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Old Mar 09, 2012, 10:48 AM
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A non-aerodynamic proof that a lifting wing pushes down on the earth

(Edit May 2013-- note the title change, to reflect the ideas described immediately below. The original title was, "a non-aerodynamic proof that you can't have lift without downwash". Please re-read the full content of this post, substituting the words "downward push on the earth" for "downwash", and consider whether or not you agree with the argument.

Whether or not this "downward push" does in fact involve some sort of "downwash", i.e. some sort of downward transfer of kinetic energy all the way to the earth's surface, is still something I'm not completely clear on. It was never my intention to suggest that a given packet of molecules left the vicinity of the wing and travelled at a constant downward velocity all the way to the earth's surface.

End edit May 2013)

(Edit May 2012-- my thoughts on this matter have now changed significantly-- I'm still convinced that the earth "feels" a downward push from the wing of an aircraft in flight, equal in magnitude to the weight of the aircraft, which is also equal to the upward gravitational attraction that the aircraft exerts on the earth, but I no longer believe that this downward force need involve any specific amount of downward momentum of the air (downwash). For more, see posts 58, 61, and 72. End edit.)

Most of you already agree w/ this-- regardless of your thoughts about airflow around the tops and bottoms of wings-- but here's another way to look at it--

0) The following will describe the true purpose of downwash, and reveal how the existence of downwash is woven into the fundamental tapestry of physics and not an accidental by-product (like the "exhaust" from an engine) of the aerodynamic creation of lift. Or, stated without the teleological language and subjective weightings and shadings, we can say:

1) The downwash behind a lifting airfoil holds the planet in place, which allows momentum to be conserved. Thus, we can predict the existence of downwash directly from the fundamental Newtonian laws, without understanding anything about what is going on in the "black box" that is the aerodynamics of the flow around the wing.

2) Consider: a planet that is not in orbit around a sun and thus can be considered to be "at rest" with regard to some inertial reference frame. Imagine an aircraft flying a tight circle around a fixed point on the ground, maintaining a constant altitude. If there is no downwash below the aircraft, then the aircraft's gravity will pull (accelerate) the planet upwards toward the aircraft. Given enough time, the planet (and the aircraft) will gain an extreme upward velocity. Clearly this violates conservation of momentum.

3) In constant-altitude flight, the downwash must exert a downward force on the surface of the planet equal to the upward pull of the aircraft's weight (mass times gravity), regardless of whether the aircraft is in ground effect or not.

4) When an aircraft is at rest on the ground, the wheels take over the job of holding the planet down in place and preventing the planet from accelerating upwards toward the aircraft. The ground "feels" the weight of the plane through the wheels in exactly the same way as the ground "feels" the weight of the plane through the downwash.

5) Climbing and descending flight may be more complex, as potential energy is being stored or released. Thrust may include an upwash or downwash which must be considered. I haven't thought this part through all the way yet.

6) A balloon transmits its "weight" (mass * gravity) to the ground in a different manner-- by displacing an equal weight of air, which ultimately has no direction to go but upwards, so that the top of the entire global atmosphere is slightly raised. This exerts an increased atmospheric pressure on the surface of the entire planet. There is no asymmetry in the mass distribution around the center of the planet, so there is no tendency for the planet to accelerate upwards due to the balloon's gravitational pull. (Technically speaking there may be some localized tidal effect on the ground if the gondola is suspended extremely far below the envelope, but no net upward acceleration of the planet as a whole.)

