# What are the contributors of lift-dependent drag?

If someone wants to plot the drag polar of an aircraft, we have

$$C_D = C_{D,o} + C_{D,i}$$

form/skin drag plus the induced.

However, as I feel, form drag and probably skin friction drag (parasite drag) also lift-coefficient dependent. For example, as the angle of attack increases, the shape will be different and so the parasite drag will be different .

Does that increment in parasite drag considered in the induced drag term because it's lift-dependent?

Where should we add this contribution of drag in terms of the drag polar formula? in the lift-independent part or in the lift-dependent part?

• It is even more complicated than that. When the wing stalls, the lift decreases, but the drag, and this is clearly form drag, increases significantly. – Jan Hudec Feb 5 '20 at 19:45

If someone wants to plot the drag polar of an aircraft, we have $$CD=CD_o+CD_i$$ form/skin drag plus the induced.

Something to note here is that there are more than one mathematical "model" to describe the relationship between lift and drag. What you have described is known as "Parabolic Drag Model", where we consider a parabolic relationship between lift and drag.

Does that increment in parasite drag considered in the induced drag term because it's lift-dependent?

Imagine an airfoil drag polar (2D polar so there is no induced drag taken into account). If this polar can be closely modelled as a skewed parabola (skewed due to camber) then $$e$$ in the induced drag term $$\frac{CL^2}{\pi*e*AR}$$ takes care of this drag rise up to some extent. This kind of a 2D airfoil drag model is usually applicable for mostly turbulent airfoils such as NACA 4 series in high Reynolds number flows.

Where should we add this contribution of drag in terms of the drag polar formula? in the lift-independent part or in the lift-dependent part?

Above said, mostly laminar airfoils such as FX163 or NLF series airfoils which operate in relatively low Reynolds numbers does not fit the above model fairly well. These airfoils exhibit a linear relationship between lift and drag at-least for the operating range which is not affected by massive separation. So in this kind a scenario its best to modify the above equation with a linear term as well.

$$CD=CD_o + k CL + \frac{CL^2}{\pi e AR}$$