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 bottom and a shot a hit point of which is closer to a top.SOLUTION: A badminton racket 2 has a shaft 4, a frame 6, and a grip 12. In the racket 2, 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)-0.2 (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 shots a shuttlecock with the racket. By the shot, 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 shot, the frame and the shaft are deformed. An attempt regarding optimization of the deformation behavior is described in Japanese Unexamined Patent Application Publication 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 smashes, lobbing, drops, clears, etc.

[0005] A smash is a shot intended to prevent the opponent player from receiving. In a smash, a player needs a skill to fly the shuttlecock in an intended trajectory. A player who frequently uses smashes hopes for stability of the trajectory (speed, height, etc.) of the shuttlecock.

[0006] Cut lobing, unlike normal lobbing, involves a cutting motion. In cut lobing, the shuttlecock rotates at high speed while flying at high speed. Cut lobing is often hit from near the net inside the player's court. Cut lobing is a shot intended to carry the shuttlecock deep into the opponent player's court. The trajectory of the shuttlecock in cut lobing is high. Advanced skill is required of the player to fly the shuttlecock at the intended height. Players who frequently use cut lobing desire stability in the trajectory (speed, height, etc.) of the shuttlecock.

[0007] In an investigation using statistical methods, typical scoring points in smashing are bottom - biased, and typical scoring points in cut lobing are top - biased. Even in shots other than smashing, the shuttlecock can be hit with bottom - biased scoring points. Even in shots other than cut lobing, the shuttlecock can be hit with top - biased scoring points.

[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 bottom - biased scoring points and shots with top - biased scoring points.

Means for Solving the Problem

[0009] A preferred badminton racket has a shaft having a butt and a tip, a grip attached to the shaft at the butt, and a frame attached to the shaft at the tip 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) of this badminton racket satisfy the following mathematical formula (1). (ωi2 / ωi1) ≧ 1.3 * (ωo2 / ωo1) - 0.2 (1)

Advantages of the Invention

[0010] A player using this badminton racket can easily perform shots with the hitting point near the bottom and can also easily perform shots with the hitting point near the top. 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, 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 from a fiber-reinforced resin. This fiber-reinforced resin has a resin matrix and a large 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] The frame 6 is annular and hollow. The frame 6 is formed of a fiber-reinforced resin. As the fiber-reinforced resin, the same base resin as that of the shaft 4 can be used. As the fiber-reinforced resin, the same reinforcing fibers as those of the shaft 4 can be used. The frame 6 is firmly coupled to the tip end 24 of the shaft 4 via the neck 8. The frame 6 has a top 26 and a bottom 28.

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

[0020] The string 14 is stretched over the frame 6. The string 14 is stretched along the width direction X and the axial direction Y. The portion of the string 14 extending along the width direction X is the cross thread 32. The portion of the 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. The face 36 generally lies along the X-Y plane.

[0021] Figure 3 is an enlarged cross-sectional view showing a part of the shaft 4 of the 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 the shaft 4.

[0022] In FIGS. 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 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, 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. In this embodiment, the outer diameter Do from the butt end 22 to the tip end 24 is substantially constant.

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

[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 for 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 the sake of 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 over the entire shaft 4. The shape of this prepreg 44 is generally rectangular. This prepreg 44 includes 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 and 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 over the entire shaft 4. The shape of this prepreg 46 is generally rectangular. This prepreg 46 includes 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 2It is so. 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 that 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. The type A prepreg configuration 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. The type B prepreg configuration will be described in detail later.

[0030] The ninth sheet group S9 includes a single prepreg 48. This prepreg 48 exists over the entire shaft 4. The shape of this prepreg 48 is generally rectangular. This prepreg 48 includes 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 It is so. The width W of this prepreg 48 is 54 mm.

[0031] FIG. 7 is a developed view showing the type A prepreg configuration, and FIG. 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 that is 240 mm away from this bad end 22. The shape of this prepreg A1 is generally rectangular. This prepreg A1 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 is. This prepreg A1 exists in the first quarter Q1.

[0033] Prepreg A2 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 A2 is generally rectangular. This prepreg A2 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 A2 exists in the first quarter Q1.

[0034] Prepreg A3 exists between the bad end 22 and a position that is 150 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 7.4 tf / mm 2 is. This prepreg A3 exists in the second quarter Q2.

[0035] Prepreg A4 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 A4 is generally rectangular. This prepreg A4 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 A4 exists in the second quarter Q2.

