JP7703967B2 - Badminton Racket - Google Patents

Description

This specification discloses a racket used in badminton.

A badminton racket has a frame, strings, and a shaft. The frame has a top and a bottom. The strings form a face. A player hits a shuttlecock with the racket. The shot causes the face to collide with the shuttlecock. The impact of the collision is transmitted from the strings to the frame and then to the shaft. The shot causes the frame and shaft to deform. An attempt to optimize the deformation behavior is described in JP 2021-23724 A.

Patent Publication No. 2021-23724

In the game of badminton, players perform different types of shots. Shots that players perform include smashes, lobs, drops, clears, etc.

Lobs are often hit from within a player's court, near the net. A lob is a shot intended to send the shuttlecock to the back of the opponent's court. The shuttlecock's trajectory in a lob is high. The player needs the skill to make the shuttlecock fly at the intended height. Players who frequently lob the shuttlecock want a consistent trajectory (speed, height, etc.).

A cut smash differs from a normal smash in that it involves a cutting motion. In a cut smash, the shuttle spins at high speed while flying at high speed. A cut smash is a shot intended to prevent the opposing player from receiving the ball. A cut smash requires the player to have advanced skill in order to make the shuttle fly on the intended trajectory. Players who frequently use cut smashes want a stable shuttle trajectory (speed, height, etc.).

A statistical study has shown that the typical impact point for a lob is closer to the top, and the typical impact point for a cut smash is closer to the bottom. For shots other than a lob, the shuttlecock may also be shot at an impact point closer to the top. For shots other than a cut smash, the shuttlecock may also be shot at an impact point closer to the bottom.

The inventor's intention is to provide a badminton racket that can reduce variation in the shuttlecock trajectory for both shots where the impact point is closer to the top and shots where the impact point is closer to the bottom.

The preferred badminton racket is
a shaft having a butt and a tip;
a grip attached to the shaft of the bat;
and a frame attached to the shaft at the tip. A ratio (ωo2/ωo1) of the out-of-plane secondary natural frequency ωo2 (Hz) to the out-of-plane primary natural frequency ωo1 (Hz) and a 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 formula (1).
(ωi2/ωi1) ≦ 1.3 * (ωo2/ωo1) - 0.6 (1)

A player using this badminton racket is more likely to hit shots with a hitting point closer to the top, and also easier to hit shots with a hitting point closer to the bottom. This racket can contribute to winning the game.

FIG. 1 is a front view showing a badminton racket according to an embodiment. FIG. 2 is a right side view of the badminton racket of FIG. 1. FIG. FIG. 3 is an enlarged cross-sectional view showing a part of the shaft of the badminton racket of FIG. FIG. 4 is an enlarged cross-sectional view taken along line IV-IV in FIG. FIG. 5 is a cross-sectional perspective view showing an example of a prepreg for the shaft of the badminton racket of FIG. 1. FIG. 6 is a development view showing a prepreg configuration for the shaft of the badminton racket of FIG. FIG. 7 is a development view showing the prepreg configuration of Type A. FIG. 8 is a schematic diagram showing a prepreg configuration of Type A. FIG. 9 is an enlarged cross-sectional view showing a part of the shaft of the badminton racket of FIG. FIG. 10 is an enlarged cross-sectional view showing a part of the shaft of the badminton racket of FIG. FIG. 11 is an enlarged cross-sectional view taken along line XI-XI of FIG. FIG. 12 is an enlarged cross-sectional view taken along line XII-XII in FIG. FIG. 13 is a schematic diagram showing a prepreg configuration of Type B. FIG. 14 is an explanatory diagram showing a method for measuring the natural frequency in the out-of-plane direction of the racket shown in FIG. FIG. 15 is a graph showing the results obtained in the measurement of FIG. FIG. 16 is an explanatory diagram showing a method for measuring the natural frequency in the in-plane direction of the racket shown in FIG. FIG. 17 is a graph showing the results obtained in the measurement of FIG. FIG. 18 is a graph showing the relationship between the ratio (ωo2/ωo1) and the ratio (ωi2/ωi1) of the badminton racket of FIG. FIG. 19 is a schematic diagram showing a prepreg configuration of Type C. FIG. 20 is a schematic diagram showing a prepreg configuration of Type D. FIG. 21 is a schematic diagram showing a prepreg configuration of Type E. FIG. 22 is a schematic diagram showing a prepreg configuration of Type F. FIG. 23 is a schematic diagram showing a prepreg configuration of Type G. FIG. 24 is a schematic diagram showing a prepreg configuration of Type H. FIG. 25 is a schematic diagram showing a prepreg configuration of Type I. FIG. 26 is a schematic diagram showing a prepreg configuration of Type J. FIG. 27 is a schematic diagram showing a prepreg configuration of Type K. FIG. 28 is a schematic diagram showing a type L prepreg configuration. FIG. 29 is a schematic diagram showing a prepreg configuration of Type M. FIG. 30 is a development view showing the prepreg configuration of Example 5. FIG. 31 is a schematic diagram showing a prepreg configuration of Type N. FIG. 32 is a schematic diagram showing a type O prepreg configuration. FIG. 33 is a development view showing the prepreg configuration of Example 6. FIG. 34 is a schematic diagram showing a type P prepreg configuration. FIG. 35 is a schematic diagram showing a prepreg configuration of Type Q. FIG. 36 is a development view showing the prepreg configuration of Comparative Example 1. FIG. 37 is a development view showing the prepreg configuration of Comparative Example 2. FIG. 38 is a schematic diagram showing a prepreg configuration of Type R. FIG. 39 is a schematic diagram showing a type S prepreg configuration. FIG. 40 is a schematic diagram showing a prepreg configuration of Type T. FIG. 41 is a development view showing the prepreg configuration of Comparative Example 3.

