1. Kansas State University Biomechanics Lab Elastic and Rigid Body Properties of Bats by Larry Noble, Professor Department of Kinesiology Kansas State University Manhattan, KS

2. Kansas State University Biomechanics Lab Acknowledgements Collaborators – –David Dzewaltowski, Professor and Head, Department of Kinesiology, Kansas State University –John Eck, Professor of Physics and Dean, College of Natural Sciences and Mathematics, Indiana University of Pennsylvania –Hugh Walker, Professor Emeritus, Department of Mechanical Engineering, Kansas State University Sponsors –Easton Aluminum, Inc. –Kansas State University Research Foundation

3. Kansas State University Biomechanics Lab Acknowledgements Graduate Research Assistants –Deanna Deppen, Rob Dorgan, Geoffrey Ringer, Marty Ponte, Christy Allen, Denise Harper, Chris Dudley, Panteleimon Ekkekakis, Kostas Pothakos, Tim Benson, Dana Davidson, Joyce McConnell, Kasee Hildenbrand

4. Kansas State University Biomechanics Lab Outline Brief history of bat development Rules on baseball and softball bats Rigid body properties –Mass –Moment of inertia –Center of percussion Elastic properties –Longitudinal vibrational nodes and modes During impact During the swing –Coefficient of restitution Is a very rigid bat or a very flexible bat more effective? What and where is the “sweet spot”

5. Kansas State University Biomechanics Lab Brief History of Bat Development: In the Beginning Began with basically a stick around 1830 In 1850’s, handle and barrel were emerging Around 1900, modern-day shape had evolved

6. Kansas State University Biomechanics Lab History of Bat Dev: Late Wood Era From the early 1900’s until ~1970, the wood bat was used exclusively with minor design changes

7. Kansas State University Biomechanics Lab History of Bat Dev: Aluminum Era Aluminum bats first appeared around 1970 Since 1980 materials with higher strength/mass ratios have emerged The plethora of recent innovations are causing concern by softball & baseball governing bodies

8. Kansas State University Biomechanics Lab Recent Softball and Baseball Bat Rule Changes Softball –Upper limit on “liveness”, or Coefficient of Restitution (COR) – Max Bat Performance Factor = 1.20 Baseball –Max barrel diameter 2.625 in (.067 m) –Length-weight diff(< 3 units diff.) –Max Ball Exit Speed Ratio (BESR) – 94 MPH (Amateur only) –Rules committee is considering a MOI rule

9. Kansas State University Biomechanics Lab Center of Percussion (COP) The COP is the point where an impact does not cause a reaction impulse at the axis, causing the axis to tend to translate Distance from axis to center of percussion (q): q = T 2 g/4 B 2 =.248387T 2 Where T = period of oscillation

10. Kansas State University Biomechanics Lab Center of Percussion Impacts on COP do not cause an impact reaction impulse at the axis (Noble & Eck, MSSE 1986) COP has a conjugate point on the handle. Each point on the handle is associated with a different COP on barrel. (Cross, Am J Phys 1998) If the conjugate point of the COP should be near the center of the hand-bat interface (approx 6 inches from knob end), then impact reaction forces will be minimized.

11. Kansas State University Biomechanics Lab Center of Percussion In most 34-in bats, COP is approx 6 in (15 cm) from barrel end if hitter grips bat on knob end COP can be displaced predictably by changing the weight distribution of the bat (Noble & Eck, Proc ISBS 1986) The best site for COP displacement is in the knob end COP displacement can cause some vibration-related problems because of the node-COP difference discussed later

12. Kansas State University Biomechanics Lab Center of Percussion & the sweet spot Earlier studies indicated that the COP is the sweet spot, the best place to hit the ball (Bryant, RQES 1977; Noble, ISB Proc 1983) The sweet spot has since been defined in terms of two criteria: –The most comfortable location The COP has a direct effect on pain/annoyance at impact (Noble, JAB 1994; Noble) Fundamental vibrational node location also has a profound effect on impact pain/annoyance (Noble, JAB 1994) –The location for maximum post-impact ball velocity Determined by characteristics other than COP (Brody, Am J Phys 1986) –e.g., bat/ball mass and bat vel/ball vel ratios Vibrational node locations

13. Kansas State University Biomechanics Lab Longitudinal vibrational modes of bat: clamped boundary condition Normal modes of oscillation for a clamped bat showing diving board mode and 1 st & 2nd harmonics (Noble & Walker, JAB 1994; Proc ISBS 1994) Diving board mode & 1 st harmonic are ~ 13 Hz & 150 HZ, respectively, for an aluminum bat (Noble, Proc ISBS 1999)

