History

1. History Newton published an article exploring the curved flight of tennis balls in 1672. New Principles of Gunnery, by B.Robins. first published in 1742 About 100 years later G. Magnus gave a similar explanation. The lateral deflecting force of a spinning sphere ball was named the Magnus Force. Magnus & Robins -- trajectories of cannon and musket balls. Robins - musket balls , slightly curved barrel. barrel bent left, ball was forced to right side, clockwise spin from above, curve to right Magnus - small cylinder rotating vertically in horizontal wind. could move laterally, not downstream. Cord wrapped around axis gives spin when pulled Magnus & Robins -- trajectories of cannon and musket balls. Robins - musket balls , slightly curved barrel. barrel bent left, ball was forced to right side, clockwise spin from above, curve to right Magnus - small cylinder rotating vertically in horizontal wind. could move laterally, not downstream. Cord wrapped around axis gives spin when pulled

2. History Many people in the last hundred years have set out to explain various aspects of baseball. In 1987, Robert K Adair was hired as the Official Physicist of the National League. Published The Physics of Baseball in 1990 Adair was good friend of Bart Giamatti, pres of NL, later commish, also an english Prof and president of Yale.Adair was good friend of Bart Giamatti, pres of NL, later commish, also an english Prof and president of Yale.

3. The Reynolds Number An object�s flow through a fluid (air) is determined by a Reynolds number � proportional to the fluid density, the fluid velocity, and the size of the object, and inversely proportional to the viscosity of the fluid. For baseball Re?2200V, with V in mph viscosity is the resistance a material has to change in form In other words it�s a measure of the "stickiness" of a fluid. (Alcohol has a lower viscosity than honey.) -To get an idea of the magnitude of the Reynolds number, consider a car moving at a speed of 55 mi/hr (= 24 m/s). An appropriate value of L would be the typical width of the car, which I would estimate to be about 1.5 m. The Reynolds number for the flow of air about the car is then 2.4*10^6 -Re is used in most situations involving fluid flow, For instance, to test a 1/3 scale car in a wind tunnel, Re=Re, so set the two equations equal to each other, find that 165mph wind in tunnel represents 55mph in real life. viscosity is the resistance a material has to change in form In other words it�s a measure of the "stickiness" of a fluid. (Alcohol has a lower viscosity than honey.) -To get an idea of the magnitude of the Reynolds number, consider a car moving at a speed of 55 mi/hr (= 24 m/s). An appropriate value of L would be the typical width of the car, which I would estimate to be about 1.5 m. The Reynolds number for the flow of air about the car is then 2.4*10^6 -Re is used in most situations involving fluid flow, For instance, to test a 1/3 scale car in a wind tunnel, Re=Re, so set the two equations equal to each other, find that 165mph wind in tunnel represents 55mph in real life.

4. Drag The retarding force on a baseball Drag is proportional to the cross sectional area of the ball, the square of the velocity of the ball, the density of air, and a drag coefficient (involving the Reynolds number).

5. Drag Turbulence caused by roughness, actually lowers the drag coefficient. So, the baseball, both rough and smooth, is found in the middle. From the previous slide, ?drag coefficient = ? drag Notice that this only true for V<155mph -> airplanes are smooth b/c faster than 155 This is why golf balls have dimples, b/c slower than 155 From the previous slide, ?drag coefficient = ? drag Notice that this only true for V<155mph -> airplanes are smooth b/c faster than 155 This is why golf balls have dimples, b/c slower than 155

6. Bernoulli�s Principle Bernoulli�s principle states that the sum of the pressure plus the kinetic energy per unit volume of a flowing fluid must remain constant: In Bernoulli�s principle P is the pressure, d is the density of the fluid, and v is the fluids speed. Pressure is said to be the ratio of force to the area over which it is applied. The second term is the kinetic energy per unit volume (kinetic energy divided by volume) of the fluid, since density is mass divided by volume. According to Bernoulli�s theorem when applied to baseball, the circulating air slows down the flow of air past the ball on one side and speeds it up on the other. In Bernoulli�s principle P is the pressure, d is the density of the fluid, and v is the fluids speed. Pressure is said to be the ratio of force to the area over which it is applied. The second term is the kinetic energy per unit volume (kinetic energy divided by volume) of the fluid, since density is mass divided by volume. According to Bernoulli�s theorem when applied to baseball, the circulating air slows down the flow of air past the ball on one side and speeds it up on the other.

