Badminton Shuttlecock Drag Trajectory

Racket Swing

Launch speed 28 m/s

Launch angle 35°

Contact height 1.2 m

Show no-drag comparison (dashed)

Flight Data

Range (drag)

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Range (no drag)

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Time of flight

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Current speed

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Peak height

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Drag decel.

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How it works

A badminton shuttlecock's cork-and-feather skirt gives it a drag coefficient roughly 10–20× higher (relative to mass) than a tennis or golf ball, so — unlike a cannonball's near-parabolic arc — its trajectory is dominated by air resistance from the moment it leaves the racket:

F_drag = ½ ρ C_d A v²   (opposing velocity, v = |velocity|)
m dv/dt = -mgŶ - F_drag · v̂
ρ=1.225 kg/m³, C_d≈0.6, A≈0.0033 m², m≈5.2 g

This simulator integrates that equation numerically (semi-implicit Euler, small fixed sub-steps) rather than using the closed-form no-drag parabola. Because drag scales with v², a hard-hit shuttlecock decelerates sharply right after contact — its outbound path is flatter and shorter than a frictionless shot at the same speed, while the return fall is steep and almost vertical. The center of mass sits forward of the center of pressure, so a real shuttlecock also self-orients nose-first in the second half of flight (the "shuttle's turn") — shown here as the flight settling into its steep terminal descent.

Launch speed / angle / height — set the racket-contact velocity vector and starting point.
Comparison trajectory (dashed) — the same launch with drag switched off, i.e. the textbook parabola, to make the drag-shortened range visible directly.
Drag decel. — instantaneous |F_drag|/m, the deceleration due to air resistance alone at the current instant of flight.

With drag (real shuttlecock) No drag (comparison)

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