# I Pressure and Lift around a Wing

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You are sort of running in circles here. The best way to address that question again goes back to the consideration of energy. A given fluid parcel has a finite total energy (represented by total pressure in Bernoulli's equation). If it is accelerated to some constant velocity further downstream (e.g. after a pipe constriction) and experiences no non-conservative forces, then it still has the same total energy but it now has higher kinetic energy. The energy stored as static pressure must therefore decrease.

#### FactChecker

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Given a fluid parcel moving along a straight streamline in the positive x-direction, I see that a pressure difference between two points (one before and one after point $P$) would cause a force $F$ on the fluid parcel which would accelerate. But what if the parcel is moving at constant speed? The force would zero and the pressure gradient would be zero. In that case, being pressure isotropic, the parcel experiences the same force from the back, from the front, from the top and from the bottom. This isotropic pressure is smaller compared to the static pressure at the same point $P$ when the fluid is not moving at all. I am not sure how to justify the fact that the speed makes the pressure smaller without using Bernoulli's equation.
After the velocity has increased and the pressure has decreased, it is hard to figure things out if you ignore what happened to cause the velocity to increase. You can't intuitively understand the difference between point A and point B while ignoring everything in between.

Suppose you wanted to compare the velocity of a car at the top of a hill with the same car after it has rolled down the hill without considering the obvious speed up as it rolled down. You want a reason why the velocity at the bottom is faster. In addition, you are trying to rule out consideration of the potential vs kinetic total energy trade-offs. That is asking for too much.

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#### fog37

Ok, thank you. I look forward to boneh3ad insight article :)

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I have a rough draft made up but it needs some figures, which may take a while to actually put together, especially with the end of the semester rapidly approaching. It might have to wait until mid-May.

#### Joseph M. Zias

For your information: I have found a very good web book on flying that includes a very readable section of wings and lift. Look up "See How it Flies" by
John S. Denker, a physicist and flight instructor.

#### sophiecentaur

Gold Member
For your information: I have found a very good web book on flying that includes a very readable section of wings and lift. Look up "See How it Flies" by
John S. Denker, a physicist and flight instructor.
That guy knows a lot about flying and planes and the book is certainly entertaining as well as informative. I didn't read from cover to cover, of course, but one bit leaped out of the screen at me:

"Downwash behind the wing is relatively easy to understand; the whole purpose of the wing is to impart some downward motion to the air."

He is obviously aware of Newton's Third Law so he is, by definition 'A Good Lad" and gets the general principle.

#### DarioC

Gold Member
I don't understand fog37's initial statement that the air flowing over the top of the wing causes a downward pressure on the top of the wing.

None the less:There was (is) an excellent video online of wind tunnel airflow over an airfoil with the flow shown by pulsed smoke. It really changed my view of what happens. What I saw was that the air velocity near the wing speeds up compared to the general tunnel flow as it goes up to the high point on the airfoil and then slows back down as it curves down to the trailing edge of the wing. This is displayed by the vertical lines of the smoke pulses.

The second part that conflicted with what I thought I knew about wings was that the "smoke lines" indicated the flow slowed down as it passed under the wing. Interestingly enough, if that is correct, it would still produce a downward vortex, and therefore lift, from the trailing edge of the wing.

I fail to see any conflict between the downward flow of air from a helicopter, the rearward flow from a propeller, or the lift from a wing. I can personally vouch for the vortex from a wing as I well remember having my light airplane flipped almost 90 degrees by a vortex from a larger corporate aircraft just as I was turning final following it

Don't have a link for that video now as it was lost on my older computer when it crashed. I'll look around and post if I find it.

#### fog37

Hello DarioC,

Let me see if I can be more clear if what I was trying to describe: if the air above the wing far from the surface is at regular atmospheric pressure and the air right above the wing surface is at pressure lower than atmospheric pressure, I would envision a pressure gradient directed toward the wing surface.

#### Joseph M. Zias

That guy knows a lot about flying and planes and the book is certainly entertaining as well as informative. I didn't read from cover to cover, of course, but one bit leaped out of the screen at me:

"Downwash behind the wing is relatively easy to understand; the whole purpose of the wing is to impart some downward motion to the air."

He is obviously aware of Newton's Third Law so he is, by definition 'A Good Lad" and gets the general principle.

