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Drag Coefficient
{{Use dmy dates|cs1-dates=ly}}
'''Drag Coefficient''' (commonly denoted as: \( c_d \), \( c_x \), or \( c_w \)) is a dimensionless quantity used to quantify the drag or resistance of an object in a fluid environment, such as air or water. It indicates how aerodynamic or hydrodynamic a body is. A lower drag coefficient corresponds to lower aerodynamic drag for a given shape.
== Definition ==
The drag coefficient \( c_d \) is defined as:
\[ c_d = \frac{2F_d}{\rho u^2 A} \]
where:
* \( F_d \) is the drag force.
* \( \rho \) is the mass density of the fluid.
* \( u \) is the flow velocity relative to the fluid.
* \( A \) is the reference area (e.g., frontal area for cars, wing area for aircraft).
== Key Points ==
* The reference area depends on the object and context.
* Airfoils use wing area; cars use projected frontal area.
* For streamlined bodies (e.g., fish, aircraft), \( c_d \) is typically lower.
* For bluff bodies (e.g., brick, sphere), \( c_d \) is higher due to flow separation and pressure drag.
== Cauchy Momentum Equation ==
In terms of local shear stress \( \tau \) and local dynamic pressure \( q \):
\[ c_d = \frac{\tau}{q} = \frac{2\tau}{\rho u^2} \]
where:
* \( \tau \) = local shear stress.
* \( q \) = \( \frac{1}{2} \rho u^2 \), the dynamic pressure.
== Drag Equation ==
The general drag force formula:
\[ F_d = \frac{1}{2} \rho u^2 c_d A \]
== Dependence on Reynolds Number ==
The drag coefficient is influenced by the Reynolds number (Re):
* Low Re: laminar flow, drag dominated by viscous forces.
* High Re: turbulent flow, drag dominated by pressure forces.
* For a sphere: \( c_d \) drops sharply at the critical Reynolds number.
== Drag Coefficient Examples ==
=== General Shapes ===
{| class="wikitable"
|-
! Shape !! \( c_d \)
|-
| Smooth sphere (Re = \( 10^6 \)) || 0.1
|-
| Rough sphere (Re = \( 10^6 \)) || 0.47
|-
| Flat plate perpendicular to flow (3D) || 1.28
|-
| Empire State Building || 1.3–1.5
|-
| Eiffel Tower || 1.8–2.0
|-
| Long flat plate perpendicular to flow (2D) || 1.98–2.05
|}
=== Aircraft ===
{| class="wikitable"
|-
! Aircraft Type !! \( c_d \) !! Drag Count
|-
| F-4 Phantom II (subsonic) || 0.021 || 210
|-
| Learjet 24 || 0.022 || 220
|-
| Boeing 787 || 0.024 || 240
|-
| Airbus A380 || 0.0265 || 265
|-
| Cessna 172/182 || 0.027 || 270
|-
| Boeing 747 || 0.031 || 310
|-
| F-104 Starfighter || 0.048 || 480
|}
== Blunt and Streamlined Body Flows ==
* **Streamlined bodies**: Flow remains attached longer; friction drag dominates.
* **Blunt bodies**: Flow separates early; pressure drag dominates.
Boundary layer behavior is critical: laminar flow = lower drag; turbulent flow = higher drag but more stable separation.
== Drag Crisis ==
At critical Reynolds numbers, \( c_d \) can drop dramatically due to a transition to turbulent boundary layer flow (e.g., golf ball dimples reduce \( c_d \)).
== See Also ==
* [[Automotive aerodynamics]]
* [[Ballistic coefficient]]
* [[Drag crisis]]
* [[Zero-lift drag coefficient]]
== References ==
# Clancy, L.J. (1975). ''Aerodynamics.'' ISBN 0-273-01120-0.
# Abbott, Ira H., and Von Doenhoff, Albert E. (1959). ''Theory of Wing Sections.''
# Hoerner, Dr. Sighard F., ''Fluid-Dynamic Drag.''
# EngineeringToolbox.com - Drag Coefficient resources.
# NASA - Shape Effects on Drag.
{{Aerospace engineering}}
{{Fluid dynamics}}
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