Wings, Propellers, and Lift

[mikegarrison]

Bernoulli's equation actually follows from the first law of thermodynamics (conservation of energy).

The equation only applies in adiabatic, inviscid flow, along a streamline. Under these conditions, no energy is added or subtracted from the flow, so by the first law the enthalpy of the fluid is conserved. Bernoulli's equation is simply a description of the trade between kinetic energy and potential energy (from both pressure and also gravity, if the gravity term is not dropped).

However, Newton's Laws also derive from the same principles, so you could start from them and work your way around to the same thing.

Bernoulli does not apply across a shock, because that is an irreversible process. Bernoulli applies only in isentropic conditions, and a shock is not isentropic. So applying Bernoulli to supersonic problems is usually a bad idea.

Turbulence and viscosity are also not isentropic, which is why Bernoulli does not apply inside the boundary layer. Nor does it apply in other regimes where viscosity is a dominant parameter, like insect flight. This is where Reynold's number comes in -- at very small speeds and sizes (small Reynold's number), viscous effects are too significant to ignore.

Edited June 26, 2019 by mikegarrison

[mikegarrison]

Kinetic energy is 1/2 * mass * velocity^2.

Potential energy from pressure is trickier. Pressure * area = force, so P = F/A. Force times distance is energy, and area times distance is volume. So multiply both F and A times distance and you get P = energy/volume, so energy = P*volume

mass = density * volume

So:

1/2 * density * velocity^2 * volume + P * volume = kinetic energy + potential energy = constant

If the fluid is incompressible then the volume is constant, so 1/2 * density * velocity^2 + Pressure = constant

When velocity is zero, the Pressure is equal to the constant. So we can call the constant "total pressure" (the total amount of the energy is in the form of pressure).

So:

1/2* density*velocity^2 + pressure = Total Pressure

And that's the familiar Bernoulli equation!

Edited June 26, 2019 by mikegarrison

[Hotel26]

Here's an idle question.  Can a wing produce more lift than 14.7 lbs / square inch?  (Atmospheric pressure at sea level, STP).

Edited June 26, 2019 by Hotel26

[wumpus]

On 6/25/2019 at 1:21 AM, Shpaget said:

Of course props have variable geometry. At the root the propeller the cord ratio is much higher than at the tip, and the entire aerofoil is twisted.

This sentence really confused me.  I think Shpaget is saying that the cross section of the propeller changes from the center to edge.  This can be confusing because the optimal angle of attack of a propeller changes in flight and many planes alter that angle (and it is called "variable geometry").  This is of course rather expensive and complicated, and is only seen on planes somewhat more expensive than a typical Cessna.

Misapplying Bernoulli's theory is as old as aviation, even Einstein famously got it wrong: http://wrightstories.com/einsteins-wing-flops/

If you think you understand the source of lift: ponder stalling (lift suddenly dropping to zero once angle of attack is too high for the given speed).  If your understanding of lift doesn't account for stalling, it is wrong (I don't understand stalling, so I'll limit my posting in this thread). 

PS: "Why planes fly" would make a great science fair exhibit (use wings/model airplanes spinning around a spindle as a "wind tunnel").  First disprove the "textbook with arrows pointing up" misunderstanding by showing a airplane flying upside down and proceed to evaluate what is really going on (hopefully including stalling.  The technical issues with the Boeing 737-MAX are mostly in the anti-stall software).

[mikegarrison]

3 hours ago, Hotel26 said:

Here's an idle question.  Can a wing produce more lift than 14.7 lbs / square inch?  (Atmospheric pressure at sea level, STP).

You know there is no generally accepted precise definition of wing area, right?

Anyway, consider a spacecraft on re-entry. The pressure on the bottom surface is far higher than the ambient pressure. Just saying that the force on the object is equal to the sum of all the pressures * all the surface areas (which is a true statement) does not mean you are restricted to the ambient static pressure for your highest pressure.

