# What New Technologies Are Teaching Us About the Game of Baseball

Save this PDF as:

Size: px
Start display at page:

## Transcription

1 What New Technologies Are Teaching Us About the Game of Baseball Alan M. Nathan University of Illinois at Urbana-Champaign October 15, 2012 Abstract The trajectory of a baseball moving through the air is very different from the one we teach in our introductory classes, in which the only force is that due to gravity. In reality, the aerodynamic drag force (which retards the motion) and the Magnus force on a spinning baseball (which causes the ball to curve) play very important roles that are crucial to many of the subtleties of the game. Despite their importance, our knowledge of how these forces affect the flight of the baseball has been qualitative at best. Recently, however, new tools have been developed for measuring accurate baseball trajectories during an actual game. These tools include both video tracking (the PITCHf/x and related systems) and the TrackMan Doppler radar system. In this article, I will discuss these new tools and give some examples of what they are teaching us about the game of baseball. 1 Introduction The flight of the ball plays an integral role in the game of baseball. Whether the ball is pitched by the pitcher, struck by the batter, or thrown by a fielder, the physics that governs the flight involves the same forces. If these are known and the initial conditions are given, the full trajectory of the ball can be predicted by solving the equations of motion. So, what are the forces on a baseball as it travels through the air? Of course there is the downward pull of gravity, which is typically the only force treated in introductory physics courses. In real life, however, gravity must be supplemented with the two aerodynamic forces of air drag F D and the Magnus force F M, the latter arising when the ball is spinning. The conventional way to parametrize the aerodynamic forces is as follows: F D = π 2 ρr2 C D v 2ˆv F M = π 2 ρr2 C L v 2 (ˆω ˆv), (1) where C D and C L are the drag and lift coefficients, respectively, v is the velocity vector, ω is the spin vector, R is the radius of the ball, and ρ is the air density. The direction of the drag is opposite to the instantaneous velocity vector, so it slows the ball without changing its direction. The direction of the Magnus force is perpendicular to both the velocity and spin vectors, so it only changes the direction of the ball. A convenient mnemonic is that the Magnus force points in the direction in which the leading edge of the rotating ball is turning. So, for example, for a ball moving horizontally with backspin, the Magnus force is directly up. As we will see in the examples that will be presented below, the aerodynamic forces play important and often subtle roles in the game of baseball. Although not the primary focus of this paper, we start by reviewing briefly the current state of our knowledge of C D and C L. New measurements of C D for a variety of sports balls are given by Kensrud and Smith.[1] For a baseball, C D is approximately 0.50 for speeds below about 40 mph. At some higher speed, it undergoes a drag crisis as the air flow in the boundary layer makes a transition from laminar to turbulant, resulting in a drop in C D to about 0.30 at a speed of around 90 mph. The range of speed over which the drag crisis occurs is not known with great precision, as different experiments seem to not agree. At 90 mph and typical air densities, the drag force is about equal to the weight of the ball. Many interesting questions abound, such as the dependence of C D on the seam orientation or the spin. One interesting feature is that most trajectories in baseball fall right in the region of the drag crisis. The lift coefficient is expected to be a function of the spin parameter S = Rω/v. Some recent measurements and a review of earlier measurements are given by Nathan.[2] The existing data are reasonably well described by the relation C L = 2.5S S. (2) For low values of spin, C L has a linear dependence on S, vanishing when the spin vanishes. For a baseball moving at v=90 mph and spinning at ω=1800 rpm values quite typi- 1

2 cal of both pitched and batted balls S=0.22 and C L =0.24; if the spin is perpendicular to the velocity, the magnitude of the Magnus force is approximately 0.8 of the weight of the ball. For high values of S, C L asymptotically approaches The fact that the drag and Magnus forces can be appreciable fractions of the weight suggests that neglecting the aerodynamic forces in trajectory calculations is not a very good approximation, as demonstrated in Fig. 1. This Figure 1: An example of a fly ball trajectory (solid curve), with the initial conditions shown. The dots show the location of the ball in 0.5-sec intervals. The other curves are the trajectories with the same initial conditions with neither drag nor Magnus (short dashed) and with drag but no Magnus (long dashed). fly ball was hit with initial parameters taken from an actual home run: launch velocity of 112 mph, vertical launch angle of 27, and backspin of 1286 rpm. Such a ball would carry nearly 700 ft in a vacuum but in reality only carries about 430 ft. Whereas the vacuum trajectory is symmetric about the apex, the effect of drag is to reduce the horizontal speed so that the ball travels farther prior to than after the apex. This particular feature is well known to baseball players, even though they are probably not aware of the physics that causes it. Also shown is a trajectory with drag but no Magnus force, which in this case is mainly in the upward direction, opposing gravity. Relative to the no-magnus trajectory, the ball rises higher, stays in the air longer, and travels farther, although the latter effect is only about 50 ft. 2 The New Technologies 2.1 The f/x Video-Based Systems The f/x systems are based on standard video technology. Most prevalent is the PITCHf/x system,[3] which is installed in all Major League Baseball (MLB) ballparks and has been used since the start of the 2007 season to track every pitch in each MLB game. The system consists of two 60-Hz cameras mounted high above the playing field with fields of view that cover most of the region between the pitching rubber and home plate and with roughly orthogonal principal axes. Proprietary software is used to identify the camera coordinates of the baseball in each image, which are then converted to a location in the field coordinate system. The conversion utilizes the camera transformation matrix, which is determined separately using markers placed at precisely known locations on the field. Depending on the details of each installation, the pitch is typically tracked in the approximate range y=5-50 ft, resulting in about 20 images per camera for each pitch, each with measurement precision of order 0.5 inch. Each trajectory is fitted using a constant-acceleration model, so that nine parameters (9P) determine the full trajectory: an initial position, an initial velocity, and an acceleration for each of three coordinates. Simulations have shown that such a parametrization is an excellent description of trajectories for most pitches.[4] The essential physics is that the aerodynamic forces on the ball, while not constant, change slowly enough and the flight path is short enough that the 9P model provides an excellent description of the actual trajectory. Using the 9P fit, various quantities of interest to both physicists (e.g, drag and lift coefficients) and baseball analysts (e.g., release speed, home plate location, movement) can be determined. The HITf/x system utilizes the same cameras to track the initial trajectory of batted balls, including the batted ball speed, vertical launch angle, and horizontal spray angle. The FIELDf/x system is an ambitious extension that tracks essentially everything on the playing field: the fielders, the base runners, the umpires, and the full trajectory of the batted baseball. 2.2 TrackMan Doppler Radar TrackMan is a phased-array Doppler radar system that is installed in a number of MLB ballparks. The system is usually mounted high above home plate and has a field of view that covers most of the playing field. A single antenna transmits at approximately 10.5 GHz. The signal reflected by the baseball is detected in a 3-antenna array, allowing the determination of the Doppler velocity and angular location of the baseball in the radar coordinate system. Together with an initial location, that is sufficient to track the full trajectory of both pitched and batted baseballs. For pitched baseballs, the measurement precision is comparable to that of PITCHf/x. The precision for batted balls is not known. Unlike PITCHf/x, the TrackMan data are not publicly available, although some MLB teams are willing to share data with researchers. 2

