Vertical Size of the Sweet Spot of the Bat

Vertical Size of the Sweet Spot of the Bat
4/9/2019 Vertical Size of the Sweet Spot of the Bat David G. Baldwin Chicago White Sox Baseball Organization A. Terry Bahill Emeritus Professor of Systems Engineering University of Arizona ©, 2018, Bahill

Reference Terry Bahill, The Science of Baseball: Modeling Bat-Ball Collisions and the Flight of the Ball, Springer Nature, NY, NY, 2018, ISBN Terry Bahill, The Science of Baseball - Batting, Bats, Bat-Ball Collisions, and the Flight of the Ball, second edition, Springer Nature, NY, NY, 2019 Baldwin, D. Snake Jazz, Xlibris Corp,

The systems engineering process
The SIMILAR process is a life-cycle model. But, it is not a serial process. It is parallel and highly iterative. 4/9/2019 © 2018 Bahill

Purpose Present a model for the batter’s probability of success depending on the bat-ball collision offset Show that the sweet spot of the bat is one-fifth of an inch high The size of the sweet spot determines the required swing accuracy for batter success 4/9/2019 © 2018 Bahill

Spahn and Sain and pray for rain
Warren Spahn, “Hitting is timing. Pitching is upsetting timing” Johnny Sain taught, never show the batter consecutive pitches of the same speed 4/9/2019 © 2018 Bahill

Bat-ball collision offset
4/9/2019 © 2018 Bahill

Performance criteria1 We need a criterion for batting success that shows the relative importance of bat weight bat shape coefficient of friction bat speed swing angle bat-ball collision offset at impact These are all under the batter’s control 4/9/2019 © 2018 Bahill

Performance criteria2 We have used
kinetic energy momentum batted-ball speed accuracy and variability of the swing launch speed launch angle batted-ball spin rate batted-ball spin axis range Most previous science of baseball studies have used maximizing batted-ball speed Where would other performance criteria be more appropriate? 4/9/2019 © 2018 Bahill

4/9/2019 Knockdown power The Colt .45 caliber APC cartridge has a muzzle kinetic energy of 500 joules (368 ft-lbm) A baseball traveling at 97 mph (43 m/s) has 137 J (101 ft-lbm) of kinetic energy A batter can be hurt, but not knocked down by a pitch The Colt .45 automatic pistol was designed for battles in the Philippines in the early years of the 20th Century, with the performance criterion of, “Knock down the charging Moro warrior before he can chop off your head with a machete.” The existing .38 would kill the warrior, but he would chop off your head before he would die As an aside, the rotational kinetic energy stored in a baseball spinning at 2200 rpm is 2 J (1.5 ft-lbm), which is much less than the translational energy. 4/9/2019 © 2018 Bahill

Performance criteria for a pitcher
Maximize batter intimidation Minimize the number of pitches per inning Minimize the number of runs Generate impressive statistics that would generate high salaries 4/9/2019 © 2018 Bahill

New performance criterion
The old batter performance criterion of maximizing batted-ball speed worked well for home runs, but less than 5% of MLB base hits are home runs We developed a new performance criterion, the probability of getting a base hit 4/9/2019 © 2018 Bahill

Bat-ball Oblique Collision model
4/9/2019 © 2018 Bahill

Normal and tangential components
The bat’s velocity and the ball’s velocity are decomposed into components normal to the collision plane and components tangent to it 4/9/2019 © 2018 Bahill

Inputs of Bat-ball Oblique Collision model
Initial velocity vector of the bat Initial normal component of the bat’s velocity vector Initial tangential component of the bat’s velocity vector Initial velocity vector of the ball at the collision Initial normal component of the ball’s velocity vector Initial tangential component of the ball’s velocity vector Collision offset distance Angle between the line of centers and the horizontal plane Vertical angle between and the horizontal plane Mass of bat Mass of ball Radius of bat at collision point Radius of ball Coefficient of restitution (CoR) of the bat-ball collision Coefficient of friction of the bat-ball collision Angular velocity of the pitch 4/9/2019 © 2018 Bahill

Definitions of vectors and angles
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Outputs of Bat-ball Oblique Collision model
Resultant velocity vector of the bat Resultant normal component of the bat’s velocity vector Resultant tangential component of the bat’s velocity vector Resultant velocity vector of ball. This is called the launch velocity Resultant normal component of the ball’s velocity vector Resultant tangential component of the ball’s velocity vector Vertical angle (φ) between the line of centers Vertical angle (λ) between the horizontal plane and This is called the launch angle. Angular velocity of the batted ball, whose magnitude is called the spin rate 4/9/2019 © 2018 Bahill

