Golf Ball Dimple Piecewise Profiles for Reduced Drag and Longer Carry
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Solution Overview
Problem
Existing golf ball dimple profiles, typically defined by parabolic, elliptical, or saucer-shaped curves, can sharply intrude into the ball's surface, leading to increased drag and insufficient carry due to suboptimal aerodynamic performance.
Innovation Solution
A golf ball dimple profile defined by a piecewise function comprising at least two distinct curves, such as a catenary and Gabriel's horn function, with a smooth transition and opposing concavities, ensuring a non-constant radius of curvature and symmetrical cross-sectional symmetry about the central axis.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Ease of manufacture
If traditional dimple profiles (parabolic, elliptical, saucer-shaped) are used, then manufacturing is simple, but drag increases and lift decreases due to sharp surface intrusion
Solution Approach 1:
The patent applies parameter changes by transitioning from traditional single-curve dimple profiles to piecewise function profiles composed of multiple curve segments (e.g., cubic bezier curves, B-splines). This allows precise control of the dimple geometry parameters including radius of curvature, depth, and width, enabling the dimple to reduce drag while maintaining manufacturability through standardized molding processes.
Solution Approach 2:
The patent utilizes curvature principles by ensuring continuous first and second derivatives at the junction points of the piecewise function segments. This creates smooth transitions with optimized radius of curvature that prevent sharp surface intrusions, thereby reducing drag and improving aerodynamic performance while maintaining simple manufacturing through rotational symmetry about the central axis.
2Ease of manufacture
If traditional dimple profiles are used, then manufacturing is simple, but carry distance is insufficient due to suboptimal aerodynamic performance
Solution Approach 1:
The patent optimizes carry distance by changing the dimensional parameters of the dimple profile through piecewise functions. By independently controlling depth, width, and curvature radius through the function parameters, the design achieves superior aerodynamic performance that extends carry distance while remaining manufacturable through conventional molding techniques.
Solution Approach 2:
The patent enhances carry distance by optimizing the curvature characteristics of the dimple profile. The piecewise function ensures continuous first and second derivatives, creating smooth surfaces that minimize turbulence and maximize lift, thereby extending ball carry distance while maintaining ease of manufacture through rotational symmetry and standardized molding processes.
3Ease of manufacture
If dimple profiles with sharp surface intrusion are used, then manufacturing is simple, but drag becomes greater than lift
Solution Approach 1:
The patent rebalances aerodynamic forces by changing the profile parameters from traditional sharp-edged designs to piecewise function profiles with controlled curvature. The continuous derivatives and optimized radius of curvature reduce drag more effectively than lift is reduced, achieving a favorable drag-to-lift ratio that improves overall aerodynamic performance while maintaining manufacturing simplicity.
Solution Approach 2:
The patent corrects the aerodynamic force balance by implementing smooth curved surfaces through piecewise functions with continuous first and second derivatives. This eliminates sharp surface intrusions that cause excessive drag, creating a dimple profile where lift exceeds drag, thereby improving aerodynamic efficiency while maintaining ease of manufacture through rotational symmetry.
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 new dimple profile enhances aerodynamic performance by reducing drag and increasing lift, providing a seamless transition that maintains momentum and improves flight distance.
Implementation Method 1
The dimples on the ball create a turbulent boundary layer around the ball, i.e., a thin layer of air adjacent to the ball flows in a turbulent manner
Implementation Method 2
The dimples on the ball create a turbulent boundary layer around the ball, i.e., a thin layer of air adjacent to the ball flows in a turbulent manner. The turbulence energizes the boundary layer of air around the ball and helps the air stay attached further around the ball to reduce the area of the wake
Implementation Method 3
Lift is the upward force on the ball that is created from a difference in pressure on the top of the ball to the bottom of the ball. The difference in pressure is created by a warpage in the air flow resulting from the ball's back spin
Data Source
AI summary
A golf ball dimple half profile is disclosed herein that can be defined by a piecewise function. The sub-functions that define the piecewise function can include, for example, a catenary function and a Gabriel's horn function. A transition between the sub-functions defining the piecewise function is smooth. The sub-functions can have opposing concavities, and at least one of the sub-functions can have a non-constant radius of curvature. The golf ball dimple half profile is rotated about the dimple's centroid to create the full dimple profile.