3 3 Studies of Pitched Baseballs The great lefthanded pitcher Warren Spahn once said, Hitting is timing. Pitching is upsetting timing. In this section, I will use the publicly available PITCHf/x data from actual MLB games[5] to explore some of the ways that pitchers can upset the timing of batters. Given the variety of possible pitches that can be thrown (e.g., fastballs, curveballs, sliders, etc.), one way to upset the timing of a batter is for the trajectory of each pitch to be nearly identical for as long as possible, giving the batter little opportunity to recognize and react to the different pitches. There is a perception among practitioners of the game that a pitched ball can deviate sharply from a straight line just before reaching the batter, giving rise to the concept of late break. From a purely physics point of view, late break is a fiction, since it is not possible to change rapidly the trajectory of a pitched baseball without enormous forces acting on it. So, it is a fair question to ask why perception is different from reality, a topic I examine in Fig. 2. Shown is a bird s eye view of an actual pitch (the solid curve) thrown by the great New York Yankee pitcher Mariano Rivera. The dotted curve is a straight line extrapolated from the initial velocity vector. The two curves are virtually indistinguishable until about 20 ft from home plate, at which point the batter has already decided where he thinks the ball will end up and whether or not to swing. The two trajectories deviate by about 0.5 ft at home plate, which is more than enough to confound the batter, who swears the solid curve broke sharply at the last moment. Clearly it did not. horizontal postion (ft) home plate Mariano Rivera's Cutter Bird's-Eye View distance from home plate (ft) Figure 2: An example of late break. Another way a pitcher can upset the timing of the batter is by varying both the speed and the movement of the pitch. The movement is defined as the deviation of the pitch from a straight line trajectory, with the effect of gravity removed. For most pitches, it is determined by the magnitude and orientation of the spin axis. An example is shown in Fig. 3, in which the direction of the movement and release speed v 0 (mph) Figure 3: Polar plot showing the pitch repertoire of Jon Lester (blue) and knuckleball pitcher Tim Wakefield (red). The radial coordinate is the release speed and the angular coordinate is the direction of the movement, as viewed by the catcher. for a few hundred pitches thrown by Boston Red Sox lefthander Jon Lester are shown as the blue points in a scatter plot, as viewed by the catcher. The spin axis is the movement angle plus 90 (see Eq. 1). For Lester, as with most MLB pitchers, the plot shows distinct clusters that serve as signatures for each of the five pitches in his repertoire. For example, the cluster at 95 mph and 65 (spin angle=155, or primarily backspin) is his primary pitch, the so-called four-seam fastball, breaking primarily upward and slightly away from a right-handed batter. The cluster near 77 mph and 225 (spin angle=315 ) is his curveball, breaking down (due to topspin) and toward a right-handed hitter. Now compare with the red points, the pitches thrown by recently retired Red Sox righthander Tim Wakefield, who occasionally throws fastballs ( 73 mph and 120 ) and curveballs (60 mph and 315 ). However, Wakefield s primary pitch is the knuckleball, shown as the amorphous ring at about 66 mph. Whereas the movement of ordinary pitches is predictable, the movement of a kunckleball is not. Given the unusual nature of the knuckleball, it is interesting to examine its behavior in more detail. It is usually thrown at a speed significantly lower than that of ordinary pitches and with very little spin. The lack of spin means that the knuckleball does not experience the Magnus force that is responsible for the movement on ordinary pitches. But it does experience movement, as seen in Fig. 3. Wind tunnel experiments have shown that the movement is due to the disruption of the air flow over the seams of the ball.[6] The seemingly erratic movement has led to the perception that the knuckleball trajectory is not smooth but undergoes abrupt changes of direction. This is an issue that can be addressed with the tracking data. To do so requires having 0 3

