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)*(cs_{1} + s_{2})} Derivation

Parallel Axis Theorem for converting RDC swingweight (I_{10}) to swingweight about the axis specified for the benchmark condition (I_{7} or I_{5}, or I_{a} which is the I used in the foregoing formulas):

I = I_{a} = I_{10} + 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