Irregular Domain Dimple Patterns for Golf Ball Aerodynamics
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Solution Overview
Problem
Existing golf ball dimple patterns struggle to achieve optimal aerodynamic efficiency and symmetry, often resulting in suboptimal surface coverage and performance due to limitations in geometric shapes and arrangements that can be used, which affects the ball's flight characteristics.
Innovation Solution
The golf ball features a unique dimple pattern arranged in multiple copies of irregular domains generated using methods such as the midpoint to midpoint method, where tetrahedrons are used to create non-straight segments that form parting lines, allowing for a uniform tessellation on the ball's surface with varying dimple diameters and patterns within different domains.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If traditional geometric shapes (circles, hexagons, triangles, Platonic solids, Archimedian solids) are used for dimple patterns, then aerodynamic symmetry is maintained, but surface coverage is suboptimal and aerodynamic efficiency is limited
Solution Approach 1:
The patent applies asymmetry by transitioning from traditional symmetric geometric shapes (Platonic solids, Archimedian solids) to asymmetric irregular domains. These irregular domains are generated through a specific mathematical process involving sphere triangulation and domain assignment algorithms that create non-uniform, asymmetric shapes. The asymmetric nature of these domains allows for more flexible and comprehensive surface coverage while maintaining aerodynamic symmetry through the overall distribution pattern of multiple domain copies across the ball surface.
Solution Approach 2:
The patent applies segmentation by dividing the golf ball surface into multiple irregular domains, where each domain is further subdivided into multiple copies. This segmentation approach allows for systematic arrangement of dimples within each domain and its copies, enabling optimized surface coverage. The segmentation into domains and their repeated copies creates a structured yet flexible pattern that improves upon traditional geometric approaches.
2Ease of manufacture
If the number of symmetric solid plane systems is limited to traditional geometric shapes, then manufacturing simplicity is maintained, but dimple arrangement flexibility and aerodynamic optimization are restricted
Solution Approach 1:
The patent applies parameter changes by transforming the fundamental geometric parameters from fixed symmetric shapes to variable irregular domains. The irregular domains are defined by specific mathematical parameters including vertex coordinates, domain boundaries, and copy distribution rules. These parameter changes enable flexible dimple arrangement while maintaining manufacturing feasibility through algorithmic generation and systematic replication of the domain patterns.
Solution Approach 2:
The patent applies mechanics substitution by replacing traditional mechanical geometric construction methods with computational algorithms. The irregular domains are generated through computer-based mathematical processes involving sphere triangulation, domain assignment, and coordinate calculation. This substitution of computational methods for traditional mechanical design enables complex irregular shapes while maintaining precision and repeatability in manufacturing.
3Ease of manufacture
If parting lines are visible in traditional dimple patterns, then manufacturing is simplified, but aerodynamic efficiency and flight stability are compromised
Solution Approach 1:
The patent applies asymmetry in the domain design to minimize the appearance of parting lines. The irregular domains are specifically shaped and positioned so that their boundaries and transitions do not create visible linear discontinuities on the ball surface. The asymmetric nature of the domains allows them to blend more naturally across what would traditionally be parting line locations, reducing visual and aerodynamic disruptions.
Solution Approach 2:
The patent applies local quality by optimizing the specific geometry and orientation of each irregular domain and its copies to minimize parting line visibility in critical areas. The domain shapes are locally adapted to smooth out transitions and reduce the prominence of boundaries. This local optimization ensures that parting lines are minimized in locations where they would most affect aerodynamic performance and visual appearance.
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 enhances the aerodynamic efficiency and symmetry of the golf ball, improving its flight stability and performance by minimizing the appearance of parting lines and allowing for greater flexibility in dimple arrangement, leading to improved aerodynamic characteristics.
Implementation Method 1
tessellating the domains onto the surface of the golf ball
Implementation Method 2
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
Implementation Method 3
Bernoulli's equation relates pressure and velocity where pressure is inversely proportional to the square of velocity
Implementation Method 4
Drag is opposite in sense to the direction of flight and orthogonal to lift. The drag force on a ball is attributed to parasitic drag forces
Implementation Method 5
dimples provide a means to energize the flow field and delay the separation of flow, or reduce the wake region behind 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.