Formulas for Evaluation of Racquet Performance

Derivations of these Formulas:

Torque

Impulse Reaction

Shock

Work

Shoulder Pull

Impact Force

Remarks on Formula Derivations

Sweet Spot (Center of Percussion) (cm from axis of rotation)
=  I / (M*r )     Derivation

Moment (Newton.meters about axis of rotation)
=  M*(r/100)*(9.81)   Derivation

Torsion, or Longitudinal Torque
= Moment * Torque   Derivation

 

 

 

 

Shoulder Crunch (Newtons)
= (2/(0.01*r + 0.61))*(Shock)   Derivation

Elbow Crunch (Newtons)
= (2/(0.01*r + 0.36))*(Shock)   Derivation

Wrist Crunch (Newtons)
= (2/(0.01*r + 0.08))*(Shock)

Tip Speed (m/s) = ((2/M) * (Work) * (e / r)^2)^1/2 
e = distance from axis to tip, in cm   Derivation

Impact Force (Newtons acting at mass center due to impact)
= (M / t)*{(1 + c)*[(2/M)*(Work)]^1/2 - (r/d)*(cs₁ + s₂)} Derivation

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Parallel Axis Theorem for converting RDC swingweight (I₁₀) to swingweight about the axis specified for the benchmark condition (I₇ or I₅, or I_a which is the I used in the foregoing formulas):

I  =  I_a  =  I₁₀ + M*[2*(10 - a)*r - (10 - a)²]    
Derivation

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New Balance Point distance (x) from original balance point, resulting from adding weight (m) at a distance (y) from the original balance point of a racquet having an original weight (M). 

x = y * (m / (M + m))     Derivation

© 1998-2000 Wilmot H. McCutchen, All Rights Reserved.

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