Research paper on th physics of golf

Research paper on th physics of golf

Message Posted By: derek
Message Posted On: January 19, 19101 at 08:37:32

In Reply To: Research paper on th physics of golf
Original Message Posted By: Sharon
Original Message Posted On: January 11, 1999 at 20:36:59:

Body of Message:
I wrote it myself... the diagrams would not paste so you might get slightly lost.

January 9, 2000
The Aerodynamics of Golf
Introduction
The other day I was watching Mike Weir hit his tee shot on a par four on TV. The camera was angled directly behind him so when I watched him take his shot I was very surprised. I was expecting the ball to go on about a forty five-degree angle up before falling to the ground at a forty five degree angle, but it did not. The ball left the club face at about a twenty five degree angle before starting a climb at which it gradually climbed to about a fifty five degree angle relative to the ground. This all took about 3 seconds, before it began to fall and it hit the ground at a fifty five-degree angle.
In diagram “A” you see the same type of ball flight I saw last weekend when I watched Mike Weir take his 287 yard drive off the tee. Diagram “B” is what I expected the ball flight to look like. Why did Mike’s shot look like this? I am going to try and figure out all the physics behind Mike Weirs drive and all the other physics of hitting the perfect drive.

Aerodynamic Forces
Why did Mike’s tee shot curve upward like that? Recall Newton’s First Law states that a body continues in a straight line at a constant speed unless a force acts on it. The upward curve on the ball tells me that there is a force greater than that off gravity. Force = Mass x Acceleration (F=MA). The mass of a golf ball is 45 grams or 0.045 Kilograms; the acceleration of gravity is 9.80 meters per second squared. So we will plug in the numbers, 0.045 kilograms multiplied by 9.80 meters per second squared (0.045kgx9.80m/s2) = 0.441 Newton’s of downward force which we will assume as a negative force. We know the net force is a positive number but we do not know what that number is. We must take into consideration that part of the positive force is from the club head hitting the mall on an upward angle, but why did the ball curve upwards before starting it’s downward fall? What possible force could be so great that it could make the ball curve upwards? The answer is the spin on the dimpled golf ball. The proper golf shot should have the top of the golf ball spinning back towards the golfer and the bottom part spinning away from the golfer. Sometimes the gold ball spins the opposite way, that is called topping the ball.
Diagram “A” is an example of a properly hit ball with plenty of backspin. Diagram “B” is a ball that is hit with no spin but is hit on an upward angle with the golf club. Diagram “C” is a shot that has been topped. A topped ball is a shot that has been hit on an upward angle with the golf club but the club hit the top of the teed ball, so it had top spin. When a shot is topped the ball starts on a seemingly normal flight pattern before suddenly snapping back down to the ground at a much higher rate that the acceleration of gravity. Why does this happen? This happens for the same reason that a properly hit ball curves upward. Backspin makes the ball curve upwards and forward spin makes the ball curve downwards. Where do these extra forces that make the balls do these weird come from? It was aerodynamic force on the dimpled spinning ball, traveling at a high speed, which was overriding the vertical force of gravity. Without the force of air on the ball, the ball would travel on a very different path than it actually does. If you through a ball a short distance, it will move accurately on a parabolic path because the force by the air on a slowly moving ball is small. When a well hit ball travels at speeds of up to 140 miles per hour, the force of the air on the ball is not small. This force, in some cases, can become even larger than the weight of the ball and can produce spectacular modifications in its flight path.
The Lifting Force on a Spinning Ball
A ball driven with spin about a horizontal axis with the top of the ball coming toward the golfer, has a lifting force on it which keeps the ball in the air much longer than would be possible that without spin. If the axes of the spinning of the ball is turned to the right or to the left then the balls flight pattern will change. If the axis is tilted left the ball will hook left and if the axis is tilted right then the ball will slice right.

