Any object moving through a fluid experiences drag - the net force in the direction of flow due to pressure and shear stress forces on the surface of the object.

The drag force can be expressed as:

F d = c d 1/2 ρ v2 A (1) where F d = drag force (N) c d = drag coefficient ρ = density of fluid (1.2 kg/m3 for air at NTP) v = flow velocity (m/s)

A = characteristic frontal area of the body (m2)



The drag coefficient is a function of several parameters like shape of the body, Reynolds Number for the flow, Froude number, Mach Number and Roughness of the Surface.

The characteristic frontal area - A - depends on the body.

Objects drag coefficients are mostly results of experiments. The drag coefficients for some common bodies are indicated below:

Type of Object Drag Coefficient

- cd - Frontal Area Laminar flat plate (Re=106) 0.001 Dolphin 0.0036 wetted area Turbulent flat plate (Re=106) 0.005 Subsonic Transport Aircraft 0.012 Supersonic Fighter,M=2.5 0.016 Streamlined body 0.04 π / 4 d2 Airplane wing, normal position 0.05 Sreamlined half-body 0.09 Long stream-lined body 0.1 Airplane wing, stalled 0.15 Modern car like a Tesla model 3 or model Y 0.23 Toyota Prius, Tesla model S 0.24 frontal area Tesla model X Sports car, sloping rear 0.2 - 0.3 frontal area Common car like Opel Vectra (class C) 0.29 frontal area Hollow semi-sphere facing stream 0.38 Bird 0.4 frontal area Solid Hemisphere 0.42 π / 4 d2 Sphere 0.5 Saloon Car, stepped rear 0.4 - 0.5 frontal area Convertible, open top 0.6 - 0.7 frontal area Bus 0.6 - 0.8 frontal area Old Car like a T-ford 0.7 - 0.9 frontal area Cube 0.8 s2 Bike racing 0.88 3.9 Bicycle 0.9 Tractor Trailed Truck 0.96 frontal area Truck 0.8 - 1.0 frontal area Person standing 1.0 – 1.3 Bicycle Upright Commuter 1.1 5.5 Thin Disk 1.1 π / 4 d2 Solid Hemisphere flow normal to flat side 1.17 π / 4 d2 Squared flat plate at 90 deg 1.17 Wires and cables 1.0 - 1.3 Person (upright position) 1.0 - 1.3 Hollow semi-cylinder opposite stream 1.2 Ski jumper 1.2 - 1.3 Hollow semi-sphere opposite stream 1.42 Passenger Train 1.8 frontal area Motorcycle and rider 1.8 frontal area Long flat plate at 90 deg 1.98 Rectangular box 2.1

Example - Air Resistance Force acting on a Normal Car

The force required to overcome air resistance for a normal family car with drag coefficient 0.29 and frontal area 2 m2 in 90 km/h can be calculated as:

F d = 0.29 1/2 (1.2 kg/m3) ((90 km/h) (1000 m/km) / (3600 s/h))2 (2 m2)



= 217.5 N

compare car air resistance with car rolling resistance

The work done to overcome the air resistance in one hour driving (90 km) can be calculated as

W d = (217.5 N) (90 km) (1000 m/km)

= 19575000 (Nm, J)

The power required to overcome the air resistance when driving 90 km/h can be calculated as

P d = (217.5 N) (90 km/h) (1000 m/km) (1/3600 h/s)

= 5436 (Nm/s, J/s, W)

= 5.4 (kW)