# Downforce Calculation for a wing Formula Source

1. Mar 19, 2015

### al_garnett

Hey guys,
The following formula is provided on the wikipedia page for downforce,

D=0.5(WS)*H*alpha*F*rho*V^2
Where:

D is downforce in newtons
WS is wingspan in metres
H is height in metres
\alpha is angle of attack
F is lift coefficient
rho, ρ, is air density in kg/m³
V is velocity in m/s

Does anybody know the source of this Formula or how its is derived? I need to reference/cite it for a university project but can't find it anywhere. We are not able to reference wikipedia articles.

Thanks

2. Mar 19, 2015

### jack action

It is based on the typical definition of lift coefficient:

Where the planform area S has been set to the product WS*H.

Someone went further by substituting the actual lift coefficient by the one defined by the thin airfoil theory, i.e. CL = 2πα or in the formula: CL = Fα , where F can vary depending on the unit for the angle of attack (which is not defined in the given formula).

I wouldn't consider that last substitution. The equation for the lift coefficient is the accurate definition (since the lift coefficient is a function of the angle of attack, Mach number and Reynold number by definition).