Roughening The Surface Helps Lifting Force

The gold ball went through many phases before eventually ending up the way it is now. It started as a smooth ball stuffed with feathers, then became a smooth ball made out of a clay type material, then came rubber balls that where scratched to make them rough. After extensive development of the design of the markings on the golf ball scientists believe that they have found the perfect design of dimples on the golf ball.
While Professor Tait was apparently the first to study the lift on a spinning ball in the game of golf, others before him had studied this effect. Sir Isaac Newton, some 220 years before Tait, recognized that a tennis ball "struck with an oblique racket" would move on a curved path. This effect is sometimes called the Magnus effect because Magnus did some careful experimental work on it. Many answers are found in some studies that were done by a scientist by the name of Daniel Bernouilli. Bernouilli found that whenever the speed of a fluid, a liquid, or a gas is caused to increase, its pressure decreases. This curious, almost paradoxical, effect can be shown to follow from Newtonian mechanics quite simply for the special case of a non-viscous incompressible fluid in streamline flow in a pipe.
Effects of Aerodynamic Forces
To display the effects of aerodynamics forces I tried an experiment. All I had to do was cut a small square piece of light cardboard, about 2 in. on a side, stick a pin or a thumbtack through its center, and place it over the end of a spool with the pin in the hole of the spool. I blew through the spool as hard as I was able. Practically everyone expects the card to be blown away, but actually the harder I blew the tighter the card clung to the end of the spool. The pin or thumbtack is essential to keep the card from slipping sideways from the spool. The behavior of the card can be understood in terms of Bernouilli's Principle. When the air flows between the card and the end of the spool its speed increases and makes the air pressure in this area lower. The air pressure on the other side of the card is greater and there is thus a resultant force from the high-pressure region holding the card firmly against the end of the spool.
There are tons of other ways that we can see Bernouilli's Principle. A Ping-Pong ball that’s mass is mere grams can be supported on a small jet of air. A larger rubber ball may be supported on an air jet from a vacuum cleaner used on its blow mode. . In each case the flow of air over the top of the ball produces a low-pressure region. The low pressure resulting from the increase in speed of the air over the topside of the wing of an airplane in conjunction with the high pressure below the wing produces the lift on the wing. As we shall see, the lift on a golf ball is another example of the Bernouilli effect.
Understanding Forces on A Spinning Ball

