Badminton racket

Abstract

To provide a badminton racket 2 which can suppress variation of a projectile path of a shuttle in both a shot a hit point of which is closer to a top and a shot a hit point of which is closer to a bottom.SOLUTION: A badminton racket 2 has a shaft 4, a frame 6, and a grip 8. In the racket, a ratio (ωo2 / ωo1) of an out-of-plane secondary natural vibration frequency ωo2(Hz) to an out-of-plane primary natural vibration frequency ωo1(Hz), and a (ωi2 / ωi1) of an in-plane secondary natural vibration frequency ωi2(Hz) to an in-plane primary natural vibration frequency ωi1(Hz) satisfy the following numerical expression (1): (ωi2 / ωi1)≤1.3*(ωo2 / ωo1)-0.6 (1).SELECTED DRAWING: Figure 1

Description

Technical Field

[0001] This specification discloses a racket for use in 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 the hit, the face collides with the shuttlecock. The impact due to the collision is transmitted from the strings through the frame to the shaft. By the hit, the frame and the shaft deform. An attempt regarding optimization of the deformation behavior is described in Japanese Patent Application Laid-Open No. 2021-23724.

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] Unlike a normal smash, a cut smash involves a cutting motion. In a cut smash, the shuttlecock flies at high speed while rotating at high speed. A cut smash is a shot intended to interfere with the opponent player's receive. In a cut smash, a player requires advanced skills to fly the shuttlecock along the intended trajectory. A player who frequently uses cut smashes desires stability in the trajectory (speed, height, etc.) of the shuttlecock.

[0007] In an investigation using statistical methods, typical hitting points in lobbing are near the top, and typical hitting points in cut smashes are near the bottom. In shots other than lobbing, the shuttlecock can be hit at hitting points near the top. In shots other than cut smashes, the shuttlecock can be hit at hitting points near the bottom.

[0008] What the present inventor intends is to provide a badminton racket capable of suppressing variations in the trajectory of the shuttlecock in both shots with hitting points near the top and shots with hitting points near the bottom.

Means for Solving the Problem

[0009] A preferred badminton racket has a shaft having a head and a tip, a grip attached to the shaft in the head, and a frame attached to the shaft in the tip. For this badminton racket, the ratio (ωo2 / ωo1) of the out-of-plane secondary natural frequency ωo2 (Hz) to the out-of-plane primary natural frequency ωo1 (Hz), and the ratio (ωi2 / ωi1) of the in-plane secondary natural frequency ωi2 (Hz) to the in-plane primary natural frequency ωi1 (Hz) satisfy the following mathematical formula (1). (ωi2 / ωi1) ≦ 1.3 * (ωo2 / ωo1) - 0.6 (1)

Advantages of the Invention

[0010] Players using this badminton racket are likely to make shots with the hitting point closer to the top and are also likely to make shots with the hitting point closer to the bottom. This racket can contribute to winning the game.

Brief Description of the Drawings

[0011]

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BEST MODE FOR CARRYING OUT THE INVENTION

[0012] Hereinafter, preferred embodiments will be described in detail while appropriately referring to the drawings.

[0013] 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 10, a grip 12, and strings 14. In FIGS. 1 and 2, arrow X represents the width direction, arrow Y represents the axial direction, and arrow Z represents the thickness direction. The width direction X is also referred to as the in-plane direction. The thickness direction Z is also referred to as the out-of-plane direction.

[0014] The shaft 4 is hollow. In FIG. 1, the arrow Ls represents the length of the shaft 4. In this embodiment, the length Ls is 340 mm. The shaft 4 has a butt 16, a middle 18, and a tip 20. The shaft 4 further has a butt end 22 and a tip end 24. In this specification, the butt 16 is defined as the zone between the butt end 22 and the position where the distance from the butt end 22 is 44% of the length Ls. The middle 18 is defined as the zone between the position where the distance from the butt end 22 is 44% of the length Ls and the position where the distance from the butt end 22 is 71% of the length Ls. The tip 20 is defined as the zone between the position where the distance from the butt end 22 is 71% of the length Ls and the tip end 24.

[0015] 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 polyetheretherketone, polyethersulfone, polyetherimide, 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] Frame 6 is annular and hollow. Frame 6 is formed of a fiber-reinforced resin. The same base resin as that of the base resin of shaft 4 can be used for this fiber-reinforced resin. The same reinforcing fibers as those of the reinforcing fibers of shaft 4 can be used for this fiber-reinforced resin. Frame 6 is firmly connected to the tip end 24 of shaft 4 via neck 8. Frame 6 has a top 26 and a bottom 28.

[0019] Grip 12 has a hole 30 extending in the axial direction (Y direction). Near the butt end 22 of shaft 4 is inserted into this hole 30. The inner peripheral surface of hole 30 and the outer peripheral surface of shaft 4 are joined with an adhesive.

[0020] String 14 is stretched over frame 6. String 14 is stretched along the width direction X and the axial direction Y. The portion of string 14 extending along the width direction X is the cross thread 32. The portion of string 14 extending along the axial direction Y is the longitudinal thread 34. The face 36 is formed by a plurality of cross threads 32 and a plurality of longitudinal threads 34. Face 36 generally lies along the X-Y plane.

[0021] FIG. 3 is an enlarged cross-sectional view showing a part of shaft 4 of racket 2 in FIG. 1. FIG. 4 is an enlarged cross-sectional view taken along line IV-IV in FIG. 3. As described above, this shaft 4 is hollow. As shown in FIG. 4, the cross-sectional shape of this shaft 4 is a circle. In other words, this shaft 4 is cylindrical. No foreign matter is accommodated inside shaft 4.

[0022] In FIGS. 3 and 4, arrow Di represents the inner diameter of shaft 4. A typical inner diameter Di is 3 mm or more and 10 mm or less. In this embodiment, the inner diameter Di from the butt end 22 (see FIG. 2) to the tip end 24 is substantially constant. In FIGS. 3 and 4, arrow Do represents the outer diameter of shaft 4. A typical outer diameter Do is 5 mm or more and 15 mm or less. In this embodiment, the outer diameter Do from the butt end 22 to the tip end 24 is substantially constant.

[0023] In FIG. 4, reference numeral SC represents the center point of the shaft 4. In the present embodiment, for convenience, the shaft 4 is divided into four zones. In FIG. 4, the zone indicated by arrow Q1 is the first quarter, the zone indicated by arrow Q2 is the second quarter, the zone indicated by arrow Q3 is the third quarter, and the zone indicated by arrow Q4 is the fourth quarter. The central angle at the point SC of each quarter is 90°. The first quarter Q1 is separated from the center point SC in the in-plane direction. The second quarter Q2 is separated from the center point SC in the out-of-plane direction. The third quarter Q3 is separated from the center point SC in the in-plane direction. The fourth quarter Q4 is separated from the center point SC in the out-of-plane direction.

