Parachute Physics: Drag, Terminal Velocity and Descent

Two forces, one balance point

A falling skydiver is caught between gravity, a constant mg pulling straight down, and drag, a force that grows with the square of speed and opposes motion. Drag depends on air density ρ, the frontal area A being pushed through the air, and a drag coefficient C_d describing how streamlined the shape is. As speed increases, drag grows quadratically while gravity stays fixed, so the two forces eventually balance exactly — that balance point is terminal velocity, and once reached, acceleration is zero and speed stays constant.

F_drag = ½ ρ v² C_d A
v_terminal = √( 2 m g / (ρ C_d A) )
m (dv/dt) = m g − ½ ρ v² C_d A       equation of motion, solved numerically each frame

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Freefall: small area, high terminal speed

Before the canopy opens, a skydiver in a belly-to-earth position presents roughly 0.6–0.9 square metres of frontal area with a drag coefficient near 1, and works out to a freefall terminal velocity around 50–55 metres per second — close to 190–200 km/h. That is not gravity accelerating a body indefinitely; it is exactly the speed at which drag has caught up to weight for that particular body shape and area.

Deployment: the area jumps, the speed can't keep up

Opening the canopy suddenly multiplies the effective area by a factor of thirty to a hundred — a sport canopy is commonly 20 to 70 square metres. Terminal velocity for that new, much larger area is far lower, often only 5–7 metres per second, but the skydiver is still moving at the old, much higher freefall speed at the instant of opening. Plugged back into the equation of motion, that mismatch produces a drag force briefly many times the jumper’s weight — the sharp deceleration felt as “opening shock” — before the body settles smoothly toward the new, much lower terminal velocity.

How the approach to terminal velocity actually looks

The equation of motion isn’t solved instantly — it’s a differential equation, and its solution approaches terminal velocity smoothly and asymptotically rather than snapping to it. Starting from rest, speed rises quickly at first (drag is small when speed is small) and the rate of increase tapers off as drag catches up with weight, approaching the terminal value but, mathematically, never exactly reaching it in finite time — which is exactly the shape the simulation traces out frame by frame as it integrates the equation.

Altitude and air density change the answer

Because terminal velocity depends on air density ρ in the denominator, and density falls with altitude, the same body in thinner high-altitude air has a higher terminal velocity than at sea level — part of why high-altitude jumps reach notably higher freefall speeds before the air thickens enough, closer to the ground, to slow the descent back toward the sea-level figure.

Frequently asked questions

Why does opening the parachute jerk you upward relative to your fall?

The canopy suddenly multiplies your effective drag area dozens of times over, but your speed is still the old, much faster freefall speed for that first instant. Plugged into the drag equation, that mismatch produces a drag force briefly far larger than your weight, which is felt as a strong upward deceleration — the opening shock — before you settle to the new, much lower terminal velocity.

Does terminal velocity depend on how much someone weighs?

Yes — directly. The terminal velocity formula has mass in the numerator under the square root, so a heavier skydiver in the same body position reaches a higher terminal velocity than a lighter one, all else being equal, because it takes more drag force (and therefore more speed) to balance the larger weight.

Why is freefall terminal velocity higher at high altitude than near the ground?

Air density ρ sits in the denominator of the terminal velocity formula, and density drops with altitude. Thinner air produces less drag at any given speed, so a jumper has to fall faster before drag catches up with weight — terminal velocity is higher high up and decreases as the jumper descends into denser air.

Try it live

Everything above runs in your browser — open Parachute and change the parameters while it is running. Nothing is installed, nothing is uploaded, the whole model lives in one tab.

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