Let a ball, similar to a golf ball except that it has a smooth surface sit a rest while air moves past it at a small velocity. This is equivalent to having the ball move with the same small velocity through air at rest. A possible flow pattern of the air past a ball is shown in Fig. 8.1(a). The lines drawn in the figure show paths of small masses of air in their motion past the ball.
Streamline and Turbulent Flow
The air shown moving is Fig.8.1(a) is an example of streamline flow. Streamline flow is very different from turbulent flow and has to be distinguished. . When a candle has been snuffed out, the smoke rises smoothly in still air for a few inches and then breaks into a disturbed motion. The lower part shows streamline flow while the upper part shows turbulent flow. As the air flows past the ball, the air close to the ball has its speed increased from A to B and then decreased from B to C. This means, according to Bernouilli, that the pressure of the air near the surface of the ball decreases from its value at A to a lower value at B and then rises to have at C the same value it had at A.
The Boundary Layer
I thought that if air moving at a very low velocity was going across a golf ball the air pressure on it would be symmetrical forward and backward and therefor would result in no net force on the ball. But some experiments have shown that there is a force on the ball even with very small air velocities. This force is caused because air is a viscous fluid. The thin layer of air around the surface of the golf ball is called the boundary layer. In the boundary layer the speed of the air varies from zero at the surface of the ball to a larger speed away from the surface out in the streamline flow. The air surrounding the surface of the ball is not moving relative to the ball. Momentum is transferred across the boundary layer from the flowing air to the surface of the ball. The force acting on the ball is measured at the rate the momentum is being transferred.
The Viscous Drag On The Ball
If you want to better understand, imagining the stirring of a kettle of some viscous fluid, such as molasses, with a spoon. As the spoon stirs the fluid, the kettle will turn along with the fluid unless the kettle is held fixed. A torque must be applied to the kettle to keep it from turning. The tangential force of the fluid on the inner surface of the kettle results from the internal viscous effects in the fluid. A similar tangential force on the surface of the ball results from the internal viscous effects in the boundary layer at the surface of the ball. The force on the ball is proportional to the relative velocity of the air past the ball at this low velocity.
Air flowing from point A to point B outside the boundary layer is going from a high-pressure region to a low-pressure region and this pressure difference helps increase the air velocity. But the air moving from B to C is moving from low pressure to high pressure loses its velocity because it is going against the pressure difference. When the viscous effect in the boundary layer becomes large enough so that the air near the surface of the ball is stopped before it reaches C, turbulent motion takes the place of the streamline flow. This happens sooner or later as the air velocity increases. The velocity of air passing a well hit golf ball will be much greater than that at which streamline flow will occur. From A to B the flow is very similar to that in the previous example. At B or a little before B the boundary layer becomes stalled and a turbulent wake extends downstream from the ball. In this turbulent wake there is considerable violent stirring of the viscous air and energy is dissipated. When a ball flies through air at rest, this energy dissipated in the turbulent wake comes from the energy of motion (kinetic energy) of the ball. There is thus a resistive force, called "drag," on the moving ball which is not related to the viscous force in the boundary layer but comes rather from the difference in the pressure on the front and on the back of the ball. This drag in this velocity range varies closely as the square of the relative velocity of the air and the ball.
Dimple Increase Turbulence in Boundary Layer
Now if we imagine the change in the flow line pattern for a small masses of air when the surface of the ball is changed from a smooth surface to that of a dimpled surface. The dimple on the surface of the ball make the boundary layer turbulent; the surface is no longer smooth and the air has to dip in and out of the dimples, stirring it up a bit. Instead of stalling at B like it did in the previous example, the high velocity air carries the turbulent boundary layer along with it, helping it move along the surface of the ball from the low pressure region at B toward the higher pressured area at C. This is shown in Fig.8.1(c).
The turbulent wake starts farther back on the surface of the ball and is smaller in cross section than in the case of a smooth ball. The drag on a dimpled ball is much smaller that that of the smooth ball because less energy is dissipated in the smaller wake. This has been proven in tests comparing the drag of a smooth ball in comparison to the drag of a rough ball.
The Spinning Ball
Fig.8.1(d) is an illustration of the flow of air past a spinning dimpled ball as it spins. In the diagram the air is moving from left to right if we are assuming the ball is at rest or if we are assuming that the air is at rest then the ball is moving for right to left.
The turbulent boundary layer is moving with the surface of the ball as it spins. This means that the air over top of the ball is moving much faster relative to the ball than that moving underneath the ball. According to Bernouilli’s Principle the pressure on top of the ball is less than that of the air directly below the ball. All this means that there should be a force, called lift, perpendicular to the direction of the ball’s motion.
