Drag Coefficient -- What is the constant K?

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SUMMARY

The drag coefficient (CD) is modeled as CD=CD0+k1CL+k2CL^2, where K represents the induced drag due to lift (CL) and is crucial for accurate modeling in varying flight conditions. The introduction of K allows for a nonlinear relationship between CD and CL, enhancing precision beyond small linearized regions. Parameters k1 and k2 must be estimated, with k1 potentially related to the induced drag coefficient, but this requires careful analysis due to the complexities of nonlinear equations. A calculator for estimating K is available at Calculatoratoz.

PREREQUISITES
  • Understanding of drag coefficients in aerodynamics
  • Familiarity with lift coefficients (CL)
  • Knowledge of nonlinear equations and their implications in flight dynamics
  • Basic proficiency in using online calculators for aerodynamic calculations
NEXT STEPS
  • Research the derivation and implications of the drag coefficient formula CD=CD0+k1CL+k2CL^2
  • Explore the concept of induced drag and its relationship with lift in finite wings
  • Learn about Taylor series expansions in the context of aerodynamics
  • Utilize the drag coefficient calculator at Calculatoratoz to practice estimating K
USEFUL FOR

Aerodynamics students, aerospace engineers, and researchers focusing on flight dynamics and drag modeling will benefit from this discussion.

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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