Drag Coefficient -- What is the constant K?

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Discussion Overview

The discussion centers around the drag coefficient in aerodynamics, specifically the introduction of a new constant, K, in the drag coefficient formula. Participants explore the implications of this constant on the relationship between drag and lift, as well as the mathematical modeling of these relationships in various flight conditions.

Discussion Character

  • Technical explanation
  • Conceptual clarification
  • Debate/contested

Main Points Raised

  • One participant presents a formula for the drag coefficient, CD, and expresses confusion about the new constant K introduced by their professor.
  • Another participant suggests that K may relate to induced drag, which is proportional to lift and not to the square of airspeed.
  • A participant explains that the new formula models CD as a function of CL and CL^2, allowing for greater accuracy in a larger range of flight conditions, while noting that k1 is likely close to ##1/(\pi A e)##, though this assertion is later corrected.
  • Another participant describes K as a constant indicating the amount of drag induced due to lift and provides a link to a calculator for estimating K.

Areas of Agreement / Disagreement

Participants express differing views on the interpretation of the constant K and its implications for the drag coefficient. There is no consensus on the exact nature or value of K, and the discussion remains unresolved regarding its precise role in the drag coefficient formula.

Contextual Notes

Some participants note that the relationship between CD and CL may become nonlinear in certain flight conditions, complicating the analysis. There is also a correction regarding the assumption about k1 being close to ##1/(\pi A e)##, indicating that further clarification is needed on this point.

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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