Golf Ball Dimple Patterns Using Irregular Polyhedral Domains
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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.
Innovation Solution
The use of irregular domains generated from polyhedrons, specifically through methods like midpoint to midpoint and center to vertex techniques, to arrange dimples on a golf ball surface in a uniform pattern, ensuring high symmetry and minimizing the appearance of parting lines.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Area of stationary object
If traditional geometric shapes (circles, hexagons, triangles) or Platonic/Archimedian solids are used for dimple patterns, then aerodynamic symmetry is maintained, but surface coverage is suboptimal and dimple arrangement flexibility is limited
Solution Approach 1:
The patent applies asymmetry by transitioning from traditional symmetric geometric shapes (circles, hexagons, Platonic solids) to asymmetric irregular domains. These irregular domains have non-uniform shapes that can be optimally packed onto the spherical surface, achieving superior surface coverage and dimple arrangement flexibility while maintaining overall aerodynamic symmetry through the tessellation pattern.
Solution Approach 2:
The patent segments the spherical surface into multiple irregular domains that are then tessellated together. This segmentation approach allows each domain to be independently optimized for dimple placement while the overall tessellation pattern ensures comprehensive surface coverage and maintains aerodynamic symmetry across the entire ball surface.
2Reliability
If dimple patterns are based on limited symmetric solid plane systems, then aerodynamic symmetry is achieved, but new pattern development becomes difficult and surface coverage is reduced
Solution Approach 1:
The patent introduces dynamics by moving from static, fixed geometric patterns based on limited symmetric solids to a more dynamic system using irregular domains. The irregular domains can be adapted and reconfigured to create new tessellation patterns, providing versatility in pattern development while maintaining aerodynamic symmetry through the overall tessellation structure.
Solution Approach 2:
The patent applies parameter changes by transforming the fundamental geometric parameters from regular shapes with fixed symmetry constraints to irregular domains with variable shapes. This allows optimization of dimple placement parameters within each domain while the tessellation pattern maintains the overall aerodynamic symmetry parameter.
3Ease of manufacture
If regular geometric patterns are used, then manufacturing simplicity is maintained, but aerodynamic efficiency and surface coverage are compromised
Solution Approach 1:
The patent applies copying by creating standardized irregular domain templates that can be repeatedly copied and tessellated across the spherical surface. This copying approach maintains manufacturing simplicity through template reuse while achieving superior aerodynamic efficiency and surface coverage compared to traditional regular geometric patterns.
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 aerodynamic efficiency and symmetry, allowing for greater flexibility in dimple arrangement and improved flight stability, while maintaining high orders of symmetry and efficient surface coverage.
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, who described it in 1853 after studying the aerodynamic forces on spinning spheres and cylinders
Implementation Method 3
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
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, which consist of pressure drag and viscous or skin friction drag
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.