Golf Ball Dimple Surface Using Bessel Function Modes
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Solution Overview
Problem
Conventional golf ball dimple designs do not effectively utilize advanced mathematical models to optimize aerodynamic performance and aesthetic appeal, limiting their ability to reduce drag and enhance flight stability.
Innovation Solution
The dimples are designed using modes or weighted superpositions of oscillations of a circular membrane, defined by Bessel functions, which create unique surface shapes that extend over the dimple diameter, allowing for customizable shapes and patterns that reduce drag and enhance aerodynamics.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Ease of manufacture
If conventional dimple designs are used, then manufacturing simplicity is maintained, but aerodynamic performance and drag reduction are limited
Solution Approach 1:
The patent applies parameter changes by transitioning from conventional simple dimple geometries to complex Bessel function-defined surfaces. The dimple shape is characterized by mathematical parameters including Bessel function order, amplitude, and phase, allowing precise control of surface geometry to optimize aerodynamic performance while maintaining manufacturing feasibility through injection molding processes.
2Object-affected harmful factors
If advanced Bessel function-based dimple surfaces are implemented, then aerodynamic performance and drag reduction are improved, but design complexity increases
Solution Approach 1:
The patent replaces traditional mechanical/geometric design approaches with mathematical field theory. Bessel functions provide a systematic framework to describe and generate optimal dimple surfaces, substituting empirical shape modification with analytically-driven surface definition. This mathematical substitution enables precise control of aerodynamic characteristics through parameter optimization rather than trial-and-error geometric adjustment.
Solution Approach 2:
The Bessel function-based dimple design provides universality by offering a single mathematical framework that can generate multiple dimple variations through parameter adjustment. The same Bessel function formulation can produce different dimple patterns, depths, and distributions across the golf ball surface, allowing one design system to address multiple aerodynamic requirements simultaneously.
3Shape
If Bessel function-based dimple shapes are used, then unique aesthetic characteristics are achieved, but manufacturing precision requirements increase
Solution Approach 1:
The patent applies preliminary action by pre-defining the dimple surface geometry through mathematical Bessel function equations before the manufacturing process. The injection mold is designed with pre-calculated Bessel function parameters, allowing the complex surface geometry to be replicated with high precision through a single-shot molding process. This preliminary mathematical definition eliminates the need for post-manufacturing adjustments and ensures consistent reproduction of the optimal surface shape.
Applied Scientific Principles
This section explains which scientific principles are used to turn an abstract innovation direction into a practical engineering solution.
Function Achieved in This Case
This approach results in golf balls with improved aerodynamic performance and aesthetic characteristics, reducing drag and enhancing flight stability by creating a turbulent boundary layer that increases pressure behind the ball.
Implementation Method 1
The dimples on a golf ball create a turbulent boundary layer around the ball. The turbulence energizes the boundary layer and helps it stay attached further around the ball to reduce the area of the wake.
Implementation Method 2
The dimples on a golf ball create a turbulent boundary layer around the ball. The turbulence energizes the boundary layer and helps it stay attached further around the ball.
Data Source
AI summary
Golf ball dimples having a surface defined by a mode, or a weighted superposition of multiple modes, of oscillation of a circular membrane are disclosed.