JOM, Vol. 64, No. 3, 2012 DOI: 10.1007/s11837-012-0288-2 Ó 2012 TMS

Feature Materials in Action Design Implementation of Bats: Reinforced Bats—A Case Study

N.M. Ravindra, Ivan Padron, Priyanka Singh, Bhumi Bhatt, Vishal Singh, and Kevin Fritz

An analysis of the physics of base- advance, rules were implemented by The rules that have been implemented bats is presented in this study. organized baseball leagues to main- are not completely consistent and of- In particular, the analysis focuses on tain a competitive balance between ten vary from one league to another. the safety of various types of baseball the teams and the players. These rules In Little League and collegiate base- bats and the numerous approaches were more focused on achieving com- ball where metal bats are prevalent, that have been taken in the industry to petitive balance than increasing - more and stricter rules have been improve their safety. In order to evalu- ty, largely because the equipment was implemented. The Little League As- ate their safety, several factors have not advanced enough to cause major sociation of America, for example, been analyzed including the baseball safety concerns. recently outlawed all bats made of EDWFRHI¿FLHQWRIUHVWLWXWLRQWKHWUDP- Starting in the 1970s, metal base- composite materials and also has rules poline effect, the durability of the bat ball bats, especially aluminum bats, regarding the maximum length of the and its constituent materials. In this became increasingly popular due to bat as well as its maximum diameter.2 study, a novel, patented, reinforced their extreme durability and improved The NCAA has gone even further re- wooden baseball bat has been exam- performance over traditional wooden garding rules for the safety of baseball ined to determine its durability and bats. More recently, bats made of bats. In addition to length and diam- safety relative to traditional wooden composite materials, which offer even eter restrictions, there are also rules EDWV5HVXOWVEDVHGRQD¿QLWHHOHPHQW better performance, have also become regarding the difference between the analysis using ANSYS software have common. As the metal and composite length and weight of the bat as well demonstrated that this reinforced bat performance continued to improve as the bat’s moment of inertia.3 Until bat reduces the stress of impact with over the years, the competitive bal- recently, the National Collegiate Ath- a baseball, increasing the useable ance between hitters and was letic Association (NCAA) also had a lifespan of the bat. Furthermore, af- increasingly disrupted, and more im- rule which required that all approved ter thorough and consistent use, re- portantly, safety began to be a major bats be tested to determine the ball sults suggest that the reinforced bat is concern. For example, given an av- exit speed ratio (BESR), which com- both more durable and safer because erage speed and bat speed, the pared the speed of the ball before and it takes longer to break than a tradi- could have as little as 0.33 sec- after collision with the bat. Bats with tional bat and, when it does break, it onds to react to a ball back at them a BESR of more than 0.728 were not cracks instead of splintering and be- in , and as little allowed in play.4 Recently, however, a coming a projectile. as 0.26 seconds in major league base- new, more stringent statistic called the ball. Another safety concern is that EDVHEDOO EDW FRHI¿FLHQW RI UHVWLWXWLRQ INTRODUCTION when wooden bats break during play, (BBCOR) has been implemented by Baseball is one of the oldest sports they often splinter, and a large chunk the NCAA which also takes into ac- in America, dating back to the mid- of the bat becomes a projectile which the “trampoline effect” caused 1800s. As would be expected with any can potentially come very close to one by metallic and composite baseball sport that has been around for more RIWKH¿HOGHUV,QIDFWSHRSOHZHUH bats. Bats with BBCOR ratings of than 150 years, there have been many killed playing youth baseball between more than 0.50 are not allowed in advances made in baseball through 1987 and 1996 and there were over competition.3 the years. Probably the biggest ad- 29,000 injuries, including over 15,000 In as well vancements have been in the area of ball-related mishaps.1 as professional Minor League Base- equipment. In the early years of base- As these incidents grew in frequen- ball, where wooden bats are used ball, there were not very many rules cy, more rules about baseball equip- exclusively, fewer rules are present regarding equipment, as most equip- ment, especially regarding baseball regarding baseball bats. While this is ment was generally very rudimentary. bats, were introduced at various levels understandable in the sense that these However, as the equipment began to of play to help make the game safer. leagues do not have to be concerned