4 access to the raw tracking data rather than the 9P fit, since we do not know how well the constant-acceleration model fits the actual data. Therefore raw data were obtained for several games from the 2011 MLB season. Here I will give a detailed analysis for one game in which 278 pitches were thrown, of which 77 were knuckleballs. Each trajectory was fit to a smooth function and the root-mean-square (rms) deviation of the data from that function was determined. The essential idea is that the smaller the rms, the better the smooth function describes the actual data. Rather than use the constant acceleration function, a more exact model was used in which the aerodynamic forces are proportional to the square of the velocity. A nonlinear least-squares fitting program was used to adjust the parameters to minimize the rms value. The result of applying this procedure is presented in Fig. 4. Figure 4: Distribution of rms values for normal (blue) and knuckleball (red) pitches. The nearly parallel linear contours of these samples indicate that they each have a Gaussian distribution with the same standard deviation but with the mean value slightly larger for knuckleballs. The rms value for each of the 201 ordinary pitches (blue) and 77 knuckleball pitches (red) is plotted as a function of the percentage of pitches in each sample having a smaller rms value. The horizontal axis is such that samples following a Gaussian distribution appear as straight lines, with the central value at 50% and standard deviation proportional to the slope. This plot shows that the distribution of rms values is very similar for the ordinary and knuckleball pitches, each being approximately Gaussian with about the same standard deviation, but with the mean value for knuckleballs (0.33 inch) only slightly larger than that for ordinary pitches (0.30 inch). If we take the mean value for ordinary pitches as a measure of the statistical precision of the tracking data (approximately 0.3 inch), then the slight increase in the knuckleball values suggests that the latter pitches deviate from smoothness by at most 0.15 inch. The conclusion is that within the precision of the tracking data, knuckleball trajectories are just as smooth as those of ordinary pitches, thereby disproving the common perception. 4 Studies of Batted Baseballs I now want to turn to a study of batted baseballs. Unfortunately, full trajectories of batted baseballs from MLB games are not yet available for analysis. However, two extremely useful pieces of information are more readily available: the initial velocity vector v 0 from either the video or radar tracking systems; and the landing point R f and flight time T, as determined either from the radar tracking or from direct observation, the latter only for batted balls that clear the fence for a home run.[7] Interestingly, this partial information is sufficient to place very tight constraints on the full trajectory, as demonstrated in Fig. 5. The data for the full trajectory shown in the figure come from a dedicated experiment in which baseballs were projected using a pitching machine and tracked using a portable version of the TrackMan system. The first 0.5 sec of the trajectory were used to determine v 0, while R f and T were directly measured by the tracking system. The trajectory was modeled using Eqs. 1-2, with three free parameters adjusted to fit R f, evaluated at the measured T : a constant drag coefficient C D and the backspin ω b and sidespin ω s components of the spin vector. The spin components are both perpendicular to v 0, with ω b and ω s lying in the horizontal and vertical planes, respectively. The curve in Fig. 5 was arrived at by this procedure. The closeness of the curve to the actual data over the full range of the trajectory demonstrates the point made above. It also shows the utility of the simplified model used in the analysis. Simulations of this procedure show that T determines ω b ; the horizontal deflection determines ω s ; and the total distance determines C D. This procedure will be used in the some of the discussion that follows. height (ft) distance (ft) Figure 5: A fly ball trajectory measured with TrackMan (points). The curve is a fit to the data in which only the data to the left of the dashed line plus the landing point and flight time were used to constrain the parameters. 4

5 D The first question I address is the dependence of fly ball distance on the initial speed v 0 and vertical launch angle θ. A total of 1257 batted balls were analyzed, using Track- Man from MLB games in St. Louis from The results are shown in Fig. 6, in which the fly balls are separated into 10 mph and 5 bins and mean values are taken for the range in each bin. Some interesting features emerge from the figure. First, the optimum θ is about 30, which is considerably smaller than the vacuum value of 45. Second, the range depends on v 0 approximately linearly, with a slope of about 5 ft/mph; in vacuum the dependence is quadratic. Finally, a ball hit with v 0 =102.5 mph at and θ=30 will carry about 405 ft. These results are in accord with expectations based on calculations of trajectories using reasonable models for C D and C L, and it is nice to see that they are confirmed by actual data. R (ft) T (F) r1-r4 R (ft) θ (deg) R 1 (ft) R 2 (ft) Figure 7: Dependence of home run distance on temperature (top) and elevation (bottom). The top plot is color-coded by vertical launch angle. The bottom plot displays the actual distance vs. the sea level distance for sea-level ball parks (blue) and Coors Field in Denver (red). Figure 6: Dependence of fly ball distance on the vertical launch angle for different 10-mph ranges of v 0, with the central value indicated in the legend. Next, I investigate the effect of temperature and altitude on fly ball distances. For this study, I analyze 8800 home runs from the MLB seasons, using v 0 from HITf/x and direct observation of R f and T. The fitting procedure described at the beginning of this section is applied to each home run to determine the average C D and the two spin components, using an air density appropriate for the known temperature and elevation. Then for each home run, two new trajectories are calculated using the same v 0, C D, and spin: one in which the temperature is set to 72.7F, the average value for the full data set, and another in which the elevation is set to sea level. For each of these a new value of the range is determined. We denote by R the difference between the actual and new value of range. In such a manner, we can determine R as a function of temperature or elevation, and these results are shown in Fig. 7. In the top part, the linear dependence of R on temperature for a given θ is evident, with the slope increasing with larger θ. The average slope, corresponding to the optimum launch angle of 30, is 2.5 ft/10f, so that a long fly ball will carry about 15 ft farther on a hot summer day at 100F than on a cold spring day at 40F. In the bottom figure, the actual distance R 1 is plotted versus the sea-level distance R 2. The blue points are those for ballparks within 200 ft of sea level, so the data is essentially a line of unit slope passing through the origin. The red points are those for Coors Field in mile-high Denver, for which there is also a line of unit slope but displaced higher by about 26 ft., from which we conclude that fly ball distances increase by about 5 ft for each 1000 ft of elevation. Finally I address the question of how well the initial velocity vector v 0 determines the landing point R f. In vacuum, of course, v 0 is completely sufficient to determine R f. The actual situation is more complicated due to the aerodynamic forces. The ideal tool for making such a study 5