[0036] Prepreg A5 exists between the bad end 22 and a position 240 mm away from this bad end 22. The shape of this prepreg A5 is generally rectangular. This prepreg A5 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 A5 exists in the third quarter Q3.

[0037] Prepreg A6 exists between a position 240 mm away from the bad end 22 and a position 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 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 A6 exists in the third quarter Q3.

[0038] Prepreg A7 exists between the bad end 22 and a position that is 150 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 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 A7 exists in the fourth quarter Q4.

[0039] Prepreg A8 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 A8 is generally rectangular. This prepreg A8 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 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. Illustrations of other sheet groups are 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 exists from the butt 16 to the middle 18, prepreg A2 exists in the tip 20, prepreg A3 exists in the butt 16, prepreg A4 exists from the middle 18 to the tip 20, prepreg A5 exists from the butt 16 to the middle 18, prepreg A6 exists in the tip 20, prepreg A7 exists in the butt 16, and prepreg A8 exists from the middle 18 to the tip 20.

[0043] FIG. 13 is a schematic diagram showing the prepreg configuration of type B. This prepreg configuration includes eight 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 butt end 22 (see FIG. 2) and a position 150 mm away from this butt end 22. The shape of this prepreg B1 is generally rectangular. This prepreg B1 includes 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 B1 exists in the first quarter Q1.

[0045] Prepreg B2 exists between a position 150 mm away from the butt end 22 and a position 340 mm away from this butt end 22. The shape of this prepreg B2 is generally rectangular. This prepreg B2 includes 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 B2 exists in the first quarter Q1.

[0046] Prepreg B3 exists between the bad end 22 and a position that is 240 mm away from this bad end 22. The shape of this prepreg B3 is generally rectangular. This prepreg B3 contains a plurality of carbon fibers arranged in parallel. The extending direction of each carbon fiber is aligned with 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 B3 exists in the second quarter Q2.

[0047] Prepreg B4 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 B4 is generally rectangular. This prepreg B4 contains a plurality of carbon fibers arranged in parallel. The extending direction of each carbon fiber is aligned with 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 B4 exists in the second quarter Q2.

[0048] Prepreg B5 exists between the bad end 22 and a position that is 150 mm away from this bad end 22. The shape of this prepreg B5 is generally rectangular. This prepreg B5 contains a plurality of carbon fibers arranged in parallel. The extending direction of each carbon fiber is aligned with 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 B5 exists in the third quarter Q3.

[0049] Prepreg B6 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 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 7.4 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 240 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 7.4 tf / mm 2 is. This prepreg B7 exists in the fourth quarter Q4.

[0051] Prepreg B8 exists between a position 240 mm away from the bad end 22 and a position 340 mm away from this bad end 22. The shape of this prepreg B8 is generally rectangular. This prepreg B8 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 B8 exists in the fourth quarter Q4.

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

[0053] Prepreg B1 exists in the butt 16, prepreg B2 exists from the middle 18 to the tip 20, prepreg B3 exists from the butt 16 to the middle 18, prepreg B4 exists in the tip 20, prepreg B5 exists in the butt 16, prepreg B6 exists from the middle 18 to the tip 20, prepreg B7 exists from the butt 16 to the middle 18, and prepreg B8 exists in 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 large, and the tensile elastic modulus E of the carbon fibers contained in prepregs A2, A6, B2, and B6 is small. 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 rigidity of the butt 16 RiM: In-plane bending rigidity of the middle 18 RiT: In-plane bending rigidity of the tip 20

[0055] In the prepreg configuration of type A, prepregs A3, A4, A7, and A8 are separated in the out-of-plane direction from the center point SC. In the prepreg configuration of type B, prepregs B3, B4, B7, and B8 are separated in the out-of-plane direction from the center point SC. The tensile elastic modulus E of the carbon fibers contained in prepregs A3, A7, B3, and B7 is small, and the tensile elastic modulus E of the carbon fibers contained in prepregs A4, A8, B4, and B8 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.

[0056] RoB < RoM < RoT RoB: Out-of-plane bending rigidity 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 includes the following formula in the bud 16. RiB > RoB This shaft 4 further includes the following formula 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 bud 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 other sheets include those containing glass fibers. Wrapping tapes are 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 matrix resin flows. Further heating causes this resin to undergo a curing reaction, and a molded body is obtained. Processing such as end face machining, polishing, and painting is performed on this molded body, 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 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 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 in a state where no part of the racket 2 is firmly fixed. In other words, the out-of-plane natural frequency under free boundary conditions is measured.