A preferred embodiment will be described in detail below, with reference to the drawings as appropriate.

A badminton racket 2 is shown in Figures 1 and 2. The racket 2 has a shaft 4, a frame 6, a neck 8, a cap 10, a grip 12, and strings 14. In Figures 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 called the in-plane direction. The thickness direction Z is also called the out-of-plane direction.

The shaft 4 is hollow. In FIG. 1, the arrow Ls indicates 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 a zone between the butt end 22 and a position where the distance from the butt end 22 is 44% of the length Ls. The middle 18 is defined as a zone between a position where the distance from the butt end 22 is 44% of the length Ls and a position where the distance from the butt end 22 is 71% of the length Ls. The tip 20 is defined as a zone between a position where the distance from the butt end 22 is 71% of the length Ls and the tip end 24.

The shaft 4 is made of fiber-reinforced resin. This fiber-reinforced resin has a resin matrix and a large number of reinforcing fibers. The shaft 4 includes multiple fiber-reinforced layers (described in more detail below).

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

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

The frame 6 is annular and hollow. The frame 6 is made of fiber-reinforced resin. The same base resin as the base resin of the shaft 4 may be used for this fiber-reinforced resin. The same reinforcing fibers as the reinforcing fibers of the shaft 4 may be used for this fiber-reinforced resin. The frame 6 is firmly connected to the tip end 24 of the shaft 4 via the neck 8. The frame 6 has a top 26 and a bottom 28.

The grip 12 has a hole 30 extending in the axial direction (Y direction). The shaft 4 is inserted near the butt end 22 into this hole 30. The inner circumferential surface of the hole 30 and the outer circumferential surface of the shaft 4 are bonded with an adhesive.

The strings 14 are strung on the frame 6. The strings 14 are strung along the width direction X and the axial direction Y. The portions of the strings 14 that extend along the width direction X are horizontal threads 32. The portions of the strings 14 that extend along the axial direction Y are vertical threads 34. The multiple horizontal threads 32 and multiple vertical threads 34 form a face 36. The face 36 generally extends along the X-Y plane.

Figure 3 is an enlarged cross-sectional view showing a portion of the shaft 4 of the racket 2 in Figure 1. Figure 4 is an enlarged cross-sectional view taken along line IV-IV in Figure 3. As described above, the shaft 4 is hollow. As shown in Figure 4, the cross-sectional shape of the shaft 4 is a circle. In other words, the shaft 4 is cylindrical. No foreign matter is contained inside the shaft 4.

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

In FIG. 4, the symbol SC represents the center point of the shaft 4. In this embodiment, for convenience, the shaft 4 is divided into four 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 spaced in the in-plane direction from the center point SC. The second quarter Q2 is spaced out of the plane from the center point SC. The third quarter Q3 is spaced in the in-plane direction from the center point SC. The fourth quarter Q4 is spaced out of the plane from the center point SC.

As mentioned above, the shaft 4 is made of fiber-reinforced resin. The shaft 4 can be manufactured by the sheet winding method. In this sheet winding method, multiple prepregs are wound around a mandrel.

Figure 5 shows an example of a prepreg 38. This prepreg 38 has multiple fibers 40 and a matrix resin 42. These fibers 40 are parallel to each other. The matrix resin 42 is not cured. The arrow θ in Figure 5 indicates the angle of the fibers 40 with respect to the Y direction.

Figure 6 is an exploded view showing the prepreg configuration for the shaft 4 of the racket 2 in Figure 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 Figure 6 is the axial direction of the shaft 4. In Figure 6, the positions of the butt end 22 and the tip end 24 are indicated by arrows. For ease of explanation, the scale in the left-right direction (axial direction) in Figure 6 does not match the scale in the up-down direction.

The first sheet group S1 includes a single prepreg 44. The prepreg 44 is present throughout the shaft 4. The shape of the prepreg 44 is generally rectangular. The prepreg 44 includes a plurality of carbon fibers arranged in parallel. The extension direction of each carbon fiber is inclined with respect to the axial direction. The angle θ of the carbon fiber is 45°. The tensile modulus E of the carbon fiber is 24 tf/ ^mm2 . The width W of the prepreg 44 is 80 mm.

The second sheet group S2 includes a single prepreg 46. The prepreg 46 is present throughout the shaft 4. The shape of the prepreg 46 is generally rectangular. The prepreg 46 includes a plurality of carbon fibers arranged in parallel. The extension direction of each carbon fiber is inclined with respect to the axial direction. The angle θ of the carbon fiber is −45°. The tensile modulus E of the carbon fiber is 24 tf/ ^mm2 . The width W of the 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 the shaft 4, the first sheet group S1 and the second sheet group S2 form a bias structure.

