Rigid floor · still air at 20 °C · g = 9.806 65 m/s²
Eighteen-Ball Drop Test
Eighteen regulation balls, largest to smallest by volume, released together from 2.00 m (measured to the bottom of each ball) onto a rigid floor. The page computes every bounce first, with air drag, buoyancy and a spring-damper contact tuned to each ball's own rebound test, then replays the result at true scale.
Height of each ball over time
Pick a ball to bring its line forward; pick it again to show all.
Results
| Ball | Mass | Diameter | Volume | COR e | From | Impact speed |
1st rebound | Contact time | Peak decel. | Max squash | Bounces ≥ 1 mm | At rest |
How the model works
- In flight each ball feels gravity, quadratic air drag ½ρCdAv² with ρ = 1.204 kg/m³, and buoyancy ρVg (1.5 % of a table tennis ball's weight, negligible for the rest).
- On the floor the ball becomes a spring and damper in parallel. Stiffness and damping are chosen so that each impact lasts the ball's typical contact time and returns exactly the coefficient of restitution e = vout / vin. That is what lets you see the squash in slow motion and read the peak deceleration.
- Where a governing body sets a drop test, e is solved backwards from it: the page simulates the official drop, with drag, and finds the exit speed that reaches the midpoint of the permitted rebound range.
- Integration is fourth-order Runge-Kutta, 0.1 ms steps in flight and 0.01 ms near and during contact. A ball counts as at rest when its next bounce would rise less than 1 mm.
- Not modelled: spin, the floor's own give, temperature and pressure drift, and the rise of e at low impact speed. Real balls of the same model also vary by several percent.
Where the numbers come from