The restriction is that the highest pressure won't be greater than the stagnation (total) pressure. So the answer to your question is yes, assuming the plane is moving (and the wing could withstand that kind of load, which most could not).

Typical wing loading is at least an order of magnitude less than that, however. To say that a wing could generate such a large wing loading is not the same thing as saying it should.

Edited June 26, 2019 by mikegarrison

[Bill Phil]

4 hours ago, Hotel26 said:

Here's an idle question.  Can a wing produce more lift than 14.7 lbs / square inch?  (Atmospheric pressure at sea level, STP).

What about dynamic pressure?

In fact dynamic pressure is a part of the simple lift and drag equations.

Edited June 26, 2019 by Bill Phil

[Shpaget]

3 hours ago, wumpus said:

This sentence really confused me.  I think Shpaget is saying that the cross section of the propeller changes from the center to edge. 

Yeah, reading that sentence back I see there's an "of" and an "h"missing. Hope these bold parts make it clearer, but you did understand what I was trying to say.

At the root of the propeller the chord ratio (ratio between the thickness of the aerofoil and the length) is much higher than at the tip (the propeller is much fatter near the center than at the edge), and the entire aerofoil is twisted (chord lines, AKA lines between leading and trailing edges near the center and near the edges are not parallel).

 

This is an extreme example:

Chord line near the center is almost parallel to the axis of rotation, while chord line at the tip is almost perpendicular. This is what i meant by "twisted".

[kerbiloid]

A multiwing

Spoiler

 

[mikegarrison]

6 hours ago, wumpus said:

If you think you understand the source of lift: ponder stalling (lift suddenly dropping to zero once angle of attack is too high for the given speed).  If your understanding of lift doesn't account for stalling, it is wrong (I don't understand stalling, so I'll limit my posting in this thread).

Lift does not suddenly fall to zero in a stall. It goes down, but not to zero.

Stalling is a turbulence phenomenon, and the Bernoulli equation does not apply to the stalled flow because it is not potential flow.

[Hotel26]

8 hours ago, mikegarrison said:

Anyway, consider a spacecraft on re-entry

Level, un-accelerated flight for this thought experiment.

The conjecture is that the airfoil applies a force to accelerate the airflow over the leading edge and in the retrograde direction.  The deflection downward is then caused by other forces[*] not applied by the wing itself.  The stream of high-speed, low-pressure air boots up a partial vacuum in the triangular lee section of the upper surface of the wing (in the shadow, so to speak).  For this reason, too, the oncoming air has a much readier path over the top of the wing rather than under it.  The result is something like a hydro-electric dam except that what it generates is a partial vacuum (providing no lift ipso facto).  But, you guessed it, now atmospheric pressure on the underside of the wing is unbalanced and this applies the direct force to the wing that we call Lift.  That, at the end of the day, Newton 3 is obeyed and the downwash matches the lift doesn't surprise me at all, but the situation is far more complicated than the simple Action-Reaction scenario of a cue ball striking a red ball and imparting energy to it.

And, in any case, Newton 3 never explains the cause, but only dictates/describes the reaction.  A rocket engine does not propel a rocket due to the mass and speed of the exhaust gases it discharges any more than the kick to my shoulder of a .303 rifle propels a bullet at supersonic speed.  The explosive expansion of gases in the engine chamber provide an unbalanced force on the "prograde" end of the engine (the cause) and those gases are expelled as the Newton 3 mandated reaction to that propulsion.

The remarkable thing about the airfoil (and Bernoulli?), though, is that a side-effect to production of the partial vacuum is that it provides a non-turbulent exit path for the upper airflow.

A corollary question is: does increasing the angle of attack (increasing the bow wave surface and the lee volume) also increase the acceleration applied to the upper wing airflow, further decreasing pressure in the partial vacuum?

 

EDIT:
* "by other forces": think meteorology and air movement (wind) caused by HI-LO pressure systems...

Edited June 26, 2019 by Hotel26

[wumpus]

2 hours ago, mikegarrison said:

Lift does not suddenly fall to zero in a stall. It goes down, but not to zero.