The third sheet group S3, the fifth sheet group S5, and the seventh sheet group S7 each have a type A prepreg configuration. The type A prepreg configuration will be described in detail later. The fourth sheet group S4, the sixth sheet group S6, and the eighth sheet group S8 each have a type B prepreg configuration. The type B prepreg configuration will be described in detail later.

The ninth sheet group S9 includes a single prepreg 48. The prepreg 48 is present throughout the shaft 4. The shape of the prepreg 48 is generally rectangular. The prepreg 48 includes a plurality of carbon fibers arranged in parallel. The extension direction of each carbon fiber is aligned with the axial direction. The angle θ of the carbon fiber is 0°. The tensile modulus E of the carbon fiber is 7.4 tf/ ^mm2 . The width W of the prepreg 48 is 54 mm.

Figure 7 is an exploded view showing the prepreg configuration of Type A, and Figure 8 is a schematic diagram thereof. 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 third sheet group S3 is approximately 4 mm, in the fifth sheet group S5 is approximately 5 mm, and in the seventh sheet group S7 is approximately 5 mm.

The prepreg A1 is present between the butt end 22 and a position 150 mm away from the butt end 22. The shape of the prepreg A1 is generally rectangular. The prepreg A1 includes a plurality of carbon fibers arranged in parallel. The extension direction of each carbon fiber is aligned with the axial direction. The angle θ of the carbon fiber is 0°. The tensile modulus E of the carbon fiber is 7.4 f/ ^mm2 . The prepreg A1 is present in the first quarter Q1.

The prepreg A2 is present between a position 150 mm away from the butt end 22 and a position 340 mm away from the butt end 22. The shape of the prepreg A2 is generally rectangular. The prepreg A2 includes a plurality of carbon fibers arranged in parallel. The extension direction of each carbon fiber is aligned with the axial direction. The angle θ of the carbon fiber is 0°. The tensile modulus E of the carbon fiber is 55 f/ ^mm2 . The prepreg A2 is present in the first quarter Q1.

The prepreg A3 is present between the butt end 22 and a position 240 mm away from the butt end 22. The shape of the prepreg A3 is generally rectangular. The prepreg A3 includes a plurality of carbon fibers arranged in parallel. The extension direction of each carbon fiber is aligned with the axial direction. The angle θ of the carbon fiber is 0°. The tensile modulus E of the carbon fiber is 55 tf/ ^mm2 . The prepreg A3 is present in the second quarter Q2.

The prepreg A4 is present between a position that is 240 mm away from the butt end 22 and a position that is 340 mm away from the butt end 22. The shape of the prepreg A4 is generally rectangular. The prepreg A4 includes a plurality of carbon fibers arranged in parallel. The extension direction of each carbon fiber is aligned with the axial direction. The angle θ of the carbon fiber is 0°. The tensile modulus E of the carbon fiber is 7.4 tf/ ^mm2 . The prepreg A4 is present in the second quarter Q2.

The prepreg A5 is present between the butt end 22 and a position 150 mm away from the butt end 22. The shape of the prepreg A5 is generally rectangular. The prepreg A5 includes a plurality of carbon fibers arranged in parallel. The extension direction of each carbon fiber is aligned with the axial direction. The angle θ of the carbon fiber is 0°. The tensile modulus E of the carbon fiber is 7.4 tf/ ^mm2 . The prepreg A5 is present in the third quarter Q3.

The prepreg A6 is present between a position 150 mm away from the butt end 22 and a position 340 mm away from the butt end 22. The shape of the prepreg A6 is generally rectangular. The prepreg A6 includes a plurality of carbon fibers arranged in parallel. The extension direction of each carbon fiber is aligned with the axial direction. The angle θ of the carbon fiber is 0°. The tensile modulus E of the carbon fiber is 55 tf/ ^mm2 . The prepreg A6 is present in the third quarter Q3.

The prepreg A7 is present between the butt end 22 and a position 240 mm away from the butt end 22. The shape of the prepreg A7 is generally rectangular. The prepreg A7 includes a plurality of carbon fibers arranged in parallel. The extension direction of each carbon fiber is aligned with the axial direction. The angle θ of the carbon fiber is 0°. The tensile modulus E of the carbon fiber is 55 tf/ ^mm2 . The prepreg A7 is present in the fourth quarter Q4.

The prepreg A8 is present between a position that is 240 mm away from the butt end 22 and a position that is 340 mm away from the butt end 22. The shape of the prepreg A8 is generally rectangular. The prepreg A8 includes a plurality of carbon fibers arranged in parallel. The extension direction of each carbon fiber is aligned with the axial direction. The angle θ of the carbon fiber is 0°. The tensile modulus E of the carbon fiber is 7.4 tf/ ^mm2 . The prepreg A8 is present in the fourth quarter Q4.

The shaft 4 is shown in FIG. 9-12. The cross section of the third sheet group S3 is shown in FIG. 9-12. The other sheet groups are not shown. As mentioned above, the third sheet group S3 has a type A prepreg structure.

As shown in Figure 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.

As shown in Figures 9-12, prepreg A1 is present in pad 16, prepreg A2 is present from middle 18 to tip 20, prepreg A3 is present from pad 16 to middle 18, prepreg A4 is present at tip 20, prepreg A5 is present in pad 16, prepreg A6 is present from middle 18 to tip 20, prepreg A7 is present from pad 16 to middle 18, and prepreg A8 is present at tip 20.

