# How to calculate aerodynamics ?

How to calculate aerodynamics ?

Aerodynamics is the study of dynamics of air. When there is a flow of air over any object, then there is a creation of lift force as well as drag force. These two forces are a result of pressure differences which are created due to flow of air over the top and bottom surface of the body and also due to shear stress on the surface of the body. However, a major contribution is of forces which are created due to pressure difference. These forces are normal and perpendicular to the flow direction.

The force which is perpendicular to the flow direction is lift force. The force which is parallel to the air flow is drag force. Lift force and drag force are both related to a coefficient, which plays a major role in calculation of these two forces. These coefficients are called lift coefficient and drag coefficient.

Lift and drag forces are proportional to the surface area, density and velocity of air. Formula to calculate the lift coefficient is

\[{c_l} = \frac{L}{{q_\infty }S}\]

and to calculate drag coefficient is

\[c_d =\frac{D}{{q_\infty }S}\]

Lift force makes any object fly. It uplifts the object from the ground. Drag force opposes the motion of the object. In order to overcome this drag force there needs to be some counteracting force. The engine of the vehicles as well as of the aircraft opposes the drag force and makes the vehicle as well as aircraft move forward. Similarly lift is balanced by weight. Lift is a good force for aircrafts and helicopters, however it is a degrading force for racing cars and vehicles.

There are different types of drag force like induced drag, pressure drag and skin friction drag and drag at supersonic speed which is wave drag. We can also calculate these drags.

Coefficient of Induced drag can be calculated as

\[ C_{D,i}=\frac{C_{L}^{2}}{\pi e AR}\]

Coefficient of lift at supersonic speed and wave drag coefficient can be calculated as,

\[c_{l}=\frac{4\alpha }{\sqrt{M_{\infty}^{2}-1}}\]

\[c_{d}=\frac{4\alpha ^{2}}{\sqrt{M_{\infty}^{2}-1}}\]

this is with respect to a flat plate at supersonic speed.