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Differential Obstruction Theory[edit]

This theory is a recent theoretical explanation of the lift of an airplane wing.


Literature on the theory is limited. It is mentioned in passing in a book on flight by Anderson, of the Smithsonian Institute. Since the publication of this explanation in 1978, it seems to have been abandoned.

Some limited details are found in the Lift talk page. I'm not aware of any other information about it.

Through the above Talk page, I am seeking to learn exactly what the theory says, and what its relationship is to the generally accepted scientific account.

Summary of the theory[edit]

DOT introduces the concept of the relative "degree of obstruction" created by a given pair of (perhaps) arbitrary curves on the wing section.

In some of its variants, the theory appears to state that the airspeed adjacent to one of the two arcs is greater there than at the other if, and only if, the "obstruction" there is greater. Because this principle allows one to determine something about the relative airspeeds above and below the wing, and thus the downward and upward forces on the wing, it provides an explanation of lift.

Beyond that, it is not clear exactly what the theory says about the airspeeds at the upper and lower surfaces, except that positive lift is always the conclusion.

Definition of obstruction[edit]

The first question that must be answered in order to understand the theory is what the definition of obstruction is. Obstruction is the central concept of the theory.

It is not clear whether there is scientific (ie, quantitative operational) definition of the degree of obstruction or not.

According to some accounts, there is a scientific definition. The "degree of obstruction" of curve A (or area A, if one considers potential flow model as an infinitely long 3D wing) is greater than that of curve B if, and only if, the arc length of A is greater. Anderson doesn't mention this definition, but it is given in the Lift:Talk page.

Other proponents state that no definition can be given, and that none is necessary, because the concept is so simple that it is intuitively obvious.

Others agree that no definition is possible or necessary, but for the opposite reason: that the definition requires complex math. According to this argument, it is not necessary to define the central concept of the theory--the degree of obstruction--because it is too complex.

So, in this case, the argument is made that there is no intuitive, non-mathematical way to determine which surface creates a higher level of obstruction.

One specific approach has been offered to determine the level of obstruction.

The first step in this procedure is to "calculate the streamlines (using for example potential-flow theory as in the NACA 0012 graphic)"

It is not specified whether the Kutta condition is to be imposed in calculating the streamlines.

Until this is answered, the rest of the procedure is meaningless. The issue is that, if the Kutta condition is NOT imposed, then the first step is itself meaningless. Potential flow theory doesn't provide the streamlines until the problem is constrained. The Kutta condition is the only physically meaningful constraint in the case of the flow over a wing. Mathematically, other constraints could be imposed, such as dictating the circulation. But to assume the circulation is to assume the lift--the thing being proved.

If the answer is, on the contrary, that the Kutta condition is to be imposed, then the entire DOT theory becomes superfluous, because we have reverted to the classical explanation of lift.

Therefore, this first step in the calculation places the theory on the horns of a dilemma.

Selection of the two curves[edit]

Some proponents appear to believe that the two curves A and B must be defined according to the conventional definition of "chord", "leading edge", "trailing edge", and "angle of attack".

This idea leads to serious concerns about the validity of the theory. All of these terms are merely conventional definitions, with no significance in Newton's laws.

Others state that the selection of the two arcs is arbitrary.

This tack avoids the above problem, but creates a more serious one. If the lengths of the two arcs is arbitrary, then so is the relative obstruction of the two arcs. The theory then becomes meaningless, since its predictions are determined by the arbitrary choice of arcs, and a wide range of mutually exclusive predictions results.

Relation to accepted science[edit]

Some proponents view the explanation as being based on the accepted scientific theory of fluid dynamics. Others seem to view it as an alternative to that theory. A third group do not accept that any accepted scientific theory exists.

Some proponents regard the theory as transcending traditional science. They state that the claims of the theory are exempt from the conventional view that any new theory must be proven to be scientifically valid.

One justification given for this exemption is that the proposition is intuitively obvious.

Another is that the claims are to be accepted as true, but are something other than a scientific theory. The argument here seems to be that, if a claim is made which the proponent doesn't regard as a "theory", then it must be accepted without any scientific validation being offered.

