Need help understanding a lift coefficient formula

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Discussion Overview

The discussion revolves around understanding the lift coefficient formula, particularly the meaning of "relevant plan area" as it appears in the equation. Participants explore its implications in the context of aerodynamics, specifically relating to airfoils and aircraft design.

Discussion Character

  • Technical explanation
  • Conceptual clarification
  • Debate/contested

Main Points Raised

  • One participant questions the definition of "relevant plan area," suggesting it might refer to the surface area of the airfoil but expressing confusion due to its placement in the denominator of the formula.
  • Another participant states that "relevant area" is considered the wing area for profiles and the frontal area for vehicles.
  • A participant notes that increasing the area required to generate a given amount of lift results in a lower lift coefficient, aligning with the formula's structure.
  • It is proposed that "relevant plan area" includes the wing area and additional areas of the aircraft that contribute to lift, such as the fuselage and other aerodynamic features.
  • One participant mentions the existence of separate lift coefficients for the wing and the entire airplane, indicating that the total lift coefficient may be lower due to the influence of the horizontal stabilizer.
  • Several participants express technical difficulties with LaTeX formatting in the discussion.
  • A participant questions the units of the lift coefficient, initially suggesting it might be in meters/second², but later finds a definition stating it is dimensionless.

Areas of Agreement / Disagreement

Participants express differing views on the definition and implications of "relevant plan area" and the units of the lift coefficient. There is no consensus on these points, and the discussion remains unresolved.

Contextual Notes

Participants highlight the complexity of defining "relevant plan area" and its dependence on specific aircraft configurations. The discussion also reveals uncertainty regarding the dimensionality of the lift coefficient.

5P@N
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Please go to this Wikipedia article on Lift Coefficients, and behold the first formula. The last part of the equation has a "S" which is supposed to stand for "relevant plan area". Now, there was no explanation of what this "relevant plan area" is or means. I was guessing that it means the surface area of the airfoil, but this cannot be so, because as "S" is in the denominator of the formula, thus as the surface area increases, there is a diminished lift coefficient, and hence a diminished lift power (so my reasoning goes). I would write down the formula here, but for some reason Latex isn't working.

So: what is the "relevant plan area" referred to?
 
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"As relevant area is considered the wing area on profiles and the front area on vehicles."
 
For a given amount of lift, if you increase the area required to generate it the lift coefficient goes down. That's precisely what is written in the article with S in the denominator.
 
Relevant plan area refers to the area that significantly contributes to lift. On a normal airplane, S would just be wing area plus the area of the fuselage between the wing roots. But it also let's the formula apply to lifting bodies, airplanes with wide fuselages, chines, strakes, lifting stabilizer, etc.
 
It does. Thanks spamanon.
 
There is a lift coefficient for the wing, and a lift coefficient for the whole airplane (a.k.a. total lift coefficient). Total CL will be less than wing CL when the horizontal stabilizer generates a down force.
 
is anyone else having trouble with Latex? For some reason I don't have it anymore.
 
is a lift coefficient in units of meters/second^2?

Anyone?

I had performed a calculation of lifting force, and in order to be in Newtons, the lift coefficient would need to have these units...
 
  • #10
5P@N said:
is a lift coefficient in units of meters/second^2?

Anyone?

I had performed a calculation of lifting force, and in order to be in Newtons, the lift coefficient would need to have these units...
The definition I found is dimensionless.
 

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