Stalling is a turbulence phenomenon, and the Bernoulli equation does not apply to the stalled flow because it is not potential flow.

My understanding is that the sudden drop is steep enough that lift often drops well below the weight of the plane, and it is easy to get in a [bad] spin.

10 hours ago, Hotel26 said:

Here's an idle question.  Can a wing produce more lift than 14.7 lbs / square inch?  (Atmospheric pressure at sea level, STP).

Mikegarrison's answer was better, but lift isn't just due to low pressure above the wing, it is due to the differential in pressure above and below the wing.  If you somehow managed to compress the air beneath the wing to higher than 14.7 lbs/in *more* than the pressure above the wing then you could pull it off.  I am unaware of any wing geometry that might pull this off (or why you would want to, the drag would be far worse than just lighter wing loading), but there shouldn't be a hard limit right there.

EDIT: If a helicopter doesn't already do this, just reduce the size of the rotors and spin faster (and cover your ears once they break the speed of sound*).  Helicopters and/or propellers seem the best bet to break the "limit".

* breaking the speed of sound with a helicopter is a good way to break the blades.  Then there's the Tu-95, which has supersonic propeller blades.  Stay far away to maintain hearing.

Edited June 26, 2019 by wumpus
mention propellers/helicopter blades

[Hotel26]

1 hour ago, wumpus said:

Mikegarrison's answer was better

You posted slightly after my conjecture above and most probably had not the opportunity to see it.  That conjecture, that the lifting force is due to unbalanced atmospheric pressure on one side of the wing, has the limit that the pressure differential across the wing (in normal flight) cannot exceed ambient pressure.  My not so idle question then was to see if that was a fatal limitation.  Not at all, I gather; and thanks for your reply, too.

[Hotel26]

There's a subtle difference between "seeking the truth" [science] and having a contest to see "who is right" [football].  I think that is what really, really offends me about this post.

I can recite Newton's Third, but that does not make me a scientist.  (No, it actually makes Isaac Newton the scientist.  He postulated it.  Science is not about knowledge, principally, but about discovery and that only comes with an open mind.)

Newton's Third applies everywhere.

But so does "3 + 4 = 7".

Newton's Third is about the application of forces and the results.  You have to identify the mechanism of the application of those forces.  I gave a scenario above in which I outlined that there may be at least two forces in operation.  Nobody has said a word for a month.

One of the proponents in this conversation seems identifiably more knowledgeable than anyone else but he's simply disparaged other opinions by saying [paraphrased] "flat earthers believe anything".  That gave me the only moment of mirth in this whole serious matter.  "Flat earthers" in the aerospace industry.  Really??  How do they hide that?

I really wish I knew how it worked and I'd be prepared to spend the time and money to do a 4-year course in aerospace to find out, but my instincts are telling me that, at the end, I would not achieve my basic goal, which is to be able to explain to my 13 year-old son how airplanes fly.  Getting the feeling that "the more you know, the less you can explain", in this field.

Perhaps the smartest person in this conversation has been the one challenged to join the "contest" who had already decided that minds weren't open here -- and declined to start.

"Air goes down so the plane has to go up to preserve Newton's Third Law"???  So, OK, that is "cargo cult science", in my opinion.

Sorry to be hard-line about this, but if nobody defends real, open enquiry (the back-bone of science), we all go back to voodoo...

Edited July 20, 2019 by Hotel26

[RCgothic]

Newton's laws always apply.

In equilibrium, the force of gravity is balanced by lift pushing on the wings. The wings push equally on the air. (3rd law).

A mass (in this case of air) experiencing a force is accelerated (2nd law). The air is pushed down.

Edited July 20, 2019 by RCgothic

[RCgothic]

On 6/27/2019 at 1:06 AM, Hotel26 said:

You posted slightly after my conjecture above and most probably had not the opportunity to see it.  That conjecture, that the lifting force is due to unbalanced atmospheric pressure on one side of the wing, has the limit that the pressure differential across the wing (in normal flight) cannot exceed ambient pressure.  My not so idle question then was to see if that was a fatal limitation.

