Drag Coefficient -- What is the constant K?

[eliasss]

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

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!

 

[Baluncore]

Welcome to PF.

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.

 

[FactChecker]

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.

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.

 

[harsh_raj]

Pressure difference across wing surface causes spillage around the wing tips. Downwash causes a local induced angle of attack with additional induced drag on a finite wing. K is a constant that shows how much of drag is induced due to lift.

This calculator may be helpul in calculating K
https://www.calculatoratoz.com/en/coefficient-of-drag-due-to-lift-calculator/Calc-5336

Hope it helps!!
Thanks