359 360 Ravindra, Padron, P. Singh, Bhatt, V. Singh, and Fritz with the negative effects of metal and a number of factors to determine the composite bat at the moment of con- composite bats, it still poses the po- reasons for better performance of tact with a ball.3 To determine a bat’s tential danger of a broken wooden bat metal bats. BBCOR rating, the NCAA has devel- LQMXULQJD¿HOGHU In regards to the studies attempting RSHG D VSHFL¿F WHVWLQJ SURFHGXUH3 A In this paper, the impact of the new to improve aspects of baseball bats, EDOOFDQQRQ¿UHVUHJXODWLRQEDVHEDOOV rules regarding metal and composite Ashley13 developed two predominant- at a stationary bat, and the velocity of bats on bat performance is analyzed. ly composite bats, one of which had the ball before and after impact is re- A new reinforced wooden bat aimed performance similar to hardwood bats corded, similarly to the BESR statis- at improving the safety of wooden but with improved durability and the tic. The difference, however, is how EDWV LV SUHVHQWHG $ ¿QLWH HOHPHQW other with performance that exceeded these velocities are used in the respec- analysis (FEA) using the ANSYS even that of aluminum bats. Both of tive calculations. The equation for the software is performed to compare the these bats contain a high-strength in- BESR statistic4 is given by the follow- stress experienced during collision by ner core made from resin-impregnated ing expression: a regular wooden bat as well as the V\QWKHWLF ¿EHUV DQG \DUQV VXUURXQG- Vv−δ reinforced bat. ed by a outer surface. Axtell, BESR = R ++05. <>ε (1) 14 Vv+δ Smith, and Shenoy also developed a I REVIEW OF THE composite reinforcement for wooden LITERATURE bats to improve durability. This com- where, VI and VR are the ball inbound There have been a number of ar- posite reinforcement consisted of an e- and rebound speeds, ε is a correction ticles analyzing the physics of base- glass braided sleeve which was placed factor, and ball bats with a variety of motivations around a regular laminated wood bat. δν and applications. These articles can be However, the main problem with = 136 mph – VContact (2) separated into three distinct catego- both of these studies is that since they ries: articles that try to understand the use composite materials, they would The BBCOR statistic is represented bat-ball collision, articles comparing not be allowed in leagues that permit as: metal and wood bats, and articles that only traditional wood bats. V present ways of improving various BBCOR = R (1+++rrC ) (3) THEORETICAL ball characteristics of baseball bats. VI BACKGROUND Among the studies attempting to where, VI and VR are the ball inbound understand the bat-ball collision, a ma- There are several important factors and rebound speeds respectively. The r jor topic of interest was the so-called to consider when analyzing both metal and Cball values are calculated from the “.” Cross tried to locate the and wooden baseball bats. These fac- following formulae: sweet spot in terms of vibration nodes WRUVLQFOXGHWKHEDW¶VFRHI¿FLHQWRIUHV- 5 or a center of percussion while Noble titution, its moment of inertia, and the Cball = 0.528 – BBCOR (4) also attempted to quantitatively de- mechanical properties of its constitu- scribe the location of the sweet spot ent materials. For metal and composite ⎡ 1 ()LBPz−−2 ⎤ as a combination of vibrational fac- bats, the so-called “trampoline effect” rm=+ ⎢ 2 ⎥ (5) tors, the center of percussion, and the is also important. ⎣W 16−−WBP()⎦ FRHI¿FLHQW RI UHVWLWXWLRQ6 Another Coefficient of Restitution study which sought to understand the where, m is the mass of the ball in bat-ball collision was Nathan, Rus- Beginning in 2005, the NCAA im- ounces, z is measured in inches from sell, and