Aerodynamic Torque on a Football

Last modified by

on

Nov 14, 2022, 4:43:58 PM

Created by

on

Aug 14, 2015, 7:39:01 AM

τ = f_{d} \cdot L \cdot sin (θ) = (\frac{1}{2} \cdot C_{d} \cdot ρ \cdot (π \cdot R^{2}) \cdot {44.74}^{2}) \cdot L \cdot sin (θ)

$tau = f_d * "L" * sin( theta ) = (1/2 * C_d * rho * (pi*R^2) * 44.74 ^2) * "L" *sin( theta )$

(V) Velocity of Ball

$(V)"Velocity of Ball"$

(L) Distance CoM to CoP

$(L)"Distance CoM to CoP"$

(θ) {Angle e}_{3} Axis to Force

$(theta)"Angle e"_3 "Axis to Force"$

Tags

UUID

87c98d5d-4257-11e5-a3bb-bc764e2038f2

The Aerodynamic Torque on a Football equation computes the aerodynamic torque experienced by a football in flight.

In the diagram the drag force, $f_{d}$ $f_d$ , acts opposite along the velocity vector and through the center of pressure (CoP). The angle between this force and the axis of symmetry for the football, the $e_{3}$ $e_3$ axis, is the angle $θ$ $theta$ .

The air resistance drag force is in the opposite direction to the velocity of the ball and acts through the CoP. The CoP is usally not coincident with the CoM. The separation of the CoM and the CoP is due to the aerodynamic drag on the leading edge of the passed football, which offsets the CoP forward of the CoM. The forward displacement of the CoP from the CoM creates the gyroscopic precession due to the torque resulting from the drag forces acting through the CoP. Torque free precession also results from the flight of the football (see

In the diagram the CoP is displaced from the CoM by a distance $L$ $L$ . Again, this displacement of the point through which the drag force acts produces torque about the CoM.

Remember Torque is the cross-product of the force vector and the displacement.

Note that despite the torque due to aerodynamic drag computed by this equation, and the wobble (precession) we see in a typical pass, the CoM follows almost perfectly a parabolic trajectory. Once the ball is released by the passer, it's center of mass -- to the greatest degree -- acts as if it is affected by gravity alone. And that is a situation we have covered in numerous equations in vCalc that concern themselves with ballistic motion.

Aerodynamic Torque on a Football

See also

Datasets

Equations and Data Items

Calculators

Equations and Data Items

Collections