I have this T-shirt that has a diagram of an airfoil and:
What part of…
F[sub]L[/sub] = (C[sub]L[/sub]Aρv[sup]2[/sup]) / 2
C[sub]L[/sub] = 2πsinθ
Don’t you understand?
I presume F[sub]L[/sub] is Lift, designated L in other equations.
C[sub]L[/sub] is the Lift coefficient
I presume A is Surface Area, designated A in other equations.
ρ is air density.
v is air velocity.
Looking online, I see this graphic that includes the equation:
L = C[sub]L[/sub] x S x (½ x ρ x v[sup]2**)
Since the ½ in that equation is within the parentheses, it does not apply to the C[sub]L[/sub] or the S. In the equation on the T-shirt, and other equations I see in search results, everything on the right side of the equation is divided by two (or multiplied by ½, if you prefer).
Which is correct?
Both equations you linked to are equivalent. Plug in some numbers and you’ll get the same result from both.
The parentheses in the graphic you linked to are superfluous - the equation would be the same without them. The 1/2 doesn’t apply to just the terms in the parentheses, it multiplies the entire equation, just like on your t-shirt.
You may be confusing the “distributive” property for addition, with multiplication.
a(b+c) = ab + ac
a(bc) = abc
If you are multiplying a sequence of numbers, as in the lift equation, the order and grouping of terms does not affect the result. Your second link probably includes the (1/2pv^2) term in parentheses because it was substituted in for another term in the derivation of the equation and the author wanted to make the derivation easy to follow, but as said, this is just for clarity and does not change the result. 1/2pv^2 is the kinetic energy density, and in the second equation, it is very clear that the lift force is the product of the coefficient of lift, surface area, and kinetic energy density.
Your t-shirt, on the other hand, just expresses the result directly, and the origin of the individual terms in the equation is less obvious.
For those of us who are more math-challenged, is it supposed to mean “take off”?
:smack:
Yeah, the parentheses fooled me. I’m used to only seeing parentheses when there is addition or subtraction, and I didn’t bother to put in some numbers to test it as I should have.