Consider flat disc moving at some arbitrarily stupidly large velocity, presenting its flat side to the airflow.

On the reverse side, every air molecule will be removed from its path. Effectively a vacuum. The limiting low pressure is -1atm gauge at standard temperature and pressure, or 0atm absolute. You can't get an air pressure lower than zero.

On the other side the plate is colliding with vast quantities of air molecules. The faster the plate goes, the more collisions, pretty much without limit. The high pressure upstream can therefore be arbitrarily high.

So there is no limit to the potential pressure differential across the plate, as determined by velocity.

Now angle the plate into the airflow. Now the pressure difference is at an angle to the airflow. Congratulations, you've now got an arbitrarily high lift component.

Everything else about aerofoil design is about chasing efficiency or operating window.

Edited July 20, 2019 by RCgothic

[mikegarrison]

9 hours ago, Hotel26 said:

There's a subtle difference between "seeking the truth" [science] and having a contest to see "who is right" [football].  I think that is what really, really offends me about this post.

I can recite Newton's Third, but that does not make me a scientist.  (No, it actually makes Isaac Newton the scientist.  He postulated it.  Science is not about knowledge, principally, but about discovery and that only comes with an open mind.)

Newton's Third applies everywhere.

But so does "3 + 4 = 7".

Newton's Third is about the application of forces and the results.  You have to identify the mechanism of the application of those forces.  I gave a scenario above in which I outlined that there may be at least two forces in operation.  Nobody has said a word for a month.

One of the proponents in this conversation seems identifiably more knowledgeable than anyone else but he's simply disparaged other opinions by saying [paraphrased] "flat earthers believe anything".  That gave me the only moment of mirth in this whole serious matter.  "Flat earthers" in the aerospace industry.  Really??  How do they hide that?

I really wish I knew how it worked and I'd be prepared to spend the time and money to do a 4-year course in aerospace to find out, but my instincts are telling me that, at the end, I would not achieve my basic goal, which is to be able to explain to my 13 year-old son how airplanes fly.  Getting the feeling that "the more you know, the less you can explain", in this field.

Perhaps the smartest person in this conversation has been the one challenged to join the "contest" who had already decided that minds weren't open here -- and declined to start.

"Air goes down so the plane has to go up to preserve Newton's Third Law"???  So, OK, that is "cargo cult science", in my opinion.

Sorry to be hard-line about this, but if nobody defends real, open enquiry (the back-bone of science), we all go back to voodoo...

Many people in this conversation have given you correct answers that you have rejected. That does not lead people to have a desire to continue to explain things to you.

If you reject answers and want experimental proofs, then it's time to do like the Wright Brothers did and build a wind tunnel in your garage. Your 13-yr-old would probably enjoy that, so I would suggest that as your next step.

[OHara]

Another thread on this topic referenced a magazine article "Bernoulli or Newton, who's really responsible for lift?".  The author could not have meant his title to be taken literally, given that birds and gliders predated Newton.  From the use of those names in the article, it seems that author used 'Newton' to represent the cause of higher pressure on the lower wing surface, and 'Bernoulli' to mean the cause of low pressure above.  It seems he was imagining the reaction force of individual packets of air to be the 'Newton' mechanism, and the higher speed of air above the wing to be 'Bernoulli'.

Bernoulli's principle is usually derived from Newton's laws, applied to air as a fluid.  The tricky part of the Bernoulli result is handling the net effect of all the packets of air pushing on each other and accelerating each other based on Newton's laws.  So you might say Newton + Air-Air-collisions = Bernoulli.

The article quotes examples from the Air and Space Museum expert, on how the pressure decrease above the wing is the larger numerical force.  From this I would conclude "the air pressing on other air is a big deal". 