Figure 13 is a schematic diagram showing a 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 approximately 4 mm, this width in the sixth sheet group S6 is approximately 5 mm, and this width in the eighth sheet group S8 is approximately 6 mm.

The prepreg B1 is present between the butt end 22 (see FIG. 2) and a position 240 mm away from the butt end 22. The shape of the prepreg B1 is generally rectangular. The prepreg B1 includes a plurality of carbon fibers arranged in parallel. The extension direction of each carbon fiber is aligned with the axial direction. The angle θ of the carbon fiber is 0°. The tensile modulus E of the carbon fiber is 7.4 tf/ ^mm2 . The prepreg B1 is present in the first quarter Q1.

The prepreg B2 is present between a position that is 240 mm away from the butt end 22 and a position that is 340 mm away from the butt end 22. The shape of the prepreg B2 is generally rectangular. The prepreg B2 includes a plurality of carbon fibers arranged in parallel. The extension direction of each carbon fiber is aligned with the axial direction. The angle θ of the carbon fiber is 0°. The tensile modulus E of the carbon fiber is 55 tf/ ^mm2 . The prepreg B2 is present in the first quarter Q1.

The prepreg B3 is present between the butt end 22 and a position 150 mm away from the butt end 22. The shape of the prepreg B3 is generally rectangular. The prepreg B3 includes a plurality of carbon fibers arranged in parallel. The extension direction of each carbon fiber is aligned with the axial direction. The angle θ of the carbon fiber is 0°. The tensile modulus E of the carbon fiber is 55 tf/ ^mm2 . The prepreg B3 is present in the second quarter Q2.

The prepreg B4 is present between a position 150 mm away from the butt end 22 and a position 340 mm away from the butt end 22. The shape of the prepreg B4 is generally rectangular. The prepreg B4 includes a plurality of carbon fibers arranged in parallel. The extension direction of each carbon fiber is aligned with the axial direction. The angle θ of the carbon fiber is 0°. The tensile modulus E of the carbon fiber is 7.4 tf/ ^mm2 . The prepreg B4 is present in the second quarter Q2.

The prepreg B5 is present between the butt end 22 and a position 240 mm away from the butt end 22. The shape of the prepreg B5 is generally rectangular. The prepreg B5 includes a plurality of carbon fibers arranged in parallel. The extension direction of each carbon fiber is aligned with the axial direction. The angle θ of the carbon fiber is 0°. The tensile modulus E of the carbon fiber is 7.4 tf/ ^mm2 . The prepreg B5 is present in the third quarter Q3.

The prepreg B6 is present between a position that is 240 mm away from the butt end 22 and a position that is 340 mm away from the butt end 22. The shape of the prepreg B6 is generally rectangular. The prepreg B6 includes a plurality of carbon fibers arranged in parallel. The extension direction of each carbon fiber is aligned with the axial direction. The angle θ of the carbon fiber is 0°. The tensile modulus E of the carbon fiber is 55 tf/ ^mm2 . The prepreg B6 is present in the third quarter Q3.

The prepreg B7 is present between the butt end 22 and a position 150 mm away from the butt end 22. The shape of the prepreg B7 is generally rectangular. The prepreg B7 includes a plurality of carbon fibers arranged in parallel. The extension direction of each carbon fiber is aligned with the axial direction. The angle θ of the carbon fiber is 0°. The tensile modulus E of the carbon fiber is 55 tf/ ^mm2 . The prepreg B7 is present in the fourth quarter Q4.

The prepreg B8 is present between a position 150 mm away from the butt end 22 and a position 340 mm away from the butt end 22. The shape of the prepreg B8 is generally rectangular. The prepreg B8 includes a plurality of carbon fibers arranged in parallel. The extension direction of each carbon fiber is aligned with the axial direction. The angle θ of the carbon fiber is 0°. The tensile modulus E of the carbon fiber is 7.4 tf/ ^mm2 . The prepreg B8 is present in the fourth quarter Q4.

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.

Prepreg B1 is present from pad 16 to middle 18, prepreg B2 is present at tip 20, prepreg B3 is present at pad 16, prepreg B4 is present from middle 18 to tip 20, prepreg B5 is present from pad 16 to middle 18, prepreg B6 is present at tip 20, prepreg B7 is present at pad 16, and prepreg B8 is present from middle 18 to tip 20.

In the prepreg configuration of Type A, prepregs A1, A2, A5, and A6 are spaced apart 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 spaced apart in the in-plane direction from the center point SC. The tensile modulus E of the carbon fibers contained in prepregs A1, A5, B1, and B5 is small, and the tensile modulus E of the carbon fibers contained in prepregs A2, A6, B2, and B6 is large. The modulus E of each carbon fiber affects the bending rigidity of shaft 4. This shaft 4 satisfies the following 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

In a prepreg configuration of Type A, prepregs A3, A4, A7, and A8 are spaced apart in the out-of-plane direction from the center point SC. In a prepreg configuration of Type B, prepregs B3, B4, B7, and B8 are spaced apart in the out-of-plane direction from the center point SC. The tensile modulus E of the carbon fibers contained in prepregs A3, A7, B3, and B7 is large, and the tensile modulus E of the carbon fibers contained in prepregs A4, A8, B4, and B8 is small. The modulus E of each carbon fiber affects the bending rigidity of shaft 4. This shaft 4 satisfies the following formula.

