Times Square Ball Drop: Descent Mechanics

Control Loop

Controller gain (aggressiveness) 1.0

Wind-gust disturbance 30%

Cable friction variation 25%

Motor response lag 0.35 s

Click the pole or the button to arm a 5‑second countdown, then the ball descends the pole under motor control — not gravity alone. Drag the canvas to pan, scroll/pinch to zoom.

Descent Readout

Elapsed

0.0 s

Target height

60 ft

Actual height

60 ft

Tracking error

0.0 ft

Motor speed

0.00 ft/s

Cable tension

1.00 × mg

The real physics

The real Times Square ball is not in free fall — it is winched down a fixed pole by a motor-driven cable and pulley system, timed so the 60‑foot descent takes exactly 60 seconds: a steady one foot per second. If the motor simply ran at a constant commanded speed, wind loading on the ball and friction variation in the pulley/cable would make it drift off that schedule.

Instead a feedback controller continuously compares the ball's actual measured height against the ideal linear schedule and nudges the motor's commanded speed by an amount proportional to that error — v_cmd = v_target + Kp·(y_target − y_actual) — with the raw command then passed through a first-order motor-lag filter (a winch motor can't change speed instantly) before it becomes real cable payout speed. Cable tension is actively regulated near m·g — it briefly exceeds or falls short of it whenever the controller commands acceleration to correct a lag, which is exactly what "controlled descent" means as opposed to a cable that simply goes slack and free-falls.

Controller gain — how hard the loop corrects position error; too low drifts off-schedule, too high overshoots and oscillates.
Wind-gust disturbance — a randomly varying aerodynamic load pushing the descent rate off target, the way real gusts hit the ball 141 feet above 1 Times Square.
Cable friction variation — simulates pulley/cable friction that isn't perfectly constant, resisting or aiding the motor unpredictably.
Motor response lag — the winch motor's own inertia/response time before it reaches a newly commanded speed.

t = 0.0 s · h = 60.0 ft

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