RACQUET SCIENCE
Using physics to help select a racquet
Formulas for evaluation of racquet performance
Derivations of these Formulas:
| Torque | Impulse Reaction | Shock | Work | Shoulder Pull | Impact Force |
Remarks on Formula Derivations
| \(M\) | = | racquet mass, in kilograms |
|---|---|---|
| \(r\) | = | distance. in centimeters, from axis of rotation to mass center |
| \(I\) | = | swingweight of the racquet about the axis of rotation, in kg·cm² |
| \(d\) | = | distance, in centimeters, from axis of rotation to point of impact |
| \(b\) | = | ball mass, in kilograms |
| \(s_1\) | = | initial velocity of the ball, in meters per second |
| \(s_2\) | = | final velocity of the ball, in meters per second |
| \(c\) | = | coefficient of restitution of the racquet/ball system (racquet bounce) |
| \(t\) | = | duration of impact (dwell time), in seconds |
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)^½ 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)]½ - (r/d)*(cs1 + s2)} Derivation
Parallel Axis Theorem for converting RDC swingweight (I10) to swingweight about the axis specified for the benchmark condition (I7 or I5, or Ia which is the I used in the foregoing formulas):
\[ I = I_a = I_10 + M \times [2 \times (10 - a) \times r - (10 - a)^2] \]
Derivation
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).
\[ x = y \times (m \div (M + m)) \]
Derivation