Momentum Transfer
The foot and ball exchange momentum through the contact force. A larger impulse, built from force over time, gives the ball a larger change in velocity.
Why this matters
Watching a powerful shot makes the motion look instant, but the useful physics happens over only a few milliseconds. In that tiny interval, the ball squashes, the foot slows down, and an impulse transfers momentum into the ball.
Understanding that collision helps explain practical questions: why a faster foot usually produces a faster shot, why a stiff but controlled ankle matters, why the ball does not leave at exactly the foot's speed, and why contact quality can matter as much as raw leg strength.
Compression: δ = xfoot - xball
Contact force: F = kδn + c·max(δ̇, 0)
Impulse: J = ∫ F dt = mΔv
Energy: kinetic energy becomes ball speed, deformation, heat, sound, and spin.
Contact force: F = kδn + c·max(δ̇, 0)
Impulse: J = ∫ F dt = mΔv
Energy: kinetic energy becomes ball speed, deformation, heat, sound, and spin.
Compression And Restitution
The ball behaves like a spring with losses. It first stores energy as deformation, then returns part of that energy as it re-expands and separates from the foot.
Technique Changes The Model
Effective foot mass, ankle stiffness, and continued drive during contact all affect the exit speed. The simulation lets you vary these factors directly.
Try the collision yourself
Use the simulator to adjust foot speed, mass, stiffness, damping, and initial ball velocity, then compare the predicted force curve, contact duration, impulse, and final ball speed with the explanation in the PDF.