Related threads:

"On the largest scale there is usually no downwash"
http://www.rcgroups.com/forums/showthread.php?t=1602562

(Appears to contradict the above, but really just makes the point that the downwash does not push (accelerate) the planet downwards, because it is counteracted by the upward pull of the plane's gravity)

"Thinking about induced drag, downwash"
http://www.rcgroups.com/forums/showthread.php?t=1605407

(Some questions about the aerodynamics of downwash, induced drag, etc )

"NASA says lift from air shoved down - can we trust NASA?"
http://www.rcgroups.com/forums/showthread.php?t=1539175

( Huge thread that included some discussions of relationship between downwash, momentum, and lift-- if lift is a force not an acceleration, then why is a downward transfer of momentum necessary for lift-- etc)

Steve
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Old Mar 09, 2012, 01:34 PM
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Imagine an aircraft flying a tight circular orbit around a point on the planet, maintaining a constant altitude over the surface of the planet.
You mean like the space shuttle in LEO?
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Old Mar 09, 2012, 02:39 PM
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You mean like the space shuttle in LEO?
No, I mean like a Piper Cub about to lower a bucket to some Amazonian tribesman.

I was using "orbit" in the non-celestial-mechanics sense. A plane flying in a tight circle staying generally above one point on the surface of the earth, at a constant altitude. Your classic "turn around a point", in no wind. I can see how there could have been some confusion because in the sentence before I used "orbit" in the other sense-- have now edited for clarity.

In the space shuttle case, the shuttle and the earth are simply co-orbiting a fixed center which is near (but not quite at) the center of the earth. No momentum issue there at all.

Steve
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Old Mar 09, 2012, 04:05 PM
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You're missing out on another option. The laws of thermodynamics.

You're suggesting that the downwash behind a plane connects to the surface of the planet. But what about the idea that the air is also a viscous gas? As such disturbances in it tend to damp out over time and the motion is converted to heat as it does so. There's lots of examples of how this works. So it's quite possible even on the vast sort of scale that you're considering that the reaction between airplane and air takes place within that mass of air only with the remaining energy being converted to heat instead of connecting the mass of the plane to the earth's mass.
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Old Mar 09, 2012, 04:27 PM
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(Edit May 2012-- my thoughts on this matter have now changed significantly-- I'm still convinced that the earth "feels" a downward push from the wing of an aircraft in flight, equal in magnitude to the weight of the aircraft, which is also equal to the upward gravitational attraction that the aircraft exerts on the earth, but I no longer believe that this downward force need involve any specific amount of downward momentum of the air (downwash). For more, see posts 58, 61, and 72. End edit.)

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You're missing out on another option. The laws of thermodynamics.

You're suggesting that the downwash behind a plane connects to the surface of the planet. But what about the idea that the air is also a viscous gas? As such disturbances in it tend to damp out over time and the motion is converted to heat as it does so. There's lots of examples of how this works. So it's quite possible even on the vast sort of scale that you're considering that the reaction between airplane and air takes place within that mass of air only with the remaining energy being converted to heat instead of connecting the mass of the plane to the earth's mass.
You may be right, bear with me as I think this through out loud and maybe reach some conclusions at the end....

From an energy point of view the situation is complex-- we are burning fuel, dumping heat out the exhaust pipe, etc--

But from a conservation of momentum point of view-- and specifically looking at conservation of momentum in the up-down direction only-- I think the situation is much simpler. In order for the earth not to be pulled upwards by the plane's gravity (mg), it must experience a downward force equal to the plane's weight (mg). This must come from the downwash.

Can a downward pressure be transmitted to the earth's surface even with no downward velocity? As we increase the plane's altitude in a series of steps, we see the cross-sectional (horizontal slice) area of the downwash (as measured at the earth's surface) increase, and we see the velocity of the downwash decrease-- but if the earth is going to "feel" the plane's weight and not accelerate upwards, don't we expect the total downward momentum of the downwash to stay the same, no matter how far below the plane we are looking?

If the downwash is losing downward momentum the further below the plane it travels, doesn't that create a new conservation of momentum problem? What specifically would cause that loss of downward momentum?

It looks to me like the downward momentum of the downwash must be conserved, all the way to the earth's surface.

Can we think of the downwash as ultimately being converted to a pressure wave that presses down on the earth with no downward momentum? But wouldn't this pressure press upwards on the plane, too, complicating the picture further?

