Simple AoA question
 

Soooo answer as simple as possible (shouldn't be too hard being pilots eh).
"Why does increasing AoA (up to the crit AoA) increase CL?" Please keep it in relation to Bernoulli's theorem

Bernoulli's theorem clearly states that students should do their own homework.

You say it's a simple question, so must have a simple answer. No?

Take PDR1's advice, do some homework. Geez, spoon fed modern generation.

....actually, I think that was the OP's question.

angrypickle

There are a great many different ways of explaining how wings create lift. As some of the above posts have revealed, the Bernoulli method is not universally accepted as being true. But you have asked the question:

So I will give you an answer to that specific question.

Bernouli’s theorem predicts that when the velocity of air increases, the static pressure will decrease.

When a wing is in flight the air stream meets it at a point known as the stagnation point. The air then splits into two streams with one flowing over the upper surface of the wing and the other flowing under the lower surface.

The speed of these two streams of air is determined by the length of the path which they take.
The length of this path is from the stagnation point to the trailing edge. If the lengths of the two paths are equal then the speeds and hence static pressure of the two streams will be equal. An example of this would be a symmetrical aerofoil at zero angle of attack. The upward force exerted by the pressure pushing up on the lower surface would be equal and opposite to the force exerted by the pressure pushing down on the upper surface. In this condition the two forces would cancel each other out, so there would be no resultant lift force and hence the Cl would be zero.

If we now pitch the wing 1 degree leading edge up, the stagnation point would move to a position slightly below the leading edge. This would increase the length of the path over the upper surface and decrease the length of the path under the lower surface. So the velocity of the air flowing over the upper surface would increase, thereby decreasing its static pressure, and the velocity of the stream flowing under the lower surface would decrease, thereby increasing the static pressure. The upward force exerted by the pressure on the lower surface would then be greater than the downward force exerted by the pressure on the upper surface, so the resultant force would be an upward (lift) force.

Gradually increasing the angle of attack further, increases this effect, thereby increasing Cl until the critical angle is reached, thereby causing the airflow over the upper surface to separate.

As I have said earlier in this post, the above arguments are not universally accepted, and it is very easy to pick holes in them. But I will leave that task to others who would prefer to show you how clever they are rather than attempting to help you.

Nothing clever Keith. Putting "Bernoulli" into a search brings up in a nano second far more information than you have provided, which would have answered the question. With pretty pictures as well. ;) You're quite entitled to your opinion of course regarding "help", rather than dissing us. :(

The reason Keith's explanation is not universally accepted is because it is incorrect.

Unfortunately, the idea keeps perpetuating because people like Keith keep peddling it.

Bernoulli states that there is a relationship between speed and pressure. In this instance, it is the pressure change that causes the speed change, not vice versa.

The air does not know it has a longer path to take, and it does not speed up because of it. The air speeds up because the wing moving through the air causes an area of lower pressure above the wing, and an area of higher pressure below.

The pressure regions above and below the wing are caused by the fact that the gas molecules in air have inertia.

Bernoulli cannot answer your question, so whoever wrote your question doesn't understand why a wing generates lift either.

Exactly why I said the answer was simple. Navier-Stokes, Prandtl, Blasius and Euler are what the OP should be reading up on IMHO.

Derfred.

I am not going to waste my time attempting to defend the Bernoulli explanation for lift, because I am well aware of its faults and some of the alternative explanations and theories.

But a few of your comments do deserve examination:

I am not peddling anything. The OP asked for an explanation based on Bernoulli’s theorem, so the only possible answer must be based on Bernoulli’s theorem. It is all very well saying “Ah but it isn’t true”, but many courses include this subject, and if the student is to pass the exams he/she must learn it. I suspect that the OP is doing such a course. If this is the case, simply saying “Bernoulli does not do it” is of no use to him/her.


You appear to be suggesting that because the air is not aware of the longer path it cannot react to it. You are of course correct in that the air has no brain, no intelligence, no self-awareness, indeed no awareness whatsoever. So it cannot ever be aware of anything. But does this lack of awareness mean that it cannot react to things around it? Let’s try a few tests:

If I place a mass of air into a sealed container then reduce the volume of the container, the air will be unaware of this reduction in volume (it is not aware of anything). Does this mean that the air pressure and temperature will not increase? Of course it doesn’t.