[0064] FIG. 15 is a graph showing the results obtained from the measurement in 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 reference numeral 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 reference numeral 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 the in-plane natural vibration of the racket 2. In this measurement method, the racket 2 is suspended by the string 50 in the same manner as the measurement method shown in FIG. 14. As shown in FIG. 16, the direction of the acceleration pickup 52 is the X direction. The point Ph of the grip 12 that faces the acceleration pickup 52 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 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 the in-plane natural vibration is calculated. The direction of the 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 the symbol 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 the symbol 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, the symbol Pr represents the points of the racket 2 shown in FIGS. 1-13.

[0068] The straight line indicated by the symbol L1 in FIG. 18 can be represented by the following mathematical formula. (ωi2 / ωi1) = 1.3 * (ωo2 / ωo1) - 0.2 As shown in FIG. 18, the point Pr is located above 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) - 0.2 (1) According to the findings obtained by the inventor, the racket 2 that satisfies this formula (1) is suitable for smashing and cutting lobbing. A player who performs smashing or cutting lobbing 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 smashing is small, and the variation in the trajectory of the shuttlecock in cutting lobbing is also small.

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

[0070] According to the findings obtained by the inventor regarding out-of-plane vibration, when the shuttlecock is hit at a portion near the bottom 28 of the face 36, the out-of-plane secondary natural frequency 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 out-of-plane primary natural frequency is mainly excited. A typical hitting point in smashing is near the bottom 28. Therefore, in smashing, mainly out-of-plane secondary natural vibration is excited. However, even in smashing, the hitting points vary. In the racket 2 with a small ratio (ωo2 / ωo1), the out-of-plane primary natural frequency ωo1 is relatively large and the out-of-plane secondary natural frequency ωo2 is relatively small. According to the findings obtained by the inventor, in smashing with a racket 2 having a large out-of-plane primary natural frequency ωo1 and a small 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 smashing. This racket 2 is also suitable for players who emphasize smashing.

[0071] As described above, typical hitting points in a smash are near the bottom 28. This racket 2 is also suitable for shots other than smashes where the shuttle is hit at a portion near the bottom 28 of the face 36.

[0072] According to the findings obtained by the inventor regarding the in-plane vibration, when the shuttle 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 shuttle is hit at a portion near the top 26 of the face 36, the vibration of the in-plane primary mode is mainly excited. Typical hitting points in cutting lobbing are near the top 26. Therefore, in cutting lobbing, the vibration of the in-plane primary mode is mainly excited. However, even in cutting lobbing, the hitting points vary. In the racket 2 with a large ratio (ωi2 / ωi1), the in-plane primary natural frequency ωi1 is relatively small and the in-plane secondary natural frequency ωi2 is relatively large. According to the findings obtained by the inventor, in cutting lobbing with the racket 2 having a small in-plane primary natural frequency ωi1 and a large in-plane secondary natural frequency ωi2, even if the hitting points vary, the variation in the initial velocity of the shuttle is small. The reason is that even if the shuttle 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 shuttle is small, the variation in the ballistic trajectory of the shuttle is also small. This racket 2 is suitable for players who frequently use cutting lobbing. This racket 2 is also suitable for players who emphasize cutting lobbing.

[0073] As described above, typical hitting points in cutting lobbing are near the top 26. This racket 2 is also suitable for shots other than cutting lobbing where the shuttle is hit at a portion near the top 26 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 smaller than the in-plane bending rigidity of the bad 16, and the out-of-plane bending rigidity of the tip 20 is larger than the out-of-plane bending rigidity of the bad 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 can be mentioned. The frame 6 having a large in-plane bending rigidity and a small 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 other 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 smashing and cutting lobbing, it is more preferable that the racket 2 satisfies the following formula. (ωi2 / ωi1) ≧ 1.3 * (ωo2 / ωo1) - 0.1 From the viewpoint of suitability for smashing and cutting lobbing, it is particularly preferable that the racket 2 satisfies the following formula. (ωi2 / ωi1) ≧ 1.3 * (ωo2 / ωo1) + 0.1

[0078] The straight line indicated by the symbol L2 in FIG. 18 can be represented by the following formula. (ωi2 / ωi1) = 1.11 * (ωo2 / ωo1) + 0.391 As shown in FIG. 18, the point Pr is located above the straight line L2. In other words, the coordinates ((ωo2 / ωo1), (ωi2 / ωi1)) of this racket 2 satisfy the following formula (2). (ωi2 / ωi1) ≧ 1.11 * (ωo2 / ωo1) + 0.391 (2) According to the findings obtained by the present inventor, the racket 2 that satisfies this formula (2) is suitable for smashing and cutting lobbing. A player who performs smashing or cutting lobbing 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 smashing is small, and the variation in the trajectory of the shuttlecock in cutting lobbing is also small.

