Introduction
The purpose of this blog is to investigate how biomechanics
can be used to maximise the displacement of golf shots. This will be done
through a discussion of the biomechanics of the golf swing and answering the
following three key questions:
- How can we utilise a biomechanical understanding of air pressure to increase the displacement of golf shots?
- How can we manipulate the time the ball is in the air to increase displacement?
- How does the initial horizontal velocity of the ball effect displacement?
Finally, this blog will discuss how this information can be
also used to improve aspects of the baseball swing.
The golf swing can be broken down into four phases; set-up,
backswing, downswing and follow through. These phases will be useful throughout in describing different functions of the golf shot.
- Set-up
- Establishing grip on the club and positioning the body with respect to the ball
- Backswing
- Preparatory movements that result in the club head rotating away from the ball
- Downswing
- Begins at the top of the back swing and ends when the club makes contact with the ball
- Follow through
- Occurs after the club has made contact with the ball.
(Hume, Keogh & Reid, 2005)
How can we utilise biomechanical understanding of air resistance to maximise placement?
When the golfer strikes the ball, more often than not, and
not meaning too, the golfer imparts spin onto the ball. As the ball flies
through the air it has a boundary layer of air that travels with it and spins
with it due to friction between the ball and the air.
When the ball spins the boundary layer of air interacts with
the air that is travelling past. When the boundary layer of air and the air
coming past are going in the same direction the resultant air velocity
increases causing a lowering of the air pressure on that side of the ball. The
opposite happens on the other side. As the air coming past the ball collides
with the boundary layer (that is they are heading in opposite directions) the
resultant velocity of the air is decreased, causing an increase of air pressure
on the other side of the ball.
When this occurs the resultant force on the ball causes the
ball to travel slightly more to the side with lower pressure, as shown in figure 1. This explains why
golfers struggle to hit the ball straight and instead perform slice or hook
shots.
Figure 1: Explanation of Swing and Hook (Blazevich, 2008, p. 188)
Golfers can utilise this knowledge to alter the swing
direction of the club to help minimise the spin on the ball, resulting in a
straighter drive and an increased displacement of the ball.
How can we manipulate the time the ball is in the air to maximise displacement?
When a golf ball is travelling through the air it is
considered a projectile and it follows a parabolic trajectory. The trajectory
is influenced by the initial angle, height and velocity with which the ball is
struck. Gravity alters the vertical velocity of the ball, while air resistance
alters the horizontal velocity of the ball (Blazevich, 2008).
To increase the time the ball is in the air, the trajectory
that the ball takes needs to be addressed. As the flight of the ball is
parabolic, the time that the ball takes to reach its peak height will be half
the total flight time of the shot (in the case that the position that the ball
is hit from and then lands is on the same plane).
The relationship between time the ball takes to reach its
peak height, initial vertical velocity and gravity can be defined with the
following equation:
Time to reach peak height = initial vertical velocity
gravity
(The Physics Classroom, 2014)
This equation indicates that increasing the initial vertical
velocity with which the ball is struck will improve the time the ball takes to
reach its peak trajectory. The equation also suggests that if gravity were to
be decreased the flight time of the ball will increase. Yet, this is not
possible as gravity is a constant force acting on the ball at a rate of -9.8ms-2,
bringing the ball back down to earth.
At the beginning of the discussion of increasing the flight
time of the shot, the trajectory of the ball was said to be parabolic and that
the total flight time is double the time the ball takes to reach peak
trajectory. This was on the condition that the ball lands at the same height it
was hit from.
In the case that a golfer is able to hit the same shot three
times but with the ball landing on different levels the displacement of the
shot will be different. When the ball lands on the same level, for example, the
fairway is completely level; the flight time can be found by doubling the time
it took for the ball to reach its peak height. In the case that there is a hill
onto which the shot is hit, then the flight time will be reduced, because the
ball does not have as far to travel through its trajectory. Finally, in the
case that the ball lands on a level below which it was shot, the flight time of
the ball will have been increased, because the ball has to travel further (Blazevich, 2008). This is demonstrated in the figure below.
This means that for the golfer to increase the flight time
of the ball to increase the displacement, the golfer should consider his/her
own positioning relative to the positioning and relative height of where they
are attempting to hit the ball. In the case that they are higher than the
target position, the displacement will be increased.