Here is an example of this argument, from Lift:Talk:

"Calling it “obstruction” theory is something unique to this talk page: Anderson does not use that label and I haven't found a source who does use the term"

Some proponents claim that there is no accepted scientific theory of lift, and so the DOT is as good as any other.


"The most import thing to remember when writing this article, I think, is that there is no universally accepted explanation of lift."

(MB, 9-Jan-2008)

One variation on this idea that has been offered is that the paradigm of science, which assumes that all physical phenomena are governed by Newton's second law, cannot be correct. The argument is that since science requires that a dynamical system obey a second order differential equation, which often results in a boundary value problem, and matter cannot solve a boundary value problem, that science cannot be correct.


The theory is based on the potential flow model, which assumes 2D steady inviscid incompressible flow.

The theory has been presented only in terms of a typical asymmetric airplane wing, with rounded leading edge, sharp trailing edge, and convex shape both above and below. It is not clear if it applies only to this shape.

The theory has been presented only in terms of a wing with zero angle of attack, with angle of attack being defined per the arbitrary customary social convention (not in terms of the actual flow or other physics-based definition). It is not clear if the theory only applies to this case or not.

Comparison to ETT[edit]

It is possible that differential obstruction theory is essentially a variant of the equal transit time theory. The latter is a fallacious but--for much of the twentieth century, widely accepted--popular explanation of lift.

One similarity is that the DOT, like ETT, seems to beg the question. That is, it assumes an airflow, and then uses this airflow to explain the airflow. The airflow that is assumed happens to be one which results in lift, so the conclusion seems to follow from the initial assumptions, for which no explanation is given. Specifically, in most explanations of the theory, it is arbitrarily assumed that the leading stagnation point is the same as the arbitrarily defined "leading edge" of the wing. This assumption is contrary to both theory and experimental fact in most cases. However, in some cases, it is at least approximately correct for a flow that obeys the Kutta condition, such as cambered wing at zero angle of attack. This may be why only these cases are ever shown in diagrams used to give the theory.

The scientifically accepted theory, which demonstrates that the Kutta condition follows from accepted scientific principles, and that lift follows from that plus Newton's laws, is nowhere mentioned in differential obstruction theory. It appears that in so doing, the theory necessarily is contradictory to the accepted science.

Some proponents explicitly reject the generally accepted theory of lift for a wing, regarding the Kutta condition. Example:

"Also, remember that the Kutta condition is not necessary for lift: where do you apply the Kutta condition on a rotating cylinder in a free stream?"

(MB, 9-Jan-08)

Celestial Dome theory[edit]

This is another of the popular explanations of lift which are printed in articles and books by pilots or sailors for an audience of pilots or sailors. These theories are not subject to peer review by scientists, and as a result, tend to contain a mixture of valid science clearly explained, and fallacies. The false science tends to get endlessly repeated by other non-scientific authors, until they become permanent fixtures of the flying or sailing culture.

According to the Celestial Dome theory, the sky is regarded in effect as a solid dome. An airplane is assumed to be flying so close to this impermeable surface that a Venturi tube is created between the sky and the upper surface of the wing. Likewise, the earth is regarded as being so close that it and the lower surface of the wing form a Venturi tube .

Lift is explained by these assumed Venturi tubes. As with most popular myths, including ETT, the case of an asymmetric section at zero angle of attack is emphasized. The reason for this bias is that all myths have the same objective of avoiding the real cause of circulation: the Kutta condition. The special case of the asymmetric wing at zero angle of attack permits a blossoming of plausible alternatives to the scientific explanation, based on the difference in shape between upper and lower surface. In this case the claim is that the "high" upper surface--relative to the chord line, which is in fact an arbitary convention, but which is invariably treated as a physically significant feature in these fallacious arguments--and the sky "squeeze" the upper flowtubes into a narrow passage. Pressure is reduced, and lift results.


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Lift doing work[edit]

I updated Dolphin51's talk page, you can go there and delete this section from here if you want.

