# When rearranging the lift force equation to solve for lift coefficient instead of lift force, why is the numerator often given as F not 2F?

the standard description of the Lift force affecting the lift surface is:

$$F={\dfrac{1}{2}}\rho v^{2} SC_{L}$$ the basic rearrangement gives the following definition of the lift coefficient: $$C_{L}={\dfrac{2F}{\rho v^{2}S}}$$

why is the above expression met so rarely? with the standard skipping the 2 multiplier? $$C_{L}={\dfrac{F}{\rho v^{2}S}}$$

I've checked 30 scientific papers, those measuring the lift\drag coefficients.

• 28 papers have had F
• 2 papers have had 2F
• Could it be related to some assumptions about S, say S in one case is for one wing and in the other case, for the total wingspan ? It really depends on the context. But to me there should definitely be a 2 factor Apr 29 '18 at 16:00
• Are you sure that there’s no 0.5 in the denominator ? Can you give a reference to confirm? Apr 29 '18 at 18:16