[0079] In FIG. 18, the straight line indicated by the reference sign L3 can be represented by the following formula. (ωi2 / ωi1) = 2.5 * (ωo2 / ωo1) - 3.42 As shown in FIG. 18, the point Pr is located on the straight line L3. In other words, the coordinates ((ωo2 / ωo1), (ωi2 / ωi1)) of this racket 2 satisfy the following formula (3). (ωi2 / ωi1) ≧ 2.5 * (ωo2 / ωo1) - 3.42 (3) According to the findings obtained by the present inventor, the racket 2 that satisfies this formula (3) is suitable for smashing and cutting lobbing. A player who performs smashing or cutting lobbing 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 smashing is small, and the variation in the trajectory of the shuttlecock in cutting lobbing is also small.

[0080] In FIG. 18, the straight line indicated by the reference sign L4 can be represented by the following formula. (ωo2 / ωo1) = 2.99 As shown in FIG. 18, the point Pr is located on the left side of the straight line L4. In other words, the ratio (ωo2 / ωo1) of the point Pr is 2.99 or less. This racket 2 is suitable for smashing. From this viewpoint, the ratio (ωo2 / ωo1) is more preferably 2.95 or less, and particularly preferably 2.94 or less. The ratio (ωo2 / ωo1) is preferably 2.50 or more.

[0081] In FIG. 18, the straight line indicated by the reference sign L5 can be represented by the following formula. (ωi2 / ωi1) = 3.61 As shown in FIG. 18, the point Pr is located above the straight line L5. In other words, the ratio (ωi2 / ωi1) of the point Pr is 3.61 or more. This racket 2 is suitable for cutting. From this viewpoint, the ratio (ωi2 / ωi1) is more preferably 3.65 or more, and particularly preferably 3.68 or more. The ratio (ωi2 / ωi1) is preferably 4.3 or less.

[0082] Hereinafter, a preferable 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 mathematical 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) smaller than that of the standard racket when the mathematical formula (1) is not satisfied. is included.

[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 preferable 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 mathematical formula (1) is satisfied based on these natural frequencies ωo1, ωo2, ωi1, and ωi2; and (C) When the following formula (1) is not satisfied, determine the characteristics of the shaft 4 or the frame 6 of the target racket 2 so as to have a ratio (ωi2 / ωi1) greater than that of the standard racket 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 should not be construed in a limited manner based on the description of this example.

[0087] [Example 1] A badminton racket shown in FIGS. 1-13 was manufactured. The out-of-plane fundamental natural frequency ωo1 of this racket was 59 Hz, the out-of-plane second natural frequency ωo2 was 172 Hz, the in-plane fundamental natural frequency ωi1 was 51 Hz, and the in-plane second natural frequency ωi2 was 200 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 width of 54 mm 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, for the first sheet group S1 and the second sheet group S2, a prepreg with a fiber elastic modulus of 30 tf / mm 2 was adopted. In this shaft, the following type of prepreg configuration was adopted. Third sheet group S3: Type I Fourth sheet group S4: Type I Fifth sheet group S5: Type I Sixth sheet group S6: Type I Seventh sheet group S7: Type J Eighth sheet group S8: Type K These prepreg configurations are shown in FIGS. 25 - 27. In this shaft, furthermore, for the ninth sheet group S9, a prepreg with a fiber elastic modulus of 30 tf / mm 2 was adopted.

[0091] [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. 28.

[0092] [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. 29.

[0093] [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. 30.

[0094] [Smash] A shuttlecock was launched with a launching machine. A player was made to perform a 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 taken, and the standard deviation of the height was determined. Based on this standard deviation, the rackets were rated. The rating criteria are as follows. The results are shown in Tables 1 and 2 below. 3: Standard deviation less than 0.06 m 2: Standard deviation of 0.06 m or more and less than 0.10 m 1: Standard deviation of 0.10 m or more

[0095] [Cutting] A shuttlecock was launched with a launching machine. A player was made to perform cutting 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 taken, and the standard deviation of the height was determined. Based on this standard deviation, the rackets were rated. The rating criteria are as follows. The results are shown in Tables 1-4 below. 3: Standard deviation less than 0.14 m 2: Standard deviation of 0.14 m or more and less than 0.20 m 1: Standard deviation of 0.20 m or more

[0096]

Table 1

[0097]

Table 2

[0098] As is clear from Tables 1 and 2, in the badminton rackets of each example, the evaluation regarding the smash stability is "3" or "2", and the evaluation regarding the cut-robbing stability is "3" or "2". On the other hand, in the rackets of each comparative example, the evaluation regarding the smash stability or the evaluation regarding the cut-robbing stability is "1". From this result, the superiority of this badminton racket is clear.

