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Old Mar 16, 2008, 10:14 AM
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Drag Polar

Hi Guys,

Could anyone tell me how to calculate the Drag Polar?

Is it:

1/(pi x A x e)

Where A = Aspect Ratio
e = Oswald Efficiency Factor
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Old Mar 16, 2008, 10:51 AM
greg
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is this the L/D plot of an aircraft obtained from the total drag of the aircraft (airfoils and body, parasitic and induced) versus lift and hence airspeed, or simply the Cl vs Cd curve for a particular airfoil? doesn't the former quite a lot of information about the aircraft and some experimental/guessimated data, and the later require wind tunnel data?
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Old Mar 21, 2008, 10:51 AM
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sligo565,

A drag polar generally refers to a plot of aircraft lift (vertical axis) versus drag (horizontal axis). The equation that you have written is part of the induced drag (drag due to lift), but it is incomplete. The induced drag is your equation, typically called k, times the lift coefficient squared.

To compute the full drag polar, you need need to take into account all components of drag, primarily parasitic drag (form drag plus skin friction and interference) plus induced drag (drag due to lift), as well as have a good understanding of the lift curve of the design, which takes into account the 3d effects of a finite span on the slope of the lift curve, along with other factors.

There are some decent websites available that can help you develop a first order model of your design, which will estimate the items above based on the geometry of your design.

Hope that helps.

Rich
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Old Mar 21, 2008, 10:58 AM
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Hey,

I used the software JAVAFOIL to produce the following graph and numbers..do i just measure off the graph at the area of zero Lift? It's just that its giving me a very high number of 0.07....can i just use the equation:

CD = CDmin + (CL - CLmindrag)^2/pi e A

To find my Drag Coefficient instead of using this such high number of CDo?!
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Old Mar 21, 2008, 11:02 AM
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Here is also a drawing of my conceptual design....its design is much like a sailplane....does anyone know an estimation of CDo of a sailplane that i could use?
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Old Mar 21, 2008, 03:16 PM
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Quote:
Originally Posted by sligo565
Hey,

I used the software JAVAFOIL to produce the following graph and numbers..do i just measure off the graph at the area of zero Lift? It's just that its giving me a very high number of 0.07....can i just use the equation:

CD = CDmin + (CL - CLmindrag)^2/pi e A

To find my Drag Coefficient instead of using this such high number of CDo?!
Yes that is the equation that you want to use. When the lift curve runs through zero lift at zero alpha, the equation reduces to the common parabolic form CD = CD0 + kCL^2. However, when the lift curve does not run through zero lift at zero alpha, which is almost always the case, you will use the full equation as you have written it. One note is that you may find the terms CD_min and CD0 interchanged, with both intended to mean minimum CD on the polar, but the CD_min terminology is the correct one.

Rich
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Old Dec 10, 2012, 11:26 AM
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I am trying to work out the drag polar of the Citation X, I have the following data. what I am confused about is that I when I wanted to work the Cd = Cd0 + KCl*2, I dont know the Cd0 and K , can someone please help me out with this. How do I find the Value of Cd0 and K>
MANY THANKS

CL=2L/(ρ V^2*S)
ρ=1.2252kg/m^3
V=146m^2
S = 50m^2
basic operating weight = 10189kg
Max payload = 5865kg
Max Fuel = 11330kg
W_max=27384kg
Cl= mg/(1⁄2ρ V^2 S)
Cl=27384/(0.5*1.2252〖146〗^2*50)=0.4114463227

Drag = CD 1⁄2 ρV^1 S

CD= CD0+K〖CLČ〗
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Old Dec 13, 2012, 10:50 AM
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Quote:
Originally Posted by Abbz View Post
I am trying to work out the drag polar of the Citation X, I have the following data. what I am confused about is that I when I wanted to work the Cd = Cd0 + KCl*2, I dont know the Cd0 and K , can someone please help me out with this. How do I find the Value of Cd0 and K>
MANY THANKS

CL=2L/(ρ V^2*S)
ρ=1.2252kg/m^3
V=146m^2
S = 50m^2
basic operating weight = 10189kg
Max payload = 5865kg
Max Fuel = 11330kg
W_max=27384kg
Cl= mg/(1⁄2ρ V^2 S)
Cl=27384/(0.5*1.2252〖146〗^2*50)=0.4114463227

Drag = CD 1⁄2 ρV^1 S

CD= CD0+K〖CLČ〗
That equation is an approximation and the parameters CD0 and K would have to come from wind tunnel or CFD data.
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Old Dec 18, 2012, 12:10 PM
Pilot Mike
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Joined Oct 2009
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I would suggest you use a program such as xfoil or avl to compute that. There are many things going on in that design that the simple equations you are using have trouble modeling. Even just a simplified planform in AVL will give you better accuracy and if you spend enough time building your model in AVL you can learn other interesting things about your design such as stability and trim states. Another program which might be nicer to a novice is XFLR5, its basically the same as AVL and xfoil but offers a GUI instead of a terminal based UI.

http://www.xflr5.com/xflr5.htm
http://web.mit.edu/drela/Public/web/xfoil/
http://web.mit.edu/drela/Public/web/avl/
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Last edited by Lost Oracle; Dec 18, 2012 at 12:14 PM. Reason: Links to programs
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