Water Polo Shot Trajectory Simulator

Shot Setup

Release speed 14.0 m/s

Launch angle 18°

Sidespin (Magnus curve) 0 rev/s

Eggbeater release height 0.55 m

Ready — press Fire Shot

Live Flight Data

Time elapsed

0.00 s

Ball height

0.55 m

Speed

14.0 m/s

Distance to goal

6.00 m

How it works

The ball is a rigid sphere (r = 0.115 m, m = 0.43 kg) launched from an eggbeater-elevated release point. Its flight is governed by Newton's second law with gravity, quadratic aerodynamic drag, and a Magnus (spin) force:

m·dv/dt = m·g + F_drag + F_magnus
F_drag   = -½ρ·Cd·A·|v|·v            (Cd ≈ 0.47, A = πr²)
F_magnus = ½ρ·Cl·A·|v|·(ω × v̂)       (Cl ∝ r·ω / |v|)

The simulator integrates this with a fixed-step RK2 (midpoint) method the instant you press Fire, producing the full arc in advance — the render loop then just walks the ball along that precomputed path in real time, so playback speed never depends on frame rate.

Release speed / angle — set the initial velocity vector, exactly like the whip of the shooting arm.
Sidespin — a positive value spins the ball so the Magnus force curves it toward the near post; negative curves it away, mimicking a wrist-snap shot around a blocker.
Eggbeater height — how high the shooter's torso rides out of the water at release; more leg-drive height flattens the angle needed to clear the crossbar.
A shot counts as a GOAL only if, at the 6 m goal line, the ball's height is between 0 and the 0.9 m crossbar and its lateral drift is within the 1.5 m half-width of the 3 m-wide goal.

This is the same drag + Magnus model used to analyze real water polo shot power, arc, and curve — the same physics that makes a well-placed skip shot or a curling wrist shot hard for a goalkeeper to read.

Ball flight path Goal frame

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