The turbulent boundary layer as it is pulled along over the top of the ball stalls farther down on the backside of the ball while the boundary layer on the underside of the ball is prevented from remaining next to the ball and stalls even before it reaches the lowest point of the ball. The wake behind the ball then starts down lower than the wake behind a non-spinning ball. The flow pattern takes on a downward component. The air must receives some downward momentum and the ball recoils in the upward direction. This is another way of looking at the origin of the Bernouilli lift on the ball.
There have been ways to measure aerodynamics of spinning golf balls invented, but it is difficult to give a quantitative description of the results of these experiments because the drag and the lift depend on at least three variables, the speed of the ball through the air, the rate of spin on the ball, and the surface texture of the ball, whether it is smooth or dimpled. So general statements are made.
The faster a ball moves through the air and the faster it spins the more drag the ball has. It may become about as large as the weight of the ball. The lift on a dimpled ball increases with the rate of spin at any given air speed and increases with air speed at any given rate of spin It may become nearly as large as the weight of the ball.
Every golfer knows that when they are hitting with the wind they will be able to drive much further than if they were hitting into the wind. This is a perfect example of the increase in drag with increased air speed at the ball. Every golfer also knows that a golf shot hit into the wind will fly at a higher trajectory than one hit with the wind. This is a perfect example of the increase in lift with the increase air speed coming at the ball.
Competing Effects of Lift and Drag
We now know that there are two major effects battling in the flight of a golf ball. It is the Lift vs. the drag of a spinning golf ball. The larger the spin the more the drag which makes the ball slow down more rapidly which makes the ball not go as far. But the larger spin also creates more lift, which allows the ball to remain in flight much longer, which lets the ball go farther. But what force over rules the other? Experience has shown that the lift do to spin is more powerful than the drag do to spin. So a shot with lots of spin and has lots of drag but also tons of lift will go farther that a shot with no drag but also no lift.
Now we know all about the flight of a ball and it is just up to us to hit the perfect drive. The perfect drive varies from person to person but you can figure out your maximum potential. First it starts of with your swing speed. Fats and strong joints will help your swing speed, but nothing will help it more that mass. People with large masses can use their weight to their advantage to gain a faster swing. To figure out the moment of your club head you will need to use the formula P=MV. Once you have your club heads momentum and you can assume the momentum of the ball on the tee is zero then you just have to remember Law of Conservation of Momentum, which is the initial momentum of an isolated system is equal to its final momentum. We know that the golf ball has a bass of 0.045 kg and has zero velocity and by weighing the club head we found that it weighed 0.650 kg and has 2.5P of momentum. If 2.5P of momentum is transferred into a 0.045 gram golf ball than the golf ball is going to leave the club face at a velocity of (2.5P \ 0.045 kg = 55.6 m/s x 60 squared divided by 1000 = 200.16 km/h. Now calculating my farthest possible shot with no spin on the golf ball would be easy, but once you calculate the spin of the ball into the picture that it becomes very complicated to find an answer. I spent about 3 hours trying to figure out what my optimum driving distance would be by measuring my wing speed and the calculating in the spin on the ball. I found the spin on the ball by screwing in a small screw into the ball and the tying a long hockey skate lace to it and the hitting it into a small wall coated with putty. Then I counted the amount of times the lace had twisted, and by using the speed of the ball which I just worked out above I found out the time and found that in 0.41 seconds the lace had been spun 51 times. To find the spins/second rate all I had to do was 1\0.41 s = 2.4 x 51 = 124.4 spins/second. Now I knew the spin rate that I shot at and the speed at which I could hit the ball so I thought I could figure out what my maximum drive potential would be. After I had all the data needed I sat down at my desk with a stack of 25 lined paper, a pencil and a calculator and spent 3 hours and went through every piece of paper trying to find my goal, what my perfect drive would be.
In conclusion I decided that there were to many variables in my equations and I was unable to find out how far I could potentially hit the ball with the perfect drive. The closest I got to an answer was when I went to the driving range and hit two buckets of golf balls. By best drive of the day was on a shot where I think I achieved my maximum club head speed and hit the ball on a perfect angle. The golf ball landed about 303 yards away and I thought that maybe I had obtained my maximum drive. But as I was driving home I realized that that could not have been my maximum drive because the ball curved upwards and towards the right. Meaning that the axis that the ball was spinning on could not have been straight. Some of the balls spinning energy was put to waist sending the ball to the right when that force could have been helping the lift. The extended lift would have let the ball remain in the air for a longer amount in time. So I realized that I had not obtained my perfect drive. But I did at least realize that my perfect drive is probably slightly more that 303 yards in the air.

