Golf Ball Dimple Patterns Using Irregular Polyhedron Tessellation
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Solution Overview
Problem
Existing golf ball dimple patterns struggle to achieve optimal aerodynamic efficiency and symmetry, with limited geometric shapes leading to suboptimal surface coverage and disadvantageous arrangements, making it difficult to devise new symmetric patterns that improve aerodynamic properties.
Innovation Solution
The method involves generating irregular domains based on polyhedrons, packing these domains with dimples, and tessellating them onto the golf ball surface using techniques like the midpoint to midpoint method, ensuring uniform patterns and preserving symmetry, which allows for greater flexibility in dimple arrangement and minimizes the appearance of parting lines.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Ease of manufacture
If traditional geometric shapes (circles, hexagons, triangles) are used for dimple patterns, then manufacturing is simple, but surface coverage is suboptimal and aerodynamic efficiency is limited
Solution Approach 1:
The patent transforms the dimple pattern from traditional geometric shapes to irregular domains generated through mathematical transformations of polyhedron vertices. This parameter change in the geometric configuration allows for optimized surface coverage and aerodynamic performance while maintaining manufacturability through systematic generation methods.
Solution Approach 2:
The patent employs three-dimensional polyhedron structures (tetrahedron, octahedron, icosahedron) as the basis for generating two-dimensional dimple patterns. By projecting and transforming 3D vertex coordinates onto the spherical surface, the method achieves superior surface coverage and aerodynamic characteristics that cannot be obtained with traditional 2D geometric approaches.
2Reliability
If symmetric geometric patterns are used, then aerodynamic symmetry is achieved, but the appearance of parting lines is prominent
Solution Approach 1:
The patent introduces asymmetry within the symmetric framework by using irregular domains with non-uniform dimple arrangements. While the overall pattern maintains rotational symmetry for aerodynamic stability, the local irregularity within each domain disrupts the visual continuity of parting lines, making them less apparent.
Solution Approach 2:
The patent applies different dimple configurations within different domains while maintaining overall symmetry. Each irregular domain has unique dimple placements and sizes, creating local variation that masks parting lines, while the global symmetric arrangement preserves aerodynamic reliability.
3Reliability
If regular polyhedron-based patterns are used, then symmetry is improved, but flexibility in dimple arrangement is reduced
Solution Approach 1:
The patent divides the spherical surface into multiple irregular domains, each generated from a portion of the polyhedron structure. This segmentation allows independent optimization of dimple arrangements within each domain while maintaining the symmetric relationship between domains, thereby achieving both high symmetry order and arrangement flexibility.
Solution Approach 2:
The patent employs dynamic algorithms to generate and optimize dimple positions within each irregular domain. The mathematical transformation methods allow for adjustable parameters that can optimize dimple distributions for different performance requirements while preserving the underlying symmetric structure.
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 higher orders of symmetry, improved dimple distribution, and enhanced flight stability, achieving better aerodynamic performance and masking the ball's parting line, while maintaining or exceeding the symmetry requirements set by the USGA.
Implementation Method 1
tessellating the domains onto the surface of the golf ball
Implementation Method 2
dimples provide a means to energize the flow field and delay the separation of flow, or reduce the wake region behind the ball
Implementation Method 3
In order to minimize pressure drag, dimples provide a means to energize the flow field and delay the separation of flow
Implementation Method 4
Lift force is perpendicular to the direction of flight and is a result of air velocity differences above and below the rotating ball. This phenomenon is attributed to Magnus, who described it in 1853
Implementation Method 5
Bernoulli's equation relates pressure and velocity where pressure is inversely proportional to the square of velocity. The velocity differential, due to faster moving air on top and slower moving air on the bottom, results in lower air pressure on top and an upward directed force on the ball
Data Source
AI summary
The present invention provides a method for arranging dimples on a golf ball surface in which the dimples are arranged in a pattern derived from at least one irregular domain generated from a regular or non-regular polyhedron. The method includes choosing control points of a polyhedron, generating an irregular domain based on those control points, packing the irregular domain with dimples, and tessellating the irregular domain to cover the surface of the golf ball. The control points include the center of a polyhedral face, a vertex of the polyhedron, a midpoint or other point on an edge of the polyhedron and others. The method ensures that the symmetry of the underlying polyhedron is preserved while minimizing or eliminating great circles due to parting lines.