

3. The badminton racket according to claim 1 or 2, wherein the above-mentioned frequency ωo2 is 179 Hz or higher.

4. The badminton racket according to claim 3, wherein the above-mentioned frequency ωo2 is 184 Hz or higher.

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