8. The Magnus Effect When a spinning object moves through a fluid it experiences a sideways force. The Magnus effect is created by an imbalance in air pressure. The strength of the Magnus Force is in direct proportion to the rate of the spin as well as the forward speed of the ball-the greater the forward speed the greater the force. The direction of the Magnus force depends only on the direction of spin. The strength of the Magnus Force is in direct proportion to the rate of the spin as well as the forward speed of the ball-the greater the forward speed the greater the force. The direction of the Magnus force depends only on the direction of spin.

9. The Magnus effect on a spinning baseball When an object is moving through the air, its surface interacts with a thin layer known as the boundary layer. When the boundary layer peels away from the surface it creates a �wake.� The wake can also be described as low-pressure region behind the ball. The front-to-back pressure difference creates a backward force on the ball, which slows its forward motion down. This is the normal air resistance, or drag, that acts on any object moving through the air. When the wake is completely deflected, that is the moment the ball breaks. The Change in momentum is cumulative, and as the ball is in flight (with top spin) it builds up pressure, then it breaks, due to any lateral force acting on it. The effect is to generate a pressure difference across the ball, creating a lateral force component that pushes the ball sideways. This force is known as the Magnus force. The Magus Force always points in the same direction that the front of the ball is turning toward.The wake can also be described as low-pressure region behind the ball. The front-to-back pressure difference creates a backward force on the ball, which slows its forward motion down. This is the normal air resistance, or drag, that acts on any object moving through the air. When the wake is completely deflected, that is the moment the ball breaks. The Change in momentum is cumulative, and as the ball is in flight (with top spin) it builds up pressure, then it breaks, due to any lateral force acting on it. The effect is to generate a pressure difference across the ball, creating a lateral force component that pushes the ball sideways. This force is known as the Magnus force. The Magus Force always points in the same direction that the front of the ball is turning toward.

10. A ball thrown with backspin does not fall as much as a ball with no spin. The Magnus force is pushing the ball with an upwards force. This pitch produces what is often called a rising fastball.A ball thrown with backspin does not fall as much as a ball with no spin. The Magnus force is pushing the ball with an upwards force. This pitch produces what is often called a rising fastball.

11. A pitch with topspin tends to drop more than a pitch with no spin. The Magnus force is pushing down.A pitch with topspin tends to drop more than a pitch with no spin. The Magnus force is pushing down.

12. The amount of Force that a baseball will curve can be determined by the equation: Where FL is the Magnus Force, K is the Magnus Coefficient, ? is the spin frequency measured in rpm, V is the velocity of the ball in mph, Cv is the drag coefficient.  Fl is the Magnus force K is the Magnus coefficient W is the rpm of the spinning ball V is the velocity in mph Cv is the drag coefficient of the air. Fl is the Magnus force K is the Magnus coefficient W is the rpm of the spinning ball V is the velocity in mph Cv is the drag coefficient of the air.

13. The Ole Number OneThe Fastball The most important person on the team is the pitcher. The pitcher must project the ball in patterns of trajectories, velocities, and placements such that the batter cannot hit the ball squarely. The focus of the fastball is to try to overpower batters. The fastball is held 2 ways: 4-seam and 2-seam. The ball is thrown directly towards the plate, and is allowed to roll off of the fingers as they are snapped down on release putting straight backspin on the ball as it travels to the plate. There is typically not a lot of movement on a fastball, it basically goes from the release to the plate. The most important person on the team is the pitcher. The pitcher must project the ball in patterns of trajectories, velocities, and placements such that the batter cannot hit the ball squarely. The focus of the fastball is to try to overpower batters. The fastball is held 2 ways: 4-seam and 2-seam. The ball is thrown directly towards the plate, and is allowed to roll off of the fingers as they are snapped down on release putting straight backspin on the ball as it travels to the plate. There is typically not a lot of movement on a fastball, it basically goes from the release to the plate.

