# The right reason for lift force on an aerofoil

## Main Question or Discussion Point

On the internet, I found two different explanations for lift force.
In one of the explanations, bernoullis equation was applied between the stream flowing under and the stream above the aerofoil(the stream above moves faster and so less pressure than the lower).
The other explanation says Bernoulis principle cannont be applied between two different streams.This explanation says that the curved path is the reason(for any mass to move along a curved path, centripetal acceleration is needed).The centripetal acceleration is given to the stream by the pressure difference (less pressure on the inside of the curve than on the outside).In this case only one of the two sides of the foil(either above or below) was analysed at a time.
Which among these would be the right explanation for lift?

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stockzahn
Homework Helper
Gold Member
I think the most comprensible explanation for the lift of an airfoil is Newton's second and third law. The air streaming along the foil is "pushed downwards" at the rear edge, which means a (downward) force must have acted on it - the (upward) reaction force lifts the airplane (or whatever).

However, the basic statement of your firstly mentioned theory is correct too. The pressure at the upside of the foil is lower than on the downside - summing up all this pressure forces must yield the same result like with the Newton-approach. The same applies for the information given by the second explanation: At curved stream lines the outside pressure is higher than the pressure at the inside. But I don't exactly see how these two statements are mutually contradictory.

I think both of the explanations are more or less correct (but neither complete nor satisfying) and you need the information of the latter to find (or understand) the pressure distribution around the foil stated by the first.

tech99
Gold Member
I think the most comprensible explanation for the lift of an airfoil is Newton's second and third law. The air streaming along the foil is "pushed downwards" at the rear edge, which means a (downward) force must have acted on it - the (upward) reaction force lifts the airplane (or whatever).
I think both of the explanations are more or less correct (but neither complete nor satisfying) and you need the information of the latter to find (or understand) the pressure distribution around the foil stated by the first.
I think the modern view is that the airstream is directed in a new direction, like a jet engine pointing slightly down, but it seems compatible with your explanation.

russ_watters
Mentor
The other explanation says Bernoulis principle cannont be applied between two different streams....

Which among these would be the right explanation for lift?
Unfortunately, people like to argue a lot on the internet, so they take the posture that if my explanation is correct, any other explanation must be wrong. But that isn't how it works.

Both explanations (if explained correctly) are correct: the Newton's 3rd Law explanation does not include a criticism of the Bernoulli explanation, but if someone is arguing that first point, they are wrong....

...that first point doesn't even make sense, and isn't how Bernoulli's principle is applied. The baseline velocity and pressure is free stream. The pressure and velocity on the surfaces of the wing get compared with that, and then each other. Of course air doesn't flow between the top and bottom surface to create the pressure difference! (insert caveat about 3d flow)

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• Mohankpvk
Unfortunately, people like to argue a lot on the internet, so they take the posture that if my explanation is correct, any other explanation must be wrong. But that isn't how it works.

Both explanations (if explained correctly) are correct: the Newton's 3rd Law explanation does not include a criticism of the Bernoulli explanation, but if someone is arguing that first point, they are wrong....

...that first point doesn't even make sense, and isn't how Bernoulli's principle is applied. The baseline velocity and pressure is free stream. The pressure and velocity on the surfaces of the wing get compared with that, and then each other. Of course air doesn't flow between the top and bottom surface to create the pressure difference! (insert caveat about 3d flow)
Nice answer.So initially the fluid along top surface of the aerofoil should be compared with the free stream.Then the stream along the bottom surface of the aerofoil should be compared with the free stream seperately.Then the effect on the top and bottom surfaces should be combined
Is there any book or other sources where I could find a derivation for the expression of lift force by this method?

I think the most comprensible explanation for the lift of an airfoil is Newton's second and third law. The air streaming along the foil is "pushed downwards" at the rear edge, which means a (downward) force must have acted on it - the (upward) reaction force lifts the airplane (or whatever).

However, the basic statement of your firstly mentioned theory is correct too. The pressure at the upside of the foil is lower than on the downside - summing up all this pressure forces must yield the same result like with the Newton-approach. The same applies for the information given by the second explanation: At curved stream lines the outside pressure is higher than the pressure at the inside. But I don't exactly see how these two statements are mutually contradictory.

I think both of the explanations are more or less correct (but neither complete nor satisfying) and you need the information of the latter to find (or understand) the pressure distribution around the foil stated by the first.

rcgldr
Homework Helper
The other explanation says Bernoulli principle cannot be applied between two different streams.
Bernoulli principle is applied separately for each stream, one above and one below a wing. The calculations are based on the streams just outside of the boundary layers above and below a wing. However, it's possible that this was a statement made using the air as a frame of reference as opposed to using the wing as a frame of reference. Normally the wing is used as a frame of reference, with the wing diverting (curving) the relative flow downwards. If the air is used as a frame of reference, which is common in the case of propellers, then Bernoulli is violated as the air flows downwards through the "plane" of air swept out by a wing, flowing downwards from the stream above to the stream below (this could explain the "two different streams" statement), where there is an increase in pressure corresponding to the work performed by a wing, resulting in a non-zero "exit velocity" (the velocity of the affected air when it's pressure returns to ambient) of air that is mostly downwards (lift) and somewhat forwards (drag). Nasa has a simplified description of this:

https://www.grc.nasa.gov/WWW/K-12/airplane/propanl.html

This type of analysis is not normally used for a wing, and instead the wing is used as a frame of reference.

As already mentioned, a wing produces lift by curving the relative flow downwards, "pulling" the air downwards from above the wing, and "pushing" the air downwards below the wing, resulting in curved flow. There is a pressure gradient nearly perpendicular to the surfaces of the wings, greater on the outside of curved flow, lesser on the inside of curved flow, and those pressure differences also affect the flow nearly parallel to the surface of the wings, in accordance with Bernoulli principle, and some mathematical models do "flow field" calculations to calculate the coexistent flow speeds and pressures just outside the boundary layers on the upper and lower surfaces of a wing, in order to calculate lift. Drag calculations are more complex.

• Mohankpvk
russ_watters
Mentor
Is there any book or other resource where I could find a derivation for the expression of lift force by this method?
I believe this is still the gold standard introductory book for aero engineering:
https://www.amazon.com/dp/0078027675/?tag=pfamazon01-20

Most of the concepts are accessible at a high school level, but actual calculations of lift and drag from geometry and airflow alone are pretty difficult.

• Mohankpvk