# How do aeroplanes fly

I am currently looking into how aeroplanes fly for a report which i am writing.

I understand the theory behind the lift force produced by different pressures above and below the wing. However, i need to use equations which i can show how to derive in the report.

I have found the following equation $\frac{1}{2}ρv^{2}AC_{L}$ but i am not sure how to derive this equation.

Thanks

There is no lengthy derivation process behind this equation. It has emerged from experimentation. Still if you want to read some background about it, pick any basic level Fluid Mechanics book.

are you sure it's experimentation?
I thought it was using a tiny volume of air (dV), and having it travel above/below the wing at constant pressure?
but yah, look at the first or second (since the first usually deals with units, SI, and stuff like that) chapter of your fluid dynamics book (or the 12th(ish) chapter of a good introductory physics book)

The problem is each place i look has different answers to my problem which is making it difficult for me to find out if any lift equations for planes are derived, or just calculated experimentally.

The equation was found using experimentation, finding the variables of a system that impact the lift and drag forces the most, and using dimensional analysis (basically it's mixing up variables with SI units that are known that eventually all cancel out to give you a term with no units, or a constant value). In this case, the coefficient of lift, CL, is the dimensionless term. The 1/2 was kind of a 'fudge factor' that made the dimensional analysis match up with the experimentation, from what I understand.

This is what I've understood from my Fluid Mechanics course. I, of course, am willing to concede if I have misrepresented the origin of the equation.

russ_watters
Mentor
The first part is just kinetic energy of air, which can be derived relatively easily. But lift coefficient can only be derived with extreme difficulty.

Gold Member
The problem is that there is no general, analytical solution for the lift on a given airfoil. The equation incorporating the lift coefficient is an empirical relation that uses the lift coefficient, $C_L$, to simplify the math, but finding that coefficient is something that often has to be done experimentally. In the situations where it can be done analytically, it would be just as easy to calculate the lift directly.

$C_L$ itself is a complicated quantity, as it depends often on the flow velocity, the angle of attack, the density of the air and the shape of the airfoil.

Thin airfoil theory can give you analytical results:
http://www.desktop.aero/appliedaero/airfoils1/tatderivation.html [Broken]

of course this only applies to thin airfoils

Last edited by a moderator:
jhae2.718
Gold Member
Introduction to Flight by Anderson is a good introductory text.

about the topic, which is a good share .thanks!

for thick airfoils, its about naca computations....

bigfooted
Gold Member
for thick airfoils, its about naca computations....
... for which you have Abbott and von Doenhoff's 'theory of wing sections'.

http://www.infoocean.info/avatar2.jpg [Broken]There is no lengthy derivation process behind this equation.

Last edited by a moderator: