Basic Concepts and Results in Aerodynamics
Freestream Vector : Velocity of the fluid far ahead of the object in the flow, undisturbed by the presence of the object.
Lift : Force perpendicular to the freestream, acting on the aircraft.
Lift = dynamic pressure X planform area X lift coefficient.
Drag = dynamic pressure X planform area X drag coefficient.
or, 
,
where is the undisturbed freestream density, is freestream speed , is the ratio of specific heats and is the freestream Mach number.
Aspect Ratio:
where is the b is the span and is the S planform area of the wing. For
a 2-D airfoil 
Lift-Curve Slope of an airfoil:
This is derived from "thin-airfoil theory" in low-speed flows where Mach number is close to 0.
In subsonic flow,
In supersonic flows,
Finite Wing Vortex system
Pressure difference between upper and lower surfaces must vanish at tips of the wing. There are two effects of this,
a ) Loss in lift, compared to 2-D airfoils.
b) Induced drag, i.e. drag induced by the force vector tilting backwards as a result of the induced downwash..
Important points
1. Since induced drag is directly related to the lift it can be calculated
by the same mathematical formulation used to calculate lift.
2. Does not require consideration of viscosity.
3. No induced drag on 2-D airfoils under steady conditions.
4. At finite Aspect ratios,
5. Ideal elliptic lift distribution implies minimum induced drag , i.e, efficiency e=1.
6. At low Mach numbers drag on well designed aircraft is primarily due to induced drag.