How does the initial horizontal velocity of the ball effect the displacement of the ball?
Coefficient of restitution
A simple way to improve the displacement of golf shots is
just through warming the golf ball before hand. This improvement is attributed
to the coefficient of restitution, which is a measure of the amount of energy
remaining in an object after a collision.
When the golf club head strikes the ball, some of the energy
of the collision will be dissipated into other forms of energy, such as sound.
When the golf ball is warmed the elasticity of the ball is increased, reducing
the amount of energy lost in when the ball is struck, increasing the horizontal
velocity of the ball, increasing the displacement of the golf ball (Blazevich,
2008).
Unfortunately, there is a lot more to the effects that
horizontal velocity of the ball has on the displacement of the ball.
Momentum of the club at impact
To examine the momentum of the club head at impact, we need
to understand momentum. The momentum of an object is equal to its mass
multiplied by its velocity.
Momentum (p) = mass x velocity
Also, the law of conservation of momentum states that the
total momentum of the club head or the ball is neither created nor destroyed,
but transferred from the club head to the ball according to the following
equation.
Initial velocity of ball = velocity of club head x mass of
club head
mass of ball
These equations suggest that to increase the momentum of the
club at impact the mass of the club head and/or the velocity of club head need
to be increased and the mass of the ball needs to be decreased.
As the rules of golf state that a golf ball must be
45.93grams (United States Golf Association, 2014) we cannot decrease the mass
of the ball, so we have to examine the linear velocity and mass of the club
head.
To further examine the momentum of the club head at impact,
the effects of the relationship between momentum and impulse will produce a
broader understanding.
The relationship between the momentum and impulse can be
described as follows:
change in mass x velocity = change in force applied over time
Δmv = ΔFt
This relationship suggests that to produce a large change in
momentum from when the swing begins to when the ball in struck the golfer needs
to apply a large amount of force over a large amount of time (Blazevich, 2008).
Therefore to increase the momentum of the club head at
impact there needs to be an increase in any or all of the following areas: mass
of the club head, velocity of the club head, force applied to the club head or
time the time the force is applied to the club head.
Mass (m) of the club head
This suggests that by increasing the mass of the club head
the momentum of it will be increased. This is on the proviso that the player is
able to manage an increase in the mass, and does not lose any coordination in
the back swing and down swing phases.
Linear velocity (v) of the club head
An increase in the linear velocity of the club head will
result in an increased horizontal velocity of the ball according to the law of
conservation, resulting in an improved displacement of the ball.
Linear velocity is a product of the angular velocity and
arm-club lever system.
Linear velocity (v) = angular velocity (ω) x arm-club lever length
(Hume, Keogh & Reid, 2005)
Angular velocity of the club head
The angular velocity of the club refers to the rate at which
the club changes its angular displacement over time. The quicker that this
occurs the larger the angular velocity of the club head. An increase in angular
velocity will result in an increase in the linear velocity of the club head.
Angular velocity (ω) = change in radians (Δθ)
change
in time (Δt)
(Blazevich, 2008)
Arm-club system length
The distance between the shoulders and the club head is
important to increasing the linear velocity. An increase in the distance
between the club head and the shoulders will result in a longer lever arm and
when combined with angular velocity will result in an increase in the linear
velocity of the club head. This implies that the player needs to have his/her
arms fully extended at the point of contact, as can be seen in figure 2 below (Hume, Keogh & Reid, 2005).
Figure 2: Adam Scott in the follow through phase (Golf Today, 2014).
Forces produced
To be able to give the club head velocity the equation
between momentum and impulse suggests that a force applied over time needs to
be applied to the club. These forces can be produced internally (e.g. by
muscles), or they can be produced externally (e.g. the ground reaction force).
The final component of discussing how to increase the displacement of a golf
shot will be to examine how the player can produce and increase the force they
impart on the club, through a discussion of the kinetic chain and the ground
reaction force (Hume, Keogh & Reid, 2005).
Ground reaction force
The first initial source of force production occurs through
the ground reaction force. The golfer utilises the newton’s third law that
states “for every force there is an equal and opposite reaction force”), as
well as the understanding that when we apply a force to an object that does not
move the object will exert an equal and opposite reaction force (Blazevich,
2008).
