Grounding golf "feel" in measurable physics
As a competitive golfer, I'd heard a lot of claims about putter design — face material, milling patterns, loft angle — and how they affect "feel" and ball roll. Most of those claims are marketing. This project was an attempt to quantify the actual physics behind putter-ball contact: how do design variables measurably affect launch conditions and roll consistency?
Coefficient of restitution as the key design variable
The coefficient of restitution (CoR) characterizes the elasticity of a collision — how much kinetic energy is preserved versus lost to deformation. For a putter striking a golf ball, CoR is determined by face material stiffness, impact velocity, and contact geometry. A higher CoR means more energy transferred to the ball per unit swing speed.
Loft angle matters because a golf ball sitting on a green is not a pure rolling contact problem at impact — the putter temporarily lifts the ball slightly before it settles into rolling, and the loft angle determines how pronounced that initial hop is. Minimizing unwanted hop leads to more consistent roll direction.
Geometry, material, and angle
Face loft angle: Standard putters have 2–4° of loft. The project modeled how varying loft across this range affects the vertical launch angle and the resulting roll transition.
Face material: Softer insert materials (polymers, aluminum) deform more on impact, reducing CoR but increasing dwell time — which golfers describe as "softer feel."
Putter geometry: Face-balanced vs. toe-weighted putters have different moment of inertia (MOI) distributions. Higher MOI reduces face rotation on off-center impacts — directly reducing directional error.
Impact velocity: CoR is not constant — it varies with impact velocity due to viscoelastic behavior in the ball cover. The model accounted for this velocity dependence.
Design decisions have quantifiable consequences
The MATLAB model quantified how changes in each variable propagated to launch angle, ball velocity, and effective roll consistency. Key findings: face loft has a more significant effect on roll initiation than face material within the standard design range, and MOI distribution is the dominant factor in directional error on off-center hits.
These findings align with published research in golf equipment engineering and validate the physics intuition that competitive golfers develop over years of play — but they make that intuition measurable.
The same analysis applies to any impact problem
Contact mechanics and coefficient of restitution are not golf-specific — they appear in crashworthiness analysis, manufacturing (stamping, forging), robotics (grasping and manipulation), and aerospace (landing gear). This project was my first serious engagement with impact dynamics as an engineering discipline, using a problem domain I could evaluate with direct physical intuition from years of competitive play.