If you would like to respond to this message, please scroll down to the form that is located at the bottom of this page and fill it in with your follow up message!

Research paper on th physics of golf - Tann da Mann! (08:49:25 10/17/102)

(0)

Magnus Force - Vanessa Freund (03:30:40 11/09/101)

(0)

Name:
E-Mail:
Subject:
Comments:	: I wrote it myself... the diagrams would not paste so you might get slightly lost. : : January 9, 2000 : The Aerodynamics of Golf : Introduction : The other day I was watching Mike Weir hit his tee shot on a par four on TV. The camera was angled directly behind him so when I watched him take his shot I was very surprised. I was expecting the ball to go on about a forty five-degree angle up before falling to the ground at a forty five degree angle, but it did not. The ball left the club face at about a twenty five degree angle before starting a climb at which it gradually climbed to about a fifty five degree angle relative to the ground. This all took about 3 seconds, before it began to fall and it hit the ground at a fifty five-degree angle. : In diagram “A” you see the same type of ball flight I saw last weekend when I watched Mike Weir take his 287 yard drive off the tee. Diagram “B” is what I expected the ball flight to look like. Why did Mike’s shot look like this? I am going to try and figure out all the physics behind Mike Weirs drive and all the other physics of hitting the perfect drive. : Aerodynamic Forces : Why did Mike’s tee shot curve upward like that? Recall Newton’s First Law states that a body continues in a straight line at a constant speed unless a force acts on it. The upward curve on the ball tells me that there is a force greater than that off gravity. Force = Mass x Acceleration (F=MA). The mass of a golf ball is 45 grams or 0.045 Kilograms; the acceleration of gravity is 9.80 meters per second squared. So we will plug in the numbers, 0.045 kilograms multiplied by 9.80 meters per second squared (0.045kgx9.80m/s2) = 0.441 Newton’s of downward force which we will assume as a negative force. We know the net force is a positive number but we do not know what that number is. We must take into consideration that part of the positive force is from the club head hitting the mall on an upward angle, but why did the ball curve upwards before starting it’s downward fall? What possible force could be so great that it could make the ball curve upwards? The answer is the spin on the dimpled golf ball. The proper golf shot should have the top of the golf ball spinning back towards the golfer and the bottom part spinning away from the golfer. Sometimes the gold ball spins the opposite way, that is called topping the ball. : Diagram “A” is an example of a properly hit ball with plenty of backspin. Diagram “B” is a ball that is hit with no spin but is hit on an upward angle with the golf club. Diagram “C” is a shot that has been topped. A topped ball is a shot that has been hit on an upward angle with the golf club but the club hit the top of the teed ball, so it had top spin. When a shot is topped the ball starts on a seemingly normal flight pattern before suddenly snapping back down to the ground at a much higher rate that the acceleration of gravity. Why does this happen? This happens for the same reason that a properly hit ball curves upward. Backspin makes the ball curve upwards and forward spin makes the ball curve downwards. Where do these extra forces that make the balls do these weird come from? It was aerodynamic force on the dimpled spinning ball, traveling at a high speed, which was overriding the vertical force of gravity. Without the force of air on the ball, the ball would travel on a very different path than it actually does. If you through a ball a short distance, it will move accurately on a parabolic path because the force by the air on a slowly moving ball is small. When a well hit ball travels at speeds of up to 140 miles per hour, the force of the air on the ball is not small. This force, in some cases, can become even larger than the weight of the ball and can produce spectacular modifications in its flight path. : The Lifting Force on a Spinning Ball : A ball driven with spin about a horizontal axis with the top of the ball coming toward the golfer, has a lifting force on it which keeps the ball in the air much longer than would be possible that without spin. If the axes of the spinning of the ball is turned to the right or to the left then the balls flight pattern will change. If the axis is tilted left the ball will hook left and if the axis is tilted right then the ball will slice right. : : Roughening The Surface Helps Lifting Force : The gold ball went through many phases before eventually ending up the way it is now. It started as a smooth ball stuffed with feathers, then became a smooth ball made out of a clay type