[0024] As described above, the shaft 4 is formed of a fiber-reinforced resin. This shaft 4 can be manufactured by the sheet winding method. In this sheet winding method, a plurality of prepregs are wound around a mandrel.

[0025] FIG. 5 shows an example of the prepreg 38. This prepreg 38 has a plurality of fibers 40 and a matrix resin 42. These fibers 40 are parallel. The matrix resin 42 is not cured. The arrow θ in FIG. 5 is the angle of the fiber 40 with respect to the Y direction.

[0026] FIG. 6 is a developed view showing the prepreg configuration of the shaft 4 of the racket 2 in FIG. 1. This prepreg configuration has nine prepreg sheet groups. Specifically, this prepreg configuration has a first sheet group S1, a second sheet group S2, a third sheet group S3, a fourth sheet group S4, a fifth sheet group S5, a sixth sheet group S6, a seventh sheet group S7, an eighth sheet group S8, and a ninth sheet group S9. The left-right direction in FIG. 6 is the axial direction of the shaft 4. In FIG. 6, the positions of the butt end 22 and the tip end 24 are indicated by arrows. For convenience of explanation, in FIG. 6, the scale in the left-right direction (axial direction) does not match the scale in the up-down direction.

[0027] The first sheet group S1 includes a single prepreg 44. This prepreg 44 exists throughout the entire shaft 4. The shape of this prepreg 44 is generally rectangular. This prepreg 44 contains a plurality of parallel carbon fibers. The extending direction of each carbon fiber is inclined with respect to the axial direction. The angle θ of this carbon fiber is 45°. The tensile elastic modulus E of this carbon fiber is 24 tf / mm 2 is. The width W of this prepreg 44 is 80 mm.

[0028] The second sheet group S2 includes a single prepreg 46. This prepreg 46 exists throughout the entire shaft 4. The shape of this prepreg 46 is generally rectangular. This prepreg 46 contains a plurality of parallel carbon fibers. The extending direction of each carbon fiber is inclined with respect to the axial direction. The angle θ of this carbon fiber is -45°. The tensile elastic modulus E of this carbon fiber is 24 tf / mm 2 is. The width W of this prepreg 46 is 80 mm. The inclination direction of the carbon fibers in the second sheet group S2 is opposite to the inclination direction of the carbon fibers in the first sheet group S1. In this shaft 4, the first sheet group S1 and the second sheet group S2 form a bias structure.

[0029] Each of the third sheet group S3, the fifth sheet group S5, and the seventh sheet group S7 has a type A prepreg configuration, which will be described in detail later. Each of the fourth sheet group S4, the sixth sheet group S6, and the eighth sheet group S8 has a type B prepreg configuration, which will be described in detail later.

[0030] The ninth sheet group S9 includes a single prepreg 48. This prepreg 48 exists throughout the entire shaft 4. The shape of this prepreg 48 is generally rectangular. This prepreg 48 contains a plurality of parallel carbon fibers. The extending direction of each carbon fiber is positioned in the axial direction. The angle θ of this carbon fiber is 0°. The tensile elastic modulus E of this carbon fiber is 7.4 tf / mm 2 is. The width W of this prepreg 48 is 54 mm.

[0031] Figure 7 is a developed view showing the prepreg configuration of type A, and Figure 8 is a schematic diagram thereof. This prepreg configuration includes 8 prepregs. The width of each prepreg corresponds to 1 / 4 of the circumference of the shaft 4 at the position of the prepreg. This width in the third sheet group S3 is about 4 mm, this width in the fifth sheet group S5 is about 5 mm, and this width in the seventh sheet group S7 is about 5 mm.

[0032] Prepreg A1 exists between the bad end 22 and a position 150 mm away from this bad end 22. The shape of this prepreg A1 is generally rectangular. This prepreg A1 contains a plurality of parallel carbon fibers. The extending direction of each carbon fiber is positioned in the axial direction. The angle θ of this carbon fiber is 0°. The tensile elastic modulus E of this carbon fiber is 7.4 f / mm 2 is. This prepreg A1 exists in the first quarter Q1.

[0033] Prepreg A2 exists between a position 150 mm away from the bad end 22 and a position 340 mm away from this bad end 22. The shape of this prepreg A2 is generally rectangular. This prepreg A2 contains a plurality of parallel carbon fibers. The extending direction of each carbon fiber is positioned in the axial direction. The angle θ of this carbon fiber is 0°. The tensile elastic modulus E of this carbon fiber is 55 f / mm 2 is. This prepreg A2 exists in the first quarter Q1.

[0034] Prepreg A3 exists between the bad end 22 and a position that is 240 mm away from this bad end 22. The shape of this prepreg A3 is generally rectangular. This prepreg A3 contains a plurality of carbon fibers arranged in parallel. The extending direction of each carbon fiber is in the axial direction. The angle θ of this carbon fiber is 0°. The tensile elastic modulus E of this carbon fiber is 55 tf / mm 2 and is. This prepreg A3 exists in the second quarter Q2.

[0035] Prepreg A4 exists between a position that is 240 mm away from the bad end 22 and a position that is 340 mm away from this bad end 22. The shape of this prepreg A4 is generally rectangular. This prepreg A4 contains a plurality of carbon fibers arranged in parallel. The extending direction of each carbon fiber is in the axial direction. The angle θ of this carbon fiber is 0°. The tensile elastic modulus E of this carbon fiber is 7.4 tf / mm 2 and is. This prepreg A4 exists in the second quarter Q2.

[0036] Prepreg A5 exists between the bad end 22 and a position that is 150 mm away from this bad end 22. The shape of this prepreg A5 is generally rectangular. This prepreg A5 contains a plurality of carbon fibers arranged in parallel. The extending direction of each carbon fiber is in the axial direction. The angle θ of this carbon fiber is 0°. The tensile elastic modulus E of this carbon fiber is 7.4 tf / mm 2 and is. This prepreg A5 exists in the third quarter Q3.