Advantage of the uppercut
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Variation in angle of descent of the pitch
The rise ball in softball can cross the plate horizontally, at an angle of zero degrees A 90 mph MLB fastball has an angle of descent of 5 degrees A 75 mph MLB curveball has an angle of descent of 10 degrees 4/9/2019 © 2018 Bahill

Effects of collision offset
Launch velocity and spin 4/9/2019 © 2018 Bahill

Collision Offset, D (in)
Launch Speed(mph) Launch Angle (deg) Backspin Rate (rpm) 0.75 92 32 2132 0.70 30 1940 0.65 28 1748 0.60 27 1557 0.55 25 1365 0.50 23 1173 0.45 22 981 0.40 20 790 0.35 18 598 0.30 17 406 0.25 15 215 0.20 14 0.15 12 -169 0.10 10 -360 0.05 9 -552 7 -744 -0.05 6 -936 4/9/2019 © 2018 Bahill

Bat-ball Oblique Collision model
4/9/2019 © 2018 Bahill

Outcomes as a function of launch angle
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Changing popups into foul tips
4/9/2019 Changing popups into foul tips Long before the game, smooth the popup to foul tip spot of the bat with fine steel wool. Be careful to not take the paint off. Before each plate appearance, lightly rub the popup to foul tip spot with sweat or saliva. 4/9/2019 © 2017 Bahill

Lick bat during world series
4/9/2019 Lick bat during world series Yasiel Puig explained why he licks his bat: "I make love to the bat and he pays me back with hits." 9:42 PM - 19 Oct 2017 Maybe he knows abut this? The umpire did not disqualify him. 4/9/2019 © 2017 Bahill

Yasiel Puig https://www.youtube.com/watch?v=sfi-81Ywq_g
You view but not download from the following 4/9/2019 © 2017 Bahill

Changing fly balls into line drives*
4/9/2019 Changing fly balls into line drives* In the future, it will be possible to see how the coefficient of friction affects the batted-ball speed. Then we will be able to decide if the varnish or paint on the bat should be made rough-textured or smooth, or if bats should be rubbed or oiled in order to improve bat performance. To confuse fielders who are trying to locate the bat-ball collision point, perhaps the bat could be painted white with random thin red lines. Or perhaps bats could be painted pink supposedly to promote breast cancer research. 4/9/2019 © 2017 Bahill

Flat front and oil can* 4/9/2019 © 2017 Bahill 4/9/2019
A little oil (or sweat or saliva) in the indicated region would change pop-ups (sure outs) into harmless foul tips. Oil would not evaporate as quickly as sweat or saliva, but oil is not as slick as snot. Also the umpire would be better able to detect oil. Do not use graphite or Molybdenum Disulfide as this would tarnish the umpire’s finger. This picture shows the flat front, the cupping and the grain. The actual size of the flat surface should not be larger than the vertical sweet spot, which is one-third of an inch high. 4/9/2019 © 2017 Bahill

Collision Offset, D (in)
Launch Speed(mph) Launch Angle (deg) Backspin Rate (rpm) Range (feet) Hang time (sec) 0.75 92 32 2132 381 5.3 0.70 30 1940 377 5.0 0.65 28 1748 370 4.7 0.60 27 1557 361 4.4 0.55 25 1365 349 4.1 0.50 23 1173 329 3.6 0.45 22 981 318 3.4 0.40 20 790 300 3.1 0.35 18 598 280 2.8 0.30 17 406 259 2.5 0.25 15 215 237 2.2 0.20 14 214 2.0 0.15 12 -169 192 1.7 0.10 10 -360 169 1.5 0.05 9 -552 147 1.2 7 -744 125 1.0 -0.05 6 -936 105 0.8 4/9/2019 © 2018 Bahill