In the case of the golf swing, for the golfer to generate a
large amount of force, they need to apply a large amount of force in the
opposite direction. Also, as the golfer wants their body to accelerate towards
the ball in the down swing (acceleration of the centre of mass toward the ball
increases the velocity of the club head) the golfer needs to produce a large
force in the opposite direction, according to newton’s second law: f=mass x
acceleration (Blazevich, 2008).
Therefore an increase in the amount of ground reaction force
the golfer is able to produce to increase the acceleration of his centre of
mass toward the ball during the downswing will increase the force with which
the ball is struck.
The kinetic chain
The kinetic chain involves certain segments of the body
working together to produce large forces to strike the ball with. This is known
as the kinetic chain. In the backswing, the muscles of the hips, shoulders and
arms are stretched, storing elastic energy in the tendons of the muscles. Then in the downswing phase each of these
tendons are released, releasing the elastic energy, and the muscles are also
shortened sequentially (from the more proximal segments to the more distal)
producing large muscle forces. This generation of force in each of the segments creates momentum, and when each of the segments decelerates sequentially they pass their moment onto the next more distal segment, until the momentum is passed into the club head, to create impart horizontal velocity onto the ball, as can be seen in video 1 below (Welch, Banks, Cook & Draovitch, 1995).
Video 1: Adam Scott 250 Yard 3-Iron (Ultra Slow Motion) (RollYourRock, 2013)
Finally, the golfer can also increase the force they apply
to the ball through creating a whip like action just before the ball is struck.
This occurs because the force produced makes the hands move with angular
velocity moving the club head with angular velocity too. When this occurs the
elasticity in the shaft of the club causes the club head to lag behind. Just
before the club head makes impact the golfer decelerates his/her hands,
transferring the momentum to the club head causing it to accelerate, maximising
the angular velocity at impact.
The Answer
To increase the distance that the
golf ball can be struck the golfer needs to think about improving three main
areas: reducing the spin imparted on the ball, thinking about where the ball is
being hit too and its relative height to the golfer, and how the golfer is
producing force to impart on the ball and how that can be improved.
How does this information apply to the baseball strike?
This information can also be useful when thinking about the biomechanics involved in striking a baseball. The baseball player uses a very similar kinetic chain and ground reaction forces as a golfer to impart momentum on the bat to strike the ball. Both skills involve the player using similar phases throughout the performance of the skill, mainly rotating the body away from the ball and loading the muscles, and then sequentially shorting the muscles of the hips, shoulders and arms to produce momentum to transfer into the bat. Whilst the force production component of the baseball swing is important to increase the distance of a baseball hit, the effects of air resistance and the time the ball spends in the air are less important (Welch, Banks, Cook & Draovitch, 1995).
References
Beaumont, S. (2011, January 25). The biomechanics of golf
(Web log post). Retrieved from http://www.insidegolf.com.au/golftips/golf-science/golf-and-baseball/.
Blazevich, A. J. (2008). Sports
Biomechanics: The Basics (2nd ed). London: Bloomsbury.
Golf Today. (2014). Adam Scott swing sequence 3 [Image].
Retrieved from http://www.golftoday.co.uk/proshop/features/2012/images/adam_scott_swing_sequence_3.jpg
Hume, P. A., Keogh, J., & Reid, D. (2005). The role of
biomechanics in maximising distance and accuracy of golf shots. The American Journal of Sports Medicine, 35(5),
429-499.
RollYourRock. (2013, August 11). Adam Scott – 250 Yard
3-Iron (Ultra Slow Motion) Aug 10, 2013 [video file]. Retrieved from http://www.youtube.com/watch?v=Dfxe4cjihVM
The Physics Classroom. (2014). Initial velocity components. Retrieved from http://www.physicsclassroom.com/class/vectors/Lesson-2/Initial-Velocity-Components
United States Golf Association. (2014). Appendix III - The ball. Retrieved from http://www.usga.org/Rule-Books/Rules-on-Clubs-and-Balls/Appendix-III-–-The-Ball/.
Welch, C. M., Banks, S. A., Cook, F. F., & Draovitch, P.
(1995). Hitting a baseball: A biomechanical description. Journal of Orthopedics and Sports Physical Theraphy, 22(5), 193-
201.