Smith, which analyzed the plemented the BESR statistic to limit the barrel end of the bat, W is the WUDPSROLQHHIIHFWXVLQJWKHFRHI¿FLHQW the performance of metal and com- weight of the bat, L is the length of of restitution.7 Finally, Drane and posite bats by placing restrictions on the bat, and BP is the balance point Sherwood (2004) found that there was the ratio of the ball speed before and relative to the knob of the bat. a 4% decrease in performance when after collision. This statistic, however, The results of this new rule have WKHEDVHEDOOZDVFRROHGVLJQL¿FDQWO\ did not provide enough safety, and EHHQ YHU\ VLJQL¿FDQW ZLWK VFRULQJ prior to use.[8] several pitchers were seriously injured dropping by over 1 per team per The studies that focused on com- after it was implemented. In response, game and average dropping paring the performance between met- the NCAA implemented the BBCOR from .305 to .279.15 al and wood bats unanimously agreed statistic in 2011, which represents the Moment of Inertia that metal bats gave better perfor- FRHI¿FLHQW RI UHVWLWXWLRQ EHWZHHQ WKH mance. Shenoy, Smith, and Axtell9 as baseball and each metal or composite Another important factor in deter- well as Greenwald, Penna, and Cris- bat model. mining a bat’s performance is its mo- co10 found that the ball’s velocity was Instead of comparing the velocity ment of inertia, or in other words, the 4–9 mph higher after colliding with a of the ball before and after impact, distribution of its weight. With bats metal bat compared to a wooden bat.11 the BBCOR statistic measures the made of a piece of wood, the Meanwhile, Crisco et al.12 analyzed bounciness or give of an aluminum or distribution of the bat’s weight is obvi- Design Implementation of Baseball Bats: Reinforced Bats—A Case Study 361

sidered as a collision between two and upsetting the balance of the game. linear springs, as in Figure 1, which THE REINFORCED BAT have different spring constants. As kball kbat VXFKERWKREMHFWVDEVRUEVRPH¿QLWH The force generated from the impact M amount of energy from each other. of a baseball on a wooden bat can often While the mass of the two objects be quite large, on the order of several m and their velocities have an impact on thousand Newtons. This violent col- the speed with which the ball leaves lision occasionally has the effect of the bat, in this model, the spring con- breaking the bat to a degree that it is Figure 1. A bat-ball collision modeled as two springs.7 VWDQWDOVRSOD\VDVLJQL¿FDQWUROH7KLV no longer useable. Sometimes when VSULQJ FRQVWDQW FDQ EH TXDQWL¿HG E\ this occurs, part of the bat becomes a considering it to be the elastic modu- VKDUSO\ SRLQWHG SURMHFWLOH ZKLFK ÀLHV RXVO\ ¿[HG PHDQLQJ WKDW DQ\ JDLQV lus, or Young’s Modulus, of the bat WRZDUGV RQH RU PRUH RI WKH ¿HOGHUV from re-positioning the bat’s weight material. The Young’s Modulus of causing a tremendous safety risk. To cannot be realized. With metal and some common bat materials are: ash, help remedy this safety risk, in this composite bats, however, the amount 12; hickory, 14; , 13; and alumi- study, a reinforced wooden baseball of material at different points along num, 69. bat has been investigated to see if it the length of the bat can be varied and A larger Young’s Modulus num- could be made more durable and safer optimized. ber means that the material requires than regular wooden bats. This rein- Bahill16 analyzed various metal and a larger force to deform by the same forced bat was designed and patented wood baseball and bats to amount. Given the much larger by Leonard Smalley.17 determine their respective moments Young’s Modulus value for aluminum In this design, as in Figure 2, four of inertia. In his analysis, he found compared to the various types of wood, small and shallow grooves are cut cir- that, as expected, the metal bats had it is obvious that the various types of cumferentially around the bat. These higher moments of inertia. To realize wood deform much more than the alu- grooves are roughly evenly distributed an increase in the moment of inertia minum, absorbing much more energy throughout the length of the bat with of a bat, Bahill recommended add- and lowering the velocity of the ball WKH¿UVWRQHFORVHWRWKHKDQGOHRIWKH ing weight near the end of the bat as it leaves the bat. Meanwhile, this