Step out of an aeroplane and, for a moment, your stomach lurches: you are falling, and gravity is hauling you downwards faster and faster. Common sense says you should just keep speeding up, on and on, until you hit the ground at a truly terrifying speed. But you don't. After a few seconds a real skydiver stops accelerating altogether and settles into a steady fall — quick, yes, but no longer speeding up. They have reached their terminal velocity.

How can something that is falling stop getting faster, without hitting anything? The answer is a quiet tug-of-war between two forces you already know: weight pulling down, and air resistance pushing back up. This page is the story of how that tug-of-war ends in a draw.

Two forces, and only one of them changes

On a falling object, two forces act along the vertical line:

• Weight pulls straight down. Weight comes from gravity, and gravity does not care how fast you are going — so weight stays exactly the same the whole way down. It is the unchanging player in our story.
• Air resistance (drag) pushes straight up, against the motion. And here is the crucial fact you met with drag: the faster you move, the bigger it grows. Sit still and there is no drag at all; fall slowly and it is small; fall quickly and it becomes a real, hefty push.

At the very first instant you let go, your speed is zero, so drag is zero too. The only force is weight, pulling down. The resultant force — what you get when you add the two forces together — is therefore the whole of your weight, downwards:

With D = 0 at the start, F_\text{resultant} = W, a big downward force. By Newton's idea that force makes things accelerate (a = F_\text{resultant} / m), you start speeding up hard.

The balance point: where the falling settles down

Now watch what your own speeding-up does to you. As you get faster, drag D grows. As D grows, the resultant force W - D shrinks — so you keep speeding up, but more and more gently. Faster still, and drag grows further, until at last it grows all the way up to match your weight exactly:

With zero resultant force, there is nothing left to change your speed: a = F_\text{resultant}/m = 0. You are not stopping — the two forces are simply balanced, so you carry on falling at one steady, unchanging speed. That steady speed is the terminal velocity. It is the fall's natural resting point, the speed at which the growing drag has finally caught up with the constant weight.

Newton's second law, applied to a fall

• The resultant force sets the acceleration: F_\text{resultant} = m\,a, where F_\text{resultant} = W - D for a falling object.
• While D < W the resultant is downward, so the object speeds up — but by less and less as D catches up.
• When D = W the resultant is zero, so a = 0: the object falls at a constant terminal velocity.

See the forces balance

Below is a skydiver whose weight (the long down-arrow) never changes. Drag the falling speed slider from a standstill up to full speed and watch the drag arrow grow upward. Notice it grows slowly at first and then races up near the end — that's because drag grows with the square of the speed. Push the speed to the top and the two arrows become equal: the resultant force drops to zero and the fall has reached its terminal velocity.

The shape that tells the whole tale: the velocity–time graph

Draw a graph of speed against time and the entire story appears in one curve. At the start the line is steep — you are accelerating hard, because drag is tiny and the resultant force is nearly your whole weight. As you speed up, drag grows, the resultant shrinks, and the line bends over, getting less and less steep. Finally it flattens into a horizontal line: constant speed, zero acceleration — terminal velocity.

A flat line on a velocity–time graph always means steady speed. So the tell-tale sign of terminal velocity is a curve that starts steep, curves over, and levels off onto a flat line. Flick the switch under the graph to open the parachute part-way down and see what it does to the story.

Opening the parachute: a bigger area, a gentler landing

A skydiver's free-fall terminal velocity — arms and legs spread — is around 50\ \text{m/s}, which is roughly the speed of a car on a motorway. Hitting the ground at that speed is not survivable. So the parachute is pulled, and suddenly the canopy spreads out an enormous area for the air to push against.

A bigger area means far more drag at any given speed. So the moment the canopy opens, drag leaps far above weight, the resultant force points upward, and the skydiver slows down — the curve on the graph plunges. But it does not slow forever: as they lose speed, drag falls again, until drag once more balances weight and they settle at a new, much lower terminal velocity, only a few metres per second — slow enough to land safely. Same weight, far bigger area, far smaller terminal velocity.

Feathers, and a place with no terminal velocity at all

The same idea explains a feather. A feather weighs almost nothing, yet it is wide and flat, so it meets a lot of air. It only has to fall a whisker's-worth of speed before the small drag on its broad surface already matches its tiny weight — so its terminal velocity is minute, and it drifts down in slow, wandering loops. Scrunch that same feather into a tight ball and its area collapses: now it must fall much faster before drag can balance its weight, so it drops noticeably quicker. Same feather, same weight — smaller area, higher terminal velocity.

And here is the clincher. Terminal velocity depends entirely on there being air to make drag. Take the air away and there is no drag to grow, so nothing ever balances the weight. On the airless Moon, a dropped hammer just keeps speeding up all the way down — there is no terminal velocity. It is only our thick blanket of air that gives falling objects on Earth a top speed at all.