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How Does an Airplane Wing Work: a Primer on Lift

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How Does an Airplane Wing Work: a Primer on Lift

Continue reading the Original PF Insights Post.

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Really nice Insight!

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Ripe for the sequel :)andNewton." That's a real missed opportunity.

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That was awesome! Could you please recommend me some literature about this topic? A bit more about fluid dynamics?

Thanks,

MJ

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For example, the go-to text for introducing undergraduate engineers to the basic principles of flight is

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I'm wondering if there's a relatively simple explanation of the effects of the component of flow perpendicular to the surface of a wing.

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The issue that I recall was that the calculation of the velocity field had to consider the effects of the flow perpendicular to the surface of a wing, not a post correction done after the velocity field was calculated.If you already know the velocity field and you know the ambient pressure outside of the region of influence of the airfoil, you can calculate the total pressure and everything else you need to calculate lift from Bernoulli's equation provided there is no separation and you already have another means of calculating the velocity field.

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I think what boneh3ad is alluding to (bh, correct me if I'm wrong), the potential flow equations (or Navier Stokes equations, if you want to be more sophisticated) you use to calculate the velocity distribution (if you are doing a model, rather than obtaining field velocity data) already take into account the accelerations you are referring to. So, provided you correctly solved the fluid dynamics equations, your results for the velocity distribution should be consistent with the Bernoulli equation, and the corresponding pressure distribution from Bernoulli equation should correctly predict the lift.

Chet

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Agreed with Bone here. You can easily engineer an airfoil to exceed below flat pitch into negative pitch. I have never used a remote control helicopter, but I am sure most of them fly upside down easily by being able to do this.

(the pitch angle of my rotor blades on my actual helicopter does not go below flat pitch, the collective just does not go down that far, lol)

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For me one of the confusing issues is the effect of the frame of reference. From the wings perspective, consider the case of an ideal wing where the relative flow is diverted with no change in speed, so no change in energy, and no work performed by the wing onto the air. From the air's perspective, the affected air ends up with a non zero "exit velocity" (it's velocity when it's pressure returns to ambient), so work is done. From this perspective, as the air crosses the plane swept by the wing, work is performned on the air, mostly in the form of a pressure jump from below ambient to above ambient. Bernoulli applies to the air as it approaches that plane from above and departs from that plane below, but Bernoulli is violated as the air crosses the plane because that is where the wing performs work on the air. It's similar to situation of a propeller as noted in this NASA article:

*We can apply Bernoulli's equation to the air in front of the propeller and to the air behind the propeller. But we cannot apply Bernoulli's equation across the propeller disk because the work performed by the engine* (propeller) * violates an assumption used to derive the equation.*

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

I always thought that the argument against Bernoulli was based on the work done using the air's frame of reference, not the validity of using Bernoulli's equation to calculate pressures given a velocity field using the wing as a frame of reference.

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

I always thought that the argument against Bernoulli was based on the work done using the air's frame of reference, not the validity of using Bernoulli's equation to calculate pressures given a velocity field using the wing as a frame of reference.

The aerobatic ones generally have a pitch angle range around +/- 12 degrees. There's a throttle versus pitch angle curve programmed into the transmitter to keep the rotor speed near constant in spite of the torque load due to higher pitch angles.radio control helicopters

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relative flow is diverted with no change in speed, so no change in energy, and no work performed by the wing onto the air.

there has to be a change in speed. Even at flat pitch for a symmetrical airfoil, the air is moving a greater distance at the same time. Seeing as how Speed is a function of time and distance, if distance increases but time remains constant, the speed must change. It does not matter that the speed above and below the airfoil is changing at the same rate, it is still changing. If the speed of air did not change going over an airfoil even at flat pitch on a symmetrical airfoil, while the distance increases and the time remains constant, there would be a vacuum on the trailing edge of the airfoil. And no one here will suggest that is happening.

Even if it is not a perfect airfoil, you can't just move something through air (at any speed) and have it result in no work is being performed.

Two particles of matter can not occupy the same place at the same time. Air is made of particles and so are the wings. Work is being performed by the wing.

Edit: just saw your reply to my RC heli post. So it has a governor to keep the rotor at a certain speed? like most modern helis. okay

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You are aware that the physics is invariant to the choice of the inertial frame of reference of the observer, correct? So as long as the wing is not accelerating relative to the ground, the analysis of the flow by an observer traveling along with the velocity of the wing yields the same results as the analysis of the flow by an stationary observer, aside from a constant velocity difference.For me one of the confusing issues is the effect of the frame of reference.

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You are aware that the physics is invariant to the choice of the inertial frame of reference of the observer, correct? So as long as the wing is not accelerating relative to the ground, the analysis of the flow by an observer traveling along with the velocity of the wing yields the same results as the analysis of the flow by an stationary observer, aside from a constant velocity difference.