bat, the second one approximately at while lightening the area close to the lack of deformation in the aluminum the middle of the bat, and the other handle. This so called “end-loading” represents the so-called “trampoline two near the end of the bat straddling effect caused a slight decrease in effect” which causes the ball to col- the “sweet spot.” Then, a sealant is put swing speed but increased the batted lide more elastically and have a higher in each groove as well as at least one ball speed, improving a given batter’s velocity after collision. strand of polymeric string. The loca- game performance. The result of this trampoline effect tion of each groove was determined The moment of inertia for baseball is twofold. First, because the ball re- HPSLULFDOO\ WKURXJK VLJQL¿FDQW UHDO bats is only mandated in one major or- bounds off of the bat with a higher ve- world testing. The end result is that the ganized baseball league—the NCAA. locity, the pitcher has less time to re- bat looks exactly the same as a tradi- Interestingly, the NCAA mandates act, which is one reason why so many tional bat, but is intended to be more a minimum moment of inertia but injuries to pitchers have occurred in durable and safer. makes no mention of a maximum mo- leagues where metal bats are used. The theory behind this design is that ment of inertia. The stated goal of this The other major result is that the ball the grooves will focus excessive vibra- rule is to force players to use heavier WHQGVWRÀ\IDUWKHUZLWKEDWVWKDWKDYH tions created from the bat-ball colli- bats, thus reducing their swing speeds a large trampoline effect. This extra sion which would otherwise propagate and improving safety. According to distance causes more home runs to throughout the entire length of the bat. Bahill’s work, however, it seems that occur and games to be higher scoring, By focusing these vibrations, the goal a maximum moment of inertia should negating the effect of skilled pitchers of this design is to prolong the life of also be mandated. Trampoline Effect 26 22  :KLOHWKHFRHI¿FLHQWRIUHVWLWXWLRQ 16 18 20 5 2 3 the bat’s mass, and its moment of in- 4 ertia are all important factors in bat 12 performance and safety, a thorough analysis of the topic would not be 4 3 14 44 52 complete without also considering the L 24 trampoline effect. The collision between a baseball Figure 2. Schematic of a reinforced baseball bat. DQGDEDWFDQEHVLPSOL¿HGWREHFRQ- 362 Ravindra, Padron, P. Singh, Bhatt, V. Singh, and Fritz

ball players reported that there was no noticeable difference in the look, feel, or most importantly, performance between traditional bats and the re- inforced bats. Of the four bats which 3.9919 1 × 107 Max 3.5487 1 × 107 were tested, all the bats were able to 3.1054 1 × 107 withstand several thousand hits over × 7 2.6622 1 10 the course of the season, and one of the 2.2189 1 × 107 1.7756 1 × 107 bats made it through the entire season 1.3324 1 × 107 without being damaged. Meanwhile, 8.8914 1 × 106 4.4588 1 × 106 the three bats that did crack (for ex- 26292 Min ample, Figure 6) after several thousand hits cracked such that instead of shat- Equivalent Stress Type: Equivalent (von-Mises) Stress tering and becoming projectiles, they Unit: Pa Figure 3. Stress concen- had very slight cracks beginning at one tration for a traditional Time: 1; 6/2/2010 1:18 PM baseball bat. of the grooves and ending at another one of the grooves. While these cracks still mark the end of the useful lives for wooden baseball bats. Also, when the wood)—Young’s modulus, 1.22 × 1010 the bats, it is important to note that they EDW ¿QDOO\ WHQGV WR EUHDN WKH JRDO LV Pa, Poisson’s Ratio, 0.371, and density, cracked in a completely controlled and to limit the crack to just the area be- 600 kg/m3; baseball—young’s modu- safe way which did not injure any of tween two such grooves so that the bat lus, 1 × 108 Pa. Poisson’s Ratio, 0.45; the participants in the game. does not completely shear and become 3 density, 4,000 kg/m . CONCLUSIONS a projectile. RESULTS The main advantages of bats made FINITE ELEMENT ANALYSIS  7KH UHVXOWV RI WKH ¿QLWH HOHPHQW with metal and composite materials are  $V D SDUW RI WKLV VWXG\ D ¿QLWH HO- analysis are shown in Figures 3 and 4, that they have greater performance and ement analysis was performed