# The Role of Physics in Golf

Physics plays an important role in the way athletes can perform; this can be seen through types of factors that influence sport performance. In golf, these factors may influence the shape of the golf clubs and how they’re made, as well as the shape and manufacturing of the golf ball. The intent in this report is to highlights certain aspects of physics that, to a great extent, influence sport performance. This will be demonstrated by in-depth analysis through the manufacturing of golf clubs and golf balls.

If it weren’t for physics behind these aspects of golf, then it would be harder to execute a more accurate and powerful shot, hence why it helps if you have a good understanding of the physics that takes place in golf. Despite someone’s lack of muscular strength, this is relevant to society because the physics are used to enhance your performance in golf through the use of many factors such as force, aerodynamics, friction, etc.

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Overall, there are four major components of physics that you will come across in golf, which are as follows: Force: According to Helmenstine (2019), force is a push or pull on an object with mass that will cause changes to its velocity. It can be represented as vector, meaning that it has magnitude and direction, (Helmenstine, A 2019).

Newton’s Second law of motion states that a force is equal to the change in momentum with a change in time, as well as mass and acceleration: F=(m_1 V_1-m_0 V_0)/(t_1-t_0 ) F=m (V_1-V_0)/(t_1-t_0 ) F=ma Force = mass x acceleration One limitation to this is when you explore force in a vertical direction; the acceleration (a) will always be equal to 9.

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8m/s2 due to the exception of acceleration due to gravity. Aerodynamics: According to Lucas (2014), “Aerodynamics is the study of how gases interact with moving bodies,” (Lucas, J 2014). The gas in which we encounter the most when dealing with aerodynamics is air. This is because of the forces of drag and lift that are caused by air passing over and around solid objects. The main course of study with aerodynamics is through flight; this can be seen through aircrafts and, of course, applied in sport.

The main aspect of aerodynamics is drag and it consists of forces that oppose an aircraft’s motion through the air. Drag is very depended on the density of the air, the square velocity, the air’s viscosity and compressibility, the size and shape of the body, and the body’s inclination to the flow, according to Hall (2015). This can be seen through the drag equation: D=Cd ×(ρ ×〖 V〗^2)/2× A Where D is the drag, Cd contains all the complex dependencies, which is usually determined experimentally, ρ, or ‘rho,’ is density, V is velocity and A is the reference area. Diagram 1: Drag Diagram (Benson, T 2014) The diagram above shows the drag equation and how it functions. Projectile Motion According to Hartsock (2019), projectile motion occurs when an object “is given an initial velocity and then follows a path determined entirely by gravity,” (Hartsock, A 2019).

Diagram 2: Projectile Motion (No Author, 2019) The above diagram shows all of the aspects when calculating the line of a projectile, also known as a trajectory. This component of physics is vital for many sports because it’s a guideline that helps determine the displacement, height, velocity, time and angle to get from point A to point B. There are many equations of motion that support this trajectory. If identified as ux then it demonstrates a horizontal pattern, however, if it’s uy then it shows a vertical pattern, hence why these two are put together to make a projectile. The equations of motion are as follows: v=u+at v^2=u^2+2a∆s ∆s=ut+1/2 at^2 Where v is final velocity, u is initial velocity, a is the acceleration, t is time and ∆s is the displacement, or distance. One limitation to this is that you are required to calculate both vertical and horizontal patterns. This is why the use of angles are vital. u_x=u sin⁡θ u_y=u sin⁡θ Either ux or uy are usually the first constants given; with this, you are able to find all of the others using the equations of motion.

Friction: According to Ghose (2013), “Friction is the resistance to motion of one object moving relative to another,” (Ghose, T 2013). Altogether, there are four types of friction, being static, sliding, rolling and fluid friction. Static friction occurs from objects that are at rest on a surface. Lastly, fluid friction occurs when an object is moving through a fluid. According to Brainard (2012), “A fluid is a substance that can flow and take the shape of its container,” (Brainard, J 2012). Diagram 3: Frictional Force: (Wood, D 2019) The above diagram explains the equation of frictional force that is static. In this report I will be analysing all of these components of physics in golf and provide justifications as to why it will work. Firstly, this will be done through the examination of the golf ball. Body Paragraph 1 (Flight of the Golf Ball): Golf balls feature some of the most important components of physics in the way that they are struck. Without its important design the golf ball may not travel as far or perfectly as it should, hence why it plays a major role in an athlete’s performance in golf. Diagram 4: Inner workings of the golf ball (Dreamstine.com, 2019) (Unknown Author, 2008)

