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Aerodynamics: The Theory of Lift

Claire Miller is an Aerospace Engineering student and casual writer. She writes about mental health issues on her blog: I Bit The Piranha.

In about 1779, Englishman George Cayley discovered and identified the four forces which act on a heavier-than-air flying vehicle: lift, drag, weight, and thrust - thus revolutionising the pursuit for human flight. Since then, understanding the aerodynamics that makes flight possible has come a long way, making travelling to different countries faster and easier, and even allowing exploration beyond Earth as well.

However, that does not mean that these four forces were completely understood as soon as they were identified. There have been a number of different theories of how lift works, many of which are now known to be incorrect. Unfortunately the most used incorrect theories are still featured in encyclopedias and educational websites, leaving students feeling confused amongst all of this conflicting information.

In this article, we will explore three main theories of lift that are incorrect, and then explain the correct theory of lift using Bernoulli's principle and Newton's Third Law of Motion.

Bernoulli's Equation

Bernoulli's equation - sometimes known as Bernoulli's principle - states that an increase in the velocity of a fluid occurs simultaneously with a decrease in pressure due to the conservation of energy. The principle is named after Daniel Bernoulli, who published this equation in his book Hydrodynamica in 1738:

aerodynamics-the-theory-of-lift

where P is pressure, ρ is density, v is velocity, g is acceleration due to gravity, and h is the height or altitude.

Newton's Third Law

Newton's Third Law of Motion, on the other hand, focuses on forces, and states that every force has an equal and opposite reaction force. The two theories complement one another, however, due to assumptions and misunderstandings as to the nature of how these principles work, a divide between supporters of Bernoulli and Newton's laws was realised.


Here are three of the main theories of lift that are now known to be incorrect.

"Equal Transit" theory

"Equal Transit" theory, also known as the "Longer Path" theory, states that because aerofoils are shaped with the upper surface longer than the bottom, air molecules that pass over the top of the aerofoil have further to travel than underneath. The theory states that the air molecules have to reach the trailing edge at the same time, and in order to do that the molecules going over the top of the wing must travel faster than the molecules moving under the wing. Because the upper flow is faster, the pressure is lower, as known by Bernoulli's equation, and thus the difference in pressure across the aerofoil produces the lift.

Figure 1 - "Equal Transit" Theory (NASA, 2015)

Figure 1 - "Equal Transit" Theory (NASA, 2015)

While the Bernoulli's equation is correct, the problem with this theory is the assumption that the air molecules have to meet the trailing edge of the wing at the same time - something that has been disproven by experimentation since. It also does not consider symmetrical aerofoils that do not have a camber and yet are still able to produce lift.

"Skipping Stone" theory

The "Skipping Stone" theory is based on the idea of air molecules hitting the underside of a wing as it moves through the air, and that lift is the reaction force of the impact. This theory completely overlooks the air molecules above the wing and makes the big assumption that it is only the underside of the wing that produces the lift, an idea that is known to be extremely inaccurate.

Figure 2 - "Skipping Stone" Theory (NASA, 2015)

Figure 2 - "Skipping Stone" Theory (NASA, 2015)

"Venturi" theory

The "Venturi" theory is based on the idea that the shape of the aerofoil acts like a Venturi nozzle, which accelerates the flow over the top of the wing. Bernoulli's equation states that a higher velocity produces a lower pressure, so the low pressure over the upper surface of the aerofoil produces the lift.

Figure 3 - "Venturi" Theory (NASA, 2015)

Figure 3 - "Venturi" Theory (NASA, 2015)

The main problem with this theory is that the aerofoil does not act like a Venturi nozzle since there is not another surface to complete the nozzle; the air molecules are not restricted as they would be in a nozzle. It also neglects the bottom surface of the wing, suggesting that enough lift will be produced regardless of the shape of the lower section of the aerofoil. This, of course, is not the case.

Correct Theories of Lift: Bernoulli and Newton

The incorrect theories all try to apply either Bernoulli's principle or Newton's Third Law, however they make errors and assumptions that do not correspond with the nature of aerodynamics.


Bernoulli's equation explains that due to the fact that air molecules are not closely bound together, they are able to flow and move freely around an object. Since the molecules themselves have a velocity associated with them, and the velocity can change depending on where the molecules are with respect to the object, the pressure changes as well.

Figure 4 - Bernoulli's Principle (Learn Engineering, 2016)

Figure 4 - Bernoulli's Principle (Learn Engineering, 2016)

The air molecules closest to the top surface of the aerofoil are kept close to the surface due to there being higher pressure at the top of the particles as opposed to the bottom of them, supplying the centrifugal force. The high pressure above the particles pushes them towards the aerofoil, which is why they stay attached to the curved surface instead of continuing on a straight path. This is known as the Coanda effect, and acts on the airflow on the lower surface of the aerofoil in the same way. The curved deflection of the air molecules creates a low pressure above the aerofoil and a high pressure below the aerofoil, and this difference in pressure generates the lift.

Figure 5 - Newton's Third Law of Motion (Learn Engineering, 2016)

Figure 5 - Newton's Third Law of Motion (Learn Engineering, 2016)

This can also be explained more simply using Newton's Third Law of Motion. Newton's Third Law states that every force has an equal and opposite reaction force. In the case of an aerofoil, the air flow is being forced downwards by the Coanda effect, deflecting the flow. So the air molecules should be pushing the aerofoil in the opposite direction with equal magnitude, and that reaction force is lift.

By fully understanding both Bernoulli's Principle and Newton's Third Law can we stop being mislead by older and incorrect theories of how lift is generated.

© 2017 Claire Miller

Comments

Patrick Fischer on October 27, 2019:

Have a look at https://www.youtube.com/watch?v=QKCK4lJLQHU. at 20:15

Here is a highly distinguished engineer dismissing the Coanda effect!

You can also watch https://www.youtube.com/watch?v=aa2kBZAoXg0 at 18:44. Again Coanda effect is stated at not relevant.

solo dolo on April 22, 2019:

this is very solo dolo fresh

nate higgers on April 22, 2019:

thankyou very much this is very cool

David White on March 30, 2019:

If you look at the bottom of the top wing of a canvas covered biplane in level cruising flight , it will be bulged out , as the top of the bottom wing is also . Since this indicates that BOTH surfaces are below ambient static pressure, then Bernoulli lift must be responsible—with the top of the wing still being below the pressure of the bottom of the wing.

No reaction force or ‘ skipping stone theory ‘ is necessary, surely , in this case . I suspect that this is true for most light aircraft in this flight attitude.

wbert on November 30, 2018:

Hello Claire,

I was doing some experiments on aerodynamics on aircraft wings. Your article above is good to explain what is wrong with the first explanations. During my research the main problem with most theory is the static and dynamic. The air is static, and the wing is dynamic, there is not much difference. Whether the high camber on the top of the wing or the surfing effect of the high speed wing the lift is derived from airflow separation just aft of the peak of the camber, or the symmetrical wing angle of attack. This is also apparent in the reason a long wing with a short cord can fly so easily. The Delta wing has the same principle.

The actual cause of this is due to air molecules are attracted to earth by gravity but repel each other this is why air gets thinner with altitude. When the wing disturbs this equilibrium the molecules above push down which causes the low pressure area just aft of the camber. By the same principle the molecules below the wing are forced to compress and push back at the wing. Both principles work together to create lift. I am interested in your opinion to this observation and explanation.

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