# In the Cl vs Cd graph, Why the drag coefficient decreases initially with the small increment in lift coefficient?

Cd = Cdo + KCl2

Total drag = Parasite drag + Induced drag

When Cl = 0 , Cd = Cdo

Increasing in Cl introduces another component of drag (Induced Drag) and therefore the total drag Cd should be increased. But, Why in this plot Cd decreases initially with the small increment in Cl?

• I don't think the origin of the graph is at (0,0), so your question may be based on an incorrect premise. – Mark Jones Jr. Oct 16 '19 at 16:27
• Can you please add the source of the image? – DeltaLima Oct 16 '19 at 16:34
• I'm not convinced that the origin is not at 0,0. – quiet flyer Oct 16 '19 at 17:43
• Possible duplicate of Is drag coefficient lowest at zero angle of attack? – Manu H Oct 17 '19 at 9:20

Think about it this way. Assume a cambered airfoil, not a symmetrical airfoil. Assume the wing has zero twist and zero incidence. To place the wing at the zero-lift angle-of-attack (zero CL), the fuselage and wing will have to fly at a somewhat nose-down pitch attitude relative to the airflow. This does not yield the lowest possible drag coefficient, regardless of whether we are looking at the wing, the fuselage, or the whole aircraft.

Bear in mind that in this part of the flight envelope (near the zero-lift angle-of-attack), drag is dominated by profile drag, not induced drag.

Now imagine using the same data to generate a graph of CD versus airspeed, assuming Lift=Weight. What would that look like? Also what would a graph of Drag versus airspeed look like?

The well-known 3D drag model of:

$$C_D=C_{D_0}+KC_L^2$$

only holds well for high aspect ratio, flap retracted wing configurations (source: ESDU Item 74035).

With flaps extended, a better model would be (source: ESDU Item 97002):

$$C_D=C_{D_0}+AC_L+BC_L^2$$

If you rearrange the terms a little bit, you get the model shown in your graph:

$$C_D=C_{D_{min}}+K(C_L-C_{L_{mindrag}})^2$$

Source: INTRODUCTION TO FLIGHT - John D Anderson

• might be copyright issues just posting part of a book like that – jk. Oct 17 '19 at 10:36