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Slide 1 - Systems Engineering of the Baseball Bat Terry Bahill Systems and Industrial Engineering University of Arizona Tucson, AZ 85721-0020 (520) 621-6561 Copyright  1989-2009 Bahill
Slide 2 - References R. G. Watts and A. T. Bahill, Keep Your Eye on the Ball: Curve Balls, Knuckleballs and Fallacies of Baseball, W. H. Freeman, 2000, ISBN 0-7167-3717-5. The slides of this presentation are available at Bahill, A.T. and Gissing, B. "Re-evaluating systems engineering concepts using systems thinking," IEEE Transactions on Systems, Man, and Cybernetics, Part C Applications and Reviews, 28(4), 516-527, 1998. A. T. Bahill, “The ideal moment of inertia for a baseball or softball bat,” IEEE Transactions on System, Man, and Cybernetics – Part A: Systems and Humans, 34(2), 197-204, 2004. 12/9/2014 2 © 2009 Bahill
Slide 3 - Definition of engineering Engineers use principles from basic science (like physics, physiology and psychology) and design things that are useful to people. 12/9/2014 3 © 2009 Bahill
Slide 4 - The SIMILAR process State the problem Investigate alternatives Model the system Integrate Launch the system Assess performance Re-evaluate. 12/9/2014 4 © 2009 Bahill
Slide 5 - The systems engineering process But, it is not a serial process. It is parallel and highly iterative. This talk is mostly about modeling. 12/9/2014 5 © 2009 Bahill
Slide 6 - Tasks in the modeling process* Describe the system to be modeled Determine the purpose of the model Determine the level of the model Gather experimental data describing system behavior Investigate alternative models Select a tool or language for the simulation Make the model Validate the model* Show that the model behaves like the real system Emulate something not used in the model’s design Perform a sensitivity analysis Show interactions with other models Integrate with models for other systems Analyze the performance of the model Re-evaluate and improve the model Suggest new experiments on the real system State your assumptions 12/9/2014 6 © 2009 Bahill
Slide 7 - 12/9/2014 7 © 2009 Bahill
Slide 8 - We teach modeling by example Modeling is usually taught by example. Here is an example. 12/9/2014 8 © 2009 Bahill
Slide 9 - The ideal bat There is an ideal baseball and softball bat for each individual. To determine the ideal bat for each player we need to consider the coefficient of restitution of the bat-ball collision, the sweet spot of the bat, the ideal bat weight, and the weight distribution of the bat. 12/9/2014 9 © 2009 Bahill
Slide 10 - 12/9/2014 10 The coefficient of restitution* CoR of a baseball-concrete floor collision is about 0.55 Drop a baseball onto a concrete floor; it will rebound CoR2 of the height. Drop it from 3 feet, it will rebound about 11 inches. CoR of a softball-concrete floor collision is around 0.47. Drop it from 3 feet, it will rebound about 8 inches. Most of the CoR of a bat-ball collision is supposed to be due to the ball. However, drop a bat from 3 feet, it will rebound 10 inches. How come? © 2009 Bahill
Slide 11 - The CoR depends on the ball and the bat, collision speed, shape of the objects, where the ball hits the bat, and temperature. (Putting bat ovens in the dugout would help!) 12/9/2014 11 © 2009 Bahill
Slide 12 - We use CoR = 1.17 (0.56 - 0.001 CollisionSpeed) for an aluminum bat and a softball and CoR = 1.17 (0.61 - 0.001 CollisionSpeed) for a wooden bat and a hardball where CollisionSpeed is in mph. 12/9/2014 12 © 2009 Bahill
Slide 13 - The sweet spot of the bat* We would like the bat-ball collision to occur near the sweet spot of the bat. The sweet spot has been defined as the center of percussion node of the fundamental vibration mode antinode of the hoop node maximum energy transfer area maximum batted-ball speed area maximum coefficient of restitution area minimum energy loss area minimum sensation area joy spot The sweet spot is centered 5 to 7 inches from the fat end of the bat. 12/9/2014 13 © 2009 Bahill
Slide 14 - The center of percussion1 When the ball hits the bat, it produces a translation that pushes the hands backward and a rotation that pulls the hands forward. When a ball is hit at the center of percussion (CoP) for the pivot point, these two movements cancel out, and the batter’s hands feel no sting. 12/9/2014 14 © 2009 Bahill
Slide 15 - The center of percussion2 To find the CoP, hang a bat by the knob (or if possible a point 6 inches from the knob) with 2 or 3 feet of string. Hit the bat with an impact hammer. Hitting it off of the CoP will make it flop like a fish out of water.* Hitting it on the CoP will make it swing like a pendulum.** 12/9/2014 15 © 2009 Bahill
Slide 16 - 12/9/2014 16 The center of percussion3 © 2009 Bahill
Slide 17 - 12/9/2014 17 © 2009 Bahill
Slide 18 - 12/9/2014 18 © 2009 Bahill
