A thrown handball follows projectile motion under gravity, decelerated by air drag, and curved sideways by the Magnus effect from its spin.
F_drag = -½ρC_d A |v|v
F_magnus = S · (ω × v)
a = g + F_drag/m + F_magnus/m
- Throw speed — initial velocity magnitude of the ball leaving the thrower's hand.
- Launch angle — vertical angle of the throw above horizontal.
- Spin (Magnus) — sidespin applied to the ball; positive curves it right, negative curves it left in flight.
- Aim (left-right) — horizontal aim offset toward the goal, combined with the Magnus curve to beat the keeper.
The goalkeeper (yellow box) reacts toward the ball's predicted crossing point — a fast, well-placed, curving shot is harder to save.