[0037] Prepreg A6 exists between a position that is 150 mm away from the bad end 22 and a position that is 340 mm away from this bad end 22. The shape of this prepreg A6 is generally rectangular. This prepreg A6 contains a plurality of parallel carbon fibers. The extending direction of each carbon fiber is positioned in the axial direction. The angle θ of this carbon fiber is 0°. The tensile elastic modulus E of this carbon fiber is 55 tf / mm 2 is. This prepreg A6 exists in the third quarter Q3.

[0038] Prepreg A7 exists between the bad end 22 and a position that is 240 mm away from this bad end 22. The shape of this prepreg A7 is generally rectangular. This prepreg A7 contains a plurality of parallel carbon fibers. The extending direction of each carbon fiber is positioned in the axial direction. The angle θ of this carbon fiber is 0°. The tensile elastic modulus E of this carbon fiber is 55 tf / mm 2 is. This prepreg A7 exists in the fourth quarter Q4.

[0039] Prepreg A8 exists between a position that is 240 mm away from the bad end 22 and a position that is 340 mm away from this bad end 22. The shape of this prepreg A8 is generally rectangular. This prepreg A8 contains a plurality of parallel carbon fibers. The extending direction of each carbon fiber is positioned in the axial direction. The angle θ of this carbon fiber is 0°. The tensile elastic modulus E of this carbon fiber is 7.4 tf / mm 2 is. This prepreg A8 exists in the fourth quarter Q4.

[0040] Shaft 4 is shown in FIGS. 9-12. FIGS. 9-12 show a cross section of the third sheet group S3. The illustration of other sheet groups is omitted. The third sheet group S3 has a prepreg configuration of type A as described above.

[0041] As shown in FIGS. 9-12, prepregs A1 and A2 are located in the first quarter Q1, prepregs A3 and A4 are located in the second quarter Q2, prepregs A5 and A6 are located in the third quarter Q3, and prepregs A7 and A8 are located in the fourth quarter Q4.

[0042] As shown in FIGS. 9-12, prepreg A1 is present in the bad 16, prepreg A2 is present from the middle 18 to the tip 20, prepreg A3 is present from the bad 16 to the middle 18, prepreg A4 is present in the tip 20, prepreg A5 is present in the bad 16, prepreg A6 is present from the middle 18 to the tip 20, prepreg A7 is present from the bad 16 to the middle 18, and prepreg A8 is present in the tip 20.

[0043] FIG. 13 is a schematic view showing the prepreg configuration of type B. This prepreg configuration includes 8 prepregs. The width of each prepreg corresponds to 1 / 4 of the circumference of the shaft 4 at the position of the prepreg. This width in the fourth sheet group S4 is about 4 mm, this width in the sixth sheet group S6 is about 5 mm, and this width in the eighth sheet group S8 is about 6 mm.

[0044] Prepreg B1 exists between the bad end 22 (see FIG. 2) and a position 240 mm away from this bad end 22. The shape of this prepreg B1 is generally rectangular. This prepreg B1 contains a plurality of carbon fibers arranged in parallel. The extending direction of each carbon fiber is in the axial direction. The angle θ of this carbon fiber is 0°. The tensile elastic modulus E of this carbon fiber is 7.4 tf / mm 2 and is. This prepreg B1 is present in the first quarter Q1.

[0045] Prepreg B2 exists between the position that is 240 mm away from the bad end 22 and the position that is 340 mm away from this bad end 22. The shape of this prepreg B2 is generally rectangular. This prepreg B2 contains a plurality of parallel carbon fibers. The extending direction of each carbon fiber is in the axial direction. The angle θ of this carbon fiber is 0°. The tensile elastic modulus E of this carbon fiber is 55 tf / mm 2 It is. This prepreg B2 exists in the first quarter Q1.

[0046] Prepreg B3 exists between the bad end 22 and the position that is 150 mm away from this bad end 22. The shape of this prepreg B3 is generally rectangular. This prepreg B3 contains a plurality of parallel carbon fibers. The extending direction of each carbon fiber is in the axial direction. The angle θ of this carbon fiber is 0°. The tensile elastic modulus E of this carbon fiber is 55 tf / mm 2 It is. This prepreg B3 exists in the second quarter Q2.

[0047] Prepreg B4 exists between the position that is 150 mm away from the bad end 22 and the position that is 340 mm away from this bad end 22. The shape of this prepreg B4 is generally rectangular. This prepreg B4 contains a plurality of parallel carbon fibers. The extending direction of each carbon fiber is in the axial direction. The angle θ of this carbon fiber is 0°. The tensile elastic modulus E of this carbon fiber is 7.4 tf / mm 2 It is. This prepreg B4 exists in the second quarter Q2.

[0048] Prepreg B5 exists between the bad end 22 and a position that is 240 mm away from this bad end 22. The shape of this prepreg B5 is generally rectangular. This prepreg B5 contains a plurality of parallel carbon fibers. The extending direction of each carbon fiber is in the axial direction. The angle θ of this carbon fiber is 0°. The tensile elastic modulus E of this carbon fiber is 7.4 tf / mm 2 is. This prepreg B5 exists in the third quarter Q3.

[0049] Prepreg B6 exists between a position that is 240 mm away from the bad end 22 and a position that is 340 mm away from this bad end 22. The shape of this prepreg B6 is generally rectangular. This prepreg B6 contains a plurality of parallel carbon fibers. The extending direction of each carbon fiber is in the axial direction. The angle θ of this carbon fiber is 0°. The tensile elastic modulus E of this carbon fiber is 55 tf / mm 2 is. This prepreg B6 exists in the third quarter Q3.

[0050] Prepreg B7 exists between the bad end 22 and a position that is 150 mm away from this bad end 22. The shape of this prepreg B7 is generally rectangular. This prepreg B7 contains a plurality of parallel carbon fibers. The extending direction of each carbon fiber is in the axial direction. The angle θ of this carbon fiber is 0°. The tensile elastic modulus E of this carbon fiber is 55 tf / mm 2 is. This prepreg B7 exists in the fourth quarter Q4.

[0051] Prepreg B8 exists between a position that is 150 mm away from the bad end 22 and a position that is 340 mm away from this bad end 22. The shape of this prepreg B8 is generally rectangular. This prepreg B8 contains a plurality of carbon fibers arranged in parallel. The extending direction of each carbon fiber is in the axial direction. The angle θ of this carbon fiber is 0°. The tensile elastic modulus E of this carbon fiber is 7.4 tf / mm 2 is. This prepreg B8 exists in the fourth quarter Q4.

[0052] Prepregs B1 and B2 are located in the first quarter Q1, prepregs B3 and B4 are located in the second quarter Q2, prepregs B5 and B6 are located in the third quarter Q3, and prepregs B7 and B8 are located in the fourth quarter Q4.

