Continuum Mechanics Definition Edit
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).
Commonly used EquationEdit
In aerospace engineering, the overall drag is generally expressed as follows:
D is the overall drag
ρ is the air density
V is the air velocity relative to the airfoil
CD is the drag coefficient (dimensionless)
S is the aircraft wing area
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 zero-lift 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.
- Leakage drag: it is due to air incoming through both holes and gaps in high-pressure 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 2-5% of the parasite drag for jet transports and 5-10% for propeller airplane or new generation fighters.
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 CDmin or CDo, as it describes the minimum possible drag the aircraft could see when no lift is produced at a subsonic velocity.
Lift-induced drag Edit
Lift-induced drag is the result of lift creation on a three-dimensional lifting body, such as the wings or fuselage of an airplane. Lift-induced 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∞.
where AR is the aspect ratio (wingspan squared over the wing area)
Since the calculation of the lift-induced drag is based on the area of the wing S, the expression of the lift-induced 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.
Wave drag Edit
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 Mcr is the dimensionless velocity at which shocks first form on the airplane. Mcr is primarily a function of airfoil thickness and sweep. A typical range for Mcr would be (0.7-0.9), depending on airfoil thickness;
- the drag divergent Mach number MDD at which the formation of shocks begins to significantly affect the drag.
For instance, Boeing definition is MDD = 1.08 Mcr.
Drag polar Edit
Plots of drag coefficient CD versus lift coefficient CL are very useful. As a first approximation CD varies as the square of CL. So a linear relation between CD and CL 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:
CD = K1.CL2 + K2.CL + CD0
- CD0 stands for parasite drag.
- K1 and K2 are dimensionless. K1.CL2 + K2.CL includes both lift-induced drag and wave drag.
Power Curve Edit
Depending on the aircraft speed, the importance of the different types of drag changes.
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.
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. 
On the other hand, if the velocity is large enough, compressibility effects have to be taken into account. CD becomes then essentially a function of M because wave drag overcomes viscous effects. CD increases dramatically in the vicinity of M = 1 because of shocks formation. For example, a sharp wing would see its CD being maximum around M = 1, whereas a more blunt airfoil would see its maximum CD right before M = 1. 
-  Fundamentals of Fluid Mechanics, 5th Ed, M.Y. Okiishi, Wiley Publications, p. 485-486
-  Dynamics of Atmospheric Flight, Bernard Etkin, Dover Publications, p. 198
-  Aicraft Design: A Conceptual Approach, 4th Ed, Daniel P. Raymer, AIAA, p. 327-347
-  http://www.aerospaceweb.org/question/aerodynamics/q0184.shtml
-  http://www.hq.nasa.gov/office/hqlibrary/aerospacedictionary/
-  Drawings by J.-B. Mercier
-  The Concorde Story, 6th Ed, Christopher Orlebar