material, then came rubber balls that where scratched to make them rough. After extensive development of the design of the markings on the golf ball scientists believe that they have found the perfect design of dimples on the golf ball. : While Professor Tait was apparently the first to study the lift on a spinning ball in the game of golf, others before him had studied this effect. Sir Isaac Newton, some 220 years before Tait, recognized that a tennis ball "struck with an oblique racket" would move on a curved path. This effect is sometimes called the Magnus effect because Magnus did some careful experimental work on it. Many answers are found in some studies that were done by a scientist by the name of Daniel Bernouilli. Bernouilli found that whenever the speed of a fluid, a liquid, or a gas is caused to increase, its pressure decreases. This curious, almost paradoxical, effect can be shown to follow from Newtonian mechanics quite simply for the special case of a non-viscous incompressible fluid in streamline flow in a pipe. : Effects of Aerodynamic Forces : To display the effects of aerodynamics forces I tried an experiment. All I had to do was cut a small square piece of light cardboard, about 2 in. on a side, stick a pin or a thumbtack through its center, and place it over the end of a spool with the pin in the hole of the spool. I blew through the spool as hard as I was able. Practically everyone expects the card to be blown away, but actually the harder I blew the tighter the card clung to the end of the spool. The pin or thumbtack is essential to keep the card from slipping sideways from the spool. The behavior of the card can be understood in terms of Bernouilli's Principle. When the air flows between the card and the end of the spool its speed increases and makes the air pressure in this area lower. The air pressure on the other side of the card is greater and there is thus a resultant force from the high-pressure region holding the card firmly against the end of the spool. : There are tons of other ways that we can see Bernouilli's Principle. A Ping-Pong ball that’s mass is mere grams can be supported on a small jet of air. A larger rubber ball may be supported on an air jet from a vacuum cleaner used on its blow mode. . In each case the flow of air over the top of the ball produces a low-pressure region. The low pressure resulting from the increase in speed of the air over the topside of the wing of an airplane in conjunction with the high pressure below the wing produces the lift on the wing. As we shall see, the lift on a golf ball is another example of the Bernouilli effect. : Understanding Forces on A Spinning Ball : Let a ball, similar to a golf ball except that it has a smooth surface sit a rest while air moves past it at a small velocity. This is equivalent to having the ball move with the same small velocity through air at rest. A possible flow pattern of the air past a ball is shown in Fig. 8.1(a). The lines drawn in the figure show paths of small masses of air in their motion past the ball. : Streamline and Turbulent Flow : The air shown moving is Fig.8.1(a) is an example of streamline flow. Streamline flow is very different from turbulent flow and has to be distinguished. . When a candle has been snuffed out, the smoke rises smoothly in still air for a few inches and then breaks into a disturbed motion. The lower part shows streamline flow while the upper part shows turbulent flow. As the air flows past the ball, the air close to the ball has its speed increased from A to B and then decreased from B to C. This means, according to Bernouilli, that the pressure of the air near the surface of the ball decreases from its value at A to a lower value at B and then rises to have at C the same value it had at A. : The Boundary Layer : I thought that if air moving at a very low velocity was going across a golf ball the air pressure on it would be symmetrical forward and backward and therefor would result in no net force on the ball. But some experiments have shown that there is a force on the ball even with very small air velocities. This force is caused because air is a viscous fluid. The thin layer of air around the surface of the golf ball is called the boundary layer. In the boundary layer the speed of the air varies from zero at the surface of the ball to a larger speed away from the surface out in the streamline flow. The air surrounding the surface of the ball is not moving relative to the ball. Momentum is transferred across the boundary layer from the flowing air to the surface of the ball. The force acting on the ball is measured at the rate the momentum is being transferred. : The Viscous Drag On The Ball : If you want to better understand, imagining the stirring of a kettle of some viscous fluid, such as molasses, with a spoon. As the spoon stirs the fluid, the