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I have found a lot of information to calculate drag coefficients and I know that total drag can be calculated by $$ D = \frac{1}{2} \rho u^2 S C_d $$ However I was wondering, if I substitute the zero lift drag coefficient into this equation is it correct to assume the value produced for the drag force would be the parasitic drag whilst the remainder of the total drag is made up of lift induced drag?

Bianfable
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Keira
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1 Answers1

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Induced drag is the portion of the lift force that opposes motion. Induced drag exists even when the drag coefficient CD in your equation is zero.

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Lift is perpendicular to the air flow relative to the wing. Imagine a wing moving right to left across your screen. The air is moving left to right relative to the wing. If there's no vertical induced airflow then the lift is vertical and there's no induced drag. However, lift deflects the air down, so typically the air relative to this wing is not moving exactly left to right, but is tilted down slightly. Hence, the lift, which is perpendicular to that airflow, is actually tilted back (right) slightly. That means a (typically small) portion of the lift is "pushing this wing back," opposing its right-to-left motion.

If you know trigonometry, induced drag is lift times the sine of the inflow angle, $ L\sin \phi $. The inflow angle is the angle of the airflow relative to the horizontal in this picture.

There's a picture of exactly this at the bottom of this page in the induced power section. (Induced power is the power required to overcome induced drag.)

Mat
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  • If lift is the component perpendicular to the air flow, as you correctly state in the second paragraph, then it cannot oppose motion. Also the question is about wing, so you shouldn't mix in factors only relevant for propellers—in which case you should also be talking about induced power, not drag. – Jan Hudec Dec 10 '20 at 23:23
  • Lift can oppose motion. This is exactly the case provided in the example. Motion is right to left, but net airflow is NOT left to right because you must include induced airflow, which "tilts it down" as shown in the picture. The reason it's called induced drag is because it's associated with this induced airflow. – Mat Dec 12 '20 at 00:10
  • No! Lift is defined as the component perpendicular to relative wind, and relative wind is defined as the free stream velocity, that is reciprocal of the aircraft motion in the air. The force due to circulation is tilted back, and this is the induced drag. But the definitions are such that this isn't what is called lift. Lift is one component of this force and induced drag is the other. – Jan Hudec Dec 12 '20 at 21:50
  • Please check wikipedia or any standard book or any aerodynamic software. It's well defined - lift is perpendicular to the flow. The flow includes more than motion, e.g. wind, induced velocity, sometimes interference from other objects. Another way to think of this is that it wouldn't make sense otherwise - a wing cannot discriminate flow due to motion from other flow sources. – Mat Dec 13 '20 at 22:50
  • Wikipedia says: “Lift is the component of this force that is perpendicular to the oncoming flow direction.” (emphasis mine). So it does not include induced velocity and other things. And of course there is no wind in the reference frame of air mass. – Jan Hudec Dec 13 '20 at 23:02
  • The Wikipedia quote is correct. The issue is that you're trying to exclude induced velocity from the oncoming flow. It and other sources of flow must be included. It wouldn't make sense otherwise. Please read https://en.wikipedia.org/wiki/Lift-induced_drag or other references carefully. If you don't understand that, maybe you could post a new thread and we could discuss there. – Mat Dec 14 '20 at 17:46
  • So lets go to the reference and flip a page from What is Lift (which is less clear than WP) to What is Drag which unambiguously states that “Drag acts in a direction that is opposite to the motion of the aircraft. Lift acts perpendicular to the motion.”. And then “The local angle of attack of the wing is increased by the induced flow of the tip vortex, giving an additional, downstream-facing, component to the aerodynamic force acting on the wing.”—note they don't call it “lift”. – Jan Hudec Dec 14 '20 at 17:52
  • I admit the NASA link for kids confuses this topic - they oversimplify definitions there. If you want to use that as your source it maybe OK for very high level talk. However, if you want to understand this this or apply it, you'd need to account for the total flow including all sources (induced flow being a significant one). Again, the prior link I provided will show you how it works. – Mat Dec 14 '20 at 18:15
  • No, they use exactly the same definition as everybody else. And remember, we are in complete agreement about the actual phenomenon. The only disagreement is whether you decompose aerodynamic force due to circulation to lift and induced drag, or decompose lift to induced drag and…. what? – Jan Hudec Dec 14 '20 at 18:18
  • I guess you are trolling. I even read the NASA link you quoted above and it clearly states the motion you quoted was "motion between the object and the fluid." They further clarify it "makes no difference whether the object moves through a static fluid, or the fluid moves past a static solid object." E.g. if you're flying 100kts (ground speed) and there's a 20kt wind, you have to include that wind. If something's (fan?) is blowing a 10kt wind down on you, must include that too. If the body is inducing a 10kt wind down, must include that too. – Mat Dec 15 '20 at 00:46
  • I am, all the time, talking about motion between the object and the fluid. Specifically, motion of the fluid far enough from the object not to be affected by it relative to the object. That's the definition of relative wind. That precisely matches what the NASA article says. That does not include any induced motion, which I understand according to the standard definition as motion of the fluid affected by the object. – Jan Hudec Dec 15 '20 at 21:41
  • Here are a couple more links. To save yourself time you can scroll right to the diagrams showing the airfoils, the total flow and the LIFT vector. What is the lift perpendicular to in all these diagrams? And how do they define induced drag? https://www.perfectedflight.com/the-truth-about-induced-drag/. http://www.ase.uc.edu/class/AEEM456/Section_2_Notes.pdf – Mat Dec 16 '20 at 01:51
  • The second one indeed defines lift as perpendicular to the local flow. The first one is funny, because it first defines it perpendicular to relative wind, then renames it to “effective lift” and redefines lift as perpendicular to local flow. Ok, so there are clearly two inconsistent definitions. – Jan Hudec Dec 16 '20 at 05:10