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Reynolds Number Calculator
Dean Pappas:
Hi Alan,
If you are looking at the plots for an airfoil: the ones with Cl and Cd on them, that is only for the profile drag of the section!
The induced drag is calculated by figuring out the Cl at which the wing is lifting. That's based on lift, airspeed and wing area. Then that gets plugged into another formula to calculate the induced drag coefficient, and that gets stuffed into yet another to get induced drag. It's not that bad.
It's late and I'll check the book tomorrow, but I'll bet wikipedia has a decent article if you just search on induced drag!
Dean
Igor Burger:
>>>If you are looking at the plots for an airfoil: the ones with Cl and Cd on them, that is only for the profile drag of the section! <<<
means infinit span or aspect ratio
limited span causes spanwise flowing and thus it will reduce the lift and enlarge the drag:
http://www.grc.nasa.gov/WWW/K-12/airplane/downwash.html
http://www.grc.nasa.gov/WWW/K-12/airplane/induced.html
the lift can be calculated also via AoA and so we something called induced AoA = - cl / (pi * AR)
or slope of lift polar is not theoretical 0.11 per 1 deg AoA as on infinite AR, but it is 0.11 * (AR/(AR+2))
Gary James:
--- Quote from: Alan Hahn on December 10, 2009, 06:22:53 PM ---Let me ask a dumb aerodynamics question (it was related to the drag issue on Igor's airfoil with flaps).
Does the coefficient of drag cd include induced drag?
--- End quote ---
Alan: That's a very GOOD question and one for which the answer isn't intuitively obvious. As best that I can explain it, SOME of the induced drag is included in those plots that you see, but on a real, 3D airplane there will be more than what you see on those plots. The plots that you see in "Theory of Wing Sections" and from computerized "wind tunnels" are supposed to represent 2 dimensional results as if the wing had infinite span.
The atmosphere can ONLY act in 2 ways on any wing surface, it can generate frictional forces and/or it can generate pressure forces. (we'll ignore the frictional forces for now). The pressure forces can ONLY act PERPENDICULAR to the surface AT THE POINT where they meet. So up near the nose of an airfoil the pressure vector is tilted a little bit forward due to the curvature of the section surface and aft of the max thickness point the pressure vector is tilted a little bit aft. Since you are a physicist, you will easily understand that the pressure vector can be resolved into two orthogonal components, one that is perpendicular to the X-axis (we'll call this lift) and the other along the Y-axis, either pointing a little bit forward or a little bit aft. We'll call that one "induced drag" since it is a force in the 'drag direction', "induced" by the production of lift. If we integrate all of these little pressure components along the X-axis we come up with the "induced drag" of the section.
NOW, if you change the angle of attack of the section, the magnitude of the pressure forces change, and also, since the chord line of the section is no longer along the X-axis you can see that the vector component of the pressure along the X-axis also increases. That is, some of the "lift" being produced is actually "tilted back" and is "dragging" the airplane backward. That's why you see the induced drag increasing as the angle of attack increases.
So, THAT part of the induced drag IS included in those 2D section plots that you see everywhere, BUT on a real, 3D airplane there is some more induced drag that comes about from the fact that real airplanes have a finite span as opposed to an "infinite" span in the 2D data. On a 3D airplane there will be drag corrections due to span-wise flow, and the energy lost in the tip vortex. On a low aspect ratio wing, it can be quite significant. THAT's why you see sailplanes with such high aspect ratios and elegantly shaped wing planforms.
So to make a long story short (too late...) Yes, the plots that you see include "most" of the induced drag, but on a real airplane the induced drag will be somewhat higher than what you see in the 2D plots.
If you remember that a "fluid" can ONLY act on a surface in two ways, friction parallel to the surface and pressure perpendicular to the surface, a lot of the aerodynamic "gobbledy gook" that we aero-types like to throw around will make a lot more sense. All those formulas are just an easy way to quantify and integrate those forces in different ways.
Douglas Ames:
--- Quote from: Gary James on December 10, 2009, 06:49:20 AM --- R%%%% Nope, I'm not costly at all anymore... my employer saw fit to declare bankruptcy, use the bankruptcy court system to cut my pay 40% and to freeze my retirement pension without providing any significant alternatives. We've had 7 suicides. Any you thought being an airline captain was glamorous. At least I have a job, even if it's not what I signed up for. R%%%%
--- End quote ---
Been there...I was a former Overhaul AMT for Eastern. Lost everything except my pride in the Strike of `89. We had 5 suicides plus hundreds of divorces nationwide. After waiting 5 yrs. I finally got my back pay and vac. - pennies on the dollar. After 30 yrs. I wonder why I never moved on to another career. Currently with A'A, at least I have a job...True.
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