Each confetti piece is a thin rigid rectangular plate (length L, width h). Unlike a point mass in free fall, its drag depends on orientation: the relative air velocity is split into a component normal to the plate (vn) and a component along it (vt), each with its own quadratic drag coefficient:
F_n = −½ρ·Cd_n·L·|v_n|·v_n (Cd_n ≈ 1.28, face-on)
F_t = −½ρ·Cd_t·L·|v_t|·v_t (Cd_t ≈ 0.02, skin friction)
a = (F_n·n̂ + F_t·t̂ + m·g) / m
Because the plate's center of pressure shifts toward the leading edge whenever it also slides sideways (v_t ≠ 0), the normal force acts off-center and produces a torque about the centroid:
τ = −F_n·(k·L/2)·(v_t / (|v_n|+|v_t|)) − c·ω|ω|
α = τ / I, I = m(L²+h²)/12
This single coupling — normal force acting at a shifting lever arm — is what makes falling paper genuinely interesting: a piece released face-down first decelerates hard (large v_n, large F_n), picks up a bit of sideways glide, and that glide generates enough torque to flip it before it can build real forward speed — so it tumbles end over end instead of gliding away. Thin, elongated pieces (high aspect ratio) have a larger moment arm and tumble more readily; near-square pieces glide more.
- Air density scales every aerodynamic force — turn it down and the pieces free-fall almost straight down with barely any flutter.
- Wind gust adds a fluctuating horizontal air velocity, shifting v_t and biasing the tumble/drift.
- Terminal v (face-on) is the analytic terminal speed √(2mg / (ρ·Cd_n·L)) for the current size/density — compare it against the measured mean fall speed.