Golf Ball Dimple Shape Using Toroid-Sphere Intersection
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Solution Overview
Problem
Conventional golf ball dimples do not adequately enhance both aerodynamic performance and aesthetics, limiting the development of novel shapes and patterns that could improve flight characteristics and visual appeal.
Innovation Solution
The use of dimples with perimeters and surface shapes derived from the intersection of a toroid and a sphere, creating unique and efficient aerodynamic features while maintaining aesthetic appeal, with various toroid shapes such as rectangular, elliptical, and twisted toroids intersecting with a spherical golf ball surface.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If conventional dimple shapes are used, then manufacturing is simple, but aerodynamic performance and aesthetics are insufficient
Solution Approach 1:
The patent applies parameter changes by varying the geometric parameters of the toroid (such as major radius R, minor radius r, and aspect ratio) to create dimples with optimized aerodynamic properties. By adjusting these parameters, the dimple shape can be tailored to achieve specific performance characteristics while maintaining manufacturability through standardized forming processes.
Solution Approach 2:
The patent utilizes spheroidality by employing a toroid (a curved three-dimensional shape) intersecting with a sphere to create the dimple geometry. This curved approach replaces conventional flat or simple geometric dimple shapes, creating a more sophisticated three-dimensional form that enhances aerodynamic performance while maintaining aesthetic appeal through its curved surfaces.
2Shape
If novel dimple shapes are developed, then aerodynamic properties and aesthetics are enhanced, but manufacturing complexity increases
Solution Approach 1:
The patent employs an intermediary approach by using the intersection of a toroid and a sphere as a mediating geometric construction to define the dimple shape. This intermediary geometry serves as a bridge between the desired novel shape and the manufacturing process, allowing complex three-dimensional forms to be created through systematic geometric operations that can be translated into manufacturable tooling and forming processes.
3Reliability
If dimple surface coverage is increased, then aerodynamic effect is enhanced, but visual appeal and packing efficiency are compromised
Solution Approach 1:
The patent applies local quality by creating dimples with non-uniform geometric characteristics - the toroid-sphere intersection produces varying curvature and surface area distribution across the dimple surface. This allows different regions of the dimple to have optimized properties for both aerodynamic performance (through controlled surface coverage) and visual appeal (through varied geometric features), achieving a balance between functional and aesthetic requirements.
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
The novel dimple shapes enhance aerodynamic properties by reducing drag and increasing pressure, while providing a visually appealing design, with improved surface coverage and packing efficiency, resulting in a golf ball with superior flight characteristics and appearance.
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
This greatly increases the pressure behind the ball and substantially reduces the drag
Data Source
AI summary
The present invention is directed to golf balls having improved aesthetics and desirable aerodynamic properties due, at least in part, to the novel shape of the dimples on the surface thereof. In particular, the present invention is directed to a golf ball that includes at least a portion of its dimples having a shape obtained from the intersection of a toroid and a sphere. The resulting curve of intersection represents the dimple perimeter and the intersecting portion of the surface of the toroid represents the dimple surface shape.