If I take a parcel of air and lift it upwards in the atmosphere, the air will be unaware of the fact that its altitude has increased (it is not aware of anything). Does this mean that it will not expand and cool down? Of course it doesn’t.

If I take a mass of air an pass it through a venturi, it will be unaware of the changes in cross-sectional-area (it is not aware of anything). Does this mean that the velocity, pressure and temperature of the air will not change? Of course it doesn’t.

We could of course do more similar tests, but hopefully you have got the point. The fact that air is not aware of anything whatsoever does not prevent it from reacting to events.

You then say:

But as we have already established, the air is not aware of anything, so how can changes in pressure cause changes in velocity. So which is it to be? Can the air react to things of which it is unaware, or can it not? You cannot have it both ways.

By all means argue that Bernoulli cannot explain how lift is generated, but please, please, try to use more rational arguments.


Those who wish to argue that airflow around wings and the generation of lift have nothing to do with Bernoulli should ask themselves a simply question. Bernoulli’s Theorem is a well established method of providing reasonably accurate predictions of how air velocity and pressure are related in a wide range of circumstance. So if Bernoulli does not apply to wings in flight, how does this come about? Does the approaching air say to itself “oh that’s just an aeroplane wing so I do not need to react in the usual bernolli-esq manner?

I read a very good article once titled something like "Why Bernoulli doesn't suck" That may not have been the correct wording but it was a play on why Bernoulli's theory didn't correctly explain the lift generated by a wing.

However it made one very good point which was In order to explain the complicated truth it is sometimes better to use a simple lie

In other words trying explain lift correctly was not easy to explain nor understand whereas the Bernoulli theory did the job well enough to explain what happened so far as a wing (or any aerofoil section) generating lift.

Keith, the mindfulness of the air molecules was just an attempt to simplify that the theory that an air molecule above the wing has to speed up in order to arrive at the trailing edge at the same time as an air molecule below the wing is completely fallacious. What I meant was, air molecules only know about the proximity of nearby molecules, and all basic physics can be explained on that basis. They certainly don't know or care where the trailing edge of the wing is, or how far they might have to travel in order to get there. And sorry to play the man like that. I just hate seeing this incorrect theory continually perpetuated. I too, was taught the Bernoulli theory of lift as a 16yo, and didn't question it until later in life.

Think of a pipe, which splits into two smaller pipes, which are then rejoined into a single pipe. However, one of the two pipes is longer than the other, and follows a wiggly path compared to the shorter straight pipe. Now pump air down those pipes. Is the air in the longer wiggly pipe going to travel faster because it has to further to go? Of course not. What an absurd suggestion.

Probably a simpler explanation is to forget the aerofoil for a minute and just imagine an inclined plane (flat plate) moving through the air. The air molecules under the plane get squashed together, increasing pressure. Behind the plane a void is created, until the air molecules above the plane rush in to fill that void, leaving an area of low pressure above the plane. Yes, it is as simple as that. A 5 year old can understand that concept, and they can re-create the void effect in the bathtub with their hand. The bath-tub experiment uses an incompressible fluid, but it demonstrates the principle at play, and is readily understandable. It is actually a far simpler explanation than Bernoulli and is the correct explanation.

Bernoulli then dictates that the air molecules below the plane will slow down due to the higher pressure, and the air molecules above the plane will speed up due to the lower pressure. This is true, however it is not this speeding up or slowing down that causes the pressure change. It is the pressure change causing the speed change. The lift is caused by the pressure differential, and the Bernoulli effect is entirely incidental.

The first few posts in this thread remind me of the story of the man who goes into a clothing shop to buy a coat.

Shop Assistant: “Good morning sir, can I help you?”

Man: “Good morning. Yes please I would like to buy one of those hooded jackets. I want it in red and it must be the smallest size you have”

Shop Assistant: Oh no sir. The blue ones would suit you much better and you will need the large size….or if I may say so, perhaps the extra large.”

Man: “No thank you I want a small red one.”

Shop Assistant: But sir, if I sell you the small red one I will be wasting your time and mine. You will be coming back tomorrow to swap it for a large blue one.”

Man: I want a small red one. It’s for my daughter who is starring in the school play….Little Red Riding Hood.”


In the case of this thread there are also a couple of posts which effectively have the shop assistant saying “why don’t you just stop being so lazy and go away and make your own coat?”


