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Baseball & softball bats - 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 swing (diving board effect)

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baseball softball bats outline
Baseball & softball bats - 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 swing (diving board effect)
      • Coefficient of restitution (trampoline effect)
  • Is a very rigid bat or a very flexible bat more effective?
  • What and where is the “sweet spot”
brief history of bat development in the beginning
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,


shape had


history of bat dev late wood era
History of Bat Dev: Late Wood Era
  • From the early 1900’s until ~1970, the wood bat was used exclusively with minor design changes
history of bat dev aluminum era
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
latest developments
Latest Developments
  • During the past three years (2002-2005) composite bats have emerged, making them even more lively and durable, and spawning more rule changes
  • This bat has a composite insert

to connect handle and barrel to

make it super flexible

  • This bat has a composite

handle and metal barrel,

and is super flexible

  • The hottest bat on the market today – it is all composite materials and it is illegal
bat incorporating nanotechnology cnt
Bat incorporating Nanotechnology (CNT)
  • Outstanding performance for 3 reasons:
  • 1. New CNT Carbon Nanotube technology (CNT)
  • 2. Composite handle giving three times greater flex than aluminum
  • 3. Sc900 Scandium alloy
  • 4.Patented ConneXion technology acts like a hinge to provide the
  • most efficient energy transfer from handle to barrel.
  • ASA and USSA approved
another cnt bat
Another CNT bat
  • Not ASA approved, but USSA approved, thus it is hotter than previous bat
  • Addition of CNT carbon nanotube technology strengthens composite structures
  • Designed for more handle flex - two times greater than aluminum
  • How do we determine if these innovations are real or bogus?
recent softball bat rule changes
Recent Softball BatRule Changes
  • USSSA Softball
    • Upper limit on “liveness”, or

Coefficient of Restitution (COR) –

Max BPF = 1.20

  • ASA Sotball2004 BBS (Batted Ball Speed) standard
    • Upper limit on “liveness”, or Coefficient of Restitution (COR)
    • Maximum BBS < 98 mph under these conditions
      • Effective January 1, 2004: Ball COR .44, Bat speed 85 mph, pitch speed 25 mph, multiple impact locations
recent baseball bat rule changes
Recent Baseball Bat Rule Changes
  • Amateur Baseball – High School and College
    • Max barrel diameter 2.625 in (.067 m)
    • Max length 42” for wood, 36” for nonwood
    • Length-weight diff(< 3 units diff.)
    • Max Ball Exit Speed Ratio (BESR) – 94 or 97 MPH
    • Rules committee is considering a MOI rule
center of percussion cop
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 = T2g/4B2

= .248387T2

Where T = period of


center of percussion
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.

center of percussion1
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, ProcISBS 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
center of percussion the sweet spot
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
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.
    • Dan Russell’s Home Page
vibrations cop impact annoyance
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 ProcISBS, 1994)
bat vibrations during swing
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
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 bending during swing and impact

Peak 41 ms PC

Begin Swing

233ms PC

Horiz Pk 38 ms PC


Peak bending and peak

torque ~ 50 ms PC

Begin swing 183 ms PC

Impact – bat still bent

back approx 20% of max

wood vs aluminum bats
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
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
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
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
Softball bat websites to check out
  • Product reviews:
    • (costs $50 per year)
  • Where to buy bats:
  • Bat testing center:
    • UMass Bat Research Center
  • Physics of bats:
    • Dan Russell’s Home Page
    • Alan Nathan’s Home Page