[0053] Prepreg B1 exists from the bad 16 to the middle 18, prepreg B2 exists at the tip 20, prepreg B3 exists at the bad 16, prepreg B4 exists from the middle 18 to the tip 20, prepreg B5 exists from the bad 16 to the middle 18, prepreg B6 exists at the tip 20, prepreg B7 exists at the bad 16, and prepreg B8 exists from the middle 18 to the tip 20.

[0054] In the prepreg configuration of type A, prepregs A1, A2, A5, and A6 are separated in the in-plane direction from the center point SC (see FIG. 4). In the prepreg configuration of type B, prepregs B1, B2, B5, and B6 are separated in the in-plane direction from the center point SC. The tensile elastic modulus E of the carbon fibers contained in prepregs A1, A5, B1, and B5 is small, and the tensile elastic modulus E of the carbon fibers contained in prepregs A2, A6, B2, and B6 is large. The elastic modulus E of each carbon fiber affects the bending rigidity of the shaft 4. This shaft 4 has the following mathematical formula. RiB < RiM < RiT RiB: In-plane bending stiffness of the butt 16 RiM: In-plane bending stiffness of the middle 18 RiT: In-plane bending stiffness of the tip 20

[0055] In the prepreg configuration of type A, prepregs A3, A4, A7, and A8 are away from the center point SC in the out-of-plane direction. In the prepreg configuration of type B, prepregs B3, B4, B7, and B8 are away from the center point SC in the out-of-plane direction. The tensile elastic modulus E of the carbon fibers contained in prepregs A3, A7, B3, and B7 is large, and the tensile elastic modulus E of the carbon fibers contained in prepregs A4, A8, B4, and B8 is small. The elastic modulus E of each carbon fiber affects the bending stiffness of the shaft 4. This shaft 4 has the following mathematical formulae.

[0056] RoB > RoM > RoT RoB: Out-of-plane bending stiffness of the butt 16 RoM: Out-of-plane bending stiffness of the middle 18 RoT: Out-of-plane bending stiffness of the tip 20

[0057] This shaft 4 further has the following mathematical formulae in the butt 16. RiB < RoB This shaft 4 further has the following mathematical formulae in the tip 20. RiT > RoT

[0058] In this specification, the tensile elastic modulus E is measured in accordance with the standard of "JIS R 7608". The tensile elastic modulus E is calculated based on the change in stress when the elongation rate changes from 0.3% to 0.7%.

[0059] As is clear from FIG. 6, the prepregs of the first sheet group S1, the second sheet group S2, and the ninth sheet group S9 exist from the butt end 22 to the tip end 24. These sheet groups can contribute to the durability of the shaft 4.

[0060] In the manufacture of this shaft 4, the sheets shown in FIG. 6 are sequentially wound around a mandrel. Other sheets may be wound around the mandrel together with these sheets. Examples of the other sheets include those containing glass fibers. A wrapping tape is further wound around these sheets. These mandrels, prepregs (sheet groups S1 - S9), and wrapping tapes are heated in an oven or the like. By heating, the resin of the matrix flows. Further heating causes this resin to undergo a curing reaction, and a molded body is obtained. This molded body is subjected to processes such as end face machining, polishing, and painting, and the shaft 4 is completed.

[0061] As described above, the material of this 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, or the like.

[0062] FIG. 14 is an explanatory diagram showing a method for measuring the out-of-plane natural frequency of the racket 2 in FIG. 1. In this method, the racket 2 is suspended by a string 50. This racket 2 does not have the string 14 (see FIG. 1). In other words, for measuring the natural frequency, the racket 2 without the string 14 is used. In FIG. 14, the axial direction (Y direction) of the shaft 4 coincides with the vertical direction. In FIG. 14, the frame 6 is located above the shaft 4.

[0063] As shown in FIG. 14, an acceleration pickup 52 is attached to the racket 2. The position of the acceleration pickup 52 is the tip of the grip 12. The direction of this acceleration pickup 52 is the Z direction. This acceleration pickup 52 has a mass of 3.5 g. A point Ph on the opposite side of the acceleration pickup 52 of this grip 12 is vibrated 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 52 are sent to a frequency analyzer (the "Dynamic Signal Analyzer" of Hewlett-Packard) via an amplifier. Based on the transfer function obtained by this device, the out-of-plane natural frequency is calculated. The direction of the out-of-plane natural vibration is mainly the Z direction. In this method, the natural frequency is measured without any part of the racket 2 being firmly fixed. In other words, the out-of-plane natural frequency under free restraint conditions is measured.

[0064] FIG. 15 is a graph showing the results obtained from the measurement of FIG. 14. In FIG. 15, the horizontal axis is the frequency (Hz), and the vertical axis is the accelerance (m / s 2 / N). What is indicated by the symbol P1 in FIG. 15 is the primary peak. The frequency at this primary peak P1 is the out-of-plane primary natural frequency ωo1. What is indicated by the symbol P2 in FIG. 15 is the secondary peak. The frequency at this secondary peak P2 is the out-of-plane secondary natural frequency ωo2.

[0065] FIG. 16 is an explanatory diagram showing a method for measuring the frequency of in-plane natural vibration of this racket 2. In this measurement method, similar to the measurement method shown in FIG. 14, the racket 2 is suspended by a string 50. As shown in FIG. 16, the direction of the acceleration pickup 52 is the X direction. A point Ph on this grip 12 that faces the acceleration pickup 52 is vibrated by an impact hammer (not shown). The input vibration measured by a force pickup of this impact hammer and the response vibration measured by the acceleration pickup 52 are sent to a frequency analyzer (the "Dynamic Signal Analyzer" of Hewlett-Packard) via an amplifier. Based on the transfer function obtained by this device, the frequency of in-plane natural vibration is calculated. The direction of in-plane natural vibration is mainly the X direction. In this method, the in-plane natural vibration frequency under free restraint conditions is measured.

[0066] FIG. 17 is a graph showing the results obtained from the measurement in FIG. 16. In FIG. 17, the horizontal axis is the frequency (Hz), and the vertical axis is the accelerance (m / s 2 / N). What is indicated by reference sign P1 in FIG. 17 is the primary peak. The frequency at this primary peak P1 is the in-plane primary natural vibration frequency ωi1. What is indicated by reference sign P2 in FIG. 17 is the secondary peak. The frequency at this secondary peak P2 is the in-plane secondary natural vibration frequency ωi2.

