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 |
| s1 | = | initial velocity of the ball, in meters per second |
| s2 | = | 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 = Ia = I10 + M*[2*(10 - a)*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 * (m / (M + m)) Derivation