14. The Four-seam Fastball In the four-seam fastball or �rising fastball�, four seams catch the air as the ball rotates, and the ball tends to float due to the lift generated by the four seams. If the ball is thrown with a backspin, the Magnus Force will point away from the ground, causing the ball to curve less. The laws of aerodynamics tell us that for a baseball to physically rise as it approaches the batter, the Magnus force would have to be greater that the weight of the ball, and the rate of spin required to generate this much force is far beyond the ability of any pitcher. So the rising fastball is an optical illusion. The ball falls less than the batter expects it to. If the ball is thrown with a backspin, the Magnus Force will point away from the ground, causing the ball to curve less. The laws of aerodynamics tell us that for a baseball to physically rise as it approaches the batter, the Magnus force would have to be greater that the weight of the ball, and the rate of spin required to generate this much force is far beyond the ability of any pitcher. So the rising fastball is an optical illusion. The ball falls less than the batter expects it to.

15. The Two-seam grip For the two-seam fastball, there are only two seams catching air, thus the ball tends to sink. The two-seam fastball is less effective in generating a Magnus effect. It is delivered with less backspin, and could cause the ball to drop down up to 3 inches�.. More or less depending on the arm angle. With only 2 seams catching the air, it is easier for pressure to build up and cause the ball to �drop� but not more than 3 inches more than the 4-seam, so a total of 7 inches in the drop. On average the two-seam fastball is 2mph slower than the four-seam. The two-seam fastball is less effective in generating a Magnus effect. It is delivered with less backspin, and could cause the ball to drop down up to 3 inches�.. More or less depending on the arm angle. With only 2 seams catching the air, it is easier for pressure to build up and cause the ball to �drop� but not more than 3 inches more than the 4-seam, so a total of 7 inches in the drop. On average the two-seam fastball is 2mph slower than the four-seam.

16. Four-Seam vs. Two-Seam The four-seam grip is called a �cross-seams fastball� The two-seam grip is also called �with the seams fastball� or �Sinking Fastball.� The Four-seam tends to float due to the lift generated by the four seams interacting with the air. The Magnus force is greater than the two-seam. Studies and calculations done between the two show that the four seam fastball reaches the plate 7 inches before the two-seam. There is a greater �hop� with the four seam, meaning it doesn�t drop as much. The Four-seam tends to float due to the lift generated by the four seams interacting with the air. The Magnus force is greater than the two-seam. Studies and calculations done between the two show that the four seam fastball reaches the plate 7 inches before the two-seam. There is a greater �hop� with the four seam, meaning it doesn�t drop as much.

17. Does a Fastball move like a Curveball? When gripped properly and thrown with enough backspin a Fastball can move side to side or even up and down. Some fastballs move more than others.Some fastballs move more than others.

18. The Sinking Fastball The sinking fastball is gripped on top of the ball with the narrow seams exposed. When releasing this fastball, you usually apply pressure against the seam with either the index or middle finger. The fingers will off the ball easier and won�t give it as much rotation, thus lowering its backspin. This reduces the Magnus Force even more than the 2-seam fastball causing the pitch to drop or �sink� more than a standard fastball. The fingers will off the ball easier and won�t give it as much rotation, thus lowering its backspin. This reduces the Magnus Force even more than the 2-seam fastball causing the pitch to drop or �sink� more than a standard fastball.