[0067] FIG. 18 is a graph showing the relationship between the ratios (ωo2 / ωo1) and (ωi2 / ωi1) of the badminton racket 2. In this graph, reference sign Pr represents the points of the racket 2 shown in FIGS. 1-5.

[0068] The straight line indicated by reference sign L1 in FIG. 18 can be represented by the following mathematical formula. (ωi2 / ωi1) = 1.3 * (ωo2 / ωo1) - 0.6 As shown in FIG. 18, the point Pr is located below the straight line L1. In other words, the coordinates ((ωo2 / ωo1), (ωi2 / ωi1)) of this racket 2 satisfy the following mathematical formula (1). (ωi2 / ωi1) ≤ 1.3 * (ωo2 / ωo1) - 0.6 (1) According to the findings obtained by the present inventors, the racket 2 that satisfies this formula (1) is suitable for lobbing and cut smash. A player who performs lobbing or cut smash using this racket 2 is likely to obtain the intended trajectory of the shuttlecock. In this racket 2, the variation in the trajectory of the shuttlecock in lobbing is small, and the variation in the trajectory of the shuttlecock in cut smash is also small.

[0069] The badminton racket 2 that satisfies the above formula has a relatively large ratio of out-of-plane vibration (ωo2 / ωo1) and a relatively small ratio of in-plane vibration (ωi2 / ωi1).

[0070] According to the findings obtained by the present inventors regarding out-of-plane vibration, when the shuttlecock is hit at a portion near the bottom 28 of the face 36, the vibration of the out-of-plane secondary mode is mainly excited. According to the findings obtained by the present inventors, when the shuttlecock is hit at a portion near the top 26 of the face 36, the vibration of the out-of-plane primary mode is mainly excited. A typical hitting point in lobbing is near the top 26. Therefore, in lobbing, the vibration of the out-of-plane primary mode is mainly excited. However, even in lobbing, the hitting points vary. In the racket 2 with a large ratio (ωo2 / ωo1), the out-of-plane primary natural frequency ωo1 is relatively small, and the out-of-plane secondary natural frequency ωo2 is relatively large. According to the findings obtained by the present inventors, in lobbing with a racket 2 having a small out-of-plane primary natural frequency ωo1 and a large out-of-plane secondary natural frequency ωo2, even if the hitting points vary, the variation in the initial velocity of the shuttlecock is small. The reason is that even if the shuttlecock is hit at a position deviated from the intended position, the reaction of the racket 2 is not extremely small. Since the variation in the initial velocity of the shuttlecock is small, the variation in the ballistic trajectory of the shuttlecock is also small. This racket 2 is suitable for players who frequently use lobbing. This racket 2 is also suitable for players who emphasize lobbing.

[0071] As described above, a typical hitting point in lobbing is near the top 26. The racket 2 is also suitable for shots other than lobbing where the shuttlecock is hit at a portion near the top 26 of the face 36.

[0072] According to the findings obtained by the inventor regarding the in-plane vibration, when the shuttlecock is hit at a portion near the bottom 28 of the face 36, the vibration of the in-plane secondary mode is mainly excited. According to the findings obtained by the inventor, when the shuttlecock is hit at a portion near the top 26 of the face 36, the vibration of the in-plane primary mode is mainly excited. A typical hitting point in cut smash is near the bottom 28. Therefore, in cut smash, the vibration of the in-plane secondary mode is mainly excited. However, even in cut smash, the hitting points vary. In the racket 2 where the ratio (ωi2 / ωi1) is small, the in-plane primary natural frequency ωi1 is relatively large and the in-plane secondary natural frequency ωi2 is relatively small. According to the findings obtained by the inventor, in a cut smash using the racket 2 where the in-plane primary natural frequency ωi1 is large and the in-plane secondary natural frequency ωi2 is small, even if the hitting points vary, the variation in the initial velocity of the shuttlecock is small. The reason is that even if the shuttlecock is hit at a position deviated from the intended position, the reaction of the racket 2 is not extremely small. Since the variation in the initial velocity of the shuttlecock is small, the variation in the ballistic trajectory of the shuttlecock is also small. This racket 2 is suitable for players who frequently use cut smash. This racket 2 is also suitable for players who emphasize cut smash.

[0073] As described above, a typical hitting point in cut smash is near the bottom 28. The racket 2 according to the present invention is also suitable for shots other than cut smash where the shuttlecock is hit at a portion near the bottom 28 of the face 36 and accompanied by a cut.

[0074] As described above, in this shaft 4, the in-plane bending rigidity of the tip 20 is greater than the in-plane bending rigidity of the badminton head 16, and the out-of-plane bending rigidity of the tip 20 is smaller than the out-of-plane bending rigidity of the badminton head 16. In the badminton racket 2 having this shaft 4, the above formula (1) can be achieved.

[0075] As another means for achieving the above formula (1), adjustment of the rigidity distribution of the frame 6 is cited. The frame 6 having a small in-plane bending rigidity and a large out-of-plane bending rigidity in the vicinity of the bottom 28 can contribute to the achievement of the above formula (1).

[0076] As still another means for achieving the above formula (1), adjustment of the rigidity distribution of the entire racket 2, adjustment of the mass distribution of the shaft 4, adjustment of the mass distribution of the frame 6, adjustment of the mass distribution of the entire racket 2, adjustment of the volume distribution of the shaft 4, adjustment of the volume distribution of the frame 6, and adjustment of the volume distribution of the entire racket 2 are exemplified.

[0077] From the viewpoint of suitability for lobbing and cut smash, it is more preferable that the racket 2 satisfies the following formula. (ωi2 / ωi1) ≦ 1.3 * (ωo2 / ωo1) - 0.7 From the viewpoint of suitability for lobbing and cut smash, it is particularly preferable that the racket 2 satisfies the following formula. (ωi2 / ωi1) ≦ 1.3 * (ωo2 / ωo1) - 0.9

[0078] The straight line indicated by the symbol L2 in FIG. 18 can be expressed by the following formula. (ωi2 / ωi1) = 1.14 * (ωo2 / ωo1) - 0.187 As shown in FIG. 18, the point Pr is located below the straight line L2. In other words, the coordinates ((ωo2 / ωo1), (ωi2 / ωi1)) of this racket 2 satisfy the following formula (2). (ωi2 / ωi1) ≦ 1.14 * (ωo2 / ωo1) - 0.187 (2) According to the findings obtained by the inventor, the racket 2 that satisfies this formula (2) is suitable for lobbing and cut smashes. A player who performs lobbing or cut smashes using this racket 2 can easily obtain the intended trajectory of the shuttlecock. In this racket 2, the variation in the trajectory of the shuttlecock in lobbing is small, and the variation in the trajectory of the shuttlecock in cut smashes is also small.