using in which it is apparent that the grooves WKH\KDYHDQHDULQ¿QLWHXVHDEOHOLIHV- ANSYS software to analyze the stress with polymeric string are able to elimi- pan. Wooden bats, on the other hand, distribution along the length of both a nate some of the stress placed on the do not achieve the same performance traditional wooden bat and the rein- bat during collision. It can be seen that and have a tendency to break or shatter forced bat during collision. Finite ele- the maximum and the minimum equiv- under consistent heavy use. It would ment analysis uses a complex system alent stress for a traditional baseball seem, then, that wooden bats are infe- of points called nodes which make a bat is higher than that of the reinforced rior to their metal and composite coun- grid called a mesh. This mesh is pro- baseball bat. This result has the effect terparts. grammed to contain the material and of relieving the stress on the rest of the A deeper analysis, however, pres- VWUXFWXUDOSURSHUWLHVZKLFKGH¿QHKRZ bat, prolonging its usable life. ents a much different picture. The in- the structure will react to certain load- The reinforced bats (Figure 5) were crease in the performance of metal bats ing conditions. Nodes are assigned at also given to the New Jersey Institute has a negative effect on other aspects a certain density throughout the mate- of Technology (NJIT) baseball team of baseball. For example, by enabling rial depending on the anticipated stress for real-world testing. The NJIT base- such tremendous performance by bat- levels of a particular area. Regions which will receive large amounts of stress usually have a higher node den- sity than those which experience little 2.6938 1 × 107 Max × 7 18 2.3945 1 10 or no stress. 2.0952 1 × 107 In this analysis, a number of param- 1.7959 1 × 107 HWHUVZHUHVSHFL¿HG)LUVWDWKUHHGL- 1.4966 1 × 107 1.1974 1 × 107 mensional version of both the standard 8.9807 1 × 106 bat and the reinforced bat were devel- 5.9878 1 × 106 2.9949 1 × 106 oped. Based on previous calculations, 1970.6 Min the force on the ball due to the pitcher was determined to be 3.94 kN and the force on the bat due to the batter’s Equivalent Stress Type: Equivalent (von-Mises) Stress - Top/Bottom swing was determined to be 3.40 kN. Unit: Pa These values, along with the follow- Time: 1 Figure 4. Stress con- 6/2/2010 1:19 PM centration for a rein- ing material constants, were included forced baseball bat. in the model: Baseball bat (maple Design Implementation of Baseball Bats: Reinforced Bats—A Case Study 363

of North Carolina at Chapel Hill, July 2001), www. scienceblog.com/community/older/2001/E/200115302. html. 2. “Little League Baseball Official Rules,” League Lineup (2011), www.leaguelineup.com/greatkills/files/ LITTLELEAGUEBASEBALLRules.pdf. 3. “National Collegiate Athletic Association Standard for Testing Baseball Bat Performance—Bat-Ball Coefficient of Restitution,” National Collegiate Athletic Association Official Website (National Collegiate Athletic Association, 21 May 2009), fs.ncaa.org/Docs/rules/ baseball/bats/NCAA%20BBCOR%20Protocol%20 FINAL%205%2009.pdf. 4. “National Collegiate Athletic Association Standard for Figure 5. A reinforced baseball bat before use. Testing Baseball Bat Performance,” National Collegiate Athletic Association Official Website (National Collegiate Athletic Association, 22 January 2009), fs.ncaa.org/ Docs/rules/baseball/bats/NCAABESRProtocol1.09.pdf. 5. Rod Cross, “The Sweet Spot of a Baseball Bat,” Amer. J. Physics, 66 (9) (1998), pp. 772–779. 6. Larry Noble, Proc. of 16 International Symposium on Biomechanics in Sports (Konstanz, Germany: University of Konstanz, 1998), pp. 86–97 7. Alan M. Nathan, Daniel A. Russell, and Lloyd V. Smith, “The Physics of the Trampoline Effect in Baseball and Softball Bats,” International Sports Engineering Association. University of California: Davis, Davis, CA. Figure 6. A reinforced baseball bat after use. Lecture (2004). 