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- Bernoulli, lift and cause & effect: looking for a clear-cut cause-and-effect and analogy.

Dear all,

for a book I'm writing I'm trying to understand the generation of lift by wings on a conceptual level. Some papers I used are given at the end. I won't talk about all the misunderstandings out there concerning the generation of lift. I'm interested, also from a pedagogical level, in the very reason why it's so damn hard to give a clear-cut cause-and-effect for how lift is generated.

Of course, in this explanation Bernoulli's law is invoked. Bernoulli's law relates pressure differences to velocity differences along a single airflow. It's a statement of energy conservation, saying that 'when pressure drops, velocity increases' and vice versa. This can be compared to dropping a stone, and saying that 'when height decreases, speed increases' and vice versa. Being a statement about energy conservation, nothing is said here about cause and effect, but for the dropping stone we know that the cause of both the decreasing height and increasing speed is gravity. Likewise, if you follow a fluid parcel along a flowline, Newton's second law tells us that the particle's velocity changes due to a pressure difference along the flow. So the pressure difference causes the velocity change, and not the other way around; we can at most conclude that if an air parcel's velocity changes, there must be a pressure difference which caused this. But then comes the paper by Doug McLean about lift (Aerodynamic Lift, Part 2: A Comprehensive Physical Explanation). In it, he says the following:

To be honest, I don't really get this, but the main lesson here is that the simple "pressure difference causes velocity difference but not the other way around"-thinking is, according to Mclean, wrong. So I was thinking about another analogous case: voltage difference and current. Usually, a voltage difference causes a current, not the other way around. However, we know from e.g. the Hall effect that if we put a conductor in an external magnetic field, a current inside that conductor can deflect, cause a charge building up at one side of the conductor, and cause a voltage difference perpendicular to the original direction of the current. A current of test charges would be driven in the perpendicular direction by this Hall voltage, which is caused by the influence of an external magnetic field on the original current. So my question: is this situation of the conductor and Hall effect with its external magnetic field comparable to a parcel of air ("current") being influenced by the movement of a wing ("the external magnetic field") such that we get a mutual interaction? Can this analogy shed more insight into how a pressure drop accelerates an air parcel around a wing, while on its turn this accelerating air parcel influences the pressure around the wing? And, of course: how would you describe the exact cause of the arising pressure regions around the wing? If I start moving a wing through air, air will collide among others at the front of the wing, such that pressure is build up there and increases. But then?

P.S. I'm not sure how much I'm allowed to copy from the paper by McLean, so please let me know or remove my quote if inappropriate due to copyright.

Doug Mclean,

Doug Mclean,

Dwight Neuenschwander,

John Denker,

Holger Babinsky,

M. D. Deshpande en M. Sivapragasam,

for a book I'm writing I'm trying to understand the generation of lift by wings on a conceptual level. Some papers I used are given at the end. I won't talk about all the misunderstandings out there concerning the generation of lift. I'm interested, also from a pedagogical level, in the very reason why it's so damn hard to give a clear-cut cause-and-effect for how lift is generated.

Of course, in this explanation Bernoulli's law is invoked. Bernoulli's law relates pressure differences to velocity differences along a single airflow. It's a statement of energy conservation, saying that 'when pressure drops, velocity increases' and vice versa. This can be compared to dropping a stone, and saying that 'when height decreases, speed increases' and vice versa. Being a statement about energy conservation, nothing is said here about cause and effect, but for the dropping stone we know that the cause of both the decreasing height and increasing speed is gravity. Likewise, if you follow a fluid parcel along a flowline, Newton's second law tells us that the particle's velocity changes due to a pressure difference along the flow. So the pressure difference causes the velocity change, and not the other way around; we can at most conclude that if an air parcel's velocity changes, there must be a pressure difference which caused this. But then comes the paper by Doug McLean about lift (Aerodynamic Lift, Part 2: A Comprehensive Physical Explanation). In it, he says the following:

How the lift and the flow details are tied

together in a set of mutual interactions:

As the flow is forced to follow the predominantly downward-

sloping surfaces of the airfoil, a set of mutual interactions

is established between the lift force, the pressure field,

and the velocity field. This is not a linear sequence of one-way

cause-and-effect relationships; the relationships are all reciprocal.