Probability of success model
4/9/2019 © 2018 Bahill

Collision Offset, D (in) Launch Angle (deg) Backspin Rate (rpm)
Range (feet) Hang time (sec) Height at the infield arc (ft) Probability of Success 0.75 32 2132 381 5.3 0.000 0.70 30 1940 377 5.0 0.007 0.65 28 1748 370 4.7 0.051 0.60 27 1557 361 4.4 0.072 0.55 25 1365 349 4.1 0.078 0.50 23 1173 329 3.6 0.087 0.45 22 981 318 3.4 0.093 0.40 20 790 300 3.1 0.138 0.35 18 598 280 2.8 0.250 0.30 17 406 259 2.5 0.525 0.25 15 215 237 2.2 1.000 0.20 14 214 2.0 0.15 12 -169 192 1.7 13 0.10 10 -360 169 1.5 9.2 0.05 9 -552 147 1.2 5.5 0.483 7 -744 125 1.0 1.8 0.490 -0.05 6 -936 105 0.8 - 0.320 4/9/2019 © 2018 Bahill

Probability of success
4/9/2019 © 2018 Bahill

Vertical size (height) of the sweet spot
4/9/2019 © 2018 Bahill

Collision Offset, D (in) Contact offset (in) Launch Angle (deg)
Backspin Rate (rpm) Range (feet) Hang time (sec) Height at infield arc (ft) Probability of Success 0.75 0.355 32 2132 381 5.3 0.000 0.70 0.332 30 1940 377 5.0 0.007 0.65 0.308 28 1748 370 4.7 0.051 0.60 0.284 27 1557 361 4.4 0.072 0.55 0.261 25 1365 349 4.1 0.078 0.50 0.237 23 1173 329 3.6 0.087 0.45 0.213 22 981 318 3.4 0.093 0.40 0.189 20 790 300 3.1 0.138 0.35 0.166 18 598 280 2.8 0.250 0.3365 0.159 546 274 2.7 0.300 0.30 0.142 17 406 259 2.5 0.525 0.25 0.118 15 215 237 2.2 1.000 0.20 0.095 14 214 2.0 0.15 0.071 12 -169 192 1.7 13 0.10 0.047 10 -360 169 1.5 9.2 0.05 0.024 9 -552 147 1.2 5.5 0.483 7 -744 125 1.0 1.8 0.490 -0.05 -0.024 6 -936 105 0.8 - 0.320 4/9/2019 © 2018 Bahill

Vertical sweet spot of the bat
Sweet spot height = = 0.183 About one-fifth of an inch 4/9/2019 © 2018 Bahill

The height of the sweet spot
The batter’s probability of success depends on the range and the hang time, which depend on dimensions of the ball field speed and reaction times of the fielders placement of the fielders velocities of the bat and ball spin of the ball size and mass of the bat and ball Diameter of the bat 4/9/2019 © 2018 Bahill

Collision Offset, D (in) Contact offset (in) Launch Angle (deg)
Backspin Rate (rpm) Range (feet) Hang time (sec) Ball height at infield arc (ft) Probability of Success 0.75 0.347 32 2190 382 5.4 0.00 0.70 0.324 30 1995 379 5.1 0.65 0.301 29 1799 372 4.8 0.04 0.6 0.278 27 1603 363 4.5 0.07 0.55 0.255 25 1408 352 4.1 0.08 0.5 0.231 24 1212 338 3.8 0.45 0.208 22 1017 321 3.5 0.09 0.4 0.185 20 821 303 3.1 0.13 0.35 0.162 19 625 283 2.8 0.23 0.33 0.149 18 547 274 2.7 0.30 0.3 0.139 17 430 261 2.5 0.48 0.25 0.116 15 234 239 2.2 1.00 0.2 0.093 14 39 217 2.0 0.15 0.069 12 -157 193 1.7 13 0.1 0.046 10 -353 170 1.5 9.3 0.05 0.023 9 -548 148 1.2 5.6 0.000 7 -744 125 1.0 0.49 -0.05 -0.023 5 -939 104 0.8 - 0.32 Bat diameter reduced from 2.61 to 2.5 inches 4/9/2019 © 2018 Bahill

Height of sweet spot with reduced bat diameter
Sweet spot height = = 0.172 About one-sixth of an inch 4/9/2019 © 2018 Bahill

Reducing bat diameter This sensitivity analysis shows that
The diameter of the bat is the second most important parameter in the model Changing from an ash bat to a maple wood bat would reduce the diameter from 2.61 inches to 2.5 inches Manufacturing does this to keep the weight down: maple wood is denser than ash This would reduce the height of the sweet spot from to inches. 4/9/2019 © 2018 Bahill

Bat shape is important The bat diameter in the region of the sweet spot should be as large as possible Manufacturers of maple wood bats are punishing batters They should enlarge the bat diameter in the region of the sweet spot and reduce the diameter in less important regions of the barrel 4/9/2019 © 2018 Bahill

