Effect of Seam-Height on Curveballs

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5-26-2015
Effect of Seam-Height on Curveballs
Joseph S. Carroll
Linfield College
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Carroll, Joseph S., "Effect of Seam-Height on Curveballs" (2015). Senior Theses. Paper 14.
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Effect of Seam-­‐Height on Curveballs Joseph Carroll A THESIS Presented to The Department of Physics LINFIELD COLLEGE McMinnville, Oregon In partial fulfillment of the requirements For the degree of BACHELOR OF SCIENCE May 2015 THESIS COPYRIGHT PERMISSIONS
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Effect
of Seam-
He ight
on
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l
Jo
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Thesis Acceptance
Linfield College
Thesis Title:
Effect of Seam-Height on Curveballs
Submitted by:
Joseph Carroll
Date Submitted:
May 2015
Thesis Advisor:
Physics Department:
Physics Department:
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Abstract The difference in seam-­‐height between raised and flat-­‐seam baseballs causes them to react differently when thrown by a pitcher. Altering the seam-­‐height on the ball changes the amount of drag force on it as it travels through the air. The goal of this experiment is to measure the difference in vertical deflection between the two types of balls when pitched with curveball topspin. It was discovered that the baseball with raised-­‐seams experiences more vertical deflection than the flat-­‐seam ball. 3 I. Introduction The flight of a projectile through the air is affected by air drag. This is evident in the sport of baseball because the laces on the ball are elevated above the surface of it enough that they significantly affect the movement of the ball through the air. In 2011, NCAA baseball adopted a new standard for bat performance that is safer for the players, but this caused the number of home runs and runs scored per game to drop drastically in the years to come [1]. In hopes of restoring the lost offensive numbers, the NCAA baseball committee implemented a new flat-­‐seam baseball in 2015 with markedly reduced seam height. The sports research lab at Washington State University and the Rawlings research lab conducted studies that launched both balls out a machine with home run trajectories, and concluded that the decreased drag from flatter seams leads to batted balls traveling greater distances [2]. Less is known about how the flatter stitching affects the movement of the baseball on its way from the pitcher’s mound to home plate. While an ideal batted ball will have backspin, creating an upward force that allows the ball to travel farther, an effective “curveball” pitch rotates forward on its way to the plate, which causes the ball to drop. Balls with backspin and topspin are demonstrated in figure 1.1. 4 Figure 1.1: Defining Topspin and Backspin. In Either case, the axis of rotation is perpendicular to the direction of motion. The Topspin ball is rotating forwards, while the backspin ball is rotating backwards. Since the distance from the pitcher’s mound to home plate is only 60 feet, compared to the batted ball testing in which baseballs traveled nearly 400 feet, the effect of drag is certainly less. Nevertheless, considering that the diameter of a baseball bat is barely greater that of a baseball, any inch of break or vertical movement that a pitcher can put on the baseball will make it more difficult for the hitter to hit. I predict that when pitched with the same velocity and spin rate, the new baseballs with flat seams will not have as much vertical drop as the raised-­‐
seam balls. The goal of this experiment is to see if the vertical drop of curveball pitches with topspin will be affected by the change in seam height. 5 667!9+(:3528,0;"#$25<!
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The drag coefficient significantly drops as the speed increases; however, the drag force is proportional 𝐶 𝑣 ! and actually increases with speed. When the ball reaches higher speeds, the airflow around it becomes more turbulent, allowing the ball to slip through the air more easily [5]. This is why the drag coefficient decreases as speed increases. Drag force was the key variable in this experiment because it is different for the two types of baseballs. The difference in seam height of the raised and flat-­‐seam baseballs means that the balls will have different values for A and 𝐶! . The seams on the baseball provide the sort of “roughness” or “smoothness” that is referred to in figure 2.1. This experiment looks at curveballs ranging between 60-­‐80 mph, and according to figure 2.1, the raised-­‐seam ball will have a lower drag coefficient over this range. However, we must not forget that the raised-­‐seam ball will also have a greater surface area, which will also contribute to drag force. The two baseballs have identical weights, so the force downwards due to gravity will be the same on both balls. The other significant force to consider is the force caused by the spin of the ball, which is perpendicular to the velocity of the ball.