The Rubber Core: The rubber core in the golf ball is vital because that is how it gets its distance. This is done because the rubber is flexible, meaning that once it’s hit, the ball will compress on contact following the clubface. After this, the ball will begin to expand and propel forward, thus providing more power in the shot. Dimples: The dimples of a golf ball are without regards one of the most important features of the game. Without it, athletes aren’t able to maximise their distance of the shot as well. According to Quintavella, the dimples on the golf ball are crucial in order to reduce wind resistance, or aerodynamic drag, and when reduced, it makes the ball go further. When a golf ball flies through the air, there will be airflow interacting the surface of the ball, which greatly affects the amount of drag. If the ball were smooth, the air will flow around the ball, creating the detached airflow behind it. Diagram 5: Drag affecting smooth and dimpled golf balls: (Kapoor, A 2018) This causes a weight deform behind the ball; this creates the low-pressure zone and this is why drag comes into play when dealing with smooth golf balls. Despite that, dimples are effective because it allows the flow of air to follow the same pattern as the dipped surfaces on the ball.

The concave shape of the dimples allows air to enter the dimple and then the air is released as it begins to reach the end of it. After this, the design allows time for the air to perfectly enter the next dimple, reducing the amount of drag immensely rather than the smooth golf ball. This is also known as turbulence, which is the allowance of air following the dimple pattern. This is also known as Euler’s principle, which states that, “separation of the boundary layer is like lot occur in regions where the pressure increases in the direction of the flow,” (Wainaina, M 2017) The amount of drag force and lift force can be determined by the acceleration equation: F_D=1/2 ρAV^2 Cd and: F_L=1/2 ρAV^2 CL Where ρ is density, which is 1.225kg/m3 according to Helmenstine (2019). A is the cross sectional area of the golf ball, which is equal to 0.00143m2 due to the golf ball radius being equal to 0.021335m. V is the velocity of the speed of the golf ball, which is 60m/s. c_d is the drag coefficient and c_L is the lift coefficient, which drag is 0.21 and lift is 0.14, according Mason (2016). Lastly FD is the frag force and FL is the lift force. Calculating drag force (FD) of golf ball: F_D=1/2 ρAV^2 C_D F_D=1/2 × 1.225 × 0.00143 × 〖60〗^2 × 0.21 F_D=0.6621615N Calculating lift force (FD) of golf ball: F_L=1/2 ρAV^2 C_L F_L=1/2 × 1.225 × 0.00143 × 〖60〗^2 × 0.14 F_L=0.441441N Use of projectile motion that determines flight: Projectile motion is another important factor of golf physics; this is because it gives the athlete an image of the trajectory required to hit the ball perfectly.

If, for instance, the golfer hit the ball at an initial velocity of 60m/s at an angle of 23o, the results are as follows: Diagram 6: (Kedia, P 2016) Finding initial vertical velocity (V_iy): V_iy=V_i sinθ V_iy=60sin23 V_iy=23.44m/s Finding initial horizontal velocity (V_ix): V_ix=V_i cosθ V_ix=60cos23 V_ix=55.23m/s Finding flight time (t): t=(-∆V_x)/a t=(-23.44-23.44)/(-9.8) t=4.78sec Finding time when ball hits peak height (t): t_y=t/2 t_y=4.78/2 t_y=2.39sec Finding maximum height (〖∆s〗_y): 〖∆s〗_y=V_iy t+1/2 gt^2 〖∆s〗_y=(23.44×2.39)+(1/2×-9.8×〖2.39〗^2 ) 〖∆s〗_y=28.03m Finding range (〖∆s〗_x): 〖∆s〗_x=V_ix t+1/2 gt^2 〖∆s〗_x=(55.23×4.78)+(1/2×0×〖4.78〗^2 ) 〖∆s〗_x=264m Final horizontal velocity (V_fx): V_fx=55.23 Final horizontal velocity (V_fy): V_fy=-23.44 Although these are theoretical values, the reality of the golf shot is that the drag will keep the ball from going this distance, hence why air resistance is a major issue for golfers.