7 [4] A web article about this analysis may be downloaded at a-nathan/pob/pitchfx_9p_model-4. pdf. [5] PITCHf/x data may be downloaded at www. brooksbaseball.net. [6] R. Watts R and E. Sawyer, Aerodynamics of a knuckleball, Am. J. Phys. 43, (1975). [7] The web site for the ESPN Home Run Tracker is at 7

### Available online at Procedia Engineering 200 (2010) (2009) In situ drag measurements of sports balls

Available online at www.sciencedirect.com Procedia Engineering 200 (2010) (2009) 2437 2442 000 000 Procedia Engineering www.elsevier.com/locate/procedia 8 th Conference of the International Sports Engineering

### Forces that govern a baseball s flight path

Forces that govern a baseball s flight path Andrew W. Nowicki Physics Department, The College of Wooster, Wooster, Ohio 44691 April 21, 1999 The three major forces that affect the baseball while in flight

### Modeling Pitch Trajectories in Fastpitch Softball

Noname manuscript No. (will be inserted by the editor) Modeling Pitch Trajectories in Fastpitch Softball Jean M. Clark Meredith L. Greer Mark D. Semon Received: date / Accepted: date Abstract The fourth-order

### Agood tennis player knows instinctively how hard to hit a ball and at what angle to get the ball over the. Ball Trajectories

42 Ball Trajectories Factors Influencing the Flight of the Ball Nathalie Tauziat, France By Rod Cross Introduction Agood tennis player knows instinctively how hard to hit a ball and at what angle to get

### ScienceDirect. Relating baseball seam height to carry distance

Available online at www.sciencedirect.com ScienceDirect Procedia Engineering 112 (2015 ) 406 411 7th Asia-Pacific Congress on Sports Technology, APCST 2015 Relating baseball seam height to carry distance

### The effect of baseball seam height on the Magnus Force

The effect of baseball seam height on the Magnus Force Shawn Bowman Physics Department, The College of Wooster, Wooster, Ohio 44691, USA (Dated: May 7, 2014) Many people do not know that Major League and

### Effects of turbulence on the drag force on a golf ball

European Journal of Physics PAPER Effects of turbulence on the drag force on a golf ball To cite this article: Rod Cross 2016 Eur. J. Phys. 37 054001 View the article online for updates and enhancements.

### THEORY OF WINGS AND WIND TUNNEL TESTING OF A NACA 2415 AIRFOIL. By Mehrdad Ghods

THEORY OF WINGS AND WIND TUNNEL TESTING OF A NACA 2415 AIRFOIL By Mehrdad Ghods Technical Communication for Engineers The University of British Columbia July 23, 2001 ABSTRACT Theory of Wings and Wind

### Available online at ScienceDirect. The 2014 Conference of the International Sports Engineering Association

Available online at www.sciencedirect.com ScienceDirect Procedia Engineering 72 ( 2014 ) 435 440 The 2014 Conference of the International Sports Engineering Association Accuracy performance parameters

### Kinematics-Projectiles

1. A volleyball hit into the air has an initial speed of 10 meters per second. Which vector best represents the angle above the horizontal that the ball should be hit to remain in the air for the greatest

### When you think of baseball, you think of a game that never changes, right? The

The Strike Zone During the PITCHf/x Era by Jon Roegele When you think of baseball, you think of a game that never changes, right? The rules are the same as they were over 100 years ago, right? The bases

### CASE STUDY FOR USE WITH SECTION B

GCE A level 135/01-B PHYSICS ASSESSMENT UNIT PH5 A.M. THURSDAY, 0 June 013 CASE STUDY FOR USE WITH SECTION B Examination copy To be given out at the start of the examination. The pre-release copy must

### THE CURVE OF THE CRICKET BALL SWING AND REVERSE SWING

Parabola Volume 32, Issue 2 (1996) THE CURVE OF THE CRICKET BALL SWING AND REVERSE SWING Frank Reid 1 It is a well known fact in cricket that the new ball when bowled by a fast bowler will often swing

### QUESTION 1. Sketch graphs (on the axes below) to show: (1) the horizontal speed v x of the ball versus time, for the duration of its flight;

QUESTION 1 A ball is thrown horizontally from a cliff with a speed of 10 ms -1 shown in the diagram at right. Neglecting the effect of air resistance and taking gravitational acceleration to be g +9.8ms

### THE BOOK--Playing The Percentages In Baseball

So as a baseball flies towards home plate, the moment when it passes from central to peripheral vision could THE BOOK ARTICLES BLOG ABOUT US The Book Tom M. Tango, Mitc... Buy New \$14.93 Privacy Information

### Georgian University GEOMEDI. Abstract. In this article we perform theoretical analysis of long jumps with the purpose to find

On the t Influence of Air Resistance and Wind during Long Jump Egoyan A. E. ( alex1cen@yahoo.com ), Khipashvili I. A. Georgian University GEOMEDI Abstract. In this article we perform theoretical analysis

### CHAPTER 1. Knowledge. (a) 8 m/s (b) 10 m/s (c) 12 m/s (d) 14 m/s

CHAPTER 1 Review K/U Knowledge/Understanding T/I Thinking/Investigation C Communication A Application Knowledge For each question, select the best answer from the four alternatives. 1. Which is true for

### ScienceDirect. Rebounding strategies in basketball

Available online at www.sciencedirect.com ScienceDirect Procedia Engineering 72 ( 2014 ) 823 828 The 2014 conference of the International Sports Engineering Association Rebounding strategies in basketball