Dr. Denker also has a LOT of comments on theorems in physics and reviews (very critical at times) on text books. Take a look at his website: http://www.av8n.com/physics/

Gold Member
That guy knows a lot about flying and planes and the book is certainly entertaining as well as informative. I didn't read from cover to cover, of course, but one bit leaped out of the screen at me:

"Downwash behind the wing is relatively easy to understand; the whole purpose of the wing is to impart some downward motion to the air."

He is obviously aware of Newton's Third Law so he is, by definition 'A Good Lad" and gets the general principle.
I am amused by his view of the purpose of a wing. I'd argue that the purpose of the wing is to hold up the plane, and imparting some downward motion to the air is the means by which it achieves this purpose, not the other way around. Otherwise I'd agree.

#### sophiecentaur

Gold Member
it achieves this purpose, not the other way around.
How would you feel about saying that the purpose of a planes propellor is to push air backwards or that an aircraft's engine is there to turn the propellor or that the fuel is put in to make the engine go? Or even that the pilot is there to make the passengers arrive at JFK.
Causes and effects.

Gold Member
How would you feel about saying that the purpose of a planes propellor is to push air backwards or that an aircraft's engine is there to turn the propellor or that the fuel is put in to make the engine go? Or even that the pilot is there to make the passengers arrive at JFK.
Causes and effects.
Well, I might argue that the pilot is there so he can earn his paycheck and eat.

#### sophiecentaur

Gold Member
Well, I might argue that the pilot is there so he can earn his paycheck and eat.
The toe bone's connected to the foot bone, the foot bone's connected to the ankle bone . . . . . now hear de word of de lawd.

#### Joseph M. Zias

I am amused by his view of the purpose of a wing. I'd argue that the purpose of the wing is to hold up the plane, and imparting some downward motion to the air is the means by which it achieves this purpose, not the other way around. Otherwise I'd agree.
From the frame of reference of the pilot - yep, keeping that plane up is Primary. Take a look at his physics site:

http://www.av8n.com/physics/

#### Joseph M. Zias

Well, I might argue that the pilot is there so he can earn his paycheck and eat.
Well as a private pilot I spend my money to fly - unfortunately the money tree has lost most of its leaves.

#### sophiecentaur

Gold Member
Well as a private pilot I spend my money to fly - unfortunately the money tree has lost most of its leaves.
I sit in my garden and watch guys like you, flying overhead every day. I can hear the cool person of hard earned cash disappearing down a black hole. As a former boat owner, I can sympathise (by a factor of ten, at least).

#### DarioC

Gold Member
Fog37, In reply I think you might want to look at what happens at the leading edge of the wing. I am getting close to the limits of my understanding here.
The air running into the leading edge curve is flung/forced upwards which compacts the air above the wing, at the same time making a lower pressure near the surface of the wing. The pressure layers higher up cannot exert downward force because they are being constantly compacted and separated from the wing by the up flow from the curved leading edge.
Thanks
DC
Added: Are you familiar with the triangular strips of metal that are put on the leading edge of the wings, near the fuselage to make that part of the wing stall before the outboard part where the ailerons are?
Rather interesting little detail on real-world wings.

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#### FactChecker

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2018 Award
This should "get you over the top" then... .

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I think this is an excellent video. As an interested amateur, I wish that I had seen this decades ago. It really gives one a clue that any simple explanation necessarily omits too much and is misleading when predicting lift and drag. That is why CFD programs are used in spite of the huge amount of computer power required and the limitations of the answers.

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OCR

#### DarioC

Gold Member
I think this is the video I mentioned. Pulsed smoke flow in wind tunnel. Check at about 47 seconds.

Gold Member
Fog37, In reply I think you might want to look at what happens at the leading edge of the wing. I am getting close to the limits of my understanding here.
The air running into the leading edge curve is flung/forced upwards which compacts the air above the wing, at the same time making a lower pressure near the surface of the wing. The pressure layers higher up cannot exert downward force because they are being constantly compacted and separated from the wing by the up flow from the curved leading edge.
Air running into the leading edge is directed both over and under the wing, not simply over it. You are correct that the pressure away from the surface does not impact it directly (only the surface pressure acts on the surface), but it is related.