[0079] In FIG. 18, the straight line indicated by reference numeral L3 can be represented by the following formula. (ωi2 / ωi1) = 1.08 * (ωo2 / ωo1) - 0.112 As shown in FIG. 18, the point Pr is located below the straight line L3. In other words, the coordinates ((ωo2 / ωo1), (ωi2 / ωi1)) of this racket 2 satisfy the following formula (3). (ωi2 / ωi1) ≦ 1.08 * (ωo2 / ωo1) - 0.112 (3) According to the findings obtained by the inventor, the racket 2 that satisfies this formula (3) is suitable for lobbing and cut smashes. A player who performs lobbing or cut smashes using this racket 2 can easily obtain the intended trajectory of the shuttlecock. In this racket 2, the variation in the trajectory of the shuttlecock in lobbing is small, and the variation in the trajectory of the shuttlecock in cut smashes is also small.

[0080] In FIG. 18, the straight line indicated by reference numeral L4 can be represented by the following formula. (ωo2 / ωo1) = 3.12 As shown in FIG. 18, the point Pr is located to the right of the straight line L4. In other words, the ratio (ωo2 / ωo1) of the point Pr is 3.12 or more. This racket 2 is suitable for lobbing. From this viewpoint, the ratio (ωo2 / ωo1) is more preferably 3.19 or more, and particularly preferably 3.25 or more. The ratio (ωo2 / ωo1) is preferably 3.80 or less.

[0081] In FIG. 18, the straight line indicated by reference numeral L5 can be represented by the following formula. (ωi2 / ωi1) = 3.45 As shown in FIG. 18, the point Pr is located below the straight line L5. In other words, the ratio (ωi2 / ωi1) of the point Pr is 3.45 or less. This racket 2 is suitable for cut smashes. From this viewpoint, the ratio (ωi2 / ωi1) is more preferably 3.42 or less, and particularly preferably 3.39 or less. The ratio (ωi2 / ωi1) is preferably 2.80 or more.

[0082] Hereinafter, a preferred method for determining the specifications of the badminton racket 2 will be described. This determination method is (A) a step of measuring the out-of-plane primary natural frequency ωo1 (Hz), the out-of-plane secondary natural frequency ωo2 (Hz), the in-plane primary natural frequency ωi1 (Hz), and the in-plane secondary natural frequency ωi2 (Hz) of the standard racket, (B) a step of determining whether or not the above-mentioned formula (1) is satisfied based on these natural frequencies ωo1, ωo2, ωi1, and ωi2, and (C) a step of determining the characteristics of the shaft 4 or the frame 6 of the target racket 2 so as to have a ratio (ωo2 / ωo1) larger than that of the standard racket when the formula (1) is not satisfied including.

[0083] Examples of the characteristics determined in this step (C) include the length of the shaft 4, the thickness of the shaft 4, the rigidity of the shaft 4, the rigidity distribution of the shaft 4, the length of the frame 6, the thickness of the frame 6, the rigidity of the frame 6, and the rigidity distribution of the frame 6.

[0084] Another preferred method for determining the specifications is (A) a step of measuring the out-of-plane primary natural frequency ωo1 (Hz), the out-of-plane secondary natural frequency ωo2 (Hz), the in-plane primary natural frequency ωi1 (Hz), and the in-plane secondary natural frequency ωi2 (Hz) of the standard racket, (B) a step of determining whether or not the above-mentioned formula (1) is satisfied based on these natural frequencies ωo1, ωo2, ωi1, and ωi2, and Step (C) of determining the characteristics of the shaft 4 or the frame 6 of the target racket 2 such that it has a ratio (ωi2 / ωi1) smaller than that of the standard racket when the following mathematical formula (1) is not satisfied. including.

[0085] Examples of the characteristics determined in this step (C) include the length of the shaft 4, the thickness of the shaft 4, the rigidity of the shaft 4, the rigidity distribution of the shaft 4, the length of the frame 6, the thickness of the frame 6, the rigidity of the frame 6, and the rigidity distribution of the frame 6.

Example

[0086] Hereinafter, the effects of the badminton racket according to the example will be clarified, but the scope disclosed in this specification based on the description of this example should not be construed restrictively.

[0087] [Example 1] A badminton racket shown in FIGS. 1-13 was manufactured. The out-of-plane first natural vibration frequency ωo1 of this racket was 54 Hz, the out-of-plane second natural vibration frequency ωo2 was 180 Hz, the in-plane first natural vibration frequency ωi1 was 59 Hz, and the in-plane second natural vibration frequency ωi2 was 202 Hz. The coordinates of this racket are indicated by the symbol Pr in FIG. 18.

[0088] [Example 2] A badminton racket was obtained in the same manner as in Example 1 except that the prepreg configuration of the shaft was changed. In this shaft, a type C prepreg configuration was adopted for the sheet groups S3-S8. In this shaft, furthermore, a prepreg with a fiber tensile elastic modulus E of 24 tf / mm 2 was adopted for the ninth sheet group S9. The type C prepreg configuration is shown in FIG. 19.

[0089] [Example 3] A badminton racket was obtained in the same manner as in Example 1 except that the prepreg configuration of the shaft was changed. In this shaft, the following type of prepreg configuration was adopted. Third sheet group S3: Type D Fourth sheet group S4: Type E Fifth sheet group S5: Type F Sixth sheet group S6: Type G Seventh sheet group S7: Type H Eighth sheet group S8: Type G These prepreg configurations are shown in FIGS. 20 - 24. In this shaft, furthermore, for the ninth sheet group S9, a prepreg with a fiber elastic modulus of 16 tf / mm 2 was adopted.

[0090] [Example 4] A badminton racket was obtained in the same manner as in Example 1, except that the prepreg configuration of the shaft was changed. In this shaft, the following type of prepreg configuration was adopted. Third sheet group S3: Type I Fourth sheet group S4: Type J Fifth sheet group S5: Type K Sixth sheet group S6: Type L Seventh sheet group S7: Type M Eighth sheet group S8: Type L These prepreg configurations are shown in FIGS. 25 - 29. In this shaft, furthermore, for the ninth sheet group S9, a prepreg with a fiber elastic modulus of 12 tf / mm 2 was adopted.