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

The shaft 4 further has the following formula in the butt 16:
RiB < RoB
The shaft 4 further comprises the following formula at the tip 20:
ＲｉＴ ＞ ＲｏＴ

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

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 are present from the butt end 22 to the tip end 24. These sheet groups can contribute to the durability of the shaft 4.

In the manufacture of this shaft 4, the sheets shown in FIG. 6 are wound in sequence around a mandrel. Other sheets may be wound around the mandrel along with these sheets. Examples of other sheets include those containing glass fiber. These sheets are then wrapped with wrapping tape. The mandrel, prepregs (sheet group S1-S9), and wrapping tape are heated in an oven or the like. The heating causes the resin in the matrix to flow. Further heating causes the resin to undergo a curing reaction, resulting in a molded body. This molded body is then subjected to end surface processing, polishing, painting, and other processes to complete the shaft 4.

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

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

As shown in FIG. 14, an acceleration pickup 52 is attached to the racket 2. The acceleration pickup 52 is located at the tip of the grip 12. The acceleration pickup 52 is oriented in the Z direction. The acceleration pickup 52 has a mass of 3.5 g. A point Ph on the grip 12 opposite 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 (Hewlett-Packard's "Dynamic Signal Analyzer") via an amplifier. The out-of-plane natural frequency is calculated based on the transfer function obtained by this device. The direction of the out-of-plane natural frequency 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 is measured under free constraint conditions.

Fig. 15 is a graph showing the results obtained from the measurement of Fig. 14. In Fig. 15, the horizontal axis is frequency (Hz) and the vertical axis is acceleration (m/ ^s2 /N). In Fig. 15, the reference symbol P1 indicates a primary peak. The frequency at this primary peak P1 is the out-of-plane primary natural frequency ωo1. In Fig. 15, the reference symbol P2 indicates a secondary peak. The frequency at this secondary peak P2 is the out-of-plane secondary natural frequency ωo2.

Figure 16 is an explanatory diagram showing a method for measuring the frequency of the natural vibration in the in-plane direction of the racket 2. In this measurement method, the racket 2 is suspended by a string 50, as in the measurement method shown in Figure 14. As shown in Figure 16, the direction of the acceleration pickup 52 is the X direction. A point Ph of the grip 12 facing 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 (Hewlett-Packard's "Dynamic Signal Analyzer") via an amplifier. The frequency of the natural vibration in the plane is calculated based on the transfer function obtained by this device. The direction of the natural vibration in the plane is mainly the X direction. In this method, the natural vibration in the plane is measured under free constraint conditions.

Fig. 17 is a graph showing the results obtained from the measurement of Fig. 16. In Fig. 17, the horizontal axis is frequency (Hz) and the vertical axis is acceleration (m/ ^s2 /N). In Fig. 17, the reference symbol P1 indicates a primary peak. The frequency at this primary peak P1 is the in-plane primary natural frequency ωi1. In Fig. 17, the reference symbol P2 indicates a secondary peak. The frequency at this secondary peak P2 is the in-plane secondary natural frequency ωi2.

Figure 18 is a graph showing the relationship between the ratio (ωo2/ωo1) and the ratio (ωi2/ωi1) of the badminton racket 2. In this graph, the symbol Pr represents the point of the racket 2 shown in Figure 1-5.

The straight line indicated by the symbol L1 in FIG.
(ωi2/ωi1) = 1.3 * (ωo2/ωo1) - 0.6
18, the point Pr is located below the straight line L1. In other words, the coordinates ((ωo2/ωo1), (ωi2/ωi1)) of the racket 2 satisfy the following formula (1).
(ωi2/ωi1) ≦ 1.3 * (ωo2/ωo1) - 0.6 (1)
According to the knowledge obtained by the inventor, the racket 2 satisfying this formula (1) is suitable for lobbing and cut smashes. A player who uses this racket 2 for lobbing or cut smashes can easily achieve the intended trajectory of the shuttlecock. With this racket 2, the trajectory of the shuttlecock in lobbing has little variation, and the trajectory of the shuttlecock in cut smashes also has little variation.

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

According to the knowledge obtained by the inventor regarding vibrations in the out-of-plane direction, when the shuttle is hit on the part of the face 36 closer to the bottom 28, vibrations in the out-of-plane secondary mode are mainly excited. According to the knowledge obtained by the inventor, when the shuttle is hit on the part of the face 36 closer to the top 26, vibrations in the out-of-plane primary mode are mainly excited. The typical impact point in lobbing is closer to the top 26. Therefore, in lobbing, vibrations in the out-of-plane primary mode are mainly excited. However, even in lobbing, the impact point varies. In a 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 knowledge obtained by the inventor, in lobbing with a racket 2 with a small out-of-plane primary natural frequency ωo1 and a large out-of-plane secondary natural frequency ωo2, even if the impact point varies, the initial velocity of the shuttle is small. The reason is that the repulsion of the racket 2 is not extremely small even if the shuttle is hit at a position that is different from the intended position. Since there is little variation in the initial speed of the shuttle, there is also little variation in the trajectory of the shuttle. This racket 2 is suitable for players who make heavy use of lobbing. This racket 2 is also suitable for players who place importance on lobbing.