Consider the streamlines as they move around the airfoil over the top. Near the leading edge they are deflected upward and have a curvature whose center points away from the airfoil. Curved motion requires a centripetal force, which here must be provided by a pressure gradient. Since the pressure far from the airfoil must be atmospheric, this means that the pressure in that region must be locally higher than atmosphere. This shouldn't be surprising because this is the result of being near the stagnation point.

After that point, the curvature flips direction as the streamlines bent to follow the curve of the airfoil over the top. Now the center of curvative is in or below the wing and the pressure must therefore decrease as you approach the surface. There is therefore a low pressure near the surface at that point.

So the pressure far from the surface does not directly impact the lift force, but it definitely plays an indirect role here.

Added: Are you familiar with the triangular strips of metal that are put on the leading edge of the wings, near the fuselage to make that part of the wing stall before the outboard part where the ailerons are?
Rather interesting little detail on real-world wings.
That's not what those triangles do. Those are vortex generators and they actually delay stall. The turbulence they induce energizes the boundary layer near the wall and makes it more resistant to separation.

I think this is an excellent video. As an interested amateur, I wish that I had seen this decades ago. It really gives one a clue that any simple explanation necessarily omits a too much and is misleading when predicting lift and drag. That is why CFD programs are used in spite of the huge amount of computer power required and the limitations of the answers.
Well, CFD is quite effective for lift. It isn't terribly accurate for drag. Computers do a terrible job of predicting laminar-turbulent transition, for example, and as a result do a terrible job predicting separation.

#### DarioC

Gold Member
On the triangles, I think somehow you have misunderstood which "triangles" I meant. The ones I am talking about are very small long strips that are located on the leading edge of the inboard part of the wing. Their purpose is to disturb the airflow at high angles of attack and cause the inboard part of the wing to "stall" before the sections outboard that have the ailerons. The desired result is the you dump a lot of the lift of the wing before you loose roll control when the aileron area stalls. It allows you to get a good comfortable sink rate during the final flare. A Beachcraft Bonanza has them as I remember and some others I am sure. I suspect they are called something like leading edge spoilers.

They are completely different in appearance and function from the various vortex generator "tabs."

Of course air goes under the wing as well as over it, but I was talking about the air going over the wing specifically, I wasn't discussing the air going under the wing, that is why I didn't write anything about that part of the airflow.

Anyone who has compared the landing characteristics of a Piper cub versus a Taylorcraft will understand the significance of the shape of the wing leading edge. Interestingly enough those two planes were designed by the same person.

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#### DarioC

Gold Member
Yes that is one. Thanks for the photo.

#### fog37

Thank you DarioC , Boneh3ad and everyone else.

I am back to thinking about the fundamentals of pressure.

In a fluid at rest, the pressure at a hypothetical point $P$ could be measured using a Bourdon vacuum pressure gauge (the higher the spring compression the higher the pressure). The measured pressure at the infinitesimal point $P$ is the same no matter the orientation of the gauge (pressure is isotropic both in hydrostatics and fluid dynamics).

But when the fluid is moving, the pressure at a particular point along a specific streamline will be dependent on the fluid speed and on the way we measure it: if we placed Bourdon gauge facing the fluid upstream, the fluid would come to rest against the measuring surface of the gauge and the measured pressure would depend on the fluid speed (stagnation point): the higher the flow speed the higher the stagnation pressure. At that same stagnation point, with the first gauge remaining in place, the pressure measured by an extra Bourdon gauge oriented perpendicularly to the first gauge would be the same since the pressure is isotropic.

What if we don't create a stagnation point but use a Bourdon gauge oriented perpendicularly to the streamline? I guess it is called a tap if we measure that pressure at the surface of the pipe (pressure does not change across the streamlines). What pressure would the gauge measure in that case? This pressure would be smaller than the pressure at the stagnation point and the faster the fluid is moving along the streamline the smaller that pressure measured by the Bourdon gauge would be. In both case (fluid at rest or moving), the pressure $p$ in Bernoulli's theorem is the same. However, it is interesting that its value changes depending on the way we measure it (facing the fluid and creating a stagnation point or perpendicularly to a streamline).

In a pipe that has a narrowing, since the fluid must accelerate to maintain the same flow rate ($m^3 / s$), the pressure in the narrowing must be smaller to have a pressure gradient.

Thanks!