Golf Ball Trajectory Research Articles

Numerical simulation and characteristics investigation of golf ball trajectory

In this study, MATrixLABoratory (MATLAB)’s ode 45 method was adopted to investigate the effects of the three main factors on golf trajectory characteristics, and the preferred striking conditions were concluded. Meanwhile, the results of interaction analysis were used to assess the dependence of carry distance and peak height on each factor. Eventually, the realistic normal swing tests were conducted in a laboratory to confirm the validation and accuracy of the mathematical model. The simulated results showed that a faster club head speed generally enabled to improve carry distance. However, once the rotational speed was more than 3,000 r·min-1, the increased tendency of carry distance turned to decrease. Moreover, the decreased tendency was aggravated as the increase of club head speed and launch angle, but the low launch angle benefited to alleviate the decrease. Compared to the carry distance, peak height always rose in any conditions. Meanwhile, the combined effects of the three factors on carry distance were more obvious than on the peak height. Finally, the optimised striking strategies were concluded for golfer-slow, golfer-medium and golfer-fast, respectively.

Simulation of Dimple Characteristics on the Trajectories of a Dimpled Sphere (Golf Ball) in Motion

A mathematical model describing the flight motion of a golf ball is developed, and the effects of dimple characteristics are studied. Using the Newton’s second law of motion, the equations governing the motion of the golf ball are developed in three dimensions. In this development the size, depth and number of dimples are taken into account. By varying the dimple size, depth and number, the effects of these characteristics are simulated via a MatLab code in which the Dormand-Prince Runge Kutta method is implemented to solve the model equations. The results of the numerical simulations that show how the golf ball trajectory is influenced by the dimple characteristics such as dimple depth, size and number within the accepted range of the Reynolds number are displayed and discussed.

A computational approach for predicting plant canopy induced wind effects on the trajectory of golf shots

Large-eddy simulation of atmospheric flow is combined with golf ball trajectory modeling that incorporates local plant canopy information to predict the trajectory of a golf shot at any hole on a golf course in a variety of wind conditions. The model is applied to examine golf shots on hole 12 of the Augusta National Golf Club, which is particularly well known for its wind-induced difficulty. The results indicate that the tree canopies around this hole play a significant role in golf ball trajectories and also induce a strong directional sensitivity on the landing spot of the ball for this hole.

Effect of Clubhead Inertial Properties and Driver Face Geometry on Golf ball Trajectories

There are many factors that influence the amount of side-spin imparted to a golf ball during impact with a driver. In general, the best golf drives are launched with minimal side-spin, producing a straight ball trajectory with maximum carry distance. During off-centre impacts, side-spin is generated due to a phenomenon known as the “gear effect.” The extent of the gear effect depends on clubhead design parameters such as the moment of inertia and centre of gravity location. The bulge of a driver is a design feature implemented to counter-act the side-spin produced by the gear effect. In this investigation, an impulse-momentum impact model and an aerodynamic ball flight model are used to (i) examine the effect of the centre of gravity depth (distance from clubface) on ball trajectory during off-centre impacts, (ii) test the efficacy of movable weight technology, and (iii) optimize the bulge radius in relation to the clubhead's centre of gravity depth and moment of inertia. In the first study, it is qualitatively shown that side-spin increases linearly with increasing centre of gravity depth. In the second study, it is found that movable weights can have a significant effect on ball trajectory, especially at higher swing speeds. In the third study, a relationship between the bulge radius, centre of gravity depth, and moment of inertia is developed, and an equation for calculating the optimum bulge radius is fit to the simulation results.

On generalized rolling of golf balls considering an offset center of mass and rolling resistance: a study of putting

This paper seeks to address the implications on putting a golf ball with an off-center mass by analyzing the effect of unbalanced mass of ball on its impact and subsequent rolling. We present the general formulation of a rigid golf ball rolling with slip that is able to transition to rolling friction on an arbitrary surface. Particular attention is given to the effects of the offset center of mass on the golf ball’s path. An experimental setup based on a USGA Stimpmeter is used to calibrate the position of contact point as the ball rolls on the green. The trajectories of the ball due to the mass imbalance were studied by numerically solving the equations of motion during putting. Theoretical predictions show that a mass imbalance has little effect on the launch conditions of the ball. However, on a level green a mass offset center of 0.2 % of the ball’s radius can impact the path of the ball with the consequences of missing the hole in a 5.8 m putt. Changing golf ball trajectories with mass offset center has implications on the development of balls and putting.

