# Drag

Figure 1: The total drag force and its components: induced drag and form drag. [1]

Drag is a component of the fluid dynamics force that acts in a direction parallel to the relative fluid flow. Lift is a fluid dynamics force component that acts in a direction perpendicular to the relative fluid flow. There are two important types of drag for incompressible flows (speeds < Mach 0.3): Parasitic drag and lift induced drag. The total drag acting on the body would be a result of both drag forces. Bluff bodies have zero lift and thus zero lift-induced drag. Parasitic drag is a type of drag that arises when a bluff body is exposed to a fluid flow as shown in Figure 2. Lift-induced drag arises due to lift forces. There is also another form of drag called wave drag, but this is more of a concern for higher speeds (sound barrier).

Figure 2: The drag force acting on a bluff body in a relative fluid flow.

#### Parasitic drag

Parasitic drag is considered to be the combination of form drag (pressure drag) and viscous skin drag (skin friction). It's parasitic drag is at times simply referred to as form drag.

The drag force is proportional to the size and shape of the body. It also grows quadratically with relative flow speed.

The drag force $\mathbf{F}_{drag}$ is:

$\mathbf{F}_{drag} = \frac{1}{2} \rho A_c C_{dp} \mathbf{v}_{rel}^2$

where $\rho$ is the fluid density (1.46 kg/m^3 for air, 1000 kg/m^3 for water), $A_c$ is the frontal face area of the body in the direction of the relative fluid flow, $C_{dp}$ is the a parasitic drag coefficient and $\mathbf{v}_{rel}$ is the relative fluid velocity vector.

#### Lift-induced drag and the total drag force

Figure 3: A description of lift-induced drag.[2]

The total drag force can be computed as:
$F_{drag} = \frac{1}{2}\rho A_c \mathbf{v}_{rel}^2 C_{dt}$

where $C_{dt}$ is the total drag coefficient, the combination of the parasitic drag coefficient and the lift-induced drag coefficient: $C_{dt} = C_{dp} + C_{di}$.

For planar wings with an elliptical lift distribution, the lift induced drag coefficient id defined as dependent on the lift coefficient $C_L$ as:

$C_{di} = \frac{C_L^2}{\pi e A_R}$

where $A_R$ is the wing's aspect ratio and $e$ is the wing span efficiency factor, typically between 0.85 an 0.95 [3] [from lifting line theory?].

#### References

[1] Figure is a vector graphics reproduction by Circuit Grove of: "Drag Curve 2" Licensed under CC BY-SA 3.0 via Wikimedia Commons.
[2] Figure is a vector graphics reproduction by Circuit Grove of: "Induce drag downwash" Licensed under CC BY-SA 3.0 via Wikipedia.
[3] http://en.wikipedia.org/wiki/Lift-induced_drag