# How Aeroplanes Fly: Deriving Equations for Lift Force

• billy92
In summary: It has emerged from experimentation. Still if you want to read some background about it, pick any basic level Fluid Mechanics book.
billy92
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.

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.

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

of course this only applies to thin airfoils

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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...

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 There is no lengthy derivation process behind this equation.

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## 1. How do aeroplanes stay in the air?

Aeroplanes stay in the air by generating lift force, which is a force that is perpendicular to the direction of motion. This lift force is created by the interaction between the wings of the plane and the air particles surrounding it.

## 2. What is the role of the wings in an aeroplane's flight?

The wings of an aeroplane are specifically designed to create lift force. This is achieved through the shape and angle of the wings, which allows air to flow over and under them, creating a difference in air pressure and therefore generating lift.

## 3. How is lift force calculated?

Lift force can be calculated using the equation: L = 1/2 * ρ * V^2 * A * CL, where ρ is the density of air, V is the velocity of the plane, A is the surface area of the wings, and CL is the coefficient of lift. This equation takes into account various factors such as air density, velocity, and wing shape.

## 4. What is the relationship between airspeed and lift force?

The relationship between airspeed and lift force is directly proportional. This means that as the speed of the plane increases, the lift force also increases. This is because as the plane moves faster, more air passes over and under the wings, resulting in a greater difference in air pressure and therefore more lift.

## 5. How does the angle of attack affect lift force?

The angle of attack is the angle between the wings and the direction of motion of the plane. As the angle of attack increases, so does the lift force. However, if the angle becomes too high, the airflow over the wings can become disrupted, resulting in a decrease in lift force and potential loss of control of the plane.

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