### Aerodynamic characteristics around the stalling angle of the discus using a PIV

10TH INTERNATIONAL SYMPOSIUM ON PARTICLE IMAGE VELOCIMETRY PIV13 Delft, The Netherlands, July 1-3, 2013 Aerodynamic characteristics around the stalling angle of the discus using a PIV Kazuya Seo 1 1 Department

### Calculate the horizontal component of the baseball's velocity at an earlier time calculated in part (a).

Ch3 Supplemental [ Edit ] Overview Summary View Diagnostics View Print View with Answers Ch3 Supplemental Due: 6:59pm on Monday, February 13, 2017 To understand how points are awarded, read the Grading

### QUESTION 1. Sketch graphs (on the axes below) to show: (1) the horizontal speed v x of the ball versus time, for the duration of its flight;

QUESTION 1 A ball is thrown horizontally from a cliff with a speed of 10 ms -1 shown in the diagram at right. Neglecting the effect of air resistance and taking gravitational acceleration to be g = +9.8ms

### LINEAR AND ANGULAR KINEMATICS Readings: McGinnis Chapters 2 and 6 DISTANCE, DISPLACEMENT, SPEED, VELOCITY, AND ACCELERATION:

LINEAR AND ANGULAR KINEMATICS Readings: McGinnis Chapters 2 and 6 1 DISTANCE, DISPLACEMENT, SPEED, VELOCITY, AND ACCELERATION: How far? Describing change in linear or angular position Distance (Scalar

### Effects of seam and surface texture on tennis balls aerodynamics

Available online at www.sciencedirect.com Procedia Engineering 34 (2012 ) 140 145 9 th Conference of the International Sports Engineering Association (ISEA) Effects of seam and surface texture on tennis

### WIND-INDUCED LOADS OVER DOUBLE CANTILEVER BRIDGES UNDER CONSTRUCTION

WIND-INDUCED LOADS OVER DOUBLE CANTILEVER BRIDGES UNDER CONSTRUCTION S. Pindado, J. Meseguer, J. M. Perales, A. Sanz-Andres and A. Martinez Key words: Wind loads, bridge construction, yawing moment. Abstract.

### A Teacher s Utilization Guide.

A Teacher s Utilization Guide www.pbs4549.org/baseball Table of Contents Credits...4 Introduction...5 108 Stitches: The Physics in Baseball...7 Video Overviews...8 Content Standards...9 Correlated Ohio

### Figure 8.45 (continued) Hit easy grounders directly to the players.

Tactics and Skills 133 3B SS 3 1 2B 1B R b 3B R SS 1 2B 3 1B c Figure 8.45 (continued) To make the game easier Hit easy grounders directly to the players. To make the game harder Hit harder ground balls.

### Why does a golf ball have dimples?

Página 1 de 5 Why does a golf ball have dimples? page 1 A golf ball can be driven great distances down the fairway. How is this possible? Is the drive only dependent on the strength of the golfer or are

### Worksheet 1.1 Kinematics in 1D

Worksheet 1.1 Kinematics in 1D Solve all problems on your own paper showing all work! 1. A tourist averaged 82 km/h for a 6.5 h trip in her Volkswagen. How far did she go? 2. Change these speeds so that

### time v (vertical) time

NT4E-QRT20: PROJECTILE MOTION FOR TWO ROCKS VELOCITY AND ACCELERATION GRAPHS II Two identical rocks are thrown horizontally from a cliff with Rock A having a greater velocity at the instant it is released

### Corked Bats, Humidors, and Steroids: The Physics of Cheating in Baseball October 29, Alan Nathan

Corked Bats, Humidors, and Steroids: The Physics of Cheating in Baseball October 29, 2011 Alan Nathan 1 News Flash 2 A great book to read. Our goal is not to reform the game but to understand it. 3 A more

Available online at www.sciencedirect.com Procedia Engineering 3 () 94 99 5 th Asia-Pacific Congress on Sports Technology (APCST) Basketball free-throw rebound motions Hiroki Okubo a*, Mont Hubbard b a

### Transcript of Ping Pong Ball Launcher Research and Design

Transcript of Ping Pong Ball Launcher Research and Design Objective To construct a mechanism to launch a ping pong ball into a garbage bin 2, 4, 6, and 8 metres away from the launcher, with restrictions:

### The validity of a rigid body model of a cricket ball-bat impact

Available online at www.sciencedirect.com Procedia Engineering 34 (2012 ) 682 687 9 th Conference of the International Sports Engineering Association (ISEA) The validity of a rigid body model of a cricket

### C) miles per hour. D) all of the above. 2) When you look at the speedometer in a moving car, you can see the car's

Practice Kinematics Questions (Answers are at the end ) 1) One possible unit of speed is. A) light years per century. B) kilometers per hour. C) miles per hour. D) all of the above.. 2) When you look at

### Two dimensional kinematics. Projectile Motion

Two dimensional kinematics Projectile Motion 1. You throw a ball straight upwards with a velocity of 40m/s. How long before it returns to your hand? A. 2s B. 4s C. 6s D. 8s E. 10s 1.You throw a ball straight

### The Visual Physics of Baseball

The Visual Physics of Baseball By Clifton Neeley The above illustration is actually a picture of a baseball being thrown digitally through four different weights of air. Baseball enthusiasts and statisticians

### ACTIVITY 1: Buoyancy Problems. OBJECTIVE: Practice and Reinforce concepts related to Fluid Pressure, primarily Buoyancy

LESSON PLAN: SNAP, CRACKLE, POP: Submarine Buoyancy, Compression, and Rotational Equilibrium DEVELOPED BY: Bill Sanford, Nansemond Suffolk Academy 2012 NAVAL HISTORICAL FOUNDATION TEACHER FELLOWSHIP ACTIVITY

### Detailed study 3.4 Topic Test Investigations: Flight

Name: Billanook College Detailed study 3.4 Topic Test Investigations: Flight Ivanhoe Girls Grammar School Questions 1 and 2 relate to the information shown in the diagram in Figure 1. z Question 1 y Figure

Slow Pitch Softball Pitching Techniques Knuckleball This is a community where softball playing Redditors can discuss any and all topics Anyone have any further tips for me to make things easier on us?