[0099] [Disclosed Items] Each of the following items is a disclosure of a preferred embodiment.

[0100] [Item 1] A shaft having a head and a tip, A grip attached to the shaft in the above head, And A frame attached to the shaft in the above 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 formula (1). (ωi2 / ωi1) ≧ 1.3 * (ωo2 / ωo1) - 0.2 (1)

[0101] [Item 2] The badminton racket according to Item 1 that satisfies the following formula (2). (ωi2 / ωi1) ≧ 1.11 * (ωo2 / ωo1) + 0.391 (2)

[0102] [Item 3] The badminton racket according to Item 1 that satisfies the following formula (3). (ωi2 / ωi1) ≧ 2.5 * (ωo2 / ωo1) - 3.42 (3)

[0103] [Item 4] The badminton racket according to any one of Items 1 to 3, wherein the ratio (ωo2 / ωo1) is 2.99 or less.

[0104] [Item 5] The badminton racket according to any one of Items 1 to 4, wherein the ratio (ωi2 / ωi1) is 3.61 or more.

[0105] [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.

[0106] [Item 7] The badminton racket according to Item 6, wherein, in the head, the tensile elastic modulus of the reinforcing fibers included in the zone away from the center point of the shaft in the in-plane direction is greater than the tensile elastic modulus of the reinforcing fibers included in the zone away from the center point of the shaft in the out-of-plane direction.

[0107] [Item 8] The badminton racket according to Item 6 or 7, wherein, in the tip, the tensile elastic modulus of the reinforcing fibers included in the zone away from the center point of the shaft in the in-plane direction is less than the tensile elastic modulus of the reinforcing fibers included in the zone away from the center point of the shaft in the out-of-plane direction.

[0108] [Item 9] The badminton racket according to any one of Items 6 to 8, wherein, in the zone away from the center point of the shaft in the in-plane direction, the tensile elastic modulus of the reinforcing fibers included in the head is greater than the tensile elastic modulus of the reinforcing fibers included in the tip.

[0109] [Item 10] The badminton racket according to any one of Items 6 to 9, wherein, in the zone 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 head is less than the tensile elastic modulus of the reinforcing fibers included in the tip.

[0110] [Item 11] 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 A method for determining the specifications of a badminton racket 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) Determining 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 (ωo2 / ωo1) 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) - 0.2 (1)

[0111] [Item 12] 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 A method for determining the specifications of a badminton racket 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) Determining whether or not the following formula (1) is satisfied based on these natural frequencies ωo1, ωo2, ωi1, and ωi2; and Step of determining the characteristics of the shaft or frame of the target racket so as to have a ratio (ωi2 / ωi1) greater than that of the standard racket when the following formula (1) is not satisfied A method for determining the specifications of a badminton racket, including the above. (ωi2 / ωi1) ≧ 1.3 * (ωo2 / ωo1) - 0.2 (1)

Industrial Applicability

[0112] 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 Signs

[0113] 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 ··· The fifth sheet group S6 ··· The sixth sheet group S7 ··· The seventh sheet group S8 ··· The eighth sheet group S9 ··· The 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 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 formula (1). (ωi2 / ωi1) ≥ 1.3 * (ωo2 / ωo1) - 0.2 (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 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 formula (1). (ωi2 / ωi1) ≥ 1.3 * (ωo2 / ωo1) - 0.2 (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 larger 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) - 0.2 (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 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) - 0.2 (1)

5. The badminton racket according to any one of claims 1 to 4, which satisfies the following mathematical formula (2). (ωi2 / ωi1) ≥ 1.11 * (ωo2 / ωo1) + 0.391 (2)

6. The badminton racket according to any one of claims 1 to 4, which satisfies the following mathematical formula (3). (ωi2 / ωi1) ≥ 2.5 * (ωo2 / ωo1) - 3.42 (3)

7. The badminton racket according to any one of claims 1 to 6, wherein the ratio (ωo2 / ωo1) is 2.99 or less.

8. The badminton racket according to any one of claims 1 to 7, wherein the ratio (ωi2 / ωi1) is 3.61 or more.

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