kettle will turn along with the fluid unless the kettle is held fixed. A torque must be applied to the kettle to keep it from turning. The tangential force of the fluid on the inner surface of the kettle results from the internal viscous effects in the fluid. A similar tangential force on the surface of the ball results from the internal viscous effects in the boundary layer at the surface of the ball. The force on the ball is proportional to the relative velocity of the air past the ball at this low velocity. : Air flowing from point A to point B outside the boundary layer is going from a high-pressure region to a low-pressure region and this pressure difference helps increase the air velocity. But the air moving from B to C is moving from low pressure to high pressure loses its velocity because it is going against the pressure difference. When the viscous effect in the boundary layer becomes large enough so that the air near the surface of the ball is stopped before it reaches C, turbulent motion takes the place of the streamline flow. This happens sooner or later as the air velocity increases. The velocity of air passing a well hit golf ball will be much greater than that at which streamline flow will occur. From A to B the flow is very similar to that in the previous example. At B or a little before B the boundary layer becomes stalled and a turbulent wake extends downstream from the ball. In this turbulent wake there is considerable violent stirring of the viscous air and energy is dissipated. When a ball flies through air at rest, this energy dissipated in the turbulent wake comes from the energy of motion (kinetic energy) of the ball. There is thus a resistive force, called "drag," on the moving ball which is not related to the viscous force in the boundary layer but comes rather from the difference in the pressure on the front and on the back of the ball. This drag in this velocity range varies closely as the square of the relative velocity of the air and the ball. : Dimple Increase Turbulence in Boundary Layer : Now if we imagine the change in the flow line pattern for a small masses of air when the surface of the ball is changed from a smooth surface to that of a dimpled surface. The dimple on the surface of the ball make the boundary layer turbulent; the surface is no longer smooth and the air has to dip in and out of the dimples, stirring it up a bit. Instead of stalling at B like it did in the previous example, the high velocity air carries the turbulent boundary layer along with it, helping it move along the surface of the ball from the low pressure region at B toward the higher pressured area at C. This is shown in Fig.8.1(c). : The turbulent wake starts farther back on the surface of the ball and is smaller in cross section than in the case of a smooth ball. The drag on a dimpled ball is much smaller that that of the smooth ball because less energy is dissipated in the smaller wake. This has been proven in tests comparing the drag of a smooth ball in comparison to the drag of a rough ball. : The Spinning Ball : Fig.8.1(d) is an illustration of the flow of air past a spinning dimpled ball as it spins. In the diagram the air is moving from left to right if we are assuming the ball is at rest or if we are assuming that the air is at rest then the ball is moving for right to left. : The turbulent boundary layer is moving with the surface of the ball as it spins. This means that the air over top of the ball is moving much faster relative to the ball than that moving underneath the ball. According to Bernouilli’s Principle the pressure on top of the ball is less than that of the air directly below the ball. All this means that there should be a force, called lift, perpendicular to the direction of the ball’s motion. : The turbulent boundary layer as it is pulled along over the top of the ball stalls farther down on the backside of the ball while the boundary layer on the underside of the ball is prevented from remaining next to the ball and stalls even before it reaches the lowest point of the ball. The wake behind the ball then starts down lower than the wake behind a non-spinning ball. The flow pattern takes on a downward component. The air must receives some downward momentum and the ball recoils in the upward direction. This is another way of looking at the origin of the Bernouilli lift on the ball. : There have been ways to measure aerodynamics of spinning golf balls invented, but it is difficult to give a quantitative description of the results of these experiments because the drag and the lift depend on at least three variables, the speed of the ball through the air, the rate of spin on the ball, and the surface texture of the ball, whether it is smooth or dimpled. So general statements are made. : The faster a ball moves through the air and the faster it spins the more