### Flight Corridor. The speed-altitude band where flight sustained by aerodynamic forces is technically possible is called the flight corridor.

Flight Corridor The speed-altitude band where flight sustained by aerodynamic forces is technically possible is called the flight corridor. The subsonic Boeing 747 and supersonic Concorde have flight corridors

### Available online at ScienceDirect. Procedia Engineering 112 (2015 )

Available online at www.sciencedirect.com ciencedirect Procedia ngineering 112 (2015 ) 443 448 7th Asia-Pacific Congress on ports Technology, APCT 2015 Kinematics of arm joint motions in basketball shooting

### A Different Approach to Teaching Engine-Out Glides

A ifferent Approach to Teaching Engine-Out Glides es Glatt, Ph., ATP/CFI-AI, AGI/IGI When student pilots begin to learn about emergency procedures, the concept of the engine-out glide is introduced. The

### Physics 11 Unit III Practice Test Projectile Motion. Instructions: Pick the best answer available in Part A and Show all your work for Part B

Physics 11 Unit III Practice Test Projectile Motion Instructions: Pick the best answer available in Part A and Show all your work for Part B 1. Which of the following is constant for all projectiles? A.

### Aerodynamically Efficient Wind Turbine Blade S Arunvinthan 1, Niladri Shekhar Das 2, E Giriprasad 3 (Avionics, AISST- Amity University, India)

International Journal of Engineering Science Invention ISSN (Online): 2319 6734, ISSN (Print): 2319 6726 Volume 3 Issue 4ǁ April 2014ǁ PP.49-54 Aerodynamically Efficient Wind Turbine Blade S Arunvinthan

### arxiv: v1 [physics.pop-ph] 31 Mar 2008

Paradoxical pop-ups: Why are they hard to catch? arxiv:0803.4357v1 [physics.pop-ph] 31 Mar 2008 Michael K. McBeath Department of Psychology, Arizona State University, Tempe, AZ 85287 Alan M. Nathan Department

### 1. A rabbit can cover a distance of 80 m in 5 s. What is the speed of the rabbit?

Chapter Problems Motion at Constant Speed Class Work. A rabbit can cover a distance of 80 m in 5 s. What is the speed of the rabbit?. During the first 50 s a truck traveled at constant speed of 5 m/s.

### What Do You Think? GOALS

Activity 3 Slinkies and Waves GOALS In this activity you will: Make a people wave. Generate longitudinal and transverse waves on a Slinky. Label the parts of a wave. Analyze the behavior of waves on a

### Biomechanics Sample Problems

Biomechanics Sample Problems Forces 1) A 90 kg ice hockey player collides head on with an 80 kg ice hockey player. If the first person exerts a force of 450 N on the second player, how much force does

### The Physics of Baseball

The Physics of Baseball Pre- Lab: America s National Pastime A Bit of History Filled with men, myths, and legends, the history of baseball is much too long to be described in any Bit of History. If you

### Introduction to Waves. If you do not have access to equipment, the following experiments can be observed here:

Introduction to Waves If you do not have access to equipment, the following experiments can be observed here: http://tinyurl.com/lupz3dh 1.1 There is a tray with water in it. This can model throwing a

### Ball Toss. Vernier Motion Detector

Experiment 6 When a juggler tosses a ball straight upward, the ball slows down until it reaches the top of its path. The ball then speeds up on its way back down. A graph of its velocity vs. time would

### Comparing the Performance of Baseball Bats

Comparing the Performance of Baseball Bats Margaret Raabe Physics Department, The College of Wooster, Wooster, Ohio 44691, USA (Dated: May 11, 2011) Experimental analysis is done on three different types

### PERFORMANCE MANEUVERS

Ch 09.qxd 5/7/04 8:14 AM Page 9-1 PERFORMANCE MANEUVERS Performance maneuvers are used to develop a high degree of pilot skill. They aid the pilot in analyzing the forces acting on the airplane and in

### Secondary Physics: The Compass Rose, Cars and Tracks

Secondary Physics: The Compass Rose, Cars and Tracks Secondary Physics at the NASCAR Hall of Fame The Great Hall and Glory Road Focus object or destination in the Hall: Compass Rose, 18 compass lines,

### Impact of a ball on a surface with tangential compliance

Impact of a ball on a surface with tangential compliance Rod Cross a Department of Physics, University of Sydney, Sydney, New South Wales 26, Australia Received 8 September 29; accepted 2 January 2 A simple

### Engineering Flettner Rotors to Increase Propulsion

Engineering Flettner Rotors to Increase Propulsion Author: Chance D. Messer Mentor: Jeffery R. Wehr Date: April 11, 2016 Advanced STEM Research Laboratory, Odessa High School, 107 E 4 th Avenue, Odessa

### Available online at ScienceDirect. Brendan Kays a, Lloyd Smith a *

Available online at www.sciencedirect.com ScienceDirect Procedia Engineering 72 ( 2014 ) 563 568 The 2014 conference of the International Sports Engineering Association Field Measurements of Ice Hockey

