🪂 Parachute Physics — Terminal Velocity & Drag

Jump from altitude, freefall to terminal velocity, then deploy the canopy and watch the drag spike. Adjust mass, parachute diameter, and deployment altitude to explore the aerodynamics of deceleration.

Parameters

Total mass 80 kg Parachute diameter 8 m Deploy altitude 1500 m Jump altitude 4000 m

⏸ READY

Telemetry

Altitude—

Velocity—

Acceleration—

Drag force—

g-load—

Terminal vel.—

Time elapsed—

Physics:
F = mg − ½ρCdAv²
ρ(h) = 1.225·e^−h/8500 kg/m³
Cd(freefall) = 1.0 · A_body=0.6 m²
Cd(canopy) = 1.5 · A_canopy=π(d/2)²

How Parachute Drag Works

During freefall, the drag force on a human body is F_drag = ½ρC_dAv², where ρ is air density (decreasing exponentially with altitude), C_d ≈ 1.0 for a prone human, and A ≈ 0.6 m². Terminal velocity is reached when drag equals gravity: v_t = √(2mg / ρC_dA). At sea level this is roughly 55 m/s (200 km/h) for a prone skydiver. When the canopy deploys, A jumps to π(d/2)² — a huge increase — and the drag spikes dramatically, causing strong deceleration. The safe landing speed is typically < 6 m/s. Air density follows the barometric formula ρ(h) = ρ₀·e^−h/8500.

About this simulation

Last updated: 7 July 2026

This simulator numerically integrates Newton's second law for a falling body every animation frame, using semi-implicit Euler steps at four times real-time speed. The net force is F = mg − ½ρ(h)CdAv², with air density following the barometric formula ρ(h) = 1.225·e^−h/8500 kg/m³. In freefall the frontal area is fixed at A ≈ 0.6 m² with Cd = 1.0; deploying the canopy — by hand or automatically at the chosen altitude — instantly swaps in a canopy area of π(d/2)² with Cd = 1.5, spiking drag and forcing a rapid approach toward a new, much lower terminal velocity. A touchdown speed under 6 m/s is scored a safe landing.

🔬 What It Shows

Drag grows with the square of speed, so it eventually balances weight at the terminal velocity v_t = √(2mg / ρCdA). Because deploying the canopy multiplies the drag area roughly a hundredfold for a typical 8 m chute, the balance point drops sharply — that sudden re-equilibration is the deceleration spike you feel in the Telemetry panel.

🎮 How To Use It

Set total mass, canopy diameter, deploy altitude, and jump altitude with the sliders, then hit Jump. Deploy the canopy yourself before the auto-deploy altitude, or let it open automatically. Watch the altitude/velocity graph and the g-load, drag force, and terminal-velocity readouts update live as physics unfolds.

💡 Did You Know?

A belly-to-earth skydiver tops out near 55 m/s (about 200 km/h), but a head-down dive can exceed 140 m/s. In 2012 Felix Baumgartner fell from the stratosphere and briefly went supersonic before his own canopy — just like in this sim — brought him back down to a survivable speed.

Frequently asked questions

Why does the velocity stop increasing during freefall?

Drag force grows with the square of speed while gravity stays constant, so the two forces converge on terminal velocity v_t = √(2mg / ρCdA). The simulator recomputes this value every frame (shown as "Terminal vel.") since it depends on the current altitude's air density and on whether the canopy is out, but the underlying reason acceleration fades to zero is always this force balance.

What actually changes when the canopy deploys?

Deployment — clicking "Deploy Canopy" or crossing the deploy altitude automatically — instantly swaps the drag area and coefficient from body values (A = 0.6 m², Cd = 1.0) to canopy values (A = π(d/2)², Cd = 1.5). For an 8 m canopy that is roughly a hundredfold jump in drag area, producing the sharp deceleration spike visible in the acceleration and drag-force readouts.

How does the simulator model air density at altitude?

It uses the barometric approximation ρ(h) = 1.225·e^−h/8500 kg/m³, which decays exponentially with a scale height of 8500 m. Thinner air at high altitude means weaker drag, so terminal velocity starts higher when you jump from 10,000 m and gradually falls toward the sea-level value as you descend.

What decides a safe landing versus a hard landing?

Once altitude reaches zero, the simulator compares impact speed against a 6 m/s threshold, a commonly cited practical limit for a controllable parachute landing. Below it, the phase badge turns green for "Safe landing"; at or above it, it turns red for "Hard landing" — so getting canopy size, deploy altitude, and total mass right all matter.

Why does total mass change the terminal velocity?

Terminal velocity scales with the square root of mass, v_t = √(2mg / ρCdA), so a heavier jumper with the same gear falls faster in both freefall and under canopy. Raising the "Total mass" slider raises every Terminal vel. readout in the simulation, which is exactly why real skydivers carrying more gear need proportionally larger canopies to land safely.