Biomechanical Considerations for Striking Implements - Background Relationship between linear motion and rotary motion –Radius of rotation –Axis of rotation Relationship between torque and rotational motion –Moment of Inertia: I = mk 2 –Radius of gyration: k = (I/m).5 –Rotational analogues of newton’s laws: T = I  Elastic properties of striking implements –Coefficient of restitution –Vibrations during the swing (bending) –Vibrations during and after impact Sweet spot determinants –Center of percussion, vibrational nodes

Relationship between linear and angular motion (kinematics)

Relationship between linear and angular motion Would you rather have a long or short baseball bat or golf club? Why?

What is Moment of Inertia (MOI)? Here, r (the radius of rotation) is equal to k (the radius of gyration), but that is not the case with extended bodies It is the resistance of a system to rotational acceleration, and is calculated at follows:

What is radius of gyration (k)? An indicator of distribution of mass about the axis. It is the distance from the axis to a point at which all the mass of a system of equal mass would be concentrated to have the MOI equal the original system. It is, then, the average weighted distance of the mass of a system to the axis. Equivalent systems k 35 k

Determining MOI & K Simple 3-segment system: –I = 3 m i d i 2 = m 1 d m 2 d m 3 d m i d i 2 –I = mk 2 ; k = (I/m).5 Irregularly shaped bodies But we can’t measure all of these small masses!

Physical pendulum properties (rigid bodies) Radius and axis of rotation Radius of gyration (K) Moment of inertia (MOI) Center of percussion

Physical pendulum method of determining MOI and K Suspend object at axis Measure mass (m), and distance from axis to COM, r Measure period of oscillation (T) –Moment of inertia (I) = T 2 mr * m/sec –Radius of gyration (K) = ( I/m).5

Rigid Body -Bat Distance from Axis to COP: q = k 2 /r = I/mr = T 2 g/4  2 = T 2

Rigid Body - Tennis Racket

Rigid Body - Golf Club

Semi-rigid (elastic) bodies) Coefficient of restitution Vibrations - nodes and modes Vibrations when bat is clamped (during swing) Vibrations when bat is free (during impact with ball)

Simpler illustration of bat vibrations during swing and impact Approx Hz Approx HZ

Bat Vibrations During Swing and Impact

Coefficient of Restitution (COR) COR is a measure of the liveliness of an object When 2 objects collide: When one object is stationary, this reduces to: An alternative way to measure COR Is to drop a ball and measure the ht Bounced compared to ht dropped:

Coefficient of Restitution (COR) COR of balls dropped or thrown at a rigid wooden surface is shown here. COR increases directly with temperature and inversely with impact velocity.

Questions What is the sweet spot of a striking implement? How do we take advantage of rigid body properties to improve implement? How do we take advantage of elastic properties to improve implement?

Evaluation methods for striking implements Apply scientific principles to evaluate mfgr claims Use it yourself, if possible Product reviews on the internet & in trade mags Consult with others who use it, or supervise its use Consult with professors, or professionals (e.g., coaches) with specialized insight and expertise Look at research available, if any –Evaluate quality of research – Extrinsic - who is sponsoring the research, where did it appear? Intrinsic – methods, procedures, statistics, conclusions

Next: Bats & Clubs Tuesday, November 1 –Lecture on golf clubs – Read Ch 9 of Kreighbaum and Smith –Submit 2 questions related to readings on golf clubs Thursday, November 3 –Guest Speaker: Chris Hay, Golf USA Tuesday, November 8 –Lecture on softball and baseball bats – Read Ch 10 of Kreighbaum & Smith –Submit 2 questions relating to readings on bats Thursday, November 10 –Review new bat products 2005 catalogues from leading bat manufacturers Bats from lab Review for exam