# 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:

F_{d}= c_{d}1/2 ρ v^{2}A (1)

where

F_{d}= drag force (N)

c_{d}= drag coefficient

ρ = density of fluid (1.2 kg/m^{3}for air at NTP)

v = flow velocity (m/s)

A = characteristic frontal area of the body (m^{2})

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 - c_{d} - | 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 ft^{2} (0.47 m^{2}) |

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 ft^{2} (0.36 m^{2}) |

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 ft^{2} (0.36 m^{2}) |

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 ft^{2} (0.51 m^{2}) |

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 m ^{2}* in

*90 km/h*can be calculated as:

*F _{d} = 0.29 1/2 (1.2 kg/m^{3}) ((90 km/h) (1000 m/km) / (3600 s/h))^{2} (2 m^{2}) *

* = 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)*

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