### The Physics of Baseball

The Physics of Baseball Pre- Lab: America s National Pastime A Bit of History Filled with men, myths, and legends, the history of baseball is much too long to be described in any Bit of History. If you

### CHAPTER 10: LINEAR KINEMATICS OF HUMAN MOVEMENT

CHAPTER 10: LINEAR KINEMATICS OF HUMAN MOVEMENT 1. Vector mechanics apply to which of the following? A. displacement B. velocity C. speed D. both displacement and velocity 2. If velocity is constant, then

### The Physics of Baseball

The Physics of Baseball Pre- Lab: America s National Pastime A Bit of History Filled with men, myths, and legends, the history of baseball is much too long to be described in any Bit of History. If you

### Kinematic Differences between Set- and Jump-Shot Motions in Basketball

Proceedings Kinematic Differences between Set- and Jump-Shot Motions in Basketball Hiroki Okubo 1, * and Mont Hubbard 2 1 Department of Advanced Robotics, Chiba Institute of Technology, 2-17-1 Tsudanuma,

### ACTIVITY THE MOTION OF PROJECTILES

Name (printed) ACTIVITY THE MOTION OF PROJECTILES First Day Stamp INTRODUCTION In this activity you will begin to understand the nature of projectiles by mapping out the paths of two projectiles over time;

### PROPER PITCHING MECHANICS

PROPER PITCHING MECHANICS While each pitcher is a different person and can display some individuality in his mechanics, everyone has similar anatomy (the same muscles, bones and ligaments in the same locations)

### Main Points Feet Balance Power Position (Power T Position)- Rotation Follow-through

Pitching Main Points 1. Feet-take a small step back with non-throwing side foot, keeping the weight over the stationary foot, which is turned parallel and touching the rubber 2. Balance Position-non-throwing

### BIOMECHANICAL MOVEMENT

SECTION PART 5 5 CHAPTER 12 13 CHAPTER 12: Biomechanical movement Practice questions - text book pages 169-172 1) For which of the following is the athlete s centre of mass most likely to lie outside of

### THE BRIDGE COLLAPSED IN NOVEMBER 1940 AFTER 4 MONTHS OF ITS OPENING TO TRAFFIC!

OUTLINE TACOMA NARROWS BRIDGE FLOW REGIME PAST A CYLINDER VORTEX SHEDDING MODES OF VORTEX SHEDDING PARALLEL & OBLIQUE FLOW PAST A SPHERE AND A CUBE SUMMARY TACOMA NARROWS BRIDGE, USA THE BRIDGE COLLAPSED

### ACTIVITY THE MOTION OF PROJECTILES

Name (printed) ACTIVITY THE MOTION OF PROJECTILES First Day Stamp INTRODUCTION In this activity you will begin to understand the nature of projectiles by mapping out the paths of two projectiles over time;

### AERODYNAMIC CHARACTERISTICS OF SPIN PHENOMENON FOR DELTA WING

ICAS 2002 CONGRESS AERODYNAMIC CHARACTERISTICS OF SPIN PHENOMENON FOR DELTA WING Yoshiaki NAKAMURA (nakamura@nuae.nagoya-u.ac.jp) Takafumi YAMADA (yamada@nuae.nagoya-u.ac.jp) Department of Aerospace Engineering,

### Chapter 3 PRESSURE AND FLUID STATICS

Fluid Mechanics: Fundamentals and Applications, 2nd Edition Yunus A. Cengel, John M. Cimbala McGraw-Hill, 2010 Chapter 3 PRESSURE AND FLUID STATICS Lecture slides by Hasan Hacışevki Copyright The McGraw-Hill

### Bending a soccer ball with math

Bending a soccer ball with math Tim Chartier, Davidson College Aerodynamics in sports has been studied ever since Newton commented on the deviation of a tennis ball in his paper New theory of light and

### The Effect of Driver Mass and Shaft Length on Initial Golf Ball Launch Conditions: A Designed Experimental Study

Available online at www.sciencedirect.com Procedia Engineering 34 (2012 ) 379 384 9 th Conference of the International Sports Engineering Association (ISEA) The Effect of Driver Mass and Shaft Length on

### 1. A tendency to roll or heel when turning (a known and typically constant disturbance) 2. Motion induced by surface waves of certain frequencies.

Department of Mechanical Engineering Massachusetts Institute of Technology 2.14 Analysis and Design of Feedback Control Systems Fall 2004 October 21, 2004 Case Study on Ship Roll Control Problem Statement:

### TEACHER ANSWER KEY December 10, Projectile Review 1

Projectile Review 1 TEACHER ANSWER KEY December 10, 2004 4 1. A baseball player throws a ball horizontally. Which statement best describes the ball's motion after it is thrown? [Neglect the effect of friction.]

### 1. downward 3. westward 2. upward 4. eastward

projectile review 1 Name 11-DEC-03 1. A baseball player throws a ball horizontally. Which statement best describes the ball's motion after it is thrown? [Neglect the effect of friction.] 1. Its vertical

### A Comparison of Jabulani and Brazuca Non-Spin Aerodynamics

A Comparison of Jabulani and Brazuca Non-Spin Aerodynamics Proc JMechE Part P: J Sports Engineering and Technology ():1 13 The Author(s) 2 Reprints and permission: sagepub.co.uk/journalspermissions.nav

### Unit 2 Review: Projectile Motion

Name: Unit 2 Review: Projectile Motion Date: 1. A projectile is fired from a gun near the surface of Earth. The initial velocity of the projectile has a vertical component of 98 meters per second and a

### My Background. Joe Wurts 1

My Background Flying RC sailplanes since 1976 First competition 1977 US Nationals, placed 2 nd Only pilot to win world champion for both FAI recognized soaring disciplines FAI world record holder for declared