The magazine-article author, and pilot, chose a catchier conclusion "So much for the 'kite' effect, or Newtonian lift. Bernoulli wins". 
That is a maybe little unfair to Newton, and not very helpful for understanding. The reason the air sped up over the wing was the ambient pressure pushing it into the space the wing has cleared for it, that ambient pressure accelerating the air per Newton's law.  And, the low pressure is allowing the ambient pressure to accelerate more air from above into the low-pressure zone, where it will join the down-wash behind the wing, part of the grand conspiracy of Nature to act according to the pattern expressed in Newton's third law.

On 6/26/2019 at 5:03 AM, Hotel26 said:

Can a wing produce more lift than 14.7 lbs / square inch?  (Atmospheric pressure at sea level, STP).

That would be 100 kPa = 10 tonnes-force per square meter.  That does make the point that air is pushing on us surprisingly hard.   Aircraft only get 500 kg-force/m² from their wings, with the upper surface pressure only reduced 5% or so.

High-altitude aircraft work at lower pressure. The SR-71 seems to get 400 kg-force/m² = 4 kPa up where the air pressure is about 4kPa.  That would seem to be a concrete example, but you might argue if that is flying like a wing, or more like kite; they call that airplane 'the sled'

Hydrofoils get more lift per square meter because the density of water is higher.  If the pressure above the foil goes to zero (or actually to the vapor pressure, small compared to 1atm) you get cavitation and the water separates from the foil.  Usually this is uneven and causes turbulence and drag, but if the craft can thrust through that drag, the flow can separate from the entire upper surface of the foil, and have nearly a vacuum over its upper surface. 

[mikegarrison]

3 hours ago, OHara said:

The article quotes examples from the Air and Space Museum expert

This reminds me of when I visited the National Air and Space Museum about 10 years ago and was surprised and disappointed to see that they had some displays in the area that is supposed to explain aerodynamics to kids that were not just simplified but actually wrong.

Although, I guess I shouldn't be too surprised. It took them about 50 40 years to admit that the Wright Brothers actually had conducted the first powered human flight. They were incredibly invested in the claim that Langley (third Secretary of the Smithsonian Institution) had been the first to achieve powered human flight.

Edited July 21, 2019 by mikegarrison
It was actually 40 years.

[mikegarrison]

Even here on their website they are a bit screwed up:

https://howthingsfly.si.edu/aerodynamics/alternative-theories-lift

Quote

 

THE MOMENTUM EXPLANATION OF LIFT

According to this explanation, the slight downward deflection of the air leaving the trailing edge of a wing is what produces lift. Since for every action there is an equal and opposite reaction, the downward push on the air must result in an upward push on the wing. But this “downwash” results from air pressure differences on the wing—it is an effect of lift, not the cause of it. The wing cannot “feel” the airstream behind it being deflected downward; but it does feel the pressure of air molecules colliding against its surface.

THE CIRCULATION THEORY OF LIFT

This is the oldest and most complex theory of lift. It explains how the difference in air speed over and under the wing results from a net “circulation” of air. Above the wing, the circulatory flow adds to the overall speed of the air; below the wing, it subtracts. But the actual force on the wing results from the difference in air pressure caused by the difference in airflow speeds.

 

These are not "alternative theories" of lift. They are alternative ways to explain and/or calculate lift. It is not an either/or situation that pressure x area = force or that the sum of the forces of the air acting on the wing and the wing acting on the air must = zero. They are both true, so both ways of looking at the problem are equally valid. And they completely misstate the purpose of using circulation to calculate lift. It's not an alternate explanation, but rather a mathematical trick (like separating a vector into two orthogonal x-y components) that allows for easier calculation.

In subsonic flight it is also outright wrong to the say that the wing cannot feel the airstream behind it. (That is correct in supersonic flight.) The pressure on the wing in subsonic flight is influenced by what happens to the the air behind the wing, so the wing does "feel" what is happening back there. Again, this is not an "alternative" to the idea that the wing feels the air pressure; it is a factor in what air pressure the wing feels.

Edited July 21, 2019 by mikegarrison

[mikegarrison]

Imagine you have some apples.