19. The Aerodynamics of a Curveball  Have you ever wondered whether a curve ball really curves, or is it just an optical illusion? A curveball is a pitch that appears to be moving straight toward home plate but is actually moving down and to the right or left depending on a pitcher. There are 2 basic factors involved in creating a curveball: The grip and air resistance A curveball is a pitch that appears to be moving straight toward home plate but is actually moving down and to the right or left depending on a pitcher. There are 2 basic factors involved in creating a curveball: The grip and air resistance

20. The Grip �Choke� the ball (wedge it down between your thumb and forefinger), and cock your wrist to the left; the ball snaps down and to the right on release. The resulting pitch should drop and curve to the left. To throw a curveball, a pitcher must hold the ball between his thumb and his index finger resting on the seam. When the pitcher comes through his motion to throw the ball, he snaps his wrist downward as he releases the ball, which gives the ball topspin. If the pitch is thrown properly the back of his hand will be facing the batter at the end of his motion. To throw a curveball, a pitcher must hold the ball between his thumb and his index finger resting on the seam. When the pitcher comes through his motion to throw the ball, he snaps his wrist downward as he releases the ball, which gives the ball topspin. If the pitch is thrown properly the back of his hand will be facing the batter at the end of his motion.

21. The flight of a Curveball This picture is shown with a 1000 rpm coming at a velocity of 60 ft/sec about its horizontal axis at right angles to the wind. The crowding together of the smoke filaments over the top of the ball shows an increased velocity in this region and a corresponding decrease in pressure, which according to Bernoulli�s Principle, would tend to deflect the ball upward across the wind stream. It will also be noted that the wake of the ball has been deflected downward. According to the principle of the conservation of momentum, this must be accompanied by a corresponding upward thrust on the ball. NOTE: If the wind is from the east to west and the ball is spinning counterclockwise about the vertical axis, then the Magnus force on the ball is directed towards the north. This picture is shown with a 1000 rpm coming at a velocity of 60 ft/sec about its horizontal axis at right angles to the wind. The crowding together of the smoke filaments over the top of the ball shows an increased velocity in this region and a corresponding decrease in pressure, which according to Bernoulli�s Principle, would tend to deflect the ball upward across the wind stream. It will also be noted that the wake of the ball has been deflected downward. According to the principle of the conservation of momentum, this must be accompanied by a corresponding upward thrust on the ball. NOTE: If the wind is from the east to west and the ball is spinning counterclockwise about the vertical axis, then the Magnus force on the ball is directed towards the north.

22. The Knuckleball There is no standard for how to throw a knuckleball. In general the ball is held as shown, pushing all of the fingers evenly out on the ball results in very little spin

23. The Knuckleball As the ball is thrown with little or no spin, the asymmetrical stitches generate large imbalances of forces and somewhat unpredictable trajectory. Low resistance turbulent air flow will be induced by stitches on one side of ball, while air flows smoothly, with more resistance on the other.

24. Knuckleball The stitches on a baseball act to push the air flow away from the leather surface just enough to form a tiny swirl of air just behind them, which most of the air happily slides past. The air moving on top of the ball goes slower, so by Bernoulli�s principles there will exist a pocket of lower pressure at the bottom and right of the ball. This lower pressure draws the ball towards it and causes a lateral deflection described earlier, the Magnus Force.The stitches on a baseball act to push the air flow away from the leather surface just enough to form a tiny swirl of air just behind them, which most of the air happily slides past. The air moving on top of the ball goes slower, so by Bernoulli�s principles there will exist a pocket of lower pressure at the bottom and right of the ball. This lower pressure draws the ball towards it and causes a lateral deflection described earlier, the Magnus Force.

25. Research by Watts and Sawyer, 1974 T=52, 310, oscillation with .18 lb amplitude at .5-1 cycle/second caused by strings on boundary layer separation T=140, 220 discontinuous jumps caused by separation point moving from in front of strings to behind. Research by Watts and Sawyer, 1974 T=52, 310, oscillation with .18 lb amplitude at .5-1 cycle/second caused by strings on boundary layer separation T=140, 220 discontinuous jumps caused by separation point moving from in front of strings to behind.

26. Impulse-Momentum theorem Impulse is the total change of momentum of a body over time. Second equation can be used for either a spinner or a non-spinnerSecond equation can be used for either a spinner or a non-spinner

27. Knuckleball without spin If the knuckleball is thrown with no spin it can only curve laterally in one direction However, if ball is thrown in position where T=52� or 310� it will have a very erratic path, this has been observed in actual pitches and is a nightmare for batters and catchers. Ball held at specific T (previous slide.) For instance, ball thrown with T=120, deflected by a force of about .1 lbs during the entire trip. Lateral displacement = 2.4 ft Ball held at specific T (previous slide.) For instance, ball thrown with T=120, deflected by a force of about .1 lbs during the entire trip. Lateral displacement = 2.4 ft

28. Model for no spin knuckle

29. Knuckleball with spin A much more realistic model is that the ball does spin on the way home, so the lateral forces it is exposed to are constantly changing on the way home. Do calculations on board now. Do calculations on board now.