One way or another the earth must "feel" the plane's weight in the form of some sort of downward force, or else the earth will accelerate upwards due to the pull of the plane's gravity. I guess the question is, whether this downward force can be imparted by some sort of pressure that involves no downward momentum, or whether there must always be downward momentum, no matter how far below the airplane we are looking. I think there must always be downward momentum, even if it is mixed to the scale where it is a vanishingly small downward velocity spread out over a vanishingly large area.

We can pose a somewhat similar problem involving thrust forces-- what ultimately happens to the rearward momentum of the propwash or jetwash, if it is not conserved indefinitely-- but since there is no planet in existence where an aircraft can travel in one linear direction indefinitely, it's really not a problem. By the time the plane has flown all the way around the earth, it has blown the propwash through a full 360 degrees so there is no net momentum imparted to the atmosphere.

Maybe I'm assuming the molecules in the atmosphere, downwash, etc are perfectly elastic when they are really not? Like, if you have a row of marbles and hit a marble against the first marble in the row, the string of collisions doesn't go on forever? How is conservation of momentum satisfied in that simpler case?

So maybe the appropriate argument is that even if the momentum of the downwash is ultimately converted to heat, this still gets expressed as a localized pressure increase that acts (pushes downward) against the surface of the earth in a localized manner and counteracts the upward pull of the plane's gravity on the earth?


This discussion is starting to branch off into several branches:

1) The earth's surface must feel a localized downward force related to the creation of lift, whether that downward force is caused by the momentum of the downwash, or a high-pressure region due to air heated by the downwash, or whatever. Otherwise the earth would accelerate upward, due to the pull of the plane's gravity, and momentum would not be conserved. The earth must "feel" the plane's weight in some manner-- in some localized manner that is fundamentally different from the "globally dispersed" way that the earth feels the weight of a balloon. The earth must be prevented from accelerating upwards toward the plane, or momentum will not be conserved. That is the key point that is less important than the details of exactly how the downwash changes as it moves down through the atmosphere.

2) But looking in more detail, if there is a downwash at distance Y below the wing (ignoring horizontal distances, just looking at the vertical distances), with downward momentum Z, then at distance Y+1 below the wing, can the downward momentum of the downwash be less than Z? If so, where has the momentum gone? Is this loss of momentum (say through inelastic collisions) still consistent with the basic Newtonian laws? And bringing the problem back around to point #1, has the momentum gone into some form (e.g. pressure) that can still transmit the "weight" of the plane to the earth, acting in a localized manner at some point more or less below the plane, so that the earth is still prevented from accelerating upward toward the plane?

(When I say localized I mean-- it doesn't really matter if the action is spread out over an entire hemisphere-- as long as the net effect is to transmit to the earth a force equal to the plane's weight-- the direction of the force must be "downwards" as defined in our inertial reference frame--meaning that all the different vectors contributing to this force point not toward the center of the earth, but rather point parallel to the plane's weight vector, which at locations very far from the plane, will no longer be aligned with local gravity i.e. no longer point toward the center of the earth. It's hard to see how these forces could be created by increasing the pressure of parcels of the atmosphere that are very far from the plane-- say on the other side of the earth-- so the action must be somewhat localized...)

Steve
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Old Mar 09, 2012, 04:36 PM
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the downwash must exert a downward force on the surface of the planet equal to the upward pull of the aircraft's weight
It sounds like you are saying the aircraft pushes air down and that that air travels downward from the plane and eventually hits the Earth, thereby enforcing Newton's laws.
Is that the premise of your argument?
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Old Mar 09, 2012, 05:09 PM
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(Edit May 2012-- my thoughts on this matter have now changed significantly-- I'm still convinced that the earth "feels" a downward push from the wing of an aircraft in flight, equal in magnitude to the weight of the aircraft, which is also equal to the upward gravitational attraction that the aircraft exerts on the earth, but I no longer believe that this downward force need involve any specific amount of downward momentum of the air (downwash). For more, see posts 58, 61, and 72. End edit.)