As mentioned above, the typical impact point for lobbing is closer to the top 26. This racket 2 is also suitable for shots other than lobbing, in which the shuttlecock is hit on a part of the face 36 closer to the top 26.

According to the knowledge obtained by the inventor regarding vibration in the in-plane direction, when the shuttle is hit on the part of the face 36 closer to the bottom 28, vibration in the in-plane secondary mode is mainly excited. According to the knowledge obtained by the inventor, when the shuttle is hit on the part of the face 36 closer to the top 26, vibration in the in-plane primary mode is mainly excited. The typical impact point in a cut smash is closer to the bottom 28. Therefore, in a cut smash, vibration in the in-plane secondary mode is mainly excited. However, even in a cut smash, the impact point varies. In a racket 2 with a small ratio (ωi2/ωi1), the in-plane primary natural frequency ωi1 is relatively large and the in-plane secondary natural frequency ωi2 is relatively small. According to the knowledge obtained by the inventor, in a cut smash with a racket 2 with a large in-plane primary natural frequency ωi1 and a small in-plane secondary natural frequency ωi2, even if the impact point varies, the initial velocity of the shuttle is small. The reason is that the repulsion of the racket 2 is not extremely small even if the shuttle is hit at a position that is different from the intended position. Since there is little variation in the initial speed of the shuttle, there is also little variation in the shuttle's trajectory. This racket 2 is suitable for players who make heavy use of cut smashes. This racket 2 is also suitable for players who place importance on cut smashes.

As mentioned above, the typical impact point in a cut smash is closer to the bottom 28. The racket 2 according to the present invention is also suitable for shots other than cut smashes in which the shuttlecock is hit on the part of the face 36 closer to the bottom 28 and involves a cut.

As described above, in this shaft 4, the in-plane bending stiffness of the tip 20 is greater than the in-plane bending stiffness of the butt 16, and the out-of-plane bending stiffness of the tip 20 is less than the out-of-plane bending stiffness of the butt 16. In a badminton racket 2 having this shaft 4, the above formula (1) can be achieved.

Another way to achieve the above formula (1) is to adjust the stiffness distribution of the frame 6. A frame 6 that has low in-plane bending stiffness and high out-of-plane bending stiffness near the bottom 28 can contribute to achieving the above formula (1).

Other examples of means for achieving the above formula (1) include adjusting the stiffness distribution of the entire racket 2, adjusting the mass distribution of the shaft 4, adjusting the mass distribution of the frame 6, adjusting the mass distribution of the entire racket 2, adjusting the volume distribution of the shaft 4, adjusting the volume distribution of the frame 6, and adjusting the volume distribution of the entire racket 2.

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

The straight line indicated by the symbol L2 in FIG.
(ωi2/ωi1) = 1.14 * (ωo2/ωo1) - 0.187
18, the point Pr is located below the straight line L2. In other words, the coordinates ((ωo2/ωo1), (ωi2/ωi1)) of the racket 2 satisfy the following formula (2).
(ωi2/ωi1) ≦ 1.14 * (ωo2/ωo1) - 0.187 (2)
According to the knowledge obtained by the inventor, the racket 2 satisfying this formula (2) is suitable for lobbing and cut smashes. A player who uses this racket 2 for lobbing or cut smashes can easily achieve the intended trajectory of the shuttlecock. With this racket 2, the trajectory of the shuttlecock in lobbing has little variation, and the trajectory of the shuttlecock in cut smashes also has little variation.

The straight line indicated by the symbol L3 in FIG.
(ωi2/ωi1) = 1.08 * (ωo2/ωo1) - 0.112
18, the point Pr is located below the straight line L3. In other words, the coordinates ((ωo2/ωo1), (ωi2/ωi1)) of the racket 2 satisfy the following formula (3).
(ωi2/ωi1) ≦ 1.08 * (ωo2/ωo1) - 0.112 (3)
According to the findings of the inventors, the racket 2 satisfying this formula (3) is suitable for lobbing and cut smashes. A player who uses this racket 2 for lobbing or cut smashes can easily achieve the intended trajectory of the shuttlecock. With this racket 2, the trajectory of the shuttlecock varies little in lobbing, and the trajectory of the shuttlecock varies little in cut smashes.

The straight line indicated by the symbol L4 in FIG.
(ωo2/ωo1) = 3.12
As shown in Fig. 18, point Pr is located to the right of line L4. In other words, the ratio (ωo2/ωo1) of point Pr is equal to or greater than 3.12. This racket 2 is suitable for lobbing. In this respect, the ratio (ωo2/ωo1) is more preferably equal to or greater than 3.19, and particularly preferably equal to or greater than 3.25. The ratio (ωo2/ωo1) is preferably equal to or less than 3.80.

The straight line indicated by the symbol L5 in FIG.
(ωi2/ωi1) = 3.45
18, the point Pr is located below the straight line L5. In other words, the ratio (ωi2/ωi1) of the point Pr is equal to or less than 3.45. This racket 2 is suitable for cut smashes. In this respect, the ratio (ωi2/ωi1) is more preferably equal to or less than 3.42, and particularly preferably equal to or less than 3.39. The ratio (ωi2/ωi1) is preferably equal to or greater than 2.80.