This spin force is called the Magnus force [6]. When a pitcher throws a curveball, he grips it in such a way that the ball rotates with topspin. As you will see in figure 2.2 the act of throwing a ball with topspin puts a downward force on the ball that causes it to drop, making it more difficult for the batter to hit. 7 Figure 2.2: Forces on a curveball. The ball is moving from left to right, and the axis of rotation is going in
or out of the page, perpendicular to the ball’s motion. Relative to the air around the ball, the top edge of the
ball has a greater speed than the bottom edge. This results in a larger drag force on the top edge of the ball.
Notice that because of the way the axis of rotation is perpendicular to the direction of travel, the speed is different on opposite edges of the ball. The larger velocity of the top edge will cause it to have a greater component of drag force than the bottom edge. The Magnus force is the net force downwards that results from adding the components. These components are proportional to the square of the velocity of the surface of the ball relative to the air. Thus the components of drag force on the lower half of the ball and the top half of the ball will be 𝑣 − 𝜔𝑟 ! and (𝑣 + 𝜔𝑟)! respectively. Finding the difference between these terms allow us to describe the Magnus force as shown in equation 2.2 [7]. 𝐹! ∝ 𝑣 + 𝑟𝜔
!
− (𝑣 − 𝑟𝜔)! ~𝑣𝑟𝑤
(2.2)
The net spin-­‐dependent force than takes the form of equation 2.3.
𝐹! = 𝑆! 𝜔𝑣!
8 (2.3)
The coefficient 𝑆! is determined from experimental measurements to have a value of !!
!
≈ 4.1x10−4 [8], where m is the mass of a baseball. The Magnus force generated by a pitcher throwing 60-­‐80 mph with a typical spin rate of 2150 rpm is about a third of the weight of a ball [9], but this will vary between raised and low seam balls. The lowered seam-­‐height of the flat seam ball reduces the amount of drag force, which causes a reduction in Magnus force as well. Part of this experiment involves calculating the trajectory of a curveball numerically, using MATLAB. Because only vertical deflection is being considered, the equations of motion of the overhand curveball can be described in two-­‐
dimensions by the following set of first-­‐order ordinary differential equations. dx
= vx
dt
B2
dvx
= − vvx
dt
m
(2.4) dy
= vy
dt
S 0 vxω
dvy
= −g −
dt
m
!
Where !! is the drag factor that includes the factors from equation 2.1, such as cross-­‐sectional area. The difference in seam heights of the two types of baseballs will lead to them having different Magnus and drag forces, which should cause differences in their vertical deflection. 9 III. Experiment/Methods The goal of this experiment is to see if the two different types of baseballs will perform differently, when thrown by a pitcher with curveball spin. In order to simulate a pitcher throwing a curveball pitch, I used a JUGS Curveball Pitching machine [10]. This pitching machine is designed for collegiate and professional baseball players to use to practice hitting curveballs that simulate a real pitcher. A photo of the pitching machine used for this experiment is shown in figure 3.1 Figure 3.1: JUGS Curveball Pitching Machine. The top wheel spins faster than the bottom wheel, according to recommended settings in the pitching machine manual, which results in realistic curveballs of any desired velocity. Photo taken of actual setup at Linfield batting cages. The pitching machine consists of two rubber wheels, one spinning clockwise, and the other spinning counter clockwise. The rotational velocity of each wheel can be manually adjusted to throw different types of pitches with different spins. The angle of the wheels can be adjusted to throw curveballs from any angle. In this 10 experiment I am only concerned with the vertical deflection due to spin, so in all trials the wheels are positioned vertically, as shown in figure 3.1. In order to give the pitch topspin, thus simulating the curveball pitch, the top wheel is set to spin faster than the bottom wheel. The dials can be set from 0-­‐100, but the best dial setting to give an overhand curveball is to keep the dials 35 units apart. For example, having the top wheel set to 70 and the bottom wheel set to 35 will fire an overhand curveball approximately 60 mph. All trials in this experiment use this same dial differential, which produces a spin rate that emulates a real college curveball, approximately 40 revolutions per second. Using the recommended dial settings produces curveballs that mimic what a real pitcher would throw. The Jugs curveball machine has the ability to send balls with speeds ranging 20-­‐104 mph, but I will only test a realistic curveball speed range of 60-­‐80 mph. The speed of the pitch was measured using a JUGS radar gun, which is shown in figure 3.2. Figure 3.2: JUGS radar gun. Standing behind the pitching machine and pointing the radar gun at the ball gives the speed of the pitch. The speed of every pitch was recorded, and the average speed of each trial was calculated. 11 The flat-­‐seamed ball has a seam height of 0.031 inches. This is shorter than the raised-­‐seam height of 0.048 inches. While this difference may not be immediately apparent by looking at the balls, the feeling is very noticeable when holding the ball. A comparison of the baseballs used can be seen in figure 3.3. Figure 3.3: Side-­‐by-­‐side comparison of the raised and flat-­‐seam baseballs with seam heights of .048 and .031 inches respectively. Studies done by WSU and Rawlings concluded that flat-­‐seam balls travel greater distances, but there has yet to be a study of their affect on curveballs. To experimentally measure how the difference in seam height affects the pitch, the balls were covered in chalk, and fired with identical dial settings at a 5x7 foot black vinyl backdrop 56 feet from the pitching machine. The balls were covered in chalk so that they would make a mark on the target when they hit it. Measuring tape extended up and down the height of the target, allowing me to collect data by quantifying the vertical impact points of the balls. This setup can be seen in figure 3.4. 