This is why scientists and engineers have crafted the dimple designed golf ball which allows minimal drag from the airflow to ensure that the ball going further. Diagram 7: (Belz, K 2019) According to diagram 7, the golf ball does not follow the usual path of a projectile, however, due to air resistance or drag, the ball with not land as far as theorised. It is evident that when the goal ball has been struck, the use of aerodynamic, force and projectile motion is in play, mainly due to airflow in the ball, despite the dimpled design. Body Paragraph 2 (Hitting the Golf Ball): The structure of the golf club weighs heavily on the amount of force it can produce, giving athletes more potential to hit the golf ball further. This is why force is a crucial component of physics in golf, because the mass of the golf club can increase the amount of force applied, meaning that the ball can be hit with greater power. As the gravity is always 9.8m/s2, the golf clubs need to cater for this in order to apply more force.

This is why metals such as titanium (most commonly used metal in golf clubs) are used; because they carry more mass and at the same time it weighs less than other materials, meaning that it can apply more force. If the average golf club weighs in at 0.33kg and the average velocity is 46.94m/s, according to Rhodes (2018): F=ma F=0.33kg × 46.94m/s F=15.49N The average amount of force applied from the golf club to the golf ball is 15.49N. In a game, a golfer can only carry 14 golf clubs, all of which belonging to one of five categories of clubs. The first one, and the most commonly used, is the woods category. This includes the driver, as well as the fairway woods. Their main function is to gain as much distance as possible in order to approach the green more efficiently. The woods, despite not being made out of wood, are usually the longer set of clubs with larger heads.

The larger head allows golfers to maximise their distance of the shot without the hassle of hitting the sweet spot of the club, hence why the larger head provides a larger flat surface. Given the fact that they have longer shafts, golfers can utilise this in order to increase the speed of the swing, thus applying this force to the golf ball and hitting it further. (Miles, J, 2016) The next type of golf clubs is the irons. The irons come in different forms, ranging from 3-iron to 9-iron. They are different to woods because the design of them shows that irons have a smaller shaft and head. The importance of these clubs is to lob the golf ball in order to accurately hit the green. As the number of irons goes up (3,4,5,6,7,8,9-iron), the loft increases while length of the shaft decreases. The next golf club is the hybrid. The hybrid is like a cross between woods and irons., hence why it’s called a hybrid. Like irons, the hybrid is numbered (2,3,4,5-hybrid), and the number represents the iron that is being replaced. Many golfers tend to replace longer irons with hybrids as they have the same purpose, but they find it easier to use. Another type of golf club is the wedge.

These come in many forms, like the pitching wedge, gap wedge, sand wedge and lob wedge. They are known as a sub-set of irons because they have the same purpose, even though their use is to get out of tough surfaces, like sand bunkers, or from extremely close range of the green. The last type of golf club is the putter. This golf club is used on the green in order to hit the golf ball into the hole. The putter has a very unique design as it does not consist of a sweet spot, thus a shot with a putter will never lift from the ground. It is also unique because instead of swinging the putter like a gold club, the golfer tends to drag the club along the ground in order to effectively use accuracy when aiming for the hole. Sweet Spots: “The centre of mass point of the club head, projected onto the club head face (in the direction that is perpendicular to the face), is commonly referred to as the sweet spot,” (Real World Physics Problems, 2019).

The sweet spot is without a doubt one of the most important components of the golf club. It allows the maximum amount of force to be applied to the golf club because the sweet spot eliminates club head twist and minimises vibration. The higher tier of golf club (tear list starts from putter all the way to drivers) the larger the sweet spot is, therefore the easier it is to generate power. Levers in golf swing: According to Raatz (2014), “The golf swing is a type of lever where a weight is on one end of a beam, a fulcrum is on the opposite end of the beam and a force is applied to the centre of the beam,” (Raatz, W 2014). The longer the lever the longer the shot, which can be seen through the size in shaft of the driver. The driver provides the most amount of power with the help of its bulky head, larger sweet spot, and longer shaft.

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