Lift theories

Hello everyone!

In my previous post, I talked about the basics of flight. I talked briefly about the forces acting on the aircraft and their origins. Well, this post highlights the most important force on the aircraft : Lift.

So, Lift as defined by Dictionary.com says:

Lift (verb): to move or bring (something) upward from the ground or other support to a higher position; hoist.

The lift force that a wing magically produces is just that. In essence, it is the driving force of the plane, allowing it to stay afloat despite of its weight. This implies that the lift must exceed the weight of the plane. The ratio of the aircraft lift to its weight is called the safety factor.

FORCES
Forces on an aircraft

But, how exactly does the wing produce lift? Well, there are a lot of theories as to how this happens and there is still no single definite theory to explain lift generation. The most popular theories include the Bernoulli’s Theory and the Newtonian Theory. Both these theories are concerned with the law of conservation of energy.

The Bernoulli Theory

The Bernoulli Theory is a bit wacky to understand. To understand it, we must first understand Bernoulli’s law of flow over surfaces. This law states that within an inviscid fluid stream, the total energy carried by a particle remains the same; it only changes in the form it is carried in.The forms of energy are Kinetic energy, Pressure Energy and The Potential energy. Every particle possesses all three forms of energy at any point of time, but, their magnitudes vary according to the flow path.

That being said, lets proceed to the explanation of Lift by this theory.

So, consider an airfoil. For the sake of explanation, consider a cambered (or curved) airfoil. This kind of airfoil has an inherently longer upper surface than the lower surface. So, when fluid flows over the upper and lower surfaces, there is a difference in velocity locally in between particles. This difference in velocity brings about a change in pressure as well, since the two are interlinked. The change in pressure is such that the faster flow on the upper surface causes a lower pressure over the upper surface. The opposite happens at the lower surface and a higher pressure is generated below. This difference in pressure causes the formation of a force which pushes the airfoil upwards, lifting it.

The problem with this theory is that this does not account for the generation of lift by a symmetric airfoil having the same length at the top and the bottom of the airfoil. The underlying assumption being that the difference in velocity of the flow stream is the only factor which induces the lift force.

Newton’s Theory of Lift

Sir Isaac Newton stated the three fundamental laws of motion in Philosophiæ Naturalis Principia Mathematica (Mathematical Principles of Natural Philosophy), published in 1687.The First Law states that a body stays in its state of rest or motion until and unless an external force acts upon it. The Second Law states that the rate of change of momentum of a body is directly proportional to the disturbing force applied. The third law of motion is commonly known as “every action has an equal and opposite reaction“. These laws can be used together to explain the generation of lift as stated below.

When an incoming airstream comes in contact with an airfoil, some parameter of the stream must be changed in order to obtain a lifting force which is basically Work. The second law implies that a change in momentum must occur with application of a force. This change in momentum is the difference in the relative velocity of the airfoil and the airstream.

NLT

Let us consider an example to illustrate this explanation. Consider an airfoil at an angle to the airstream (known as the angle of attack). The airstream hits the lower side and due to the shape of the airfoil, it is deflected downwards. This downward deflection of the airstream causes an equal and opposite force on the airfoil, which is nothing but the lift generated. This is in accordance with the 3rd Law.

The only fallacy of this theory is that it relies on the explanation of lift by the deflection of the airstream by the lower surface only. This theory fails to explain the landing behaviour of any commercial aircraft. All commercial airplanes use the control surface known as the spoiler during landing to reduce the lift. The spoiler deflects air and is located on the upper surface of the wing.

DSCF0645.JPG
Spoilers employed during Landing

Conclusion

To conclude, I would summarize by saying that both Bernoulli’s Theory and Newton’s theory explain lift correctly in their own right. However, both theories have their own fallacies which can be proven in practical situations. I personally feel that Lift generated in an aircraft is the result of both these effects. What’s even more amazing to me is that both the theories described were not even formulated by either Newton or Bernoulli with the intention of describing lift generation.

On this note, I’ll end it for today. Hope this was educational!

Until Next Time! 🙂

References and further reading:

  1. http://www.aviation-history.com/theory/lift.htm
  2. https://www.youtube.com/watch?v=aFO4PBolwFg
  3. http://www.grc.nasa.gov/WWW/K-12/airplane/bernnew.html
  4. https://en.wikipedia.org/wiki/Bernoulli%27s_principle

 

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