# Force components acting on an airfoil

## Summary:

Are these formulas for lift and drag correct ?

## Main Question or Discussion Point

Hi,

I have a simple question but I want to be 100% sure that my reasoning is correct. Take a look at this picture showing forces acting on an airfoil:

Green forces (X and Y components) are known from CFD software but I need the values of blue components (lift and drag). Of course for zero angle of attack they will be equal to each other but I need formulas for nonzero angle. In the literature I've found the following equation for lift: $$F_{L}=F_{X} \sin{\alpha} - F_{Y} \cos{\alpha}$$ From this I figured out the formula for drag: $$F_{D}=F_{X} \cos{\alpha} + F_{Y} \sin{\alpha}$$ Are these equations correct ? If not then how they should look like ?

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Y axis should be inverted in diagram above for equation you provide to be correct.

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It's always the part that one is most confident about that turns out to be wrong. So be careful of any "of course" statements. :>)

Thanks for reply. Is the first formula (for lift) correct and second one (for drag) wrong ? Could you tell me what should be changed ? Only sign so that it becomes $F_{D}=F_{X} \cos{\alpha}- F_{Y} \sin{\alpha}$ ?

FactChecker
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Either change your diagram or change every sign of $F_Y$ in your equations.

PS. Always test the cases of $\alpha=0$ and $\alpha=90$ to make sure that your sign convention is correct.

So, just to make sure, for the diagram I attached to my first post the correct formulas are: $F_{L}=F_{X} \sin{\alpha}+ F_{Y} \cos{\alpha}$ and $F_{D}=F_{X} \cos{\alpha}- F_{Y} \sin{\alpha}$, right ?

FactChecker
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Looks good to me.

Thank you very much. Apparently there was an error in the article where I’ve found the first formula which confused me and I couldn’t figure out how to derive it.

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