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 = mk2

– 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 massabout the axis. It is the distance fromthe axis to a point at which all themass of a system of equal masswould be concentrated to have the MOI equal the original system. Itis, then, the average weighted distance of the mass of a systemto the axis.

Equivalent systems

k 35

k 35

Determining MOI & K • Simple 3-segment system:

– I = mi di2 = m1 d1

2 + m2 d22+

m3 d32 + . . . . . . .+ mi di

2

– I = mk2 ; 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) = T2 mr * .248387 m/sec

– Radius of gyration (K) = ( I/m).5

Rigid Body -BatDistance from Axis to COP:

q = k2/r = I/mr = T2g/42 = .248387T2

Rigid Body - Tennis Racket

Rigid Body - Golf Club

Semi-rigid (elastic) bodies)•Coefficient of restitution

•Vibrations - nodes and modesVibrations 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 10-20 Hz Approx 150-250 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