Kansas State University Biomechanics Lab Center of Percussion & the sweet spot Earlier studies indicated that the COP is the sweet spot, the best place

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


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.


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)


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


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?


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


Bat Vibrations During Swing & Impact

-4

-3

-2

-1

0

1

2

3

4

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7

Time (s)

Str

ain

(v

)

Horiz DirVert DirMagnitudeHoriz DirVert DirMagnitude

Begin Swing 233ms PC

Peak 41 ms PC

Horiz Pk 38 ms PC

Bat bending during swing and impact



Begin swing 183 ms PC

Peak bending and peak torque ~ 50 ms PC

Impact – bat still bentback approx 20% of max


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


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


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


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?


Softball bat websites to check out

• Technical notes on bats: Baseball & Softball Knowledge Base

• Product reviews: http://www.batreviews.com/

http://www.bandnsoftball.com/ (costs $50 per year)

• Where to buy them: BallGloves.com

• Physics of baseball bats - Alan Nathan

• UMass Bat Research Center

• Physics and acoustics of bats - Dan Russell

Documents

Kansas State University Biomechanics Lab Center of Percussion & the sweet spot Earlier studies indicated that the COP is the sweet spot, the best place