The Physics Of Golf

.. ollision is greater than 3000lb[1] and high speed photography has shown the ball to be considerably flattened against the club head.[1] The elastic properties of the ball come into place at this point because it is those properties that allow the ball to be compressed and then spring away from the face of the club at a high velocity. Although there is no scientific proof of what exactly happens at the point of impact, through the use of physics, several educated guesses can be made. Momentum is conserved: Since the club head is at the end of a somewhat flexible shaft, one may, to a fair degree of approximation, assume that the club head in its horizontal motion at the bottom of the swing acts as a free body.[4] Therefore, the horizontal momentum of the club head before the collision must be the same as the sum of the horizontal momentum of the club head and the ball after the collision. It is important to note that the vertical momentum is not conserved because the arms and shoulders pull up with a force on the club head. The collision is inelastic: By simply holding a golf ball and feeling how firm it is, one can easily see that is not perfectly elastic.

Therefore, some mechanical energy must be lost. Newton was the first to experiment with this property of collisions. He found that the ratio of the speed with which the ball leaves the floor to that with which the ball approaches the floor to be practically a constant over a large range of speeds.[ ] The constant is called the coefficient of restitution. For a perfectly elastic ball the coefficient is one. For a ball that does not rebound at all, the coefficient would be zero.

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This also applies to collisions that happen at an angle such as with the face of the golf club and the ball. The ball slides and rolls on the clubface: Consider this example as an explanation for how a golf ball generates its spin from the uneven surface of the face of a golf club. As anyone who has thrown a bowling ball will attest to, the ball slides down the alley at first. Since there is some amount of friction between the ball and the lane, the ball slows down, which allows the ball to begin rolling. After the ball has traveled some distance it no longer slides and just purely rolls.

The same is true for the face of the golf club. As the collision occurs the ball begins to slide toward the top of the face of the club. However, because the friction force between the ball and clubface is so great it quickly begins to spin (roll) off the top of the club. This generates the tremendous amount of spin necessary to keep the ball a loft for drives at or above 230 yards. It is these three factors together that the quantity known as effective loft is derived from.

The effective loft of any club is given as EL = L + a(i) – B(i) Y. L is the loft of the club a(i) and B(i) are angles that are dependant upon each swing and each person performing the swing and Y is the back swing angle of the arm. From effective loft of the club, one can estimate the components of drag and lift on the golf ball. The following table expresses the variations that are possible during the swing. B(0) – B(i) – EL + Spin + Lift + B(0) + B(i) + EL – Spin – Lift – Y – B(i) + EL – Spin – Lift – Y + B(i) – EL + Spin + Lift + TS + B(i) – EL + Spin + Lift + Al + B(i) – EL + Spin + Lift + As an example, the third line reveals that when the back swing angle of the arms is decreased, the effective loft is decreased, the spin is decreased, and the lift is decreased. As one can see through the material presented above, the golf swing is a multi-stage process.

It is not simply the swing, or the transfer of energy, or the flight of the ball that is subject to the laws of physics. The first aspect of the golf stroke, which is based upon physical principals, is the downswing of the golf club. The golfer must do two things in order to have a successful shot. He must first generate enough energy to hit the ball a significant distance. And then he must transfer this energy into the golf club.

The energy is derived from the muscles in the golfers body. As was previously stated it takes at least 32lbs of muscle to generate the necessary two horsepower for hitting the golf ball. Most of this energy comes from the legs and back of the individual. Then, the golfer uses his body and arms, along with the shaft of the golf club like a whip. Just as a whip transfers energy from its large mass at the handle down to the tip causing a dramatic acceleration, the golfer transfers the energy through his body into the shaft of the golf club, which flexes. When the golfer snaps his wrist at the point of impact, all of the energy is transferred into the club head allowing it to achieve a velocity of 100mph or even greater.

At the point of impact, more physical properties take over. As the club comes in contact with the ball, two important factors are most prevalent. First, the ball is semi- elastic and therefore the ball flattens somewhat when it comes in contact with the face of the club. This allows the ball to spring away at a tremendous velocity, which is also based on the principal of conservation of momentum. The other important factor that happens at impact is the generation of spin.

At first, the ball begins to slide up the face of the club toward the top, however, because of the large coefficient of friction; the ball stops sliding and begins rolling. This action gives the ball a rotation around its horizontal axis, which creates lift and drag. Lift and drag are the final aspects of how physics relates to golf. As the ball spins, it creates lift by disturbing the flow of air around the ball. The dimples help greatly with this.

However, drag is also produced, which threatens to pull the ball back toward the earth. It is the job of the golfer and the golf ball manufacturer to generate enough lift either through the swing or the dimpled design of the golf ball so that the upward lifting force counteracts the downward forces of gravity and drag. As anyone who has played a round of golf has observed, the spin created with modern clubs and ball design more then compensates for drag and gravity and allows the ball to stay aloft for a long time. Because of the unique challenges that physics present during a game of golf, it will be a long time before anyone is able to master the game. In an endeavor to improve scores many miracle products have claimed to lower ones score, however it is evident that only those ideas and products, which have a basis in science, have stayed on the market. The golf ball is a prime example of this.

