Game of Golf


The game of golf has really been around since the 15th century. For more than five hundred years people have been trying to hit a small ball with a long club to send it into a distant hole. It should be a simple game because this process is governed by laws of physics that have been known for a long time. In reality, however, as any golfer would tell you, it is not a simple game. Let us show you some of the parameters that a golfer has to consider in his quest to sink the ball into a hole.

Clubhead Speed

A golfer rotates his body during the swing reaching maximum speed of rotation at the moment the club is about to hit the ball. For most golfers this speed is fairly constant in most of their swings. This means that their out-stretched hands complete the path around the dashed circle (see figure below) in the same time during every swing. The clubhead moves faster because it follows the larger dashed circle during the same time as the shorter arms. Most golfers describe their ability to rotate by giving the clubhead speed of a driver. This speed varies between 160 mph (experts) and 70 mph for inexperienced golfers.

rotation

Golf Clubs

Golfers have at their disposal a set of clubs consisting of woods (#1 (driver) to #9) and irons (#1 to #9). In addition, golfers carry a pitching wedge (PW), a sand wedge (SW) and a putter. The length of woods range from 45" for drivers to 41" for wood #9, while the length of irons range from 40" for #1 to 36" for iron #9. Both the pitching wedge and the sand wedge are 35.5". Note that the clubhead speed decreases as the length of the club decreases. Why?

Direction of Motion

The face of each club makes a different angle with the vertical. This angle is called the loft. The loft of woods range from 10° for #1 to 27° for #9. The loft of irons range from 15° for #1 to 42° for #9. The sand wedge has the largest loft at 55°. When the golf ball is hit it will acquire a velocity in some direction q above horizontal. The angle q increases as the the length of the club decreases. It is likely that a ball hit with the sand wedge will have initial velocity in a direction close to 55° above horizontal. On the other hand, hitting the ball with the driver will cause the ball to have initial velocity close to 10° above horizontal.

Range

In conclusion, as the "number" of a club increases the slower the clubhead speed and the higher the loft. Both of these quantities have an impact on the distance the ball will travel. This distance is called the range. Physics helps us to compute the range of the golf ball if we can assume that only gravity pulls the ball downward. In other words, if we can assume that the impact of air can be neglected. In this case the range can be computed as follows:

In this equation, R stands for the distance between the point where the ball was hit and the point where it landed on the ground, v0 is the initial velocity of the ball, the angle q is the direction of the initial velocity and g is the gravitational acceleration 9.8 m/s2.

Impact of air

The effect of the air on the flight of a ball may appear to be simple. The work done by friction between the ball and the air takes away some of the kinetic energy of the ball.

Without rotation

If the ball does not rotate then the air resistance simply slows it down and the range of the ball is shorter than it would be in vacuum.

With rotation

When the ball rotates after the hit, the flow of air just above the ball is different than the flow of air just below the ball. The consequence of this difference in the flow above and below the ball is a force that acts upward against gravity. This force causes the ball to remain in the air longer than it would without air and consequently, the rotating golf ball has a range which is longer than the range of a golf ball in vacuum. As you probably know, golf balls have dimples. The effect of these dimples is to amplify the force lifting the ball up against gravity. The figure below indicates the trajectories of a golf ball. The parabolic trajectory (black) is the path of the ball in vacuum, the blue trajectory shows the path of the ball through air without rotation and the red trajectory indicates the path of the ball rotating through the air. Golfers who can send a ball off with large rotation become famous as long hitters. For example, Tiger Woods is known for driving balls farther than 300 yards.

rotation

Unfortunately, there is no simple formula for computing the range of a rotating golf ball. The effect of the upward force on the trajectory also depends on the direction of motion and the velocity of the ball and therefore it varies during flight. To simplify the task we will restrict our consideration to the flights of non-rotating balls

Experiment

We will show you a simulation of a golf course where your task is to hit a hole-in-one - a rare event on a golf course!

  1. Hole-in-one No Air
  2. Hole-in-one With Air. Try the same experiment with "Air" on (but don't make any calculations).

Since the ranges shown in the simulation are in m and the velocities in m/s you may need to convert units: 1 yard = 0.9 m; 1 mph = 0.44 m/s and 1" = 0.025 m.


Physics of Golf > Instruction