I love you

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The two frames of reference in question here are related by a simply Galilean transformation and are otherwise functionally identical (already stated by @Chestermiller while I was typing this). The work done in each frame of reference is the same. The lift calculated is the same.

As for why Bernoulli's equation applies here, consider that Bernoulli's equation is an energy conservation statement at its heart, where total energy in the flow is represented by total pressure. If it applies along a streamline, then if every streamline originates in a region with the same total pressure, then it applies everywhere that hasn't been acted on by a non-conservative process (i.e. where flow energy has been conserved). Since Bernoulli's equation generally only applies in an inviscid flow, it is therefore valid everywhere here.

I'll also remind everyone that we are considering lift here. If you want to calculate an accurate value for drag (which in general cannot be done) you cannot neglect viscosity.

Nothing requires any sort of "same time" constraint here.

As for why Bernoulli's equation applies here, consider that Bernoulli's equation is an energy conservation statement at its heart, where total energy in the flow is represented by total pressure. If it applies along a streamline, then if every streamline originates in a region with the same total pressure, then it applies everywhere that hasn't been acted on by a non-conservative process (i.e. where flow energy has been conserved). Since Bernoulli's equation generally only applies in an inviscid flow, it is therefore valid everywhere here.

I'll also remind everyone that we are considering lift here. If you want to calculate an accurate value for drag (which in general cannot be done) you cannot neglect viscosity.

Even at flat pitch for a symmetrical airfoil, the air is moving a greater distance at the same time.

Nothing requires any sort of "same time" constraint here.

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That would either one, make a vacuum in our atmosphere or two, make the air occupy the same space as the airfoil.

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S=D/T

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Air frame of reference - From some old notes: Cessna at cruise speed, downwash speed ~= 4.5 m/s, mass flow ~= 2500 kg/s, work done per second ~= 25,300 joules (25,300 watts ~= 34 horsepower). How do I get this from the wing's frame of reference?work done ... frame of reference

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Your s=d/t claim only works if you assume t is constant. What I'm saying is that is not necessarily true. It is *not* true if the object is producing lift. The wing certainly does change the speed but there's no reason that the time of a particle moving from front to back has to be the same as the time of a particle moving the same distance in the free stream. That is not the mechanism by which the air is accelerated. Now, it may work out that a symmetric airfoil at zero angle of attack exhibits this property, but it's not a general rule.

Now that I think a little more, except for the small region near the airfoil where viscosity has sapped some of the energy, it's quite possible that a symmetric airfoil at zero angle of attack would exhibit an equal (or very close to it) time for a particle to move from one edge to the other near the airfoil as compared to the same distance in the free stream. That's just not a general rule.

Just take a look at this video. In the beginning part where they just release the small puffs of smoke, it's clear that the regions near the airfoil are traveling the same distances are regions in the undisturbed air in dramatically different amounts of time. That's what I'm trying to illustrate.

@rcgldr Where are those numbers from and what do they mean? The idea of a mass flow doesn't even make sense without some area through which it is traveling. A single velocity doesn't make sense either, as the wake behind a wing will have a much more complicated profile. Do have a diagram to explain what you mean here, because I'm not following.

Now that I think a little more, except for the small region near the airfoil where viscosity has sapped some of the energy, it's quite possible that a symmetric airfoil at zero angle of attack would exhibit an equal (or very close to it) time for a particle to move from one edge to the other near the airfoil as compared to the same distance in the free stream. That's just not a general rule.

Just take a look at this video. In the beginning part where they just release the small puffs of smoke, it's clear that the regions near the airfoil are traveling the same distances are regions in the undisturbed air in dramatically different amounts of time. That's what I'm trying to illustrate.

@rcgldr Where are those numbers from and what do they mean? The idea of a mass flow doesn't even make sense without some area through which it is traveling. A single velocity doesn't make sense either, as the wake behind a wing will have a much more complicated profile. Do have a diagram to explain what you mean here, because I'm not following.

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I thought it was a Cessna, but the numbers are off (too low). These are old notes. Doing a web search I found an article that mentions Cessna, downwash, and mass flow, but that's not where I got my old (over 15 , maybe 20 years old) notes from.Where are those numbers from and what do they mean?

http://www.allstar.fiu.edu/aero/airflylvl3.htm

It's easier to consider the case of a high end glider like the Nimbus with a 60:1 glide ratio. At 60 mph, descent rate is 1 mph, average weight 1500 lbs. The decrease in (the gliders) gravitational potential energy, and increase in total energy of the air translates into 4 hp. Most of the energy added to the air would be mechanical, some of it thermal. This is a better example to show energy is added to the air by the glider, from the air's frame of reference. How would I convert this data to the glider's (wing) frame of reference?