Having observed the way the thread was developing I was tempted to give the answer which the OP had requested. I knew from previous experience that this would cause me to be met by a crowd of people who would inevitably conclude that I must be a supporter of the Bernoulli explanation and they would by eager to demonstrate their superior knowledge. In an (unsuccessful) attempt to avoid this tedium I included the following comments in my post:

And

And in a later post:


Sadly all of those comments were ignored and, as expected a number of posters have set about convincing me that I and Bernoulli are wrong.

Well here is a news flash folks:

1. I have never argued that the Bernoulli explanation is correct.
2. I do not believe that the Bernoulli explanation is correct.
3. You do not need to waste your time and mine by attempting to convince me that
the Bernoulli explanation is wrong (see note 2 to understand why.).


But just to keep the thread going:



That is true. It is also true that Newton knew nothing about space flight but his laws of motion are used everyday in designing and operating spacecraft. Bernoulli’s Theorem is based on the laws of conservation of energy. These laws apply to aircraft just as much as they do to anything else. But of course this does not make the Bernoulli explanation of lift correct.


Absolutely correct.


Although you appear to have modified your views on the “awareness” capabilities of air molecules, you are still wrong. Air molecules have no awareness of events whatsoever, regardless of whether the events are close at hand or far aware. The movements of the molecules are determined by the forces acting upon them. Nothing more, nothing less. In using your “awareness” concept to explain things you are using a lie to simplify your explanation, in the same way that anyone using the “long path/short path” explanation of lift is using a lie to simplify their explanation. The use of such lies does make things easier simply because it eliminates the need for much of the explanation.

And I thought it was all down to viscosity and circulation......!

A wing operates in a single body of air. Air moving along a pipe may not be the same body of air, as air in another pipe. Once it's not the same body of air, the rules of one body of air don't apply. But, let's consider the air in the wiggly pipe for a moment - when the air goes around the wiggle corners in the pipe, does the air on the outside of corner speed up and become less dense than the air slowing down on the inside of the same corner? 'Cause that is the same body of air - the body of air in the one pipe?

But if:

Why would the air molecules rush in to fill a void? What to they know?

Considering the flat plate + AoA as the mechanism by which lift is created (as opposed to the air having to speed across the upper surface to reconnect with the shorter path lower surface), How does an airfoil wing, operating at zero AoA create any lift? Wings don't suddenly stop lifting the aircraft when AoA is reduced to less than zero - In some cases, they gradually develop less lift as AoA reduces to zero, then maybe negative a degree or two. But the lift does not instantly become zero, when the molecules stop being squashed under the plane of a wing.

Consider the aerfoil of the wing of an American Champion Citabria, and Decathlon:

Wikipedia:

Why would the same type of plane (Citabria vs Decathlon) have different airfoils, if it were not an effort to extract the different positive vs negative lift? The Decathlon semi symmetrical airfoil is designed so the air does have about the same distance to travel top over bottom, other than the difference induced by the AoA, and moved stagnation point. In the Decathlon, AoA is pretty important to lift, less so during upright flight of the Citabria. I have flown Citabrias with zero apparent AoA, and they still flew fine, supporting most, if not all of their weight by the wings....

According to NASA:

neither Newton nor Bernoulli ever attempted to explain the aerodynamic lift of an object...

Bernoulli's equation relates the pressure in a gas to the local velocity. Adding up (integrating) the pressure variation times the area around the entire body determines the aerodynamic force on the body. Now adding up the velocity variation around the object instead of the pressure variation also determines the aerodynamic force. The integrated velocity variation around the object produces a net turning of the gas flow. From Newton's third law of motion, a turning action of the flow will result in a re-action (aerodynamic force) on the object. So both "Bernoulli" and "Newton" are correct...

Arguments arise because people mis-apply Bernoulli and Newton's equations and because they over-simplify the description of the problem of aerodynamic lift...

The most popular incorrect theory of lift arises from a mis-application of Bernoulli's equation. The theory is known as the "equal transit time" or "longer path" theory. In reality, the velocity on the upper surface of a lifting wing is much higher than the velocity which produces an equal transit time...

There is also an incorrect theory which uses Newton's third law applied to the bottom surface of a wing. It neglects the physical reality that both the lower and upper surface of a wing contribute to the turning of a flow of gas...