12 Figure 3.4: Curveball target. Measuring tape was attached to the vinyl target, allowing the impact points of chalk-­‐covered baseballs to be collected. Trials at velocities between 60-­‐80 mph were done for both types of baseballs, and their average impact height for each trial was compared to see the difference in vertical break. There is a significant amount of experimental error due to the uncertainty of the machine. The machine is fairly inconsistent, and the same baseballs under the same conditions do not always hit the same spot. As I mentioned earlier, the wheels are positioned vertically, in order to give the ball perfect topspin. However, the variation in horizontal impact that can be seen in figure 3.4 tells us that the balls are not exiting the pitching exactly the same every time. This could be partially due to the ball not being oriented exactly the same every time it touches the wheels. I 13 attempted to give them the same orientation every time by placing them between the spinning wheels by hand. I placed them between the wheels with 4-­‐seam orientation, which is where you grip the ball across the horseshoe shaped seams, allowing 4 seams to cut through the air with every rotation. 4-­‐seam orientation is shown in figure 3.5. Figure 3.5: 4-­‐Seam orientation. Placing the balls in the machine with 4-­‐seams minimizes any horizontal deflection that may occur when air interacts with the seams. Also, establishing a certain way to feed the ball into machine minimizes any variation that would occur from the balls being oriented differently from pitch to pitch. The marks from balls on the target do not have the same vertical impact point every pitch, but by analyzing the data I am able to find a value for their average vertical location. The average location of both types of balls in each of the various trials was then compared. Because the difference in seam height leads to 14 different drag and spin forces on the baseballs, the different balls generally group around two different locations. I was able to obtain plausible results from this experimental method, but uncertainty of the pitching machine motivated me to create a computational model for comparison. Modeling the overhand curveball trials computationally allows us to see what should happen without the uncertainties inherent in the experimental setup, and gives us something to confirm the reasonableness of the experimental results. The motion of a pitched baseball can be described by the ordinary differential equations in equation 2.4. The preferred method, and the simplest method for solving these equations is Euler’s method, which gives us a numerical solution to equations that would be difficult to solve analytically [11]. Euler’s method is helpful for any situation that involves calculating an unknown curve that has a given starting point and satisfies a given differential equation. Thus, this method allows us to investigate the motion of a pitched baseball, and gives us an accurate approximation of that motion. Initial values for x and y are given based on the distance between the pitcher and home plate, and the typical height at which a pitcher releases a curveball. At this starting point the slope and tangent line are calculated using the differential equations. A small time step is taken along the tangent line and then the slope is calculated again. This is an approximation, but by making the time step small enough, the error between the approximation and the unknown curve can be minimized. After a sufficient amount of time steps and slope calculations, the result is a good approximation of an overhand curveball. 15 6?7!F$%8/*%!+,0!',+/<%&%!
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To put the significance of this difference in vertical deflection in perspective, note that the diameter of a baseball bat is less than 3 inches, and typical strike zone has a height of about 30 inches. Baseball is a game of inches, and any small difference of where the ball hits the bat affects the outcome. The standard deviation bars in figure 4.1 are large enough that the average raised-­‐seam height falls within the standard deviation of the low-­‐seam, and vice-­‐versa. This motivated the computational model of the same pitch illustrated in figure 4.2. Y (feet) X (feet) Figure 4.2: Computational model of the 77 mph curveball in figure 4.1. The red line represents the flat-­‐seam ball, and the raised-­‐seam ball is in blue. Both were given the same starting point, velocity, and spin rate. The raised-­‐seam ball has a 2.2 % larger cross-­‐sectional area, which contributes to a greater drag and magus forces. There are uncertainties present in the experimental trials, due to the inability of the pitching machine to hit the same point of impact consistently. While the grouping of raised seam pitches appears to generally fall below the grouping of low seam pitches, the large standard deviation from the average makes it less 17 %'04-0%-0.P!<0!'3>$3!&'!#23&/$3!-04$7&-.)&$!&/$!7$)*!/$-./&[7!$##$%&!'0!4$3&-%)6!
