1. 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

2. 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.

3. 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)

4. 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

5. 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?

6. Kansas State University Biomechanics Lab Bat Flexibility Field Test Effects of bat handle flexibility on performance and preferences 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 An examination of bat bending characteristics during the swing followed this study

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

8. Kansas State University Biomechanics Lab

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

10. Kansas State University Biomechanics Lab Wood vs Aluminum Bats 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

11. Kansas State University Biomechanics Lab Conclusions: Bat Vibrations During Swing and Impact 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

12. 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

13. Kansas State University Biomechanics Lab Criteria for evaluating baseball & softball bats Overall feel, grip, how does it fit your hand(s) Post impact ball response –Control –Power Durability –Resistance to denting, cracking, etc. under normal playing conditions Forgiveness – size of sweet spot Construction quality –End cap, knob, welds, finish Would you buy the same bat again?

14. Kansas State University Biomechanics Lab Softball bat websites to check out Technical notes on bats: Baseball & Softball Knowledge BaseBaseball & Softball Knowledge Base Product reviews: http://www.batreviews.com/http://www.batreviews.com/ http://www.bandnsoftball.com/http://www.bandnsoftball.com/ (costs $50 per year) Where to buy them: BallGloves.comBallGloves.com Physics of baseball bats - Alan Nathan UMass Bat Research Center Physics and acoustics of bats - Dan Russell