# Need help understanding a lift coefficient formula

## Main Question or Discussion Point

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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fresh_42
Mentor
"As relevant area is considered the wing area on profiles and the front area on vehicles."

Gold Member
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 lets the formula apply to lifting bodies, airplanes with wide fuselages, chines, strakes, lifting stabilizer, etc.

See if this image helps.

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...

fresh_42
Mentor
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.