Slide 19 - The node of the fundamental mode The node of the fundamental vibration mode is the point where the fundamental vibration mode of the bat has a null point. To find this node, with your fingers and thumb grip a bat about six inches from the knob. Tap the barrel at various points with an impact hammer. The point where you feel no vibration and hear almost nothing is the node. 12/9/2014 19 © 2009 Bahill
Slide 20 - Hoop mode Only hollow metal & composite bats Trampoline effect Wood bats don’t deform. All of the energy is stored in the ball. Most of the losses are in the ball. A ball has both a contribution to CoR and a stiffness. A stiff ball will deform the bat more, and therefore store more energy in the bat. BPFs of 1.2 are common. 12/9/2014 20 © 2009 Bahill
Slide 21 - How big is the sweet spot? The node of the fundamental vibration mode is about a ¼ of an inch wide. The center of percussion is a few inches wide. The least vibrational sensation point is a few inches wide. 12/9/2014 21 © 2009 Bahill
Slide 22 - 12/9/2014 22 © 2009 Bahill
Slide 23 - Bunts Do batters bunt the ball at the end of the bat rather than at the sweet spot in order to deaden the bunt? 12/9/2014 23 © 2009 Bahill
Slide 24 - Ideal bat weight™* There is an ideal bat weight™ for each baseball and softball player. It makes the ball go the fastest. Measure bat swings. Make a model for the human. Couple the model to equations of physics. Compute ideal bat weight. 12/9/2014 24 © 2009 Bahill
Slide 25 - 12/9/2014 25 © 2009 Bahill
Slide 26 - Ideal bat weight™ 12/9/2014 26 © 2009 Bahill
Slide 27 - Outlawing aluminum bats^ For most college batters, outlawing aluminum bats would produce faster batted-ball speeds, thus endangering pitchers. 12/9/2014 27 © 2009 Bahill
Slide 28 - System Design 12/9/2014 28 © 2009 Bahill
Slide 29 - Rules of thumb for recommending bats 12/9/2014 29 © 2009 Bahill
Slide 30 - 12/9/2014 30 © 2009 Bahill
Slide 31 - Sweet spot versus center of mass* speedsweet-spot = 1.15 * speedcenter-of-mass But the standard deviation is large: 0.06 12/9/2014 31 © 2009 Bahill
Slide 32 - 12/9/2014 32 © 2009 Bahill The variable moment of inertia bat experiments
Slide 33 - The beginnings^ In 1988 we conducted our first variable moment of inertia bat experiments. Lack of funding and the large variability in the data caused us to quit doing those experiments. With retrospective analysis we now know that most of the variability was due to player life experiences: the Chinese students who had never played baseball fell into one group, the Americans who grew up playing baseball fell in to another group, and the university women softball players fell into another group. 12/9/2014 33 © 2009 Bahill
Slide 34 - The beginnings (continued) Furthermore, the first three UofA women softball players we measured turned out to have the biggest positive slope, the biggest negative slope and a zero slope (on the next slide). What bad luck! 12/9/2014 34 © 2009 Bahill
Slide 35 - Results of the variable moment of inertia experiments 12/9/2014 35 © 2009 Bahill
Slide 36 - Moment of inertia experiments Weight distribution is characterized by moment of inertia. It takes a sweet-spot speed of 50 mph, producing a batted-ball speed of 71 mph, to drive a perfectly hit softball over the left field fence (200 feet) of Hillenbrand stadium. About half of these players can doing this. Which of these batters would profit from using an end-loaded bat? 12/9/2014 36 © 2009 Bahill
Slide 37 - Batted-ball speed 12/9/2014 37 © 2009 Bahill
Slide 38 - End-loaded bats The data for each player can be fit with a line of the form vbat-before = slope Iknob + intercept Batters with positive slopes would definitely profit from using end-loaded bats. 12/9/2014 38 © 2009 Bahill
Slide 39 - Optimal inertia 12/9/2014 39 © 2009 Bahill
Slide 40 - Moment of inertia summary* 12/9/2014 40 © 2009 Bahill
Slide 41 - Moment of inertia conclusions* Batters with positive slopes should definitely use end loaded bats. We calculated the optimal moment of inertia for the 40 batters in our study. They would all profit from using end-loaded bats. 12/9/2014 41 © 2009 Bahill
Slide 42 - Assess performance The University of Arizona softball team has won the collegiate world series six times in the last dozen years. 12/9/2014 42 © 2009 Bahill
Slide 43 - 12/9/2014 43 The distance the ball travels depends on where the ball hits the bat* © 2009 Bahill
Slide 44 - Integrate Outlawing aluminum bats would endanger pitchers. All of the batters in our study would profit from using an end-loaded bat. There is an ideal bat (weight & moment of inertia) for each person. 12/9/2014 44 © 2009 Bahill
Slide 45 - 12/9/2014 45 © 2009 Bahill
Slide 46 - Seminar materials Convict of SE cards bat on wire ball impact hammer 12/9/2014 46 © 2009 Bahill