30. Knuckle with spin Too much spin will result in a small deflection, so the spin is critical Approximating the curve seen in the handout, with an Amplitude=.08lbs we find that a K-ball at 40mph with 2 revolutions on the way home will only be deflected .048ft or .6 inches An important note, when rotating ball should go through one of the 4 erratic angles shown in the handout.An important note, when rotating ball should go through one of the 4 erratic angles shown in the handout.

31. Knuckleball By numerically integrating 2nd equation from impulse momentum slide, with an initial orientation of 90�, Watts and Sawyer came up with this diagram -As you can see, the � revolution pitch would be hard to hit, but the � revolution pitch would make you think it would surely be off the plate. Two theories about hitting a knuckleball, unfortunately neither work By numerically integrating 2nd equation from impulse momentum slide, with an initial orientation of 90�, Watts and Sawyer came up with this diagram -As you can see, the � revolution pitch would be hard to hit, but the � revolution pitch would make you think it would surely be off the plate. Two theories about hitting a knuckleball, unfortunately neither work

32. Pictures of a knuckleball as it rotates. The blue areas are areas of turbulence, which causes less resistance and lower pressurePictures of a knuckleball as it rotates. The blue areas are areas of turbulence, which causes less resistance and lower pressure

33. Downfalls of the Knuckle Catchers must use their glove and their body to at least block a knuckler, if they are unsuccessful, the ball will pass them, resulting in stolen bases or the batters advancement to first. If a knuckleball does not break much, due to too much spin or bad orientation of the pitch, it will end up in the bleachers One successful knuckle catcher was once asked how he handled the pitch, he replied its easy, I just wait till it stops rolling and pick it up.One successful knuckle catcher was once asked how he handled the pitch, he replied its easy, I just wait till it stops rolling and pick it up.

34. Illegally Modified Baseballs Possible ways a pitcher can cheat to gain a bigger advantage over the hitter.

35. The �Spit-Ball� When a lubricant is applied to a baseball it can have the trajectory of a knuckleball with the speed of a fastball. Saliva, sweat, vacillating any type of lubricant will cause the ball to �slip� off your fingers with no spin. The process of the sinking fastball can be exaggerated by liberating the fingers to make them slide off the ball even more readily. The result of a spit ball is that it can hardly have any rotation, but yet have the speeds of a regular fastball.Saliva, sweat, vacillating any type of lubricant will cause the ball to �slip� off your fingers with no spin. The process of the sinking fastball can be exaggerated by liberating the fingers to make them slide off the ball even more readily. The result of a spit ball is that it can hardly have any rotation, but yet have the speeds of a regular fastball.

36. What happens you have a scuffed baseball Scuffing can produce asymmetric forces on the ball and irregular trajectories. Scuffing the ball can increase the drag on one side and cause the ball to move in that direction. Good pitchers can throw the ball so that the effect of seams is symmetric. SO if a ball was scuffed on one end of the rotation the ball will veer to the scuffed area, and the ball will remain fixed on the side with the scrape. These situations can produce unexpected curving trajectories coupled with high speeds. That is why both of these techniques are illegal. Good pitchers can throw the ball so that the effect of seams is symmetric. SO if a ball was scuffed on one end of the rotation the ball will veer to the scuffed area, and the ball will remain fixed on the side with the scrape. These situations can produce unexpected curving trajectories coupled with high speeds. That is why both of these techniques are illegal.

37. Summary People have been studying these phenomenon since Newton The course the baseball takes while it is in flight is dependant upon the axis of spin, the amount of spin, and the orientation of the ball. These factors effect trajectories because of the Magnus Effect and Drag Force