[0091] [Example 5] A badminton racket was obtained in the same manner as in Example 1, except that the prepreg configuration of the shaft was changed. This prepreg configuration is shown in FIG. 30. The prepreg configuration of Type N is shown in FIG. 31. The prepreg configuration of Type O is shown in FIG. 32.

[0092] [Example 6] A badminton racket was obtained in the same manner as in Example 1, except that the prepreg configuration of the shaft was changed. This prepreg configuration is shown in FIG. 33. The prepreg configuration of Type P is shown in FIG. 34. The prepreg configuration of Type Q is shown in FIG. 35.

[0093] [Comparative Example 1] A badminton racket was obtained in the same manner as in Example 1 except that the prepreg configuration of the shaft was changed. This prepreg configuration is shown in FIG. 36.

[0094] [Comparative Example 2] A badminton racket was obtained in the same manner as in Example 1 except that the prepreg configuration of the shaft was changed. This prepreg configuration is shown in FIG. 37. The prepreg configuration of Type R is shown in FIG. 38. The prepreg configuration of Type S is shown in FIG. 39. The prepreg configuration of Type T is shown in FIG. 40.

[0095] [Comparative Example 3] A badminton racket was obtained in the same manner as in Example 1 except that the prepreg configuration of the shaft was changed. This prepreg configuration is shown in FIG. 41.

[0096] [Lobbing] The shuttlecock was launched with a launching machine. The player was made to perform lobbing on this shuttlecock, and the trajectory of the shuttlecock was photographed. The image was analyzed, and the height of the shuttlecock passing over the net was measured. Twenty measurements were made, and the standard deviation of the height was determined. Based on this standard deviation, the rackets were graded. The grading criteria are as follows. This result is shown in Tables 1 and 2 below. 3: Standard deviation is less than 0.14 m 2: Standard deviation is 0.14 m or more and less than 0.20 m 1: Standard deviation is 0.20 m or more

[0097] [Cut Smash] The shuttlecock was launched with a launching machine. The player was made to perform a cut smash on this shuttlecock, and the trajectory of the shuttlecock was photographed. The image was analyzed, and the height of the shuttlecock passing over the net was measured. Twenty measurements were made, and the standard deviation of the height was determined. Based on this standard deviation, the rackets were graded. The grading criteria are as follows. This result is shown in Tables 1 and 2 below. 3: Standard deviation is less than 0.06 m 2: The standard deviation is 0.06 m or more and less than 0.10 m 1: The standard deviation is 0.10 m or more

[0098]

Table 1

[0099]

Table 2

[0100] As is clear from Tables 1 and 2, in the badminton rackets of each example, the evaluation regarding the stability of lobbing is "3" or "2", and the evaluation regarding the stability of cut smash is "3" or "2". On the other hand, in the rackets of each comparative example, the evaluation regarding the stability of lobbing or the evaluation of the stability of cut smash is "1". From this result, the superiority of this badminton racket is clear.

[0101] [Disclosed Items] Each of the following items is a disclosure of a preferred embodiment.

[0102] [Item 1] A shaft having a head and a tip, A grip attached to the above-mentioned shaft on the above-mentioned head, And A frame attached to the above-mentioned shaft at the above-mentioned tip Comprising, A badminton racket in which the ratio (ωo2 / ωo1) of the out-of-plane secondary natural frequency ωo2 (Hz) to the out-of-plane primary natural frequency ωo1 (Hz), and the ratio (ωi2 / ωi1) of the in-plane secondary natural frequency ωi2 (Hz) to the in-plane primary natural frequency ωi1 (Hz) satisfy the following mathematical formula (1). (ωi2 / ωi1) ≦ 1.3 * (ωo2 / ωo1) - 0.6 (1)

[0103] [Item 2] The badminton racket according to Item 1 that satisfies the following mathematical formula (2). (ωi2 / ωi1) ≤ 1.14 * (ωo2 / ωo1) - 0.187 (2)

[0104] [Item 3] The badminton racket according to Item 1, which satisfies the following formula (3). (ωi2 / ωi1) ≤ 1.08 * (ωo2 / ωo1) - 0.112 (3)

[0105] [Item 4] The badminton racket according to any one of Items 1 to 3, wherein the ratio (ωo2 / ωo1) is 3.12 or more.

[0106] [Item 5] The badminton racket according to any one of Items 1 to 4, wherein the ratio (ωi2 / ωi1) is 3.45 or less.

[0107] [Item 6] The badminton racket according to any one of Items 1 to 5, wherein the material of the shaft is a fiber-reinforced resin containing a plurality of reinforcing fibers.

[0108] [Item 7] In the above-mentioned badminton racket, the tensile elastic modulus of the reinforcing fibers contained in the zone in the in-plane direction away from the center point of the shaft is smaller than the tensile elastic modulus of the reinforcing fibers contained in the zone in the out-of-plane direction away from the center point of the shaft, according to Item 6.

[0109] [Item 8] In the above-mentioned tip, the tensile elastic modulus of the reinforcing fibers contained in the zone in the in-plane direction away from the center point of the shaft is larger than the tensile elastic modulus of the reinforcing fibers contained in the zone in the out-of-plane direction away from the center point of the shaft, according to Item 6 or 7.

[0110] [Item 9] In a zone that is farther away from the center point of the shaft in the in-plane direction, the tensile elastic modulus of the reinforcing fibers included in the bad is smaller than the tensile elastic modulus of the reinforcing fibers included in the tip, the badminton racket according to any one of Items 6 to 8.

[0111] [Item 10] In a zone that is farther away from the center point of the shaft in the out-of-plane direction, the tensile elastic modulus of the reinforcing fibers included in the bad is larger than the tensile elastic modulus of the reinforcing fibers included in the tip, the badminton racket according to any one of Items 6 to 9.