The real details of how an object generates lift are very complex and do not lend themselves to simplification.

Along with countless others I was taught that it was all down to Bernoulli and his theory of a faster flow over the top of the wing. I realise now that it's probably not the case but I still find myself teaching it, and glossing over what I know to be an elephant in the classroom. To proffer anything else would have done far more than raise the eyebrows of any trapper during a CFS check all those years ago.

The flat plate theory - or a streamlined one - does make a lot more sense, and when explained along the lines of sticking ones hand out of a car window makes it easy to visualize that when lift is generated, so too is drag. It's also pretty easy to prove that symmetrical airfoils work very well indeed - just look at any of the advanced aerobatic types in production.

A symmetrical aerofoil at zero AoA creates no lift, but it does create drag.

Explain how this drag is generated. Please keep it in relation to Bernoulli's theorem.

I'll stab a guess.

The symmetrical at zero AoA will not generate induced drag but it will suffer the penalty of parasite drag. Parasite drag is the product of the skin friction coefficient, the surface area and the effect of pressure drag and airspeed.

My best guess is that Bernoulli's theory might have something to do with the pressure drag?

And therein lies the problem. The explanation used in flight schools must be sufficiently simple to enable the typical student pilot to understand it, but the simplification process inevitably reduces its accuracy.

In the past I spent quite a few years running a ground school which provided theoretical knowledge training for PPL and ATPL students. The vast majority of them would have dropped out of the course if I and my instructors had attempted to explain lift in term of Navier-Stokes, Prandtl, Blasius or Euler. This level is OK for an engineering degree course in which something like six months might be devoted to the subject, but in a typical pilot training course, be it PPL or ATPL, the time devoted to this subject is usually less than 1 hour. Having used a single 50 minute lesson to deal with the subject of flow through convergent-divergent ducts, one student who had recently completed an aeronautical engineering degree said, “well that’s six months of thermodynamics dealt with in less than 1 hour. My lesson had obviously involved a lot of simplification, but the majority of the students had understood the essentials of the subject.


Ah now, do you really want the small red coat or are you just checking out the shop assistants?

Explanation 1 (loosely based on Bernoulli)
Bernoulli’s Theorem is based upon the assumption that the total energy of the air will be constant at all points along the flow. For this to be true there must be no energy added and no energy lost due to factors such as friction. In reality some energy is lost due to friction, so Bernoulli cannot provide the whole explanation. This lost energy is of course the “Friction Drag”.

The air which strikes the leading edge of the wing at the stagnation point is brought to rest, so all of its dynamic pressure is converted into static pressure. This increased static pressure exerts a rearward force which opposes the forward motion of the wing. Air slightly above and slightly below the stagnation point is not brought to rest, but its velocity is reduce, so some of its dynamic pressure is converted into static pressure. This adds to the rearward force opposing the forward motion of the wing. This sequence of reducing deceleration continues as the distance above and below the stagnation point increase. The overall effect of all of this is an area of increased static pressure acting in a rearward direction on the leading edge.

As the air flows past the leading edge its velocity gradually increases, so some of the static pressure is converted into dynamic pressure. It may be tempting to imagine that the sum of this static pressure plus dynamic pressure acting on the rearward facing surfaces of the wing would provide a forward force which would be equal and opposite to the rearward force on the leading edge. But this is not the case for two reasons:

1. As discussed earlier friction causes the air stream to lose energy, so the total pressure over the rearward facing surfaces is less than that over the forward facing surfaces.

2. Although static pressure acts in all directions, dynamic pressure acts only in the direction of flow (the downstream direction). So the dynamic pressure does not tend to push the wing forward.

The overall effect of all of this is that the changes in velocity and pressure which are caused by the movement of the wing through the air, exert a rearward force on the wing. This together with the friction force is the zero-lift drag.

Explanation 2 (Based on the awareness principle)
Air molecules are inherently lazy, so they really do not like to be disturbed by things flying through them.

When they become aware of an approaching aircraft they bunch-up together to produce an area of increased static pressure. This increased static pressure opposes the forward motion of the aircraft. This is the zero-lift drag.

Both of the above explanations are of course simple but inaccurate.

Keith you have (albeit by your own admission, inaccurately) explained the drag, can you now explain what generates the lift - with or without Bernoulli.