  • Jeffareid wrote about the lift force doing work on the air. My view is that, when we are viewing an airplane in flight from the inertial reference frame attached to the atmosphere, lift never does work because it is, by definition, the component of the aerodynamic force perpendicular to the velocity of the airplane. Even though lift is perpendicular to the direction of an aircraft, it's not perpendicular to the surfaces of the wings which have an effective angle of attack and divert the air downwards. There is a non-zero vertical component of distance that the surfaces of a wing (both upper and lower) interact with the air. It would seem that the work done would equal lift times this non-zero component of distance. Using the air as a frame of reference, after an aircraft flies through a volume of air, most of the resultant air flow is downwards, corresponding to lift, and some forwards, corresponding to drag. Note that the downwards force applied by gravity onto the aircraft, and from the aircraft onto the air, is eventually transmitted through the air onto the surface of the earth (spread out over a much larger area), which "reacts" with an equal and opposing upwards force. The downforce of the atmosphere onto the the earths surface includes the weight of the air and any object that the air is supporting (after taking into account vertical components of acceleration). Without getting into how it happens, a wing works because it diverts (accelerates) the air downwards (lift), at the cost of diverting some air forwards (drag). Jeffareid (talk) 11:12, 16 February 2009 (UTC)
You wrote
"Even though lift is perpendicular to the direction of an aircraft, it's not perpendicular to the surfaces of the wings which have an effective angle of attack and divert the air downwards."
Agree, it's not relevant that lift is normal to direction of motion of the aircraft. By the definition of work, any small surface whose normal has a component in the direction of motion of the adjacent parcel of air is doing positive work on that parcel.
Likewise, on the upper surface of the wing aft of the max chord point, the air is doing positive work on the wing, losing energy and transferring it to the (talk) 22:46, 16 February 2009 (UTC)
I call this "void theory", if an air flow doesn't follow (or fill in via turbulence) a convex surface, then a void would be created. Because air has momentum (and viscosity), it can't fill in the void instaneously, so the result is an acceleration of air towards the "void" region, coexisting with a reduction in pressure. I've been acused (or credited?) of inventing "void theory", but the Wiki article on wing mentions the same concept: In that case a low pressure region is generated on the upper surface of the wing which draws the air above the wing downwards towards what would otherwise be a void after the wing had passed. Wing. It's similar to form drag, except that it results in acceleration of air perpendicular to the direction of travel because of an effective angle of attack. Jeffareid (talk) 00:32, 17 February 2009 (UTC)
I picture something like what you call "void theory" when I do a thought experiment to explain to myself why the flow always remains tangent to the surface or zero. This is one of the boundary conditions required to solve either equation: Napier-Stokes or PFT. Unless the wing's made of thin cloth.
I picture the known flow (PFT, or real, depending on mood). The velocities and pressures are constant. The flow at some little area is tangent to the surface.
I ask myself, "If this flow were subjected to a random small perturbation (butterfly flapping its wings in the Amazon for example), in which the flow at this spot were suddenly not tangent, would the system restore its original state automatically?" In other words, is it in equilibrium?
If you have a concrete feeling for why a dynamical system is in equilibrium, then you understand the system. If you don't, you don't.
For example, suppose the tiny surface region is on the top, is perfectly flat (a funny wing, maybe a reject) and located near the trailing edge. Therefore, the surface normal points up and to the right (aft, downwind).
The sideways force (relative to its local direction) on the neighboring air parcel is zero, by F=mA, and it is moving in a straight line. Its x speed is positive, and its y speed is negative. The pressure gradient sideways to motion is zero. The pressure gradient in the direction of motion? Let's postpone that...too much to think about and not important we hope.
What if the perturbation caused it to turn slightly left (more upward) for a moment?
Here the experimenter must choose between treating it as solid for a moment or as plastic, as one does in every other case. I usually try both.
To be continued. Thoughts welcome. (talk) 18:57, 17 February 2009 (UTC)
why the flow always remains tangent to the surface or zero. I think of it as a dynamic situation, where the flow accelerates perpendicular to the surface, resulting in a flow towards the surface as it recedes and moves out of the way. Perhaps it's more easily understood by imagining the air flow at the back of a bus, where a moving void is introduced into the air, drawing the air into the direction of the trailing surface of the bus. The upper surface of a wing also introduces a void, but since the vertical component of surface movement is much less than the horizontal component, the air takes the path of least resistance, accelerating and flowing mostly downwards towards the surface and only a bit forwards. The same principle explains why land speed record vehicles (Bonneville) use long tapered tail sections to reduce drag; to gradually introduce a void that can be filled by the air flowing at a relatively small inwards speed instead of a very fast forward speed. Jeffareid (talk) 08:25, 18 February 2009 (UTC)
You wrote
"I think of it as a dynamic situation, where the flow accelerates perpendicular to the surface..."
"...resulting in a flow towards the surface as it recedes "
You mean parallel to, not towards, right?
I meant towards, using the air as a frame of reference. From the wing point of reference the flow isn't quite parallel, near the wing, the flow is less than parallel. Going back to the air as a frame of reference, both the acceleration and airflow over most of the wing is downwards and a bit forwards. Less than parallel - there's a boundary later that thickens and normally becomes turbulent along the upper (and sometimes lower) surface of a wing. The first diagram here is an exaggerated example: laminar_flow.htm
"why land speed record vehicles (Bonneville) use long tapered tail sections to reduce drag; to gradually introduce a void that can be filled by the air flowing at a relatively small inwards speed instead of a very fast forward speed."
If we assume there is a steady flow and no friction, why would avoiding a very fast forward speed at the back of the object reduce drag? (talk) 18:36, 19 February 2009 (UTC)
I'm not sure what you're getting at with friction. Even if a bus had frictionless skin, it introduces a large flat moving void at the back end of the bus that the air has to partially fill in by accelerating inwards and forwards. This creates a large amount of drag. If a long tapered tail was added to the bus, it would have much less drag, because most of the void would be filled by relatively slow inwards acceleration of air.Jeffareid (talk) 22:00, 19 February 2009 (UTC)
No, with no friction, there's no drag. Here's why. The air's pushed around the back corners by a very high pressure zone (relative to the pressure at the surface of the bus at the corners). As it approaches the stagnation line, the air turns again, this time downwind. The large force for this high acceleration is provided by a high pressure zone at the stagnation point. The force of this aft pressure zone pushing the bus forward equals the force at the front stagnation point pushing the bus backward. The net force on the bus is zero. (talk) 22:36, 22 February 2009 (UTC)
You wrote:
"I meant towards, using the air as a frame of reference...
When you say "the air", which parcel of air do you mean? If you choose a parcel of air that is accelerating, then Newton's laws don't apply. (talk) 18:47, 22 February 2009 (UTC)

