Basketball Shot Trajectory: Drag & Magnus Effect Simulator

Shot Setup

Ready — press Shoot

Release angle 48°

Release speed 7.6 m/s

Backspin 28 rev/s

Hoop distance 6.0 m

Live Trajectory

Time of flight

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Apex height

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Entry angle

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Range (drag+Magnus)

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How it works

The ball's flight is not scripted — its position comes from numerically integrating Newton's second law every frame, with three real forces acting on the center of mass: gravity, quadratic aerodynamic drag opposing velocity, and the Magnus lift force generated by backspin.

F_drag  = −½ρ|v|Cd·A · v̂
F_magnus = ½ρ|v|Cl·A · (ω × v̂)
a = (F_drag + F_magnus)/m + g

ρ = 1.225 kg/m³ (air density), Cd ≈ 0.47 (sphere drag coefficient), A = πr² with a regulation r ≈ 0.121 m ball, m ≈ 0.62 kg. The lift coefficient Cl is modeled from the dimensionless spin parameter S = ωr/|v| (Cl ≈ min(1, S), the standard sphere-lift approximation), so backspin only bends the path when the ball is actually spinning fast relative to its speed — exactly like a real jump shot's rotation flattening the arc and stretching its range.

Release angle / speed — the initial velocity vector fed into the ODE at t=0.
Backspin — sets ω for the Magnus term; more backspin lifts the trajectory, extending range and steepening the entry angle into the rim.
Hoop distance — where the rim (0.457 m diameter, 3.05 m high) sits; the sim finds where the integrated path crosses rim height and classifies swish (center, steep enough entry) vs rim-graze vs miss from that real intersection, not a script.

Real-world relevance: real shooters use backspin for exactly this reason — a "soft touch" with more backspin gives a flatter Magnus-assisted arc and a larger margin for error on the rim, which is why coaches teach a full wrist snap on release.

Ball trajectory Backboard / rim No-drag reference arc