This sensitivity analysis shows
The speed of the bat is the most important variable If the bat speed is increased, then the height of the sweet spot decreases A higher bat speed gives a higher launch velocity and a longer range It will be easier for the ball to get into the outfielder ellipses The batter must compensate by reducing the launch angle In summary, increasing bat speed decreases the vertical size of the sweet spot 4/9/2019 © 2018 Bahill

Increasing ball speed decreases the sweet spot
Increasing launch speed (e.g. by increasing bat speed or CoR), increases the ball’s range and the sweet spot height will be smaller Launch a ball at 92 mph, at an 18-degree angle with 780 rpm of backspin. It will travel 250 feet with a hang time of 2.8 seconds. probability of success = 0.502 Launch a ball at 94 mph. It will travel 257 feet with a hang time of 2.9 seconds probability of success = 0.355 Therefore, increasing the launch speed decreases the vertical size of the sweet spot of the bat 4/9/2019 © 2018 Bahill

4/9/2019 Desired Range model Assume the MLB batter wants the ball to go over the infielders and hit the grass in front of the outfielders He wants the ball to hit the ground between 140 and 270 feet from home plate. The contact offsets corresponding to 140 and 270 feet are and inches Therefore, the vertical size of the sweet spot of the bat is inches This is about one-seventh of an inch This number is smaller than the one-fifth of an inch derived with our Probably of Success model, because this Desired Range model does not utilize the gaps between the fielders and it ignores line drive and ground ball base hits. 4/9/2019 © 2018 Bahill

Height of sweet spot for a softball bat
An NCAA (college) softball player wants to hit a line-drive/fly-ball She also wants the ball to go over the infielders and hit the grass in front of the outfielders. She wants the ball to hit the ground between 115 and 180 feet from home plate. Desired Range model for NCAA softball Desired range of the batted-ball Resulting contact offsets Vertical size (height) of the sweet spot 115 to 180 feet 0.121 and 0.320 0.199 inches, one-fifth of an inch. 4/9/2019 © 2018 Bahill

4/9/2019 Performance criteria The old criterion of maximizing batted-ball speed, was designed for home runs. It recommended increasing batted-ball launch speed for all situations. Our new performance criteria of maximizing the probability of a base hit, was designed for singles. It recommends controlling batted-ball speed and launch angle. MLB batters who had very high bat swing speeds also had large variabilities and therefore less accuracy. They also had less success in MLB. When we presented Fig in chapter 4, we commented that swing speed data for the MLB batter had small variability for physiological data. We now see why. It is very important for batters to have all swings be alike. So, batters train to reduce variability of bat swing speeds This keeps the size of the sweet spot constant. In a different vein, on a change up, the batter must delay the onset of the swing but keep the swing speed constant. 4/9/2019 © 2018 Bahill

Variability The vertical size of the sweet spot depends on
4/9/2019 Variability The vertical size of the sweet spot depends on dimensions of the ball field speed and reaction times of the fielders placement of the fielders size and mass of the bat and ball velocities of the bat and ball coefficient of restitution spin of the ball bat-ball collision offset at impact Velocities are vectors with magnitude and direction 4/9/2019 © 2018 Bahill

Reliability of sweet spot estimates
We presented all of this variability to help understand the reliability of our sweet spot estimates Applying this variability to the Probability of Success model and considering all approximations and uncertainties, we conclude that the sweet spot of a bat is one-fifth of an inch high with a range of one-sixth to one-fourth of an inch 4/9/2019 © 2018 Bahill

Summary of Chapter 8 (eight)
The most important properties affecting the range of the batted-ball are, in decreasing order of importance, CoR Wind velocity Air density Initial spin of the batted-ball Launch speed Drag coefficient The values stated on television broadcasts and internet sites for the range of home run balls probably have an estimated margin of error of around ± 10% 4/9/2019 © 2018 Bahill

Summary of Chapter 9 The most important properties affecting the batter’s probability of success (height of the sweet spot) are, in decreasing order of importance, Bat swing speed Bat diameter at sweet spot Bat swing angle CoR Pitch speed Bat weight After studying the variation produced by all these properties, we conclude that the sweet spot of the bat is about one-fifth of an inch high (5 mm) 4/9/2019 © 2018 Bahill

Vertical Size of the Sweet Spot of the Bat

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