# 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

## 2 Answers

The definition of the coefficients differs between countries/regions. The factor ½ is used in most of Europe and in Russia, because it is part of the dynamic pressure equation. In the USA the 2 is incorporated in the coefficient.

• Not contradicting anybody, just note the(1/2) factor in the lift force comes directly from Bernoulli equation Jun 19 '19 at 11:37

The total aerodynamic force acting on a body is usually thought of as having two components, lift and drag.

By definition, the component of force parallel to the oncoming flow is called drag

and the component perpendicular to the oncoming flow is called lift

It is convenient to express the induced drag as an expression having similarities with that of the lift, thus by taking the ratio of lift to drag the « 2 multiplier » disappears, but considering solely the lift coefficient the expression you are giving is correct.