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It sounds like you are saying the aircraft pushes air down and that that air travels downward from the plane and eventually hits the Earth, thereby enforcing Newton's laws.
Is that the premise of your argument?
Basically.

The plane's gravity pulls upwards on the earth with a force equal to mg.

Something must be stopping the earth from accelerating upwards toward the plane, because a steady and indefinite upward acceleration of the planet is very inconsistent with conservation of momentum.

The thing that stops the acceleration can only be a downward push equal to the plane's weight (mg), which is somehow or another transmitted to the surface of the earth near the plane. I'm proposing that the downwash is the mechanism that imparts the downward force, equal to the plane's weight (mg), upon the surface of the earth near the plane.

Please see especially the last three paragraphs (starting with "This discussion is starting to branch off into several branches: ") of my last post above.

Steve
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Old Mar 09, 2012, 05:45 PM
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(Edit May 2012-- my thoughts on this matter have now changed significantly-- I'm still convinced that the earth "feels" a downward push from the wing of an aircraft in flight, equal in magnitude to the weight of the aircraft, which is also equal to the upward gravitational attraction that the aircraft exerts on the earth, but I no longer believe that this downward force need involve any specific amount of downward momentum of the air (downwash). For more, see posts 58, 61, and 72. End edit.)

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2) But looking in more detail, if there is a downwash at distance Y below the wing (ignoring horizontal distances, just looking at the vertical distances), with downward momentum Z, then at distance Y+1 below the wing, can the downward momentum of the downwash be less than Z? If so, where has the momentum gone? Is this loss of momentum (say through inelastic collisions) still consistent with the basic Newtonian laws?
My understanding may be fuzzy but my understanding is that momentum in any particular direction must be conserved even if the collisions are inelastic. Am I wrong?

I just googled "downwash momentum weight" and found the following-- do you feel that this is in error? Please follow this link and see what you think. (The link should open to a heading "Section 1.8 Incompressible Flow over Finite Wings", which is at the top of page 79. ) The author is arguing that the downward momentum of the downwash is in fact conserved all the way to the ground. Source: the textbook "Mechanics of Flight" by Warren F. Phillips. Actually, the author's argument is so similar to mine one might think that I am stealing it from him-- and I believe I actually own this book, haven't read it all the way through-- but if you've followed my posts over the lasts several weeks I think you can see I originated these ideas clumsily and independently, anyway nothing here is fundamentally new to science, it's all familiar ground in one form or another....

Steve

http://books.google.com/books?id=6-_...weight&f=false
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Old Mar 09, 2012, 05:53 PM
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While I follow what you're suggesting it's also compounded by the fact that the air is being acted on by gravity as well and in a way is part of the mass of the globe. And that due to how the air dissapates motion and pressure any locallized effect is spread out into a larger volume and mass of air. If it were not the case then we'd feel pressure pulses from aircraft as they pass overhead even at a great height.

And there was that formula from Mark Drela that was useful for determining the magnatude of the pressure pulse at some distance below the path of a plane. The nature of the equation showed that the effect diminished VERY fast. This further adds to the idea that the air mass spreads out the effect quickly into the volume and mass in a wide angle conical manner below the aircraft and to the sides. So once again I'm not sure that a description that uses the air to transfer the aircraft's weight to the earth is valid or not.

Certainly the earth is pulling the airplane towards its center and to some extent the airplane's mass is pulling the earth up towards it as well. I'm just overwhelmed though at what part the air itself plays. That of simply a medium or does the mass of the air become part of the earth to some extent from not at all to a lot.
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Old Mar 09, 2012, 05:56 PM
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(accidental repeat post)
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Old Mar 09, 2012, 06:56 PM
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If you use the bound vortex theory and extend the vortex sheets back to the point at which the take off roll began then You can conclude that the downwash inside the vortex is equal to the upwash outside of it. QED.
(Think of a giant smoke ring, or more correctly a series of them that stretches from the take off point to the plane in flight. IN an ideal fluid vortices always form complete rings, or terminate against a surface as happens with a tornado)

The only reason we don't see these giant vortex rings is because the energy is eventually dissipated in the air's viscosity.