It has made dramatic changes from being made of dried goose feathers to the two piece dimpled design of today. All of the improvements on the ball were based around trying to give the golfer and edge in lowering his score and working around some of the laws of physics, which prevent him from reaching perfection. Appendix 4 The following terms will be defined based on their relevance to the physics of golf: momentum, moment of inertia, torque, centripetal force, and centrifugal force Momentum: Newtons first law defines a property of a body called inertia, which describes what happens to a body when no force acts on it; the inertia of a body is said to be measured by its mass. When acted upon by a constant unbalanced force, the body will experience acceleration proportional to the mass of the body. The mass of a body is proportional to its weight. Momentum is then defined as the mass of a body multiplied by its velocity.

Like velocity, momentum, has a direction as well as magnitude, making it a vector quantity. From the definition of momentum, for constant mass the rate of change of momentum is the product of the mass and its acceleration. Newtons second law suggests that an unbalanced force on a body is associated with its acceleration. For the purpose of this paper, Newtons second law states that the mass of a body multiplied by its acceleration is proportional to the force acting on it, and the acceleration is in the direction of the force. The way in which momentum applies to golf is through the transfer of momentum from the golf club to the golf ball.

Before the collision, the club head is moving at a speed of 100mph along the horizontal. After the collision, for a club without loft, the ball is moving off at a high velocity, and the club head continues in the follow-through at a somewhat reduced velocity. For a club without loft, these velocities will also be horizontal. The momentum is such that the total momentum before the collision is equal to that of the momentum of the club head after the collision plus the momentum of the ball. Moment of Inertia: The linear acceleration of a body when acted upon by a constant force depends on its mass, which as already stated is quantity proportional to its weight. The larger the mass is, the smaller the acceleration will be for a given force. Similarly, when a constant torque acts on a body, its angular acceleration will depend on the mass of the body and on how the mass is distributed in the body. The combination of mass and its distribution in the body is called its moment of inertia.

When the axis of rotation of the body is chosen such that more of the mass is far from the axis, the moment of inertia will be larger. Thus the moment of inertia will depend of the choice of axis. This concept is easily demonstrated with the help of a golf club. When the club is help at the grip end between two fingers and let hang so that the shaft is along a vertical line, it is very easy to rotate the club along a vertical axis. But when the club is held near the center of the shaft, where it balances between the same two fingers, the same torque produces a much smaller angular acceleration.

The moments of inertia in the two cases differ by a factor of 10.[ ] This same affect can be observed when a club is first waggled about the grip in the usual way and then waggled while holding the head. Torque: Torque is the term used to describe twist in a quantitative manner. Two factors, the amount of force applied and the distance over which it is applied determine torque. The size of the torque is found by multiplying the size of the force by the length of the lever arm, the lever arm being the shortest distance from the line along which the force acts to the axis about which the body may rotate. The force must be in a plane perpendicular to the axis of the rotation.

Centrifugal Force: This force can be observed when a golf ball is placed on the dashboard of an automobile just inside the windshield and is observed while the vehicle travels around turns. One will notice that the ball will always roll to the outside of the curve and rolls more quickly the tighter the turn. Actually, the ball does not accelerate; it appears to accelerate since there is no centripetal force to make it turn in the same path as the car. Its motion is the result of a lack of centripetal force rather than the result of an outwardly directed force being applied to the ball. Centripetal Force: According to Newtons Second Law, the centripetal force on a body moving in a circle is proportional to the mass of a body multiplied by its centripetal acceleration. The centripetal acceleration increases with the radius of the circle on which it moves and with the square of the angular velocity of the motion. Appendix 1 The following curves were drawn based on the information gathered and analyzed with the use of a computer. The curves are calculations for the energies present during a swing.

Curve A shows the total kinetic energy as it develops throughout the swing. Curve B shows how the kinetic energy of the arms varies throughout the downswing. Curve C shows how the kinetic energy of the club alone varies throughout the swing. Curve D shows the work done by the golfer as he applies the torque by his arms to the system. (graph taken from source #5) Appendix 2 (original drawings but concept from source #5) These drawings illustrate the forces on a golf ball during its flight.

The first set of pictures shows how the air moves around the ball during its flight. The first pictures show that when there is some spin, the air pressure around the ball is changed because of the turbulence created by the rotation. The picture below that shows how the air would move if there were no spin. The other two pictures demonstrate how using spin can change the flight of the ball. For example, the top picture is showing that a ball spinning on a vertical axis in a clockwise direction will travel to the right because of the airflow around the ball.

The bottom picture on that side is illustrating another example of how air can flow around a ball with no spin. The other two illustrations show a three-dimensional (on the top) and a two-dimensional (on the bottom) view of some of the vectors involved with the flight of a golf ball. The illustrations show the effective loft of the club, the lifting vector as well as the path of the golf club and the angle at which the face points. Appendix 3 This is a graph of the five-torques acting on the arms as they vary throughout the downswing. Curve A shows the constant torque TS of the golfer on the system. Curve B shows the torque that depends mainly on the acceleration of the wrist-cock-angle.

The torque represented by curve C depends mainly on the square of the velocity of the wrist-cock-angle. Curves D and E show the torques resulting from action of gravity and the golfers weight shift respectively. The torque T shows how the sum of the five-torques on the arms varies during the downswing and becomes very large just prior to the club colliding with the ball. (graph from source #1) Bibliography 1. Abrahams, Jonathan (1994).

Club Smarts. New York: Lyons & Burford. 2. Andrisani, John. (1997). The Tiger Woods Way.

New York: Random House. 3. Beard, James (1982). Turf Management for Golf Courses. New York: McMillan. 4.

Jones, Trent (1993). Golf By Design. New York: Little, Brown, and company. 5. Kroen, William. (1992).

The Why Book Of Golf. California: Price Stern Sloan. Physics.