Tennis Racket Stiffness Tuning for Spin and Face Stability
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Solution Overview
Problem
Existing tennis rackets fail to achieve an optimal balance among repulsion performance, spin performance, and face stability, which are crucial for enhancing player performance.
Innovation Solution
The racket design incorporates specific stiffness indices and moment of inertia parameters, including an in-plane stiffness index Gi ≥ 1.40, out-of-plane stiffness index Go of 60000 to 85000, moment of inertia Mi of 13500 to 15000 g·cm², and index of inertia Ii ≥ 0.150, achieved through a combination of fiber reinforced resin and reinforcement fibers with controlled inclination angles.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Speed
If the racket design prioritizes repulsion performance through high stiffness values, then ball speed improves, but face stability and spin performance deteriorate
Solution Approach 1:
The patent applies parameter changes by precisely controlling the in-plane stiffness index Gi within 1.05-1.35 and out-of-plane stiffness index Go within 50000-70000. These specific parameter ranges optimize the balance between repulsion (ball speed) and face stability, preventing excessive stiffness that would harm stability while maintaining sufficient stiffness for speed.
Solution Approach 2:
The patent uses composite materials consisting of fiber reinforced resin with reinforcement fibers arranged at specific inclination angles (10°-30° from the longitudinal direction). This composite structure allows simultaneous optimization of in-plane and out-of-plane stiffness properties, achieving both repulsion performance and face stability that cannot be obtained with single materials.
2Power
If the racket design increases stiffness for better repulsion, then kinetic energy transfer improves, but spin performance and control deteriorate
Solution Approach 1:
The patent controls the in-plane stiffness index Gi within 1.05-1.35 to optimize kinetic energy transfer while maintaining spin performance. This parameter range ensures sufficient stiffness for power transfer but prevents excessive stiffness that would reduce string deformation and spin generation capability.
Solution Approach 2:
The fiber reinforced resin composite with controlled fiber inclination angles (10°-30°) provides optimized stiffness characteristics that enable both effective kinetic energy transfer for power and sufficient flexibility for spin generation, resolving the contradiction between power and ease of operation.
3Speed
If the racket uses higher stiffness values for improved repulsion, then ball flying speed increases, but the balance with spin performance and face stability is lost
Solution Approach 1:
The patent simultaneously controls multiple parameters: in-plane stiffness index Gi (1.05-1.35), out-of-plane stiffness index Go (50000-70000), and reinforcement fiber inclination angles (10°-30°). This multi-parameter optimization ensures balanced performance across repulsion (ball speed), face stability, and spin performance, preventing over-optimization of any single attribute.
Solution Approach 2:
The fiber reinforced resin composite structure with specifically oriented reinforcement fibers enables simultaneous optimization of multiple performance attributes. The composite material provides anisotropic stiffness properties that can be tuned to achieve balanced repulsion, stability, and spin performance that homogeneous materials cannot provide.
Data Source
AI summary
A racket 2 includes a frame 4, a grip 6, a grommet 10, and a string 12. In the racket 2, an in-plane stiffness index Gi, which is a ratio of a top pressure stiffness value Git (kgf/cm) to a side pressure stiffness value Gis (kgf/cm), is 1.40 or greater; an out-of-plane stiffness index Go, which is a product of a throat stiffness value Gos (kgf/cm) and a ball-hitting face stiffness value Goh (kgf/cm), is from 60000 to 85000; a moment of inertia Mi about an axis of the racket 2 is from 13500 g·cm2 to 15000 g·cm2; and an index of inertia Ii is 0.150 or greater, which is calculated by the following mathematical formula: Ii=Mi/(Wr·Lc) (where Wr is a mass (g) of the racket, and Lc is a distance (mm) from a grip end to a center of gravity of the racket).