Air resistance, also called air drag, is the force that air exerts on a moving object in the direction opposite to its motion. At everyday speeds it is calculated with the drag equation F = ½ ρ v² Cd A, where ρ is air density, v is speed, Cd is the drag coefficient and A is the frontal area. Because the force grows with the square of speed, doubling your speed makes air resistance four times larger.
The air resistance formula
| Symbol | Meaning | SI unit |
|---|---|---|
| Fd | Drag force (air resistance) | newton (N) |
| ρ | Density of air, about 1.225 kg/m³ at sea level and 15 °C | kg/m³ |
| v | Speed of the object relative to the air | m/s |
| Cd | Drag coefficient, depends on shape and surface | no unit |
| A | Frontal (reference) area facing the flow | m² |
For very small or very slow objects, such as dust particles or droplets in fog, air flows smoothly and the force is closer to Stokes’ law, F = 6πηrv, which grows only linearly with speed. The v² formula above applies to cars, balls, cyclists, aircraft and most engineering problems.
Typical drag coefficients
| Object | Approximate Cd |
|---|---|
| Streamlined body (teardrop) | 0.04 |
| Modern car | 0.25 – 0.35 |
| Sphere (ball) | about 0.47 |
| Cyclist, upright | about 0.9 |
| Cube face-on | about 1.05 |
| Flat plate facing the flow | about 1.2 |
What affects air resistance?
- Speed: the biggest factor, since drag rises with v².
- Shape: streamlined shapes let air close smoothly behind the object and reduce the low-pressure wake, lowering Cd.
- Frontal area: a larger area meets more air. Cyclists crouch and skydivers spread out for exactly this reason.
- Air density: air is thinner at altitude and on hot days, so drag is lower. Aircraft cruise high partly to save fuel this way.
- Surface texture: roughness usually adds skin friction, although the dimples on a golf ball actually cut drag by delaying flow separation.
The two components of air resistance
- Form (pressure) drag: caused by high pressure on the front and a low-pressure wake behind. It dominates for blunt objects like trucks and parachutes.
- Skin friction drag: caused by air rubbing along the surface in the thin boundary layer. It matters most for long, streamlined bodies such as aircraft fuselages.
Aircraft wings also have induced drag, a by-product of producing lift.
Solved examples
1. Drag on a car at 100 km/h. Cd = 0.30, A = 2.2 m², v = 100 km/h = 27.8 m/s, ρ = 1.225 kg/m³.
F = ½ × 1.225 × 27.8² × 0.30 × 2.2 = ½ × 1.225 × 772.8 × 0.66 ≈ 312 N.
Power needed just to push through the air = F × v = 312 × 27.8 ≈ 8.7 kW. At 120 km/h the power rises to about 15 kW, because drag power grows with v³. That is why fuel economy drops quickly at highway speeds.
2. Terminal velocity. A falling object stops accelerating when air resistance equals its weight: ½ ρ v² Cd A = mg, so vt = √(2mg ÷ (ρ Cd A)). For an 80 kg person with CdA = 0.7 m²: vt = √(2 × 80 × 9.81 ÷ (1.225 × 0.7)) ≈ 43 m/s (about 155 km/h). Opening a parachute increases CdA enormously and brings this down to about 5 m/s.
Everyday examples
- A feather falls slowly because its drag is large compared to its tiny weight; in a vacuum it falls as fast as a coin.
- Racing cyclists ride in a tight group (a peloton) to shelter from the wind and save energy.
- Trucks fit roof deflectors to smooth airflow over the trailer.
- Bullet trains and aircraft have long pointed noses to cut pressure drag.
Frequently asked questions
What is the formula for air resistance?
F = ½ ρ v² Cd A, where ρ is air density, v is speed, Cd is the drag coefficient and A is the frontal area.
What is the SI unit of air resistance?
Air resistance is a force, so its SI unit is the newton (N).
What is the drag coefficient?
The drag coefficient is a dimensionless number that describes how aerodynamic a shape is. A modern car is about 0.3, a sphere about 0.47 and a flat plate about 1.2.
Does air resistance increase with speed?
Yes. At normal speeds it increases with the square of speed, so doubling the speed makes the drag force four times larger.
References
- NASA Glenn Research Center – What is Drag?
- NCERT Class 11 Physics, “Mechanical Properties of Fluids” (viscous drag and terminal velocity).
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