8. P.J. Drane and J.A. Sherwood, “Characterization of the Effect of Temperature on Baseball COR Performance,” The Engineering of Sport, 5 (2) (2004), ters, the effect of a team’s pitching that the trademark is pointed directly pp. 59–65. ability becomes almost inconsequen- up or down, the ball will collide with 9. Mahesh M. Shenoy, Lloyd V. Smith, and John T. tial, upsetting the balance of the game. the grain of the bat instead of against Axtell, “Performance Assessment of Wood, Metal, and 19 Composite Baseball Bats,” Composite Structures, 52 (3- More importantly, the tremendous the grain, increasing the lifespan of 4) (2001), pp. 397–404. speed with which the ball leaves a the bat. Therefore, it seems that this re- 10. Richard M. Greenwald, Lori H. Penna, and Joseph metal bat causes the pitcher to have al- inforced wooden bat is the best blend J. Crisco, “Differences in Speed With Wood and Aluminum Baseball Bats: A Study,” J. most no time to react when a ball is hit of performance, safety, and durability Applied Biomechanics 17 (2001), p. 241–252. directly at them. This lack of reaction among the currently available types of 11. N.M. Ravindra, Sikha Sushil K., and Padron Ivan, time has caused many serious injuries baseball bats. “Physics of Baseball Bats—An Analysis,” Int. J. Sports Science and Eng., 3 (2009), pp. 34–42. through the years to pitchers at differ- ACKNOWLEDGEMENTS 12. Joseph J. Crisco, Richard M. Greenwald, Jeffrey D. ent levels of baseball. Blume, and Lorraine H. Penna, “Batting Performance of Wooden bats, on the other hand, The authors acknowledge with Wood and Metal Baseball Bats,” Medicine & Science in Sports & Exercise, 34 (10) (2002), pp. 1675–1684. have maintained the gentle balance WKDQNVWKHSDUWLDO¿QDQFLDOVXSSRUWRI 13. Steven Ashley, “Wood-Composite Baseball Bates between pitchers and batters for over the New Jersey Institute of Technology. Take the Field,” Mechanical Engineering, 113 (8) (1991), 150 years and their slightly less potent They thank Drs. Donald Sebastian, pp. 43–45. 14. John T. Axtell, Lloyd V. Smith, and Mahesh M. performance allows the pitchers a little Priscilla Nelson, James Geller, and Shenoy, “Effect of Composite Reinforcement on the more time to react when a ball is hit di- Rose Federici for their keen interest in Durability of Wood Baseball Bats,” Proc. of 32nd rectly at them. The main concern, then, the project. Several bat manufacturers International SAMPE Technical Conference (SAMPE: Covina, CA 2000), pp. 687–697. with wooden bats is that they tend to including Radial Bats, MDS/Leonard 15. Pat Borzi, “Making Metal Bats Play Like Wood,” The break under heavy use, potentially be- Smalley and Akadema supplied bats Times (18 June 2011), SP4. coming a dangerous, sharp projectile. for this study. The study was made 16. A. Terry Bahill, “The Ideal Moment of Inertia for a Baseball or Softball Bat,” Systems, Man and These disadvantages, however, are possible by the participation and sup- Cybernetics, Part A: Systems and Humans, IEEE remedied by the reinforced bat which port of the NJIT baseball team and the Transactions on, 34 (2) (2004), pp. 197–204. was tested as part of this study. Our re- coaches, Lenny Kaplan, Brian Calla- 17. “Reinforced Wooden Baseball Bat, Leonard Smalley,” assignee, U.S. patent 7,448,971 (11 Nov. 2008). sults show that this bat kept the same han and Mike Cole. The assistance of 18. Peter Widas, “Introduction to Finite Element performance standards of wooden Pradeep Bheemarthi, Shanmugamur- Analysis,” Va Tech–Lab for Scientific Visual Analysis bats but experienced dramatically less thy Lakshmanan, Gaurav Devrani, (Virginia Tech Material Science and Engineering, 8 Apr. 1997), www.sv.vt.edu/classes/MSE2094_ stress on impact, prolonging its lifes- Rene Rivero, Tsezar Seman and Vijay NoteBook/97ClassProj/num/widas/history.html. pan. Furthermore, when the bats did Kasisomayajula during the early part 19. http://www.youtube.com/watch?v=W2wpSfVRa0w ¿QDOO\ FUDFN WKH\ FUDFNHG LQ D YHU\ of this project is acknowledged with N.M. Ravindra, Ivan Padron, Priyanka Singh, controlled manner between two of the thanks. Bhumi Bhatt, and Vishal Singh are with the New grooves as opposed to shearing along Jersey Institute of Technology, Newark, New Jer- References the grain of the bat and becoming a sey 07102; Kevin Fritz is with the University of 1. “New Study Shows 13 Little League Players Died Pennsylvania, Philadelphia, Pennsylvania 19104. sharp projectile which could injure a from Baseball Injuries from 1987–96,” ScienceBlog.com Dr. Ravindra can be reached at nmravindra@ player. Also, by holding the bat such | Science News Straight from the Source (University gmail.com.