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

Question

C_d = C_d_o + KC_l²

Total drag = Parasite drag + Induced drag

When C_l = 0 , C_d = C_d_o

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

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
Possible duplicate of Is drag coefficient lowest at zero angle of attack? — Manu H, Oct 17 '19 at 09:20

quiet flyer · Accepted Answer · 2019-10-16T19:05:33.310

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.

Related: Is drag coefficient lowest at zero angle of attack?

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?

https://aviation.stackexchange.com/questions/62357/is-drag-coefficient-lowest-at-zero-angle-of-attack — Nirmal, Oct 16 '19 at 18:29
Right, now incorporated, thanks. I guess it's a duplicate question or nearly so. Zero a-o-a and zero-lift a-o-a are not exactly the same thing. — quiet flyer, Oct 16 '19 at 19:02

score 5 · Answer 2 · answered Oct 16 '19 at 16:51

5

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:

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

answered Oct 16 '19 at 16:51

JZYL

11,066
2
15
49

I don't think the flaps are the cause of the $C_{D_{mindrag}}$ and $C_{D_0}$ discrepancy. This phenomenon also occurs when the flaps are retracted (due to the reasons mentioned by quiet flyer). Also, it's not clear to me how the rearrangement of terms (in which equation, the one with the flaps?) should lead to the final result – ROIMaison Mar 21 '24 at 12:39

score 2 · Answer 3 · answered Oct 17 '19 at 06:22

2

Source: INTRODUCTION TO FLIGHT - John D Anderson

answered Oct 17 '19 at 06:22

Nirmal

319
1
3
10

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

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

3 Answers3