14. Kansas State University Biomechanics Lab Longitudinal vibrational modes of bat: free-free boundary condition Diving board mode is missing from hand-held bat (Brody, Am J Phys 1990) Bat behaves as a free-free body during impact Fundamental frequency involves most of the displacement and ranges from 150 to 300 Hz in most aluminum bats First harmonic ranges from 500 to 1000 Hz Impact time ~1.5 ms for baseball and ~3.5 ms for softball

15. Kansas State University Biomechanics Lab Longitudinal vibrational modes of bat: Antinode of all modes is at barrel end Frequency can be changed substantially by changing stiffness/mass ratio (Noble & Walker, Proc ISBS 1994) Higher freq vibrations are dampened quicker with a tight grip Time for waves to travel up and down the bat is >2 ms, longer than impact time (Cross, Proc ISBS 1999)

16. Kansas State University Biomechanics Lab Impact vibrations and annoyance Node of fund mode approx 17 cm (6.7 in) from each end and 170 Hz (Cross, Am J Phys 1998) First harmonic is approx 530 Hz with nodes at approx 13 cm from BE, 5 cm from COM toward hands, and 7 cm from KE. Impacts on the node will not excite that mode. Mode excitation increases linearly with impact-node distance Thus we have a “sweet vibrations” zone approx 13-17 cm (5-6.7 in) from BE.

17. Kansas State University Biomechanics Lab Vibrations, COP & Impact Annoyance Node-COP distance is determinant of bat preference (Noble & Dzewaltowski, Tech Report to Easton Aluminum1994) Impact annoyance is least at a point between node of fundamental & COP (Noble & Walker Proc ISBS, 1994)

18. Kansas State University Biomechanics Lab Vibrations and Post-impact Ball Velocity Theoretical model included lowest 20 vibrational modes of a standard wood bat was developed to estimate ratio of exit to initial speed of a baseball in a 1 m/s impact on standard wood bat which is initially stationary. Red curve is calculated result for a flexible bat, blue curve is estimate for a rigid bat. Points with error bars are empirical measurements. (Nathan, Am J Phys 2000.

19. Kansas State University Biomechanics Lab Vibrations and Post-impact Ball Velocity Estimates of post-impact ball velocity of wood and aluminum bat Aluminum bats are better because –COR is higher –Length and weight are independent –Aluminum bats have lower Moment of inertia –Stiffness can be a design feature –Node-COP location can be a design feature

20. Kansas State University Biomechanics Lab Vibrations and Post-impact Ball Velocity Estimates of exit speed with 90 mph ball colliding with wood bat with COM speed of 54 mph and rotational speed about COM of 51 sec -1. Red curve is for rigid bat, blue curve is for flexible bat. More recently, empirical data supports these estimates

21. Kansas State University Biomechanics Lab Bat Vibrations During Swing Manufacturer’s are claiming “diving board effect” This implies that bat bends back during the swing and “releases the stored elastic energy at impact, as depicted here Is this implication valid?

22. Kansas State University Biomechanics Lab Bat Flexibility Field Test First, a controlled blind field test involving 6 different bat flexibilities with 32 elite softball players was funded by a bat manufacturer Results indicated that these hyper-flexible bats resulted in greater post-impact velocity and were preferred by elite slow-pitch hitters over stiffer bats (Noble, Tech Rep to Easton Aluminum 1994) An examination of bat bending characteristics during the swing followed this study (Noble, Proc ISBS 2001)

23. Kansas State University Biomechanics Lab Begin Swing 233ms PC Peak 41 ms PC Horiz Pk 38 ms PC Bat bending during swing and impact

24. Kansas State University Biomechanics Lab

25. Begin swing 183 ms PC Peak bending and peak torque ~ 50 ms PC Impact – bat still bent back approx 20% of max

26. Kansas State University Biomechanics Lab Bat Vibrations During Swing and Impact: Conclusions During the swing, the bat bends back and stores elastic energy that is released during impact Thus, a more flexible bat would appear to be more effective if the ball impacts at the sweet spot During impact, the bat behaves as a free-free body A stiffer bat would appear to be more effective if the ball does not impact at the sweet spot. Perhaps a stiff bat is better for baseball and fast-pitch softball and a flexible bat is better for slow-pitch softball

27. Kansas State University Biomechanics Lab So, Where and What is Sweet Spot? It is the best place on the bat to hit the ball, considering –Annoyance/comfort –Post-impact ball velocity This location is: –Location of minimal vibrations (approx 6.5 in from barrel end) –Location of COP with axis approx 6 in from knob end (approx 6 in from barrel end) –Preferably these two areas are close together References for this presentation are on this course website in word format under filename “ acsmpresbiblio.rtf “ acsmpresbiblio.rtf

28. Kansas State University Biomechanics Lab References for this presentation can be found on this website: http://www:ksu-personal.edu/~lnoble