Aerodynamic Torque Calculator on Football

\( V \) (Velocity of Ball):

\( L \) (Distance CoM to CoP):

\( \theta \) (Angle e₃ Axis to Force):

\( C_d \) (Drag Coefficient):

\( R \) (Radius of Ball):

Torque (\( \tau \)) in N·m:

Torque (\( \tau \)) in N·in:

1. What is the Aerodynamic Torque Calculator?

Definition: This calculator determines the aerodynamic torque (\( \tau \)) on a football based on its velocity, distance from the Center of Pressure (CoP) to the Center of Mass (CoM), angle of force, drag coefficient, and radius.

Purpose: It assists engineers, physicists, and sports scientists in analyzing the rotational effects of air resistance on a football.

2. How Does the Calculator Work?

The calculator uses the relationship:

\[ \tau = f_a \cdot L \cdot \sin(\theta) = \left( \frac{1}{2} \cdot C_d \cdot \rho \cdot (\pi \cdot R^2) \cdot V^2 \right) \cdot L \cdot \sin(\theta) \]

Where:

\( \tau \) — Aerodynamic torque (in N·m or N·in)
\( f_a \) — Aerodynamic force
\( C_d \) — Drag coefficient (unitless)
\( \rho \) — Air density (1.225 kg/m³)
\( R \) — Radius of the ball (m)
\( V \) — Velocity of the ball (m/s)
\( L \) — Distance from CoP to CoM (m)
\( \theta \) — Angle between force and rotational axis (radians)

Explanation: Enter velocity, distance, angle (0-180°), drag coefficient, and radius, and the calculator computes torque in N·m and N·in.

3. Importance of Aerodynamic Torque

Details: Aerodynamic torque affects the spin and stability of a football, influencing its trajectory in sports and aerodynamics studies.

4. Using the Calculator

Tips: Enter positive values for velocity, distance, angle (0-180°), drag coefficient, and radius, then click "Calculate." Results show torque in N·m and N·in (to 5 decimal places, or scientific notation if less than 0.0001).

Favorite