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V. Conclusion The data shows that for overhand curveballs ranging between 65-­‐80 mph, the raised-­‐seam baseball experiences more vertical deflection than its flat-­‐seam replacement. The change in seam height was enough to reduce the baseball’s vertical deflection by several inches. The data also shows that the baseballs experience the most change in vertical deflection in the 65 mph trial, and this change in vertical deflection decreases as velocity increases. My assumption is that the 65 mph pitches experience the most difference because the longer path to home plate allows more time for the laces to alter the motion of the ball. A computational model of the experiment yielded consistent results, concluding that the raised-­‐seam ball drops more, with a decreasing difference in drop as velocity increases. I believe that most of the experimental error in this experiment can be attributed to the pitching machine’s inconsistent nature. Regardless of what kind of ball is being used or what rate the wheels are spinning, the standard deviation of the balls impact point was greater than the difference between the average impact heights of the two baseballs. I attempted to minimize the inconsistency of the machine by placing the balls between the spinning wheels the same way each time, but access to a more consistent pitching machine would help me achieve more convincing results. It is also possible that because of the difference in seam-­‐height, the baseballs might interact with the wheels differently and not spin at the same rate. For future research, I would like to be able to measure the drag force on the raised and flat-­‐seam baseballs in a wind tunnel. Because I did not have the ability to 21 use a wind tunnel for this experiment, I was unable to measure the exact drag coefficient of the baseballs. Knowing the drag coefficient values would help improve my computational model and make it a more accurate approximation. In my computational model, I assumed the baseballs had the same drag coefficient value and simply applied the difference in cross-­‐sectional area. Also, a realistic curveball is not perfectly overhand. A typical curveball has moves in three dimensions, with both vertical and horizontal deflection due to spin. In addition to testing a more realistic curveball, I think that game films of current pitchers who have pitched with both baseballs should be analyzed. Comparing film of pitches from past seasons and this current season could possibly reveal a difference in curveball performance. 22 Acknowledgements I would like to thank the members of my faculty thesis committee for their help and support throughout this process. Dr. Murray for her guidance and ideas, as well as Dr. Heath and Dr. Crosser for taking the time to provide advice and make corrections. I would also like to thank every Professor in the department for their wisdom and encouragement over my 4 years at Linfield. Thank you to my fellow classmates, who have worked alongside me on their own thesis projects and still taken the time to give feedback. I would especially like to thank my parents for their unconditional love and support, as well as my teammates and coaches on the baseball team for making my experience at Linfield unforgettable. Lastly, a special thank you to my roommates, teammates, and girlfriend Aubrey Nitschelm for assisting me in setting up my experiment as well as collecting data. 23 References: [1] Boyles, Donald J. "NCAA Changes Measure of Bat Performance." College Baseball Daily. CBB News, 8 Oct. 2008. Web. [2] Fitt, Aaron. "NCAA Concludes Study On Ball Seams." Baseball America. The Enthusiast Network, 2 Oct. 2013. Web. [3] Giordano, Nicholas J., and Hisao Nakanishi. "Realistic Projectile Motion." Computational Physics. 2nd ed. Upper Saddle River, NJ: Pearson/Prentice Hall, 2006. pg 22. Print. [4] Giordano, 33. [5] Giordano, 32. [6] Fitzpatrick, Richard. "The Magnus Force." Integration of ODE's. N.p., 29 Mar. 2006. Web. [7] Giordano, 38. [8] Giordano, 38. [9] Nathan, Alan M. "The Effect of Spin on the Flight of a Baseball." American Journal of Physics Am. J. Phys. 76.2 (2008): 119. Scitation.aip.org. Web. [10] Owners Manual (2008). JUGS Curveball Pitching Machine. JUGS Sports, Tualatin, Oregon. [11] Giordano, 2. 24 25