Golf Ball Dimples Using Cycloid Curves for Aerodynamic Optimization
Find Innovative SolutionsGenerate Solutions
Solution Overview
Problem
Existing golf ball dimple designs, particularly those using circular arcs, are complex and time-consuming to optimize for aerodynamic performance, making it difficult to determine optimal dimple characteristics like size and volume, which hinders the ball's distance and stability in flight.
Innovation Solution
The golf ball features dimples with cross-sectional shapes defined by cycloid or trochoid curves, allowing for efficient quantification and arrangement of dimple sizes and volumes, improving aerodynamic performance and distance traveled.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If circular arcs are used to describe dimple cross-sectional shapes, then dimple characteristics can be quantified, but the optimization process becomes complicated and time-consuming
Solution Approach 1:
The patent changes the mathematical parameter basis from circular arcs to cycloid or trochoid curves. These curves are defined by simpler parametric equations that directly relate dimple depth, diameter, and volume through a small number of parameters, enabling rapid calculation and optimization without the complexity of circular arc combinations.
Solution Approach 2:
The patent extracts and eliminates the complicated mathematical relationships inherent in circular arc-based dimple designs. By adopting cycloid/trochoid curves, it removes the need for complex numerical quantification while retaining the ability to precisely control dimple characteristics, thus reducing optimization time.
2Volume of moving object
If double dimple shapes are used to enlarge dimple volume, then distance traveled is extended, but the cross-sectional shape becomes complex and difficult to quantify
Solution Approach 1:
The patent applies cycloid or trochoid curves to create dimple cross-sections that achieve large volumes through controlled parameter variations (depth, diameter, curvature) rather than through complex nested geometries. The parametric nature of these curves allows volume optimization while maintaining mathematical simplicity.
Solution Approach 2:
The patent utilizes the inherent curvature properties of cycloid and trochoid curves to create smoothly contoured dimple cross-sections. These curves naturally provide the desired curvature distribution to maximize dimple volume while maintaining simple, manufacturable shapes without requiring complex nested or multi-arc constructions.
3Reliability
If more dimples are formed on the ball, then aerodynamic performance is improved, but the complexity of determining optimal dimple characteristics increases
Solution Approach 1:
The patent establishes a systematic parameter-based approach using cycloid/trochoid curves that allows rapid determination of optimal dimple characteristics for any given number of dimples. The parametric equations enable quick calculation of depth, diameter, and volume relationships, making it feasible to optimize configurations with numerous dimples without overwhelming complexity.
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 design enhances aerodynamic performance by simplifying the determination of dimple characteristics, leading to increased distance and stability in flight, while maintaining manufacturability and quality.
Implementation Method 1
air resistance during flight be reduced by dimples arranged on the surface of the ball
Data Source
AI summary
The invention provides a golf ball having numerous dimples on a surface thereof, wherein at least one dimple cross-sectional shape is a cycloid curve or a trochoid curve. By thus optimizing the cross-sectional shape of the dimples, the aerodynamic performance due to the dimple effect is enhanced, enabling the distance traveled by the ball to be increased.