# Lift

Lift is a component of the fluid dynamics force that acts in a direction perpendicular to the relative fluid flow. Drag is a fluid dynamics force component that acts in a direction parallel to the relative fluid flow. An airfoil is a streamline shape that produces significantly more lift than drag.

Figure 1: The lift and drag force generated by an airfoil.

#### Determining the lift on an airfoil

The drag force $\hat{F}_{lift}$ is:

$F_{lift} = \frac{1}{2} \rho A_p C_{L} v_{rel}^2$

where $\rho$ is the fluid density, $A_p$ is the planform area of the body in the direction of the relative fluid flow, $C_L$ is the a lift coefficient, $v_{rel}$ is the relative fluid velocity vector and $\hat{L}$.

There are a few ways to explain how the lift force is generated. One is based on Newton's law and the other on Bernoulli's principle. The Newton's law explanation says that Lift is a reaction force. The flow coming off the airfoil has a downward velocity which means the foil applied a force on the fluid [needs a figure]. Newton's 3rd law says that every force has an equal and opposite reaction force. That means the force the foil exerted on the fluid is the force the fluid exerted on the foil.

The Bernoulli principle says that for an inviscid fluid, an increase in fluid velocity causes a decrease in pressure. For lift producing shapes, the fluid must travel faster over the shape than under which mean the pressure below is higher than above.

#### Kutta–Joukowski theorem

The Kutta-Joukowski theorem is a fundamental theorem of aerodynamics that states that the lift acting on a body is equal to the relative velocity of the surrounding fluid, $v_{rel}$, times the density of the surrounding fluid, $\rho$, times the circulation around the body, $\Gamma$:

$F_{lift} = \rho v_{rel} \Gamma$

The circulation, an important concept in aerodynamics, is the line integral of the relative fluid velocity around the 2D airfoil's perimeter, a closed curve:

$\Gamma = \oint V ds$