The Influence of Golf Ball Dimples on Aerodynamic Characteristics

Aerodynamic forces act on a golf ball during flight. For that purpose in order to develop a golf ball with high performance, it is important to analyze aerodynamic characteristics of the golf ball. On the other hand, dimple pattern of a golf ball is complicate and the influence of dimples hasn’t been investigated in detail. Therefore the influence of golf ball dimples on aerodynamic characteristics was investigated using a wind tunnel and rotating device. Some golf balls whose dimples have different depths were measured. As a result, it was found that the shallower the dimple was, the larger the lift coefficient was. However, when the depth of the dimples was much shallower, the lift coefficient was extremely-little on the slow velocity, i.e. under 30m/s. When the golf ball trajectory which was launched with a driver was calculated under various initial conditions, the ball velocity became under 30 m/s over the vertex of the trajectory in many cases, including professional male golfers and female golfers. Therefore, if the lift coefficient of the velocity of 30m/s becomes smaller, distances will become shorter. Dimple patterns that had a high lift coefficient at all velocities was researched. As a result, it was found that a golf ball with a dimple pattern that has extremely small dimples between large shallow dimples has a high lift coefficient at all velocities, including under 30m/s. In order to investigate the cause of the results, a flow visualization experiment was conducted. Visualization of flow around a golf ball was conducted by generating smoke. Moreover pictures of flow were taken by high-speed video and analyzed by PIV (Particle Image Velocimetry). As a result, there was the difference in the streamline distribution between golf balls.

Measurement of Putting Golf Balls Motion Using a Vision Sensor

This paper presents measurement of a putting golf ball jump motion using a vision sensor. After putting, a golf ball experiences bouncing, sliding and rolling sequentially. In particular, ball jump motion contains lots of important information related to impact such as jump number, height and length. Putting is simulated as a simple pendulum and golf ball jumps are measured using a vision sensor. The golf ball jump changes significantly according to impact errors such as impact timings. If an IMU sensor is attached on the putter head and relationship between variations of golf ball trajectory and IMU sensor signal is characterized, coaching information of golf putting to correct various impact errors can be provided only using IMU sensor.

골프볼 비행 궤적에 관한 연구

The purpose of this study is to develop the 3-dimensional(3D) trajectory of golf ball impacted by the various club head speed. The prediction of golf ball trajectory is very difficult for the air turbulence during the golf ball flight. This golf ball experiences the dragging force, lifting force and gravitational force(weight) during the flight in the air. These forces control the flight motion or trajectory of golf ball, these forces also determine the carry distance and run distance of golf ball. The developed KH Golf Profiler is examined by the very large data of PGA and LPGA measured by the golf ball radar Trackman during the last 4 years, the KH Golf Profiler has shown less than 3% differences compared with the PDA and LPGA data for 11~12 golf clubs.

Optimization of the clubface shape of a golf driver to minimize dispersion of off-center shots

The objective was to optimize the post-impact conditions of a golf driver and golf ball in order to minimize dispersion of a drive for off-center hits. When a golf ball is struct by a clubhead at a point away from the “sweetspot” on the clubface, spin is induced on the ball which makes it curve during flight. Over the years, clubmakers have made the clubface slightly convex in shape in order make off-center hits land as close to the fairway as possible. A general, three-dimensional impact model using principles of momentum conservation on rigid bodies was used to extract the spin and velocity vectors of the ball after impact. An aerodynamic model including drag, lift and skin friction was then used to obtain the landing position of the ball. An optimization routine was used to calculate the optimum clubface shape to minimize golf ball dispersion from the middle of the fairway, for off-center hits. In order to have an accurate simulation of impact on a computer, the mass and inertia tensor of the clubhead was experimentally measured. The clubface shape relative to the center of gravity of the clubhead was also measured. The impact computer program and golf ball trajectory computer programs were verified by using the golfing robot “Iron Byron” to hit various shots on the clubface of a particular driver. The computer simulation yielded results of ball landing positions from the middle of the fairway that fell within the standard deviations of those experimentally measured. The optimization routine was used to find the optimum clubface shape to minimize golf ball dispersion for off-center hits, for a particular driver swung at a certain initial velocity in a certain direction. The clubface shape was modeled in the impact program as an ellipsoid. After running the optimization program, the average dispersion from the middle of the fairway for the worst possible off-center hit locations was reduced on the average from 8.075 to 2.198 yards. The optimization program demonstrated its effectiveness in determining the optimum clubface to minimize dispersion of off-center hits.

Golf green visualization

Nonrealistic rendering techniques that enhance viewer perception of golf green topography and how that topography affects putting are discussed. Conventional computer graphics and numerical analysis techniques are combined with application-specific modeling and analysis algorithms to enhance a viewer's understanding of the golf green and model golf ball trajectories and putting difficulty. The coding of the system in LYMB and implementation of the system in broadcasts of two golf tournaments are described.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Maximum projectile range with drag and lift, with particular application to golf

This paper explores the interesting problem of projectile motion without the vacuum idealization. Particular attention is paid to golf ball trajectories with and without lift. No lift trajectories with linear and quadratic drag are considered first. Then, trajectories with lift and linear drag are investigated. Projection angles for maximum range are determined for all these cases. Computer solutions are used throughout, with a Runge–Kutta routine used for all cases except for the well-known closed solution for the no lift, linear drag projectile.