drag the ball has. It may become about as large as the weight of the ball. The lift on a dimpled ball increases with the rate of spin at any given air speed and increases with air speed at any given rate of spin It may become nearly as large as the weight of the ball. : Every golfer knows that when they are hitting with the wind they will be able to drive much further than if they were hitting into the wind. This is a perfect example of the increase in drag with increased air speed at the ball. Every golfer also knows that a golf shot hit into the wind will fly at a higher trajectory than one hit with the wind. This is a perfect example of the increase in lift with the increase air speed coming at the ball. : Competing Effects of Lift and Drag : We now know that there are two major effects battling in the flight of a golf ball. It is the Lift vs. the drag of a spinning golf ball. The larger the spin the more the drag which makes the ball slow down more rapidly which makes the ball not go as far. But the larger spin also creates more lift, which allows the ball to remain in flight much longer, which lets the ball go farther. But what force over rules the other? Experience has shown that the lift do to spin is more powerful than the drag do to spin. So a shot with lots of spin and has lots of drag but also tons of lift will go farther that a shot with no drag but also no lift. : Now we know all about the flight of a ball and it is just up to us to hit the perfect drive. The perfect drive varies from person to person but you can figure out your maximum potential. First it starts of with your swing speed. Fats and strong joints will help your swing speed, but nothing will help it more that mass. People with large masses can use their weight to their advantage to gain a faster swing. To figure out the moment of your club head you will need to use the formula P=MV. Once you have your club heads momentum and you can assume the momentum of the ball on the tee is zero then you just have to remember Law of Conservation of Momentum, which is the initial momentum of an isolated system is equal to its final momentum. We know that the golf ball has a bass of 0.045 kg and has zero velocity and by weighing the club head we found that it weighed 0.650 kg and has 2.5P of momentum. If 2.5P of momentum is transferred into a 0.045 gram golf ball than the golf ball is going to leave the club face at a velocity of (2.5P \ 0.045 kg = 55.6 m/s x 60 squared divided by 1000 = 200.16 km/h. Now calculating my farthest possible shot with no spin on the golf ball would be easy, but once you calculate the spin of the ball into the picture that it becomes very complicated to find an answer. I spent about 3 hours trying to figure out what my optimum driving distance would be by measuring my wing speed and the calculating in the spin on the ball. I found the spin on the ball by screwing in a small screw into the ball and the tying a long hockey skate lace to it and the hitting it into a small wall coated with putty. Then I counted the amount of times the lace had twisted, and by using the speed of the ball which I just worked out above I found out the time and found that in 0.41 seconds the lace had been spun 51 times. To find the spins/second rate all I had to do was 1\0.41 s = 2.4 x 51 = 124.4 spins/second. Now I knew the spin rate that I shot at and the speed at which I could hit the ball so I thought I could figure out what my maximum drive potential would be. After I had all the data needed I sat down at my desk with a stack of 25 lined paper, a pencil and a calculator and spent 3 hours and went through every piece of paper trying to find my goal, what my perfect drive would be. : In conclusion I decided that there were to many variables in my equations and I was unable to find out how far I could potentially hit the ball with the perfect drive. The closest I got to an answer was when I went to the driving range and hit two buckets of golf balls. By best drive of the day was on a shot where I think I achieved my maximum club head speed and hit the ball on a perfect angle. The golf ball landed about 303 yards away and I thought that maybe I had obtained my maximum drive. But as I was driving home I realized that that could not have been my maximum drive because the ball curved upwards and towards the right. Meaning that the axis that the ball was spinning on could not have been straight. Some of the balls spinning energy was put to waist sending the ball to the right when that force could have been helping the lift. The extended lift would have let the ball remain in the air for a longer amount in time. So I realized that I had not obtained my perfect drive. But I did at least realize that my perfect drive is probably slightly more that 303 yards in the air.
User WWW URL:
UserLink Title:

High Graphics
Low Graphics