Downforce Calculation for a wing Formula Source

In summary, the formula for downforce provided on Wikipedia is based on the definition of lift coefficient, with the planform area being set to the product of wingspan and height. The lift coefficient has been substituted with the one defined by the thin airfoil theory. However, this substitution may not be accurate as it depends on the unit for the angle of attack. The source of this formula is unknown and cannot be referenced for university projects.
  • #1
al_garnett
9
0
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
 
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  • #2
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).
 

1. What is downforce and why is it important in racing?

Downforce is the downward force created by the wings or aerodynamic components on a race car. It is important because it helps increase the traction and grip of the tires, allowing the car to corner faster and maintain stability at high speeds.

2. How is downforce calculated for a wing?

Downforce calculation for a wing involves several factors such as the wing's surface area, angle of attack, air density, and velocity. These factors are used in the formula: Downforce = 0.5 x Surface Area x Air Density x Velocity^2 x Coefficient of Lift. The coefficient of lift is determined by the shape and design of the wing.

3. What is the source of the formula used for downforce calculation?

The formula for downforce calculation for a wing is derived from Bernoulli's principle, which states that an increase in the speed of a fluid (in this case, air) results in a decrease in pressure. This pressure difference creates a force that is perpendicular to the flow of air, known as lift or downforce in the case of wings.

4. How does the angle of attack affect downforce?

The angle of attack refers to the angle at which the wing is positioned relative to the airflow. A higher angle of attack will result in a greater downforce, up to a certain point. If the angle is too high, the airflow will become turbulent, reducing the effectiveness of the wing and decreasing downforce.

5. Are there any limitations to downforce calculation for a wing?

Yes, there are limitations to downforce calculation for a wing. Factors such as wind conditions, surface roughness, and changes in air density can affect the accuracy of the calculation. Additionally, the formula assumes a constant air density and does not take into account the effects of other aerodynamic components on the car.

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