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# Drag Coefficient

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:

Fd = cd 1/2 ρ v2 A                      (1)

where

Fd = drag force (N)

cd = 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:

Drag Coefficients vs. Type of Objects
Type of ObjectDrag 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
Bicycle - Streamlined Velomobile 0.12 5 ft2 (0.47 m2)
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
Bike - Drafting behind an other cyclist 0.5 3.9 ft2 (0.36 m2)
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 ft2 (0.36 m2)
Bicycle 0.9
Tractor Trailed Truck 0.96 frontal area
Truck 0.8 - 1.0 frontal area
Person standing 1.0 – 1.3
Bike - Upright Commuter 1.1 5.5 ft2 (0.51 m2)
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:

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

= 217.5 N

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

Wd = (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

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

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

= 5.4 (kW)

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