[0112] [Item 11] A shaft having a bad and a tip, A grip attached to the shaft in the bad, And A frame attached to the shaft in the tip A method for determining the specifications of a badminton racket provided with, (A) A step of measuring the out-of-plane primary natural frequency ωo1 (Hz), the out-of-plane secondary natural frequency ωo2 (Hz), the in-plane primary natural frequency ωi1 (Hz), and the in-plane secondary natural frequency ωi2 (Hz) of a standard racket, (B) A step of determining whether or not the following mathematical formula (1) is satisfied based on these natural frequencies ωo1, ωo2, ωi1, and ωi2, And (C) When the following mathematical formula (1) is not satisfied, a step of determining the characteristics of the shaft or the frame of the target racket so as to have a ratio (ωo2 / ωo1) larger than that of the standard racket A method for determining the specifications of a badminton racket including. (ωi2 / ωi1) ≦ 1.3 * (ωo2 / ωo1) - 0.6 (1)

[0113] [Item 12] A shaft having a bad and a tip, A grip attached to the shaft in the bad, And A frame attached to the shaft in the above tip A method for determining the specifications of a badminton racket having the same, comprising: (A) Measuring the out-of-plane first natural frequency ωo1 (Hz), out-of-plane second natural frequency ωo2 (Hz), in-plane first natural frequency ωi1 (Hz), and in-plane second natural frequency ωi2 (Hz) of a standard racket; (B) Judging whether or not the following formula (1) is satisfied based on these natural frequencies ωo1, ωo2, ωi1, and ωi2; and (C) When the following formula (1) is not satisfied, determining the characteristics of the shaft or frame of the target racket so as to have a ratio (ωi2 / ωi1) smaller than that of the standard racket A method for determining the specifications of a badminton racket, including the above steps. (ωi2 / ωi1) ≦ 1.3 * (ωo2 / ωo1) - 0.6 (1)

Industrial Applicability

[0114] The above-mentioned badminton racket is suitable for players with a style that frequently uses smashes and cut dropshots. This racket is also suitable for players with a style that frequently uses other shots with a bottom-oriented hitting point and other shots with a top-oriented hitting point and accompanied by a cut.

Explanation of Symbols

[0115] 2 ··· Badminton racket 4 ··· Shaft 6 ··· Frame 8 ··· Neck 10 ··· Cap 12 ··· Grip 14 ··· String 16 ··· Bad 18 ··· Middle 20 ··· Tip 22 ··· Bad end 24 ··· Tip end 26 ··· Top 28 ··· Bottom 36 ··· Face 38 ··· Prepreg 40 ··· Fiber 42 ··· Matrix Resin 44 ··· Prepreg 46 ··· Prepreg 48 ··· Prepreg S1 ··· First Sheet Group S2 ··· Second Sheet Group S3 ··· Third Sheet Group S4 ··· Fourth Sheet Group S5 ··· Fifth Sheet Group S6 ··· Sixth Sheet Group S7 ··· Seventh Sheet Group S8 ··· Eighth Sheet Group S9 ··· Ninth Sheet Group

Claims

1. A shaft having a head and a tip, a grip attached to the shaft in the head, and a frame attached to the shaft in the tip are provided, the material of the shaft is a fiber-reinforced resin containing a plurality of reinforcing fibers, in the head, the tensile elastic modulus of the reinforcing fibers contained in the zone away from the center point of the shaft in the in-plane direction is smaller than the tensile elastic modulus of the reinforcing fibers contained in the zone away from the center point of the shaft in the out-of-plane direction, A badminton racket in which the ratio (ωo2 / ωo1) of the out-of-plane secondary natural frequency ωo2 (Hz) to the out-of-plane primary natural frequency ωo1 (Hz) and the ratio (ωi2 / ωi1) of the in-plane secondary natural frequency ωi2 (Hz) to the in-plane primary natural frequency ωi1 (Hz) satisfy the following mathematical formula (1). (ωi2 / ωi1) ≦ 1.3 * (ωo2 / ωo1) - 0.6 (1)

2. A shaft having a head and a tip, a grip attached to the shaft in the head, and a frame attached to the shaft in the tip are provided, the material of the shaft is a fiber-reinforced resin containing a plurality of reinforcing fibers, in the tip, the tensile elastic modulus of the reinforcing fibers contained in the zone away from the center point of the shaft in the in-plane direction is larger than the tensile elastic modulus of the reinforcing fibers contained in the zone away from the center point of the shaft in the out-of-plane direction, A badminton racket in which the ratio (ωo2 / ωo1) of the out-of-plane secondary natural frequency ωo2 (Hz) to the out-of-plane primary natural frequency ωo1 (Hz) and the ratio (ωi2 / ωi1) of the in-plane secondary natural frequency ωi2 (Hz) to the in-plane primary natural frequency ωi1 (Hz) satisfy the following mathematical formula (1). (ωi2 / ωi1) ≦ 1.3 * (ωo2 / ωo1) - 0.6 (1)

3. A shaft having a head and a tip, a grip attached to the shaft in the head, and a frame attached to the shaft in the tip are provided, the material of the shaft is a fiber-reinforced resin containing a plurality of reinforcing fibers, in the zone away from the center point of the shaft in the in-plane direction, the tensile elastic modulus of the reinforcing fibers contained in the head is smaller than the tensile elastic modulus of the reinforcing fibers contained in the tip, A badminton racket in which the ratio (ωo2 / ωo1) of the out-of-plane second natural frequency ωo2 (Hz) to the out-of-plane first natural frequency ωo1 (Hz), and the ratio (ωi2 / ωi1) of the in-plane second natural frequency ωi2 (Hz) to the in-plane first natural frequency ωi1 (Hz) satisfy the following mathematical formula (1). (ωi2 / ωi1) ≦ 1.3 * (ωo2 / ωo1) - 0.6 (1)

4. A shaft having a butt and a tip, a grip attached to the shaft in the butt, and a frame attached to the shaft in the tip are provided, the material of the shaft is a fiber-reinforced resin containing a plurality of reinforcing fibers, in a zone away from the center point of the shaft in the out-of-plane direction, the tensile elastic modulus of the reinforcing fibers contained in the butt is greater than the tensile elastic modulus of the reinforcing fibers contained in the tip, A badminton racket in which the ratio (ωo2 / ωo1) of the out-of-plane second natural frequency ωo2 (Hz) to the out-of-plane first natural frequency ωo1 (Hz), and the ratio (ωi2 / ωi1) of the in-plane second natural frequency ωi2 (Hz) to the in-plane first natural frequency ωi1 (Hz) satisfy the following mathematical formula (1). (ωi2 / ωi1) ≦ 1.3 * (ωo2 / ωo1) - 0.6 (1)

5. The badminton racket according to any one of claims 1 to 4, which satisfies the following mathematical formula (2). (ωi2 / ωi1) ≦ 1.14 * (ωo2 / ωo1) - 0.187 (2)

6. The badminton racket according to any one of claims 1 to 4, which satisfies the following mathematical formula (3). (ωi2 / ωi1) ≦ 1.08 * (ωo2 / ωo1) - 0.112 (3)

7. The badminton racket according to any one of claims 1 to 6, wherein the ratio (ωo2 / ωo1) is 3.12 or more.

8. The badminton racket according to any one of claims 1 to 7, wherein the ratio (ωi2 / ωi1) is 3.45 or less.

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