Nor are the relationships ordered in time; in a steady

flow they are all simultaneous.

[...]

At the overall flowfield level, the lift force and the pressure

field support each other in a mutual interaction: The pressure

field exerts the upward lift force on the airfoil, and at the

same time the existence of the pressure field is a result of the

equal-and-opposite downward force exerted by the airfoil

on the air. The relationship is reciprocal, consistent with the

reciprocity between action and reaction inherent in Newton’s

third law.

[...]

To grasp the pressure-velocity interaction intuitively, it

helps to note that a pressure difference can exist only because

the air acted on by the pressure difference is able to “push

back” against the unbalanced pressure force. When a parcel of

air is subjected to different pressures on opposing sides, the

parcel’s neighbors exert a net force on the parcel as illustrated

in Fig. 3. According to Newton’s third law, this force must be

opposed by an equal-and-opposite “pushback” exerted by the

parcel on its neighbors. The “pushback” is provided by the

inertia of the air in the parcel as it is accelerated by the

pressure difference, in accordance with Newton’s second law. This is why

the mass of the air is important, and why lift depends on air density.

So the pressure field that exerts the lift force arises

as part of a mutual interaction with the lift force itself and at the same time

is sustained in a mutual interaction between the pressure

and the vector velocity of the flow. Upward and downward

deflections of the flow and different flow speeds above and

below the airfoil are all essential parts of this interaction. The

pressure differences follow naturally from Newton’s second

and third laws and from the fact that the flow along the surface

is forced to follow the predominantly downward-sloping

contours of the airfoil associated with angle of attack and/or

camber. And of course the fact that the air has mass is crucial

to the interaction.

From: Doug Mclean,"Aerodynamic Lift, Part 2: A Comprehensive Physical Explanation."In ‘The American Association of Physics Teachers’. AAPT, 2018.

To be honest, I don't really get this, but the main lesson here is that the simple "pressure difference causes velocity difference but not the other way around"-thinking is, according to Mclean, wrong. So I was thinking about another analogous case: voltage difference and current. Usually, a voltage difference causes a current, not the other way around. However, we know from e.g. the Hall effect that if we put a conductor in an external magnetic field, a current inside that conductor can deflect, cause a charge building up at one side of the conductor, and cause a voltage difference perpendicular to the original direction of the current. A current of test charges would be driven in the perpendicular direction by this Hall voltage, which is caused by the influence of an external magnetic field on the original current. So my question: is this situation of the conductor and Hall effect with its external magnetic field comparable to a parcel of air ("current") being influenced by the movement of a wing ("the external magnetic field") such that we get a mutual interaction? Can this analogy shed more insight into how a pressure drop accelerates an air parcel around a wing, while on its turn this accelerating air parcel influences the pressure around the wing? And, of course: how would you describe the exact cause of the arising pressure regions around the wing? If I start moving a wing through air, air will collide among others at the front of the wing, such that pressure is build up there and increases. But then?

P.S. I'm not sure how much I'm allowed to copy from the paper by McLean, so please let me know or remove my quote if inappropriate due to copyright.

Doug Mclean,

*Aerodynamic Lift, Part 1: The Science.*In ‘The American Association of Physics Teachers’. AAPT, 2018.Doug Mclean,

*Aerodynamic Lift, Part 2: A Comprehensive Physical Explanation.*In ‘The American Association of Physics Teachers’. AAPT, 2018.Dwight Neuenschwander,

*How Airplanes Fly: Lift and Circulation.*In ‘Elegant Connections in Physics’, 2015.John Denker,

*See How It Flies. A new spin on the perceptions, procedures, and principles of flight.*Online te lezen, 2001.Holger Babinsky,

*How do wings work?*In ‘Physics Education (2003).M. D. Deshpande en M. Sivapragasam,

*How Do Wings Generate Lift? 1. Popular myths, what they mean and why they work.*In ‘Resonance’, 2017.