From the wing's frame of reference, the air is slowed down due to drag.amount of time in general.

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If I do that, than what was 0 velocity from the air's frame of reference becomes a negative velocity from the plane's frame of reference.You would essentially just subtract off the free stream velocity of the plane.

From the planes frame of refrence, the slight decrease in speed due to drag is multiplied by the relative flow: 1/2 m (v - Δv)^2 - 1/2 m v^2 ~= - m v Δv. So from the plane's frame of reference, it would seem the loss in energy due to drag would be greater than the increase in energy due to downwash, which I assume is a fraction of the relative flow speed. From a wing frame of reference, I don't see how diversion of flow could increase the energy of the air. It's easier to see this if only drag is considered, like a bus. From the air's frame of reference, the energy of the air is increased by the bus, but from the bus frame of reference (bus moving with no wind, or bus not moving with an oncoming wind), the relative flow is slowed down, decreasing the energy of the air. Maybe I'm missing something here.

I did find this old quote from Mark Drela related to my point about curved flow

Date: Wed, 17 Feb 1999 14:19:57 GMT

Newsgroups: rec.models.rc.air

In article <7a9l31$23u$1@pale-rider.INS.CWRU.Edu> ...

Professor Mark Drela, MIT Aero and Astro wrote:

"Bending the free airstream causes pressure gradients" on the wingsurface

(wing at an AOA) This wing deflection of the airflow also causes vertical

momentum on the inert airmass (downwash).

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As to your other paragraph, I'm really having a tough time deciphering your language. The bottom line is that if you think from the frame of the wing and moving air, the wing deflects air downward. In oother words, the wake is going to have a downward component to its velocity. If you change the reference frame by subtracting the free stream velocity, that doesn't affect the downward velocity at all. The downward momentum change remains the same in both frames, ergo so does the lift.

If you want to talk drag, the wake coming off of an airfoil is going to be slightly slower than the free stream in the wing's frame, so when you subtract off the free stream velocity, that results in a slight forward velocity, which you also frequently cite.

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What I was trying to get at is that the pressure differentials are due to the pressure gradient's that are perpendicular to the relative flow, coexistant with the curved flow. The idea is that a wing produces lift by curving (diverting) the relative flow. The air travels faster above a wing because the pressure gradient related to curved flow coexists with a low pressure zone just above the wing's surface.That quote has nothing to do with your point. That quote simply says that the air flow bends around the wing and the pressure varies, which corresponds with the velocity bending.

My issue isn't about the change in momentum, since that is the same in both frames of reference. My issue is about the change in energy of the air by the wing. The change in energy of the air is affected by the frame of reference.As to your other paragraph, I'm really having a tough time deciphering your language. ... momentum ...

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Also, of course the kinetic energy changes. Energy is frame dependent. What is not frame dependent is conservation of energy, so the change in total energy should be the same either way. After all, you've removed all of the kinetic energy associated with the free stream velocity both upstream and downstream of the airfoil.

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The shape of the airfoil, angle of attack, and free stream velocity could be considered as the causes. As you stated, everything else, pressure gradient normal to and in the direction of flow, change in velocity of the affecte air, ... , are coexistent.It isn't really a cause and effect thing. It's two sides of the same coin.

Using the glider model, from the air frame of reference (no wind), the decrease in gravitational potential energy is offset by the increase in the air's energy (mostly mechanical, some thermal). From the glider's frame of refernce, it's not clear to me.conservation of energy

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Otherwise, I'm honestly not sure how I can be any more clear. The flow fields in the two frames are exactly the same only offset by the free stream velocity. Forces such as lift are the direct result of the change of momentum, not energy, and the momentum change is identical in each case.

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I meant the decrease in gravitational potential energy of the glider, which is offset by the increase in the energy of the air (since the glider is in a steady descent and not accelerating). It's a 1500 lb glider descending at 1 mph, 4 hp, 550 ft lbs of energy every second. Sorry I didn't make it clear I was referring to the potential energy of the glider.The increase in gravitational potential energy is negligible in a flow like that. It is air

However, the same issue exists for something simpler, like a parachutist with parachute deployed in a vertical and steady descent. From the ground / air (no wind) frame of reference, the decrease in gravitational potential energy is offset by an increase in energy of the air. From the parachutist's frame of reference ... ? So I'm not sure this was going anywhere.

... but I see your point, the energy issue shouldn't matter, it's the momentum change that corresponds to lift (and drag).

and thanks for creating the primer.

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https://en.wikipedia.org/wiki/User:Rolo_Tamasi

Lift on a wing is the result of differential radial forces over the wing surface.

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