Looked at this way you don't have to worry about gravity, the curvature of the earth or anything beyond the air/plane system.

Pat MacKenzie
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Old Mar 09, 2012, 07:13 PM
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Thank you Pat, that's exactly what I had in mind.

Steve, I agree that the momentum of the system you have defined is conserved. My disagreement is the way the force is transmitted. I do not think that the air molecules that leave the wing travel to the ground.

We can see this clearly in the 2D case in the picture I posted earlier
http://static.rcgroups.net/forums/at...treamlines.jpg
Strealines are essentially a frictionless wall. By definition, the air flow cannot cross a streamline. With this in mind, it is clear that the air going past the wing does not really change in altitude much after it is downstream from the wing.
The 2D case demonstrates the effect of the bound vortex, so this example does not demonstrate the effect of the trailing vortices.
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Old Mar 09, 2012, 07:15 PM
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But in that case, what would be holding the earth down, preventing the earth from rising up toward the plane as it flies in circles?

(Conclusion-- no planet can exist whose atmosphere is an ideal fluid-- or flight can never be invented on such a planet? )

Steve

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Originally Posted by pmackenzie View Post
If you use the bound vortex theory and extend the vortex sheets back to the point at which the take off roll began then You can conclude that the downwash inside the vortex is equal to the upwash outside of it. QED.
(Think of a giant smoke ring, or more correctly a series of them that stretches from the take off point to the plane in flight. IN an ideal fluid vortices always form complete rings, or terminate against a surface as happens with a tornado)

The only reason we don't see these giant vortex rings is because the energy is eventually dissipated in the air's viscosity.

Looked at this way you don't have to worry about gravity, the curvature of the earth or anything beyond the air/plane system.

Pat MacKenzie
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Old Mar 09, 2012, 07:26 PM
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The 2D case demonstrates the effect of the bound vortex, so this example does not demonstrate the effect of the trailing vortices.
That may be important-- conclusion-- no wing of infinite span may exist (or at least, take to the air), as it would violate the law of conservation of momentum?
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Old Mar 09, 2012, 07:35 PM
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(Edit May 2012-- my thoughts on this matter have now changed significantly-- I'm still convinced that the earth "feels" a downward push from the wing of an aircraft in flight, equal in magnitude to the weight of the aircraft, which is also equal to the upward gravitational attraction that the aircraft exerts on the earth, but I no longer believe that this downward force need involve any specific amount of downward momentum of the air (downwash). For more, see posts 58, 61, and 72. End edit.)

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Steve, I agree that the momentum of the system you have defined is conserved. My disagreement is the way the force is transmitted. I do not think that the air molecules that leave the wing travel to the ground.
Certainly not the same molecules. But must the downward momentum be conserved all the way to the ground? Consider this both from the perspective of

A) the need to generate a downward force to prevent the ground from being attracted upward toward the plane by the plane's gravity, and

B) simple consideration of the law of conservation of momentum-- once the downward momentum of the downwash is initially generated, may it be dissipated to zero before it reaches the ground? This is non-obvious to me.

We can all agree that the ground is not forced downward. I suppose if the ground is not being forced downward, then there is no reason that the first layer of molecules touching the ground needs to be forced downward either, and so on and so forth counting upwards-- the non-movement of the ground could be transmitted upwards to the overlying molecules of air, in which case the downward force that prevents the planet from rising could be transmitted to the ground in the form of a pressure rather than a momentum? I.e. simply define the lowermost part of the atmosphere as "part of the ground"?

Food for thought....

Steve
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