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

Is drag coefficient lowest at zero angle of attack?What is the true formula for parasite drag?Is induced drag caused because of the tilt of the wing backwards?Do wingtip vortices cause a decrease in the lift component of aerodynamic force, and do planes need to pull more AoA to compensate?Why is the thrust/drag increase much lower at a lower FL with weight the only variable?How significant is the lift induced drag contribution to total drag of aircraft at cruise speed?How to calculate the induced drag coefficient?How does wing aspect ratio influence lift and drag?Why is a reduction in lift called 'drag'?Why do Wingtip Vortices affect the upwash ahead of the aerofoil?How is the total drag variation with velocity related to altitude?

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4

1

$begingroup$

C_d = C_do + KC_l²

Total drag = Parasite drag + Induced drag

When C_l = 0 , C_d = C_do

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?

lift drag

share|improve this question

asked Oct 16 at 16:19

NirmalNirmal

17566 bronze badges

$endgroup$

• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  I don't think the origin of the graph is at (0,0), so your question may be based on an incorrect premise.
  $endgroup$
  – Mark Jones Jr.
  Oct 16 at 16:27
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  Can you please add the source of the image?
  $endgroup$
  – DeltaLima
  Oct 16 at 16:34
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  I'm not convinced that the origin is not at 0,0.
  $endgroup$
  – quiet flyer
  Oct 16 at 17:43
  

  
  
  
  


• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  $begingroup$
  Possible duplicate of Is drag coefficient lowest at zero angle of attack?
  $endgroup$
  – Manu H
  Oct 17 at 9:20
  

  
  
  
  

add a comment
 | 

4

1

$begingroup$

C_d = C_do + KC_l²

Total drag = Parasite drag + Induced drag

When C_l = 0 , C_d = C_do

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?

lift drag

share|improve this question

asked Oct 16 at 16:19

NirmalNirmal

17566 bronze badges

$endgroup$

• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  I don't think the origin of the graph is at (0,0), so your question may be based on an incorrect premise.
  $endgroup$
  – Mark Jones Jr.
  Oct 16 at 16:27
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  Can you please add the source of the image?
  $endgroup$
  – DeltaLima
  Oct 16 at 16:34
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  I'm not convinced that the origin is not at 0,0.
  $endgroup$
  – quiet flyer
  Oct 16 at 17:43
  

  
  
  
  


• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  $begingroup$
  Possible duplicate of Is drag coefficient lowest at zero angle of attack?
  $endgroup$
  – Manu H
  Oct 17 at 9:20
  

  
  
  
  

add a comment
 | 

$begingroup$

C_d = C_do + KC_l²

Total drag = Parasite drag + Induced drag

When C_l = 0 , C_d = C_do

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?

lift drag

share|improve this question

asked Oct 16 at 16:19

NirmalNirmal

17566 bronze badges

$endgroup$

share|improve this question

asked Oct 16 at 16:19

NirmalNirmal

17566 bronze badges

share|improve this question

asked Oct 16 at 16:19

NirmalNirmal

17566 bronze badges

asked Oct 16 at 16:19

NirmalNirmal

17566 bronze badges

asked Oct 16 at 16:19

NirmalNirmal

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3 Answers
3

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7

$begingroup$

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?

share|improve this answer

edited Oct 16 at 19:05

answered Oct 16 at 17:32

quiet flyerquiet flyer

6,7941010 silver badges4646 bronze badges

$endgroup$

• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  aviation.stackexchange.com/questions/62357/…
  $endgroup$
  – Nirmal
  Oct 16 at 18:29
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  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.
  $endgroup$
  – quiet flyer
  Oct 16 at 19:02
  
  

  
  
  
  

add a comment
 | 

4

$begingroup$

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:

$$C_D=C_D_min+K(C_L-C_L_mindrag)^2$$

share|improve this answer

answered Oct 16 at 16:51

JimmyJimmy

3,89611 gold badge55 silver badges2828 bronze badges

$endgroup$

add a comment
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1

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Source: INTRODUCTION TO FLIGHT - John D Anderson

share|improve this answer

answered Oct 17 at 6:22

NirmalNirmal

17566 bronze badges

$endgroup$

• 
  
  
  

