Air Resistance and Fluid Drag

Air resistance (drag) is the force that a fluid such as air exerts on an object moving through it, directed opposite to the motion, and it increases with speed, cross-sectional area and the density of the fluid. In brief: at higher speeds the drag force is approximately F = ½ρC_dAv², so doubling the speed multiplies the drag by four. A falling object accelerates until the drag equals its weight, reaching a constant terminal velocity.

A feather falls slowly, a skydiver reaches a steady speed, and cars are designed with smooth shapes. All of these are effects of drag. This guide explains the origin of drag and the factors that influence it, describes terminal velocity, compares ways of changing drag in a table, works through a drag and terminal velocity calculation and corrects common mistakes.

What is drag?

When an object moves through a fluid (a gas or liquid), it has to push the fluid aside, and the fluid exerts a resisting force called drag. In air it is called air resistance. It acts opposite to the velocity of the object relative to the fluid. Drag always opposes motion, and unlike dry friction it increases with speed and goes to zero for an object at rest.

What does drag depend on?

Speed: at low speeds for small objects in viscous fluids the drag is roughly proportional to the speed (laminar flow). At the higher speeds of everyday objects such as cars and cyclists, it is proportional to the square of the speed (turbulent flow).
Cross-sectional area A: the larger the frontal area, the greater the drag. A skydiver with a parachute open has a much bigger area.
Shape (drag coefficient C_d): streamlined shapes have low C_d (about 0.04 for an airfoil, 0.25 to 0.35 for a modern car), and flat plates facing the flow have high values (about 1.1 to 1.3).
Fluid density ρ: water is about 800 times denser than air, so the drag in water is much higher at the same speed. Air at sea level has ρ = 1.2 kg/m³.

For turbulent flow the quadratic drag law is F = ½ρC_dAv².

What is terminal velocity?

A dropped object begins with only weight, mg, acting on it, and accelerates at g. As it speeds up, the drag increases, so the net force and acceleration decrease. When the drag equals the weight, the net force is zero, and the object falls at constant velocity: the terminal velocity, v_t = √(2mg ÷ ρC_dA). A skydiver in a spread position reaches about 55 m/s (200 km/h), and with an open parachute only about 5 m/s. A raindrop reaches a few meters per second, depending on its size.

Speed of the 80 kg skydiver from the worked example (C_d = 1.0, A = 0.70 m²), calculated with quadratic drag. The curve starts with slope g (dotted line), flattens as drag grows, and approaches the terminal speed of 43 m/s (dashed line), where drag equals the 784 N weight.

Changing drag

Examples of reducing or increasing drag
Aim	Method	Example
Reduce drag	Streamline the shape	Cars, aircraft, racing cyclists in a crouched position
Reduce drag	Reduce frontal area	Folded wings of a diving falcon
Increase drag	Increase the area	Parachute, airbrakes
Reduce drag	Lower the speed	Slower driving saves fuel

Worked example: a skydiver

A skydiver of mass 80 kg has a frontal area of 0.70 m² and C_d = 1.0. Air density is 1.2 kg/m³. Use g = 9.8 m/s².

Weight: mg = 80 × 9.8 = 784 N.
Drag at 50 m/s: F = ½ × 1.2 × 1.0 × 0.70 × 50² = 0.42 × 2500 = 1,050 N. This is greater than the weight, so at 50 m/s the skydiver is slowing down.
Terminal velocity: set drag equal to weight: 0.42 × v² = 784, so v² = 1,867 and v = 43 m/s (about 156 km/h).
Acceleration at 20 m/s: drag = 0.42 × 400 = 168 N, net force = 784 − 168 = 616 N, a = 616 ÷ 80 = 7.7 m/s², which is less than g.

How was drag studied?

Leonardo da Vinci and Galileo noted the effect of air on falling bodies. Newton derived a drag law in the Principia, and George Stokes calculated the drag on a small sphere in a viscous fluid in 1851. The Wright brothers measured lift and drag of wing shapes in a wind tunnel in 1901, and Ludwig Prandtl’s boundary layer theory (1904) explained how the drag on bodies arises.

Which mistakes are common?

Mistake 1: Thinking that heavier objects always fall faster

With drag, a heavier object of the same shape has a higher terminal velocity, but in a vacuum all objects fall together.

Mistake 2: Assuming that drag is constant

Drag increases with speed, which is why the acceleration decreases as a body falls.

Mistake 3: Thinking that terminal velocity means zero force

The forces are balanced (zero net force), but the weight and the drag are both large.

Mistake 4: Forgetting that drag depends on the fluid

Moving through water requires much more force than through air at the same speed.