### PRE-TEST Module 2 The Principles of Flight Units /60 points

PRE-TEST Module 2 The Principles of Flight Units 1-2-3.../60 points 1 Answer the following questions. (20 p.) moving the plane (4) upward / forward. Opposed to that is 1. What are the names of the four

### Kick precision and spin rate in drop and torpedo punts

Available online at www.sciencedirect.com Procedia Engineering 60 ( 2013 ) 448 452 6 th Asia-Pacific Congress on Sports Technology (APCST) Kick precision and spin rate in drop and torpedo punts Franz Konstantin

### BROCK UNIVERSITY. Name: Student #: Page 1 of 12

Name: Student #: BROCK UNIVERSITY Page 1 of 12 Final Exam: July 2016 Number of pages: 12 (+ formula sheet) Course: PHYS 1P21/1P91 Number of students: 104 Examination date: 9 July 2016 Number of hours:

### Pitching Skills and Drills

Pitching Skills and Drills Copyright Notice -IT IS ILLEGAL TO POST THIS DOCUMENT ONLINE The material enclosed is copyrighted. You do not have resell rights or giveaway rights to the material provided herein.

Parasite Drag by David F. Rogers http://www.nar-associates.com Copyright c 2005 David F. Rogers. All rights reserved. How many of you still have a Grimes rotating beacon on both the top and bottom of the

### Hornady 4 Degree of Freedom (4 DOF) Trajectory Program

Hornady 4 Degree of Freedom (4 DOF) Trajectory Program Table of Contents Introduction. 2 Gyroscopic Stability.. 6 Zero Angle....... 7 Muzzle velocity Correction. 7 Spin Drift.. 9 Aerodynamic Jump... 9

### Ch. 2 & 3 Velocity & Acceleration

Ch. 2 & 3 Velocity & Acceleration Objective: Student will be able to Compare Velocity to Speed Identify what is acceleration Calculate velocity and acceleration from an equation and from slope of a graph.

### j~/ ... FIGURE 3-31 Problem 9.

9. () An airplane is traveling 735 kmlh in a direction 41S west of north (Fig. 3-31). (a) Find the components of the velocity vector in the northerly and westerly directions. (b) How far north and how

### AERODYNAMICS SPORTS BALLS

Ann. Rev. Fluid Mech. 1985.17:151~9 Copyright 1985 by Annual Reviews Inc. All rights reserved AERODYNAMICS SPORTS BALLS OF Rabindra 1 D. Mehta Aerodynamics Research Branch, NASA Ames Research Center, Moffett

### Wind loads investigations of HAWT with wind tunnel tests and site measurements

loads investigations of HAWT with wind tunnel tests and site measurements Shigeto HIRAI, Senior Researcher, Nagasaki R&D Center, Technical Headquarters, MITSUBISHI HEAVY INDSUTRIES, LTD, Fukahori, Nagasaki,

### AN31E Application Note

Balancing Theory Aim of balancing How an unbalance evolves An unbalance exists when the principle mass axis of a rotating body, the so-called axis of inertia, does not coincide with the rotational axis.

### Instruction and Practice Manual

Instruction and Practice Manual Axiom Sports Manufacturing A Division of Fitec International 3525 Ridge Meadow Parkway Memphis, TN 38175 (901) 366-9144 www.axiomsports.com 1 Thank you for purchasing the

### Hitting with Runners in Scoring Position

Hitting with Runners in Scoring Position Jim Albert Department of Mathematics and Statistics Bowling Green State University November 25, 2001 Abstract Sportscasters typically tell us about the batting

### Report for Experiment #11 Testing Newton s Second Law On the Moon

Report for Experiment #11 Testing Newton s Second Law On the Moon Neil Armstrong Lab partner: Buzz Aldrin TA: Michael Collins July 20th, 1969 Abstract In this experiment, we tested Newton s second law

### Characteristics of modern soccer balls

Available online at www.sciencedirect.com Procedia Engineering 34 (01 ) 1 17 9 th Conference of the International Sports Engineering Association (ISEA) Characteristics of modern soccer balls Takeshi Asai

### Activity P07: Acceleration of a Cart (Acceleration Sensor, Motion Sensor)

Activity P07: Acceleration of a Cart (Acceleration Sensor, Motion Sensor) Equipment Needed Qty Equipment Needed Qty Acceleration Sensor (CI-6558) 1 Dynamics Cart (inc. w/ Track) 1 Motion Sensor (CI-6742)

### Power efficiency and aerodynamic forces measurements on the Dettwiler-wind turbine

Institut für Fluiddynamik ETH Zentrum, ML H 33 CH-8092 Zürich P rof. Dr. Thomas Rösgen Sonneggstrasse 3 Telefon +41-44-632 2646 Fax +41-44-632 1147 roesgen@ifd.mavt.ethz.ch www.ifd.mavt.ethz.ch Power efficiency

### Mechanical Engineering Journal

Bulletin of the JSME Mechanical Engineering Journal Vol.5, No.1, 2018 Effect of seam characteristics on critical Reynolds number in footballs Kiyoshi NAITO*, Sungchan HONG**, Masaaki KOIDO**, Masao NAKAYAMA**,

### Wind Regimes 1. 1 Wind Regimes

Wind Regimes 1 1 Wind Regimes The proper design of a wind turbine for a site requires an accurate characterization of the wind at the site where it will operate. This requires an understanding of the sources

### Ground Forces Impact on Release of Rotational Shot Put Technique

Brigham Young University BYU ScholarsArchive All Theses and Dissertations 2014-12-01 Ground Forces Impact on Release of Rotational Shot Put Technique Niklas B. Arrhenius Brigham Young University - Provo