Is Bernoulli's Law Correct for Calculating Lift on Airplane Wings?

[50936]

Hi everyone,

I read on a website that the Bernoulli's expression can be applied to airplane wings by using the equation:

Difference in pressure above and below wing
= 1/2 x air density x [(airflow velocity below wing)^2 - (airflow velocity above wing)^2]


I tried using it but the units don't seem to add up correctly when I use the metric system (kg/m^3 for density, m/s for velocity).
The website uses (slugs/ft^3) for density, and (ft/s) for velocity.

Can anybody tell me if this equation is correct?

 

[cesiumfrog]

Before that, how do you intend to determine the difference in airflow velocities?

 

[50936]

There is a simulator of an airfoil in flight on a NASA website.

http://www.grc.nasa.gov/WWW/K-12/airplane/foil2.html

It gives readings of the velocity of air at any point around the wing.

 

[rcgldr]

I read on a website that the Bernoulli's expression can be applied to airplane wings by using the equation: Difference in pressure above and below wing
= 1/2 x air density x [(airflow velocity below wing)^2 - (airflow velocity above wing)^2]
This equation is correct?

The equation is correct, but it's not quite that simple, as the relative air flow speed (using a wing based frame of reference) across a wing isn't constant, and there's a non-Bernoulli component due to the fact that lift isn't "free" and some work is done on the air. Somewhere during the process of generating lift, the total energy of the air is increased, meaining that kinetic energy was increased without an equal decrease in pressure energy or vice versa.

Also take the case where the air is the frame of reference, most of the air flow is downwards (corresponding to lift) and a small amount forwards (corresponding to drag). This is a more difficult to understand example, because you have the dynamics of a moving wing and downwards airflow as the wing passes through a volume of air. So it's easier to use a wing based frame of reference to calculate pressures based on flow perpendicular to the surface of an airfoil, but these calculations have to be adjusted to take into account work done, and the issue of turbulent airflow.

The goal of a wing is to accelerate air downwards, which causes an equal and opposite reaction force from the air to generate lift. If this could be done without requiring any work performed on the air, then a true Bernoulli like transition would occur in the downwards acceleration of air. This isn't possible, but some very long wing span high end gliders get verly close to this ideal situation, with an overall lift to drag ratio around 60 to 1.

How wings accomplish efficient downwards acceleration of air is complicated. The bottom of a wing accelerates air downwards through mechanical interaction. Above a wing, "Coanda like" effects (friction, viscosity, void effects), cause the air to tend to follow the upper surface of a wing, which also accelerates air downwards.

 

[Gear300]

For flight, what is needed is a thrust that can overcome drag. What is also needed is lift that can overcome the weight. For such lift, Bernoulli's principle can be applied. That is how the scientist does it...to come up with the concept. Now we need the inventor/engineer to make the concepts happen...which requires specifics (situations aren't as easily generalized)...and at that point, we realize that there are also limits to these concepts based on how far we've progressed (so we're either capable of doing it at the moment or not).

The use of airplane wings can be based on Bernoulli's principle, but if you want data, it also depends on the design of the wings and so forth (more specific things).

 

[stewartcs]

Hi everyone,

I read on a website that the Bernoulli's expression can be applied to airplane wings by using the equation:

Difference in pressure above and below wing
= 1/2 x air density x [(airflow velocity below wing)^2 - (airflow velocity above wing)^2]


I tried using it but the units don't seem to add up correctly when I use the metric system (kg/m^3 for density, m/s for velocity).
The website uses (slugs/ft^3) for density, and (ft/s) for velocity.

Can anybody tell me if this equation is correct?

Take what you read on the internet with a grain of salt.

http://home.comcast.net/~clipper-108/Lift_AAPT.pdf

CS

 

[rcgldr]

Regarding Bernoulli, a very efficient wing manages to produce lift with very little work done on the air. One way to accomplish this is to minimize the total kinetic energy added to the air, which is why very high apect ratio wings (long wingspans) are so efficient. The other way is to produce most of the kinetic energy via conversion of pressure energy into kinetic energy (a Bernoulli like conversion) which is determined by the air foil shape. Still, no energy conversion process is 100% efficient, and there are non-Bernoulli factors involved in producing lift.

 

[50936]

I really appreciate all the replies, but I'm having a bit of a hard time understanding.

Initially, I had the idea that the Bernoulli effect and the Newton action-reaction force were two separate effects, and that both of them add up to produce the total lift for an aircraft.

And thus, my research question is to figure out to what extent each of them contribute to producing the TOTAL lift.

But by reading the posts, it seems like the Bernoulli effect and Newton action-reaction force are interrelated.
So maybe my question needs changing...

What do you guys think?

 

[rcgldr]

Newton's 3rd law - Whenever an object exerts a force on another object, the other object exerts an equal an opposite force on the initial object. In some cases, the opposing force is a reaction force due to acceleration of the other object.

Bernoulli - In the ideal case where there is no work done on a gas or fluid, the total energy remains constant, and if there is a "work free" transition that causes a change in kinetic energy, then an equal an opposite transition occurs in the pressure energy. (Temperature energy is also a component of total energy, but it's ignored in the "classic" Bernoulli case).

Newton's 3rd law and lift - Wings produce lift by appying a downwards force to the air, which which responds with an equal and opposite lift force. Since the air is free to move, the result of the force applied to the air is a downwards acceleration of the air, and it's the reactive response to this acceleration that results in the reactive lift force from the air.

Bernoulli and lift - If a wing were 100% efficient, no work would be required, and all of the increase in kinetic energy of the air would correspond to an equal and opposite decrease in pressure energy.

Wings are not 100% efficient. When a wing passes through a volume of air, the result is a downwards and slightly forwards acceleration of air. The forwards component corresponds to drag. Newtons 3rd law still applies in this case, the only difference is the direction and magnitude of the force; the wing applies a downwards and somewhat forwards force on the air, and the air reacts with an equal and opposing upwards and somewhat backwards force. The Bernoulli relationship is impacted by efficiency; the increase in kinetic energy of the air is more than the decrease in pressure energy, and this work related component is a "non-Bernoulli" aspect of a wings interaction of the air. In addition, there is some change in air temperature, especially at higher air speeds, which also affects Bernoulli, but not Newton's 3rd law.

Wings work via a combination of forward speed and effective angle of attack (zero effective angle of attack means zero lift), which is how a wing applies a downwards (and forwards) force to the air. As mentioned before, the bottom of a wing accelerates air downwards through mechanical interaction, and above a wing, "Coanda like" effects (friction, viscosity, void effects), cause the air to tend to follow the upper surface of a wing, which also accelerates air downwards.

Getting back to your original post, the lift on a wing can be approximated by integrating the sum of pressures across the chord of the wing, using the speed at each point near the surface of a wing to calculate pressures via the Bernoulli relationship. However this process needs to be modified to compensate for work done on the air ("non-Bernoulli" like transitions in pressure, kinetic, and temperature energy), and take into account that the air stream is somewhat detached from the surface of a wing (there's a shear boundary layer than transitions from zero relative speed to the speed of the air). Except for about the leading 1/3rd of the wing chord, the flow is turbulent, small horizontal eddies, so an effective "average" speed has to be used to account for these eddies (or the turbulent flow is ignored and treated as "semi-laminar"). Although this approach might be good for approximating lift mathematically, it's not a good method for explaining lift, since lift is a reaction force to downwards acceleration of a very large volume of air per unit of time, not just the air streams near the surface of a wing.