• 1 big green apple
• 1 small green apple
• 1 big red apple
• 1 small green apple

Now some people say the proper explanation for how many apples you have is the "color method". 3 green + 1 red = 4.

Others say the real explanation is the "size grouping". 2 big apples + 2 small apples = 4.

LET THE HOLY WARS BEGIN!

[Hotel26]

I'll start by making an apology for adopting a-possibly-bit-too-extreme stance in my previous.

For context, my objection and involvement in this thread has been about the dispensation of Bernoulli altogether.  That's probably been a misunderstanding engendered by casual language in the original thread.

I've persisted only because, if this is just Newton, one  should be able to identify some forces.  Not so simple because fluid dynamics is involved.  But I can accept that the two are equivalent perspectives on the same thing.  And that flight is just not simple to explain (hence the long confusion and debate in the 'industry').  A simple statement of Newton alone is necessarily a simplistic explanation of a complex mechanism.  One thing is evident, that the upper wing airflow *is* accelerated and therefore the Bernoulli effect *is* in play.  You could say that the mathematics is so difficult that it was inevitable that the feasible wing had to be discovered by trial (why wind tunnels are/were indispensable), especially given the precedent in Nature.

The bigger picture, at least for this layman, is that the modern wing and a plank work fundamentally the same way (wincing saying that), but what makes the wing so entirely different is that it presents a curve the airflow can be accelerated along (deflected) without breaking into turbulence.

Edited July 21, 2019 by Hotel26

[mikegarrison]

4 minutes ago, Hotel26 said:

The bigger picture, at least for this layman, is that the modern wing and a plank work fundamentally the same way (wincing saying that), but what makes the wing so entirely different is that it presents a curve the airflow can be accelerated along (deflected) without breaking into turbulence.

Yes, this is simplified but fairly true.

[kerbiloid]

Spoiler

3 hours ago, mikegarrison said:

Imagine you have some apples.

• 1 big green apple
• 1 small green apple
• 1 big red apple
• 1 small green apple

Now some people say the proper explanation for how many apples you have is the "color method". 3 green + 1 red = 4.

Others say the real explanation is the "size grouping". 2 big apples + 2 small apples = 4.

LET THE HOLY WARS BEGIN!

According to google, the task looks even more funny in French:
grande pomme verte
petite pomme verte
grande pomme rouge
petite pomme rouge

So, humans should just start using proper languages instead of their tribal speech:

stock
<< apple (big | green)
<< apple (small | green)
<< apple (big | red)
<< apple (small | red)
;

 

Edited July 21, 2019 by kerbiloid

[RCgothic]

The reason that accelerated flow exhibits a lower pressure is that a greater proportion of the air molecules are moving in the same direction. In highly simplified form, if all the air molecules are moving parallel to a surface, they are not colliding with that surface so zero pressure. Bernoulli is just Newton for air.

Obviously it's more complicated than that because fluid flows do not behave simply.

[doggonemess]

On 6/26/2019 at 6:54 PM, Hotel26 said:

And, in any case, Newton 3 never explains the cause, but only dictates/describes the reaction.  A rocket engine does not propel a rocket due to the mass and speed of the exhaust gases it discharges any more than the kick to my shoulder of a .303 rifle propels a bullet at supersonic speed.  The explosive expansion of gases in the engine chamber provide an unbalanced force on the "prograde" end of the engine (the cause) and those gases are expelled as the Newton 3 mandated reaction to that propulsion.

I agree with what you're saying, and I'm certain that you know far more about this topic than I do, but I'm having trouble with this analogy. 

I thought about the forces involved, and I think it breaks down like this:

gunpowder = rocket fuel

bullet = rocket 

barrel = engine

shoulder = atmosphere (?)

Or is there no equivalent in the rocket's case - was your intention to show that the bullet leaving the gun has nothing to do with your shoulder, and that it still would have left the gun if the rifle was floating in space? 

I'm just trying to figure this out. Definitely correct me if I'm being a dope.