A method for determining the preferable specifications of the badminton racket 2 will be described below.
(A) 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) determining whether or not the above-mentioned formula (1) is satisfied based on these natural frequencies ωo1, ωo2, ωi1, and ωi2;
and (C) if formula (1) is not satisfied, determining the characteristics of the shaft 4 or frame 6 of the target racket 2 so as to have a ratio (ωo2/ωo1) greater than that of the standard racket.

Examples of the characteristics determined in step (C) include the length of shaft 4, the thickness of shaft 4, the stiffness of shaft 4, the stiffness distribution of shaft 4, the length of frame 6, the thickness of frame 6, the stiffness of frame 6, and the stiffness distribution of frame 6.

Another preferred method for determining the specifications is
(A) 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) determining whether or not the above-mentioned formula (1) is satisfied based on these natural frequencies ωo1, ωo2, ωi1, and ωi2;
and (C) determining the characteristics of the shaft 4 or frame 6 of the target racket 2 so as to have a ratio (ωi2/ωi1) smaller than that of the standard racket if the following formula (1) is not satisfied.

Examples of the characteristics determined in step (C) include the length of shaft 4, the thickness of shaft 4, the stiffness of shaft 4, the stiffness distribution of shaft 4, the length of frame 6, the thickness of frame 6, the stiffness of frame 6, and the stiffness distribution of frame 6.

The effects of the badminton racket according to the embodiment will be explained below, but the scope of the disclosure in this specification should not be interpreted as being limited based on the description of this embodiment.

[Example 1]
The badminton racket shown in Fig. 1-13 was manufactured. The out-of-plane primary natural frequency ωo1 of this racket was 54 Hz, the out-of-plane secondary natural frequency ωo2 was 180 Hz, the in-plane primary natural frequency ωi1 was 59 Hz, and the in-plane secondary natural frequency ωi2 was 202 Hz. The coordinates of this racket are indicated by the symbol Pr in Fig. 18.

[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 prepreg configuration of Type C was adopted for sheet groups S3-S8. In this shaft, a prepreg having a fiber tensile modulus E of 24 tf/ ^mm2 was further adopted for the ninth sheet group S9. The prepreg configuration of Type C is shown in FIG.

[Example 3]
A badminton racket was obtained in the same manner as in Example 1, except that the prepreg structure of the shaft was changed. In this shaft, the following type of prepreg structure 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 Figures 20 to 24. Furthermore, in this shaft, a prepreg having a fiber elastic modulus of 16 tf/ ^mm2 was used for the ninth sheet group S9.

[Example 4]
A badminton racket was obtained in the same manner as in Example 1, except that the prepreg structure of the shaft was changed. In this shaft, the following type of prepreg structure 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 Figures 25 to 29. Furthermore, in this shaft, a prepreg having a fiber elastic modulus of 12 tf/ ^mm2 was used for the ninth sheet group S9.

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

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

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

[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 Figure 37. The prepreg configuration of Type R is shown in Figure 38. The prepreg configuration of Type S is shown in Figure 39. The prepreg configuration of Type T is shown in Figure 40.

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

[Robbing]
A shuttlecock was launched from a launching machine. A player lobbed the shuttlecock, and the trajectory of the shuttlecock was photographed. The image was analyzed to measure the height of the shuttlecock as it passed over the net. Twenty measurements were taken, and the standard deviation of the height was calculated. Based on this standard deviation, the rackets were rated. The grading criteria are as follows. The results are shown in Tables 1 and 2 below.
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

[Cut Smash]
A shuttlecock was launched from a launching machine. A player performed a cut smash on the shuttlecock, and the trajectory of the shuttlecock was photographed. The image was analyzed to measure the height of the shuttlecock as it passed over the net. Twenty measurements were taken, and the standard deviation of the height was calculated. Based on this standard deviation, the rackets were rated. The grading criteria are as follows. The results are shown in Tables 1 and 2 below.
3: Standard deviation is less than 0.06 m 2: Standard deviation is 0.06 m or more and less than 0.10 m 1: Standard deviation is 0.10 m or more

As is clear from Tables 1 and 2, the badminton rackets of each embodiment were rated "3" or "2" for lob stability, and "3" or "2" for cut smash stability. On the other hand, the rackets of each comparative example were rated "1" for lob stability or cut smash stability. From these results, the superiority of this badminton racket is clear.

[Disclosure items]
Each of the following sections is a disclosure of a preferred embodiment.

[Item 1]
a shaft having a butt and a tip;
a grip attached to the shaft of the bat;
and a frame attached to the shaft at the tip,
A badminton racket in which a ratio (ωo2/ωo1) of the out-of-plane secondary natural frequency ωo2 (Hz) to the out-of-plane primary natural frequency ωo1 (Hz) and a 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) - 0.6 (1)

[Item 2]
A badminton racket according to item 1, which satisfies the following formula (2).
(ωi2/ωi1) ≦ 1.14 * (ωo2/ωo1) - 0.187 (2)

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

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

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

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

[Item 7]
7. The badminton racket according to item 6, wherein in the bat, the tensile modulus of reinforcing fibers included in a zone away from the center point of the shaft in an in-plane direction is smaller than the tensile modulus of reinforcing fibers included in a zone away from the center point of the shaft in an out-of-plane direction.

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

[Item 9]
9. A badminton racket according to any one of items 6 to 8, wherein in a zone away from the center point of the shaft in an in-plane direction, the tensile modulus of elasticity of the reinforcing fibers included in the butt is smaller than the tensile modulus of elasticity of the reinforcing fibers included in the tip.