  
  

  
  
  
  
  
  

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

  
  
  
  

add a comment
 | 

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7

$begingroup$

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?

share|improve this answer

edited Oct 16 at 19:05

answered Oct 16 at 17:32

quiet flyerquiet flyer

6,7941010 silver badges4646 bronze badges

$endgroup$

• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  aviation.stackexchange.com/questions/62357/…
  $endgroup$
  – Nirmal
  Oct 16 at 18:29
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  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.
  $endgroup$
  – quiet flyer
  Oct 16 at 19:02
  
  

  
  
  
  

add a comment
 | 

7

$begingroup$

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?

share|improve this answer

edited Oct 16 at 19:05

answered Oct 16 at 17:32

quiet flyerquiet flyer

6,7941010 silver badges4646 bronze badges

$endgroup$

• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  aviation.stackexchange.com/questions/62357/…
  $endgroup$
  – Nirmal
  Oct 16 at 18:29
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  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.
  $endgroup$
  – quiet flyer
  Oct 16 at 19:02
  
  

  
  
  
  

add a comment
 | 

$begingroup$

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?

share|improve this answer

edited Oct 16 at 19:05

answered Oct 16 at 17:32

quiet flyerquiet flyer

6,7941010 silver badges4646 bronze badges

$endgroup$

share|improve this answer

edited Oct 16 at 19:05

answered Oct 16 at 17:32

quiet flyerquiet flyer

6,7941010 silver badges4646 bronze badges

answered Oct 16 at 17:32

quiet flyerquiet flyer

6,7941010 silver badges4646 bronze badges

answered Oct 16 at 17:32

quiet flyerquiet flyer

6,7941010 silver badges4646 bronze badges

4

$begingroup$

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:

$$C_D=C_D_min+K(C_L-C_L_mindrag)^2$$

share|improve this answer

answered Oct 16 at 16:51

JimmyJimmy

3,89611 gold badge55 silver badges2828 bronze badges

$endgroup$

add a comment
 | 

4

$begingroup$

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:

$$C_D=C_D_min+K(C_L-C_L_mindrag)^2$$

share|improve this answer

answered Oct 16 at 16:51

JimmyJimmy

3,89611 gold badge55 silver badges2828 bronze badges

$endgroup$

add a comment
 | 

$begingroup$

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:

$$C_D=C_D_min+K(C_L-C_L_mindrag)^2$$

share|improve this answer

answered Oct 16 at 16:51

JimmyJimmy

3,89611 gold badge55 silver badges2828 bronze badges

$endgroup$

share|improve this answer

answered Oct 16 at 16:51

JimmyJimmy

3,89611 gold badge55 silver badges2828 bronze badges

answered Oct 16 at 16:51

JimmyJimmy

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answered Oct 16 at 16:51

JimmyJimmy

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1

$begingroup$

Source: INTRODUCTION TO FLIGHT - John D Anderson

share|improve this answer

answered Oct 17 at 6:22

NirmalNirmal

17566 bronze badges

$endgroup$

• 
  
  
  

  
  

  
  
  
  
  
  

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

  
  
  
  

add a comment
 | 

1

$begingroup$

Source: INTRODUCTION TO FLIGHT - John D Anderson

share|improve this answer

answered Oct 17 at 6:22

NirmalNirmal

17566 bronze badges

$endgroup$

• 
  
  
  

  
  

  
  
  
  
  
  

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

  
  
  
  

add a comment
 | 

$begingroup$

Source: INTRODUCTION TO FLIGHT - John D Anderson

share|improve this answer

answered Oct 17 at 6:22

NirmalNirmal

17566 bronze badges

$endgroup$

share|improve this answer

answered Oct 17 at 6:22

NirmalNirmal

17566 bronze badges

answered Oct 17 at 6:22

NirmalNirmal

17566 bronze badges

answered Oct 17 at 6:22

NirmalNirmal

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