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About this book

This book simulates the complete trajectories (flight and subsequent ground run) of golf shots using the aerodynamic and material properties of golf balls, and establish the significance of wind’s impact on gameplay. It also presents insight into how physical parameters like launch conditions (speed, angle and spin-rate) and wind conditions affect the trajectory of a golf ball. It discusses the specific effects of wind on the flight trajectory and explore the consequences of effect of wind direction; impact of golf club selection on the wind-induced deviation; strategies and their effectiveness to counter the diversion due to wind; and the sensitivity of the trajectory to aerodynamic characteristics of golf balls. Furthermore, the impact of wind on a player's strategy is elucidated with cases studies on the renowned holes of three golf courses: (i) Hole 17, TPC Sawgrass, (ii) Hole 8, Muirfield Golf Club, and (iii) Hole 18, Pebble beach Golf links. It presents an integrated mathematical model and quantitative data on ball trajectory accompanied by insights and illustrations for players, golf-course designers, ball manufacturers, scientific community, and golf enthusiasts. This book will be useful for researchers and professionals in the fields of aerodynamics engineering, sports science and physics. Additionally, this book will be a good read for golf players and coaches, golf-course designers, as well as golf-ball manufacturers.

Table of Contents

Frontmatter

Chapter 1. Introduction

Abstract
Golf, one of the most high-speed ball sports, is popularly referred to as the “Gentleman’s Game”. The objective of the game is simple: the players need to start from the tee (which lies in the teeing box) and deliver the ball into the hole (which lies in the putting green) by hitting a series of shots using a club. A golf course consists of several holes each having a unique layout design. Once all the competing golfers successfully play all the holes, the player who played the least number of shots wins the game. Despite its simple objective, golf is one of the most difficult ball sports due to the challenges it poses on the players. Apart from the teeing box and the hole, a golf course contains several other features that make up its architecture. These include hills, valleys, trees, sand bunkers and water bodies like lakes, ponds and sometimes even seas and ocean (see Fig. 1.1). While these features provide an aesthetic touch to the golf course, their primary role is to act as obstacles for the golfer during a game. In order to gain a competitive edge, the golfers need to minimise the number of shots they play. Hence, they need to properly plan their route taking into account the distance to be covered, as well the obstacle and hazards, that may come in the way. If a poorly planned (or poorly delivered) shot lands the ball in any of the hazards, it yields additional shots to the player which, in turn, manifests as a competitive disadvantage.
Shantanu Malik, Sandeep Saha

Chapter 2. Understanding the Motion and the Environment

Abstract
In this chapter, we discuss various physical models that govern the motion of a golf ball. The flight of a golf ball is governed by the laws of aerodynamics and projectile motion. The dimples on the ball’s surface help the ball fly over a larger distance by reducing the drag, while the backspin enhances the upward Magnus force acting on it due to its airspeed. On the other hand, bouncing and rolling motions are governed by the ball’s material properties, the grass type and the local terrain profile. The ball’s interaction with the golf course plays a vital role in the gameplay. Therefore, it is essential to understand and model the golf course architecture itself. The local wind conditions are modelled using a logarithmic velocity profile, that captures the effect of the atmospheric boundary layer. Finally, we end with a discussion on various design styles and par rating of a golf course.
Shantanu Malik, Sandeep Saha

Chapter 3. Simulating the Motion in a Synthesised Environment

Abstract
In this chapter, we discuss the algorithm and numerical techniques that we use to simulate a golf ball’s motion in a synthesised golf course environment. The physical models that govern the motion of the ball are integrated with the golf course environment in the form of a computer algorithm which comprises of four subroutines: flight, bounce, roll and validity check. In the flight subroutine, the ball’s flight trajectory is computed as an initial value problem using numerical schemes. When the ball hits the ground, the bounce subroutine computes the rebound velocity and spin rate vector from the impact velocity and spin rate vector. When the balls motion transitions from bouncing to pure rolling, the roll subroutine takes over and numerically computes the motion. Finally, we describe the procedure we use to model a real or an arbitrary golf course and explain how we incorporate it in the simulation programme so that the ball interacts with it.
Shantanu Malik, Sandeep Saha

Chapter 4. How Does Wind Impact Gameplay?

Abstract
The flight of a golf ball is majorly governed by aerodynamic forces acting on the ball. Since these forces depend on the relative airspeed of the ball, wind has a direct impact of the golf ball’s trajectory. Moreover, the impact of wind is much more significant than that of other parameters like ball speed, spin rate and launch angle. Therefore, the effect of wind becomes a vital subject in the game of golf. In this chapter, we present a detailed quantitative analysis of the variation in wind-induced deviations with respect to three parameters that govern the ball’s trajectory: wind conditions, launch conditions and aerodynamic characteristics. We find that the effect of headwind is more profound than that of a tailwind of the same magnitude. Also, the wind-induced deviations are higher for more lobbed shots compared to flat shots. Finally, the trajectory of a golf ball having hexagonal dimples undergoes a higher deflection in the presence of wind, as compared to that of a conventional golf ball having circular dimples.
Shantanu Malik, Sandeep Saha

Chapter 5. Gameplay, the Course and Wind

Abstract
In this chapter, we view the results obtained from the quantitative analysis in Chap. 4 from the perspective of a golfer. First, we describe the common techniques used by the golfer to adapt his launch conditions such that the wind-induced deviation is nullified. We explain how these techniques work through simulations of realistic golf shots and also discuss their limitations. Next, we discuss how wind impacts a real golf game by simulating golf shots under the effect of wind in modelled environments of three real golf courses having different design styles: (1) hole 17 of Tournament Players’ Club in Florida (penal style), (2) hole 8 of Muirfield Golf Club in Scotland (strategic style) and (3) hole 18 of Pebble Beach Golf Links in California (heroic style). We find that wind has a decisive effect on the gameplay strategy in each of the courses, wherein wind tends to enhance the key characteristic of the course and hence helps in clearly distinguishing between amateurs and experts.
Shantanu Malik, Sandeep Saha

Chapter 6. Concluding Thoughts

Abstract
The flight of a golf ball is majorly governed by aerodynamic forces acting on the ball. Since these forces depend on the relative airspeed of the ball, wind has a direct impact on the golf ball’s trajectory. Moreover, the impact of wind is much more significant than that of other parameters like ball speed, spin rate and launch angle. Therefore, the effect of wind becomes a vital subject in the game of golf. However, since the wind has varying degrees of impact on different physical settings and golf course layouts, it is important to understand the impact of wind on the game as a whole, as opposed to just on individual flight trajectories.
Shantanu Malik, Sandeep Saha
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