Drag and Terminal Velocity

Drag — the resistive force on a body moving through a fluid, always acting opposite to the direction of motion.

What drag depends on — the speed of the body, its cross-sectional area, its shape, and the density and viscosity of the fluid. The key point for this course is that drag increases with speed, which is what makes terminal velocity possible.

Terminal velocity — the constant velocity reached when the resistive forces exactly balance the driving force, so the resultant force and therefore the acceleration are zero.

How it develops, for a falling object

At release, the speed is zero so the drag is zero. The only force is the weight, so the object accelerates at g.

As it speeds up, the drag grows. The resultant force (weight minus drag) falls, so the acceleration falls — the object is still speeding up, but less rapidly.

Eventually the drag equals the weight. The resultant force is zero, the acceleration is zero, and the velocity stays constant from then on.

Example: the acceleration decreasing is the part most often described wrongly. Between release and terminal velocity the object never slows down — it simply gains speed more and more slowly, and the velocity–time graph is a curve flattening towards a horizontal asymptote.

A skydiver opening a parachute — the cross-sectional area increases sharply, so the drag becomes much greater than the weight. The resultant force is now upwards, so the skydiver decelerates. As the speed falls the drag falls too, until it again equals the weight and a new, much lower terminal velocity is reached.

Shape and streamlining — a streamlined shape lets the fluid flow smoothly around it, reducing drag and raising the terminal velocity. This is why a raindrop falls faster than a snowflake of the same mass.