Continuum Mechanics Definition Edit
A body moving through a fluid is submitted to an interaction between its outer surface and the fluid.[1] This can be described as a stress including two terms :
The integrated or resultant aerodynamic effects of these distributions is a force. This force can be split in two terms: lift and drag.
The drag is the resultant force in the direction of the upstream velocity U relative to the airfoil. When specifically considering an aircraft, the drag force is in the opposite direction of the freestream velocity (or flight path).[1]
Commonly used EquationEdit
In aerospace engineering, the overall drag is generally expressed as follows:
where:
D is the overall drag ρ is the air density V is the air velocity relative to the airfoil C_{D} is the drag coefficient (dimensionless) S is the aircraft wing area  n.b.

Types of Drag Edit
There are essentially three types of drags that can affect a body traveling through a fluid:
 parasite drag (including leakage and protuberance drag)
 lift induced drag (including trim drag)
 wave drag
Parasite drag Edit
Parasite drag (also called parasitic drag or zerolift drag) is made up of the following components :
 Form drag: loss due to the shape of a wetted surface changing the flow direction of a viscous fluid.
 Skin friction drag: loss in the boundary layer due to the roughness of a wetted surface .
 Interference drag: the proximity of several bodies creating mutual interferences in the air flow around each different element.[3]
 Leakage drag: it is due to air incoming through both holes and gaps in highpressure zones over the fuselage, wings, empennage,...This air is exiting the aircraft's skin towards low pressure zones. Loss due to incoming airflow contributes directly to drag while exiting air increases airflow separation.
 Protuberances drag: protuberances are elements added on the "clean" body that spoil the airflow. They include antennas, door edges, control surface hinges as well as protruding rivets.
Leakage and protuberance drag is difficult to predict but it roughly represents 25% of the parasite drag for jet transports and 510% for propeller airplane or new generation fighters.[3]
A well designed aircraft in subsonic flight will have parasitic drag mostly due to skin friction plus small drag due to turbulent air mixing behind it. The parasite drag coefficient is denoted as C_{Dmin} or C_{Do,} as it describes the minimum possible drag the aircraft could see when no lift is produced at a subsonic velocity.[3]
Liftinduced drag Edit
Liftinduced drag is the result of lift creation on a threedimensional lifting body, such as the wings or fuselage of an airplane. Liftinduced drag includes the creation of vortices above the wings as well as the additional viscous drag.
The lift is perpendicular to the freestream velocity V_{∞} and the induced drag is perpendicular to the lift. In most cases, the aircraft is symmetric and the induced drag is collinear to the freestream velocity V_{∞}.[2]
The liftinduced drag coefficient. C_{Di. }is approximated to vary proportionally to the square of the lift coefficient C_{L}. [2]
where AR is the aspect ratio (wingspan squared over the wing area) 
Since the calculation of the liftinduced drag is based on the area of the wing S, the expression of the liftinduced drag must be completed by the trim drag. This additional drag is caused by the horizontal tail (or canard) force that is instantaneously required to balance the aircraft total pitching moment around its center of gravity.[2]
Wave drag Edit
Wave drag (also called compressibility drag) is due to the formation of shocks. A shock is the supersonic phenomenon.[3]
Though, even if the aircraft is flying at a subsonic speed some areas of its fuselage may encounter supersonic airflow . This is especially true above the wings where the airflow is strongly accelerated. Therefore wave drag starts to appear in transonic flight (Mach 0.8 to 1.2) and is still present in supersonic flights (Mach > 1,2).
As an airplane accelerates through the transonic regime, the increase of drag is due to the formation of shocks and the importance of the compressibility drag tends to dominate other forms of drag as the aircraft's speed increases towards Mach 1.0.
Two Mach Number are then defined:
 the critical Mach number M_{cr} is the dimensionless velocity at which shocks first form on the airplane. M_{cr} is primarily a function of airfoil thickness and sweep. A typical range for M_{cr } would be (0.70.9), depending on airfoil thickness;
 the drag divergent Mach number M_{DD} at which the formation of shocks begins to significantly affect the drag.
For instance, Boeing definition is M_{DD} = 1.08 M_{cr}.[3]
Drag polar Edit
Plots of drag coefficient C_{D }versus lift coefficient C_{L }are very useful. As a first approximation C_{D} varies as the square of C_{L}. So a linear relation between C_{D} and C_{L} ² can be plotted for a aircraft at a given Mach number.
To be more accurate, a linear term can be taken into account and we get the relation:
C_{D} = K_{1}.C_{L}^{2} + K_{2}.C_{L} + C_{D0}
where:
 C_{D0} stands for parasite drag.
 K_{1} and K_{2} are dimensionless. K_{1}.C_{L}^{2} + K_{2}.C_{L} includes both liftinduced drag and wave drag.
Power Curve Edit
Depending on the aircraft speed, the importance of the different types of drag changes.
At lower speeds, induced drag is the most important because of the high angle of attack required to produce sufficientlift. [2]
As velocity increases, the induced drag decreases (as well as the angle of attack) but parasite drag increases since the airflow surrounding the aircraft is faster, generating more skin friction. At transonic speed, the wave drag has to be taken into account.
The overall drag can be plot as a function of the aircraft velocity to obtain the power curve. This curve presents a point at which the drag is minimum: this is the velocity at which the range is maximum. This velocity is different from the velocity at which the endurance is maximized.
Influence of Mach and Reynolds numbersEdit
The drag coefficient depends largely on the velocity of the flow. Since the Mach number and the Reynolds number vary both proportionally with the airflow speed, drag can be seen as a function of both Re and M.[1]
If the Mach number, M < 0.5, C_{D} is mostly a function of Re because most of the drag is due to friction between the aircraft and air.
For streamlined bodies like a wing, the drag coefficient increases when the boundary layer surrounding it becomes turbulent because most of the drag is due to the shear force. So the drag increases with the flow speed and the surface roughness of the wing. Hence, the more the surface roughness of the wing, the smaller the Reynolds number at which the boundary layer becomes turbulent. [1]
On the other hand, if the velocity is large enough, compressibility effects have to be taken into account. C_{D} becomes then essentially a function of M because wave drag overcomes viscous effects. C_{D }increases dramatically in the vicinity of M = 1 because of shocks formation. For example, a sharp wing would see its C_{D }being maximum around M = 1, whereas a more blunt airfoil would see its maximum C_{D } right before M = 1. [1]
References Edit
 [1] Fundamentals of Fluid Mechanics, 5th Ed, M.Y. Okiishi, Wiley Publications, p. 485486
 [2] Dynamics of Atmospheric Flight, Bernard Etkin, Dover Publications, p. 198
 [3] Aicraft Design: A Conceptual Approach, 4th Ed, Daniel P. Raymer, AIAA, p. 327347
 [4] http://www.aerospaceweb.org/question/aerodynamics/q0184.shtml
 [5] http://www.hq.nasa.gov/office/hqlibrary/aerospacedictionary/
 [6] Drawings by J.B. Mercier
 [7] The Concorde Story, 6th Ed, Christopher Orlebar