[Item 10]
10. A badminton racket according to any one of items 6 to 9, wherein in a zone away from the center point of the shaft in the out-of-plane direction, the tensile modulus of elasticity of the reinforcing fibers included in the butt is greater than the tensile modulus of elasticity of the reinforcing fibers included in the tip.

[Item 11]
a shaft having a butt and a tip;
a grip attached to the shaft of the bat;
and A method for determining specifications for a badminton racket having a frame attached to the shaft at the tip, comprising the steps of:
(A) 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) determining whether or not the following formula (1) is satisfied based on these natural frequencies ωo1, ωo2, ωi1, and ωi2;
and (C) a method for determining specifications for a badminton racket, the method including the step of determining characteristics of a shaft or frame of a target racket so that it has a ratio (ωo2/ωo1) greater than that of a standard racket if the following formula (1) is not satisfied:
(ωi2/ωi1) ≦ 1.3 * (ωo2/ωo1) - 0.6 (1)

[Item 12]
a shaft having a butt and a tip;
a grip attached to the shaft of the bat;
and A method for determining specifications for a badminton racket having a frame attached to the shaft at the tip, comprising the steps of:
(A) 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) determining whether or not the following formula (1) is satisfied based on these natural frequencies ωo1, ωo2, ωi1, and ωi2;
and (C) a method for determining specifications for a badminton racket, the method including a step of determining characteristics of a shaft or frame of a target racket so that the target racket has a ratio (ωi2/ωi1) smaller than the ratio of a standard racket if the following mathematical formula (1) is not satisfied.
(ωi2/ωi1) ≦ 1.3 * (ωo2/ωo1) - 0.6 (1)

The badminton racket described above is suitable for players who use a style that makes heavy use of smashes and cut lobs. This racket is also suitable for players who use a style that makes heavy use of other shots with a bottom-up impact point and other shots with a top-up impact point and cuts.

Reference Signs List 2: Badminton racket 4: Shaft 6: Frame 8: Neck 10: Cap 12: Grip 14: String 16: Butt 18: Middle 20: Tip 22: Butt 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 (8)

a shaft having a butt and a tip;
a grip attached to the shaft of the bat;
and a frame attached to the shaft at the tip,
The shaft is made of a fiber-reinforced resin containing a plurality of reinforcing fibers,
In the butt, the tensile modulus of elasticity of the reinforcing fibers included in a zone away from the center point of the shaft in an in-plane direction is smaller than the tensile modulus of elasticity of the reinforcing fibers included in a zone away from the center point of the shaft in an out-of-plane direction,
A badminton racket in which a ratio (ωo2/ωo1) of the out-of-plane secondary natural frequency ωo2 (Hz) to the out-of-plane primary natural frequency ωo1 (Hz) and a 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) - 0.6 (1) a shaft having a butt and a tip;
a grip attached to the shaft of the bat;
and
a frame attached to the shaft at the tip
Equipped with
The shaft is made of a fiber-reinforced resin containing a plurality of reinforcing fibers,
In the tip, the tensile modulus of reinforcing fibers included in a zone away from the center point of the shaft in an in-plane direction is greater than the tensile modulus of reinforcing fibers included in a zone away from the center point of the shaft in an out-of-plane direction;
A badminton racket in which a ratio (ωo2/ωo1) of the out-of-plane secondary natural frequency ωo2 (Hz) to the out-of-plane primary natural frequency ωo1 (Hz) and a 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) - 0.6 (1) a shaft having a butt and a tip;
a grip attached to the shaft of the bat;
and
a frame attached to the shaft at the tip
Equipped with
The shaft is made of a fiber-reinforced resin containing a plurality of reinforcing fibers,
In a zone away from a center point of the shaft in an in-plane direction, the tensile modulus of elasticity of the reinforcing fiber included in the butt is smaller than the tensile modulus of elasticity of the reinforcing fiber included in the tip;
A badminton racket in which a ratio (ωo2/ωo1) of the out-of-plane secondary natural frequency ωo2 (Hz) to the out-of-plane primary natural frequency ωo1 (Hz) and a 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) - 0.6 (1) a shaft having a butt and a tip;
a grip attached to the shaft of the bat;
and
a frame attached to the shaft at the tip
Equipped with
The shaft is made of a fiber-reinforced resin containing a plurality of reinforcing fibers,
In a zone away from the center point of the shaft in an out-of-plane direction, the tensile modulus of elasticity of the reinforcing fiber included in the butt is greater than the tensile modulus of elasticity of the reinforcing fiber included in the tip;
A badminton racket in which a ratio (ωo2/ωo1) of the out-of-plane secondary natural frequency ωo2 (Hz) to the out-of-plane primary natural frequency ωo1 (Hz) and a 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) - 0.6 (1) 5. A badminton racket according to claim 1, which satisfies the following formula (2).
(ωi2/ωi1) ≦ 1.14 * (ωo2/ωo1) - 0.187 (2) 5. A badminton racket according to claim 1, which satisfies the following formula (3).
(ωi2/ωi1) ≦ 1.08 * (ωo2/ωo1) - 0.112 (3) 7. The badminton racket according to claim 1 , wherein the ratio (ωo2/ωo1) is 3.12 or greater. A 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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