Presets
Playback
Release
Where the ball starts and how fast it is thrown. Spin is positive for backspin.
Surface and ball
Restitution e, friction mu and the inertia factor k = I/(m r^2).
World and clock
Gravity can be changed to any planet.
Camera
Layers
Quality
Model checks
The science
What this bench shows
A football is released from a height onto mown turf. At every bounce the surface gives the ball a normal impulse and a friction impulse along the ground. Whether the ball slips or grips decides how much speed and spin it keeps. The 3D ball, its trail, the contact marks and all graphs come from one small impulse model, the same one as the 2D companion.
1. Normal bounce
The vertical velocity reverses and shrinks by the restitution: vy' = e vn. The normal impulse per unit mass is Jn = (1 + e) vn.
2. Friction: slip or stick
The contact point (bottom of the ball) moves at u = vx + ω r (ω counter-clockwise on screen = backspin for a ball travelling right). The ball has moment of inertia I = k m r2 (solid sphere k = 0.4, thin shell k = 2/3). The impulse that would exactly stop the slipping is Jstick = -u k/(1 + k). If |Jstick| ≤ μ Jn the ball sticks; otherwise it slips and Coulomb friction delivers Jt = -μ Jn sign(u). Then vx' = vx + Jt and ω' = ω + Jt/(k r).
3. A conservation law that checks the model
Friction acts at the contact point, so the angular momentum about that point, Lc = I ω - m r vx per unit mass (k r ω - vx) r, does not change in the bounce. The fourth graph shows it before and after every impact.
4. After the last bounce
On the ground the ball skids with kinetic friction until u = 0, then rolls. The end speed is vx = (vx0 - k r ω0)/(1 + k), independent of μ (Model check 1).
What to try
Compare Backspin (the ball checks up or even comes back) with Topspin (it kicks forward) and Wet pitch (small μ keeps almost all the speed). The third graph sweeps the incoming spin and shows the outgoing speed for the current surface.
Honest simplifications
Rigid sphere, instantaneous contact, constant e and μ (no dependence on impact speed), no air drag or Magnus force, flat rigid turf, no rolling resistance. Real balls deform and turf grabs; the trends are right, the numbers are illustrative. Ball radius is 0.11 m.