# Lift and Drag

## Body - like an airfoil - in fluid flow

### Lifting Force

The lifting force acting on a body in a fluid flow can be calculated

*F _{L} = c_{L} 1/2 ρ v*

^{2}

*A (1)*

*where *

*F _{L}* = lifting force (N)

*c _{L} = lifting coefficient*

*ρ = density of fluid (kg/m*^{3}*)*

*v = flow velocity (m/s)*

*A = body area (m*^{2}*)*

### Drag Force

The drag force acting on a body in fluid flow can be calculated

*F _{D} = c*

_{D}

*1/2 ρ v*

^{2}

*A (2)*

*where *

*F _{D} = drag force (N)*

*c _{D} = drag coefficient*

*ρ = density of fluid (kg/m*^{3}*)*

*v = flow velocity (m/s)*

*A = body area (m*^{2}*)*

### Required Thrust Power to overcome Drag Force

The thrust power required to overcome the drag force can be calculated

*P = F_{D} v (3)*

*where *

*P = power (W)*

### Example - Aeroplane and Airfoil Lift - Drag and required Thrust Power

For an aeroplane with velocity *100 m/s*, wing area *20 m ^{2}*, a drag coefficient

*0.06*and a lift coefficient

*0.7 -*the lifting force acting on the airfoil can be calculated

*F _{L}* = 0.7 1/2 (1.2 kg/m

^{3}) (100 m/s)

^{2}

*(20 m*

^{2})* = 84000 (N)*

* = 84 (kN)*

The drag force can be calculated

*F _{D}* = 0.06

*1/2 (*

*1.2 kg/m*

^{3}) (100 m/s)^{2}

*(20 m*

^{2})* = 7200 (N)*

* = 7.2 (kN)*

Required thrust power to overcome the drag force:

*P = (7200 N) (100 m/s)*

* = 720000 (W)*

* = 720 (kW)*