Drag Coefficient -- What is the constant K?

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The drag coefficient (CD) is initially represented as CD=CD0+CL/πAe, assuming a linear relationship with lift (CL) for small flight conditions. A new formula introduced by the professor, CD=CD0+k1CL+k2CL^2, incorporates constants k1 and k2, allowing for a more accurate representation of CD over a broader range of flight conditions where the relationship begins to curve. The constant K reflects the induced drag due to lift, which is influenced by factors like pressure differences and downwash around the wing. Estimating k1 and k2 is essential for accurate modeling, though it complicates the analysis due to nonlinearity. Understanding these constants is crucial for analyzing drag in various flight scenarios.
eliasss
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TL;DR
What is the constant K in the drag coefficient?
As I understand, the drag coefficient looks as follows:

CD=CD0+CL/πAe

however, the professor threw in a new constant, K, and I am having trouble understanding what this means. The formula now looks like this:

CD=CD0+k1CL+k2CL^2

could someone help? Thanks!
 
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Maybe one is the induced drag, that is due to air moving around the end of the wing.
Induced drag is proportional to lift, not to the square of the airspeed.
 
eliasss said:
TL;DR Summary: What is the constant K in the drag coefficient?

As I understand, the drag coefficient looks as follows:

CD=CD0+CL/πAe
This assumes that CD is a linear function of CL, which is an ok assumption as long as you are linearizing in a small region of flight condition.
There are good reasons to analyze stability and control in small flight condition regions using linearized equations.
eliasss said:
however, the professor threw in a new constant, K, and I am having trouble understanding what this means. The formula now looks like this:

CD=CD0+k1CL+k2CL^2
This models CD as a function of CL and CL^2. It allows more accuracy for a larger region of flight condition where the relationship between CD and CL has begun to curve. The parameters, k1 and k2 need to be estimated. k1 is probably very close to ##1/(\pi A e)##. But a lot of analysis gets much more difficult when the equations are nonlinear.
CORRECTION: There is no reason to think that k1 is close to ##1/(\pi A e)##. I was thinking that it was a Taylor series expansion around the linearization point.
 
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