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Downforce Calculation for a wing Formula Source

  1. Mar 19, 2015 #1
    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. jcsd
  3. Mar 19, 2015 #2

    jack action

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    Science Advisor
    Gold Member

    It is based on the typical definition of lift coefficient:

    17e3deb4158e74360b161739fc2548e4.png

    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).
     
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