Lifting bodies - conflict with obstruction theory[edit]

How would "obstruction theory" or "Kutta condition" explain these lifting body airfoils with "humps" on the bottom and "thick" trailing edges? M2_F2_glider.jpg M2_F3_rocket_powered.jpg originally posted in Talk:Lift_(force), now in archive 2 Jeffareid (talk) 11:31, 16 February 2009 (UTC)

The differential obstruction theory cannot explain the lift on anything, in my opinion. I think it is a fallacy.
By "Kutta condition" I assume you mean the accepted theoretical model used to predict or explain lift based on potential flow theory ("PFT" for now) plus the Kutta condition. In this model, the Kutta condition is imposed in order to get a unique solution (ie, to fix the circulation) to the flow for the case of a wing with a sharp trailing edge. The scientific explanation of why the Kutta condition occurs is external to the PFT: the theory of viscid flow explains why the Kutta condition occurs, and PFT is by definition an INVISCID theory.
There is nothing about humps on the bottom of a wing that affects the application of this theory. If the wing has a single trailing edge, PFT plus Kutta condition will give the flow and the lift--zero, negative, or positive, regardless of humps and bumps as long as they are smooth.
It will be as accurate as expected: not very. Real wing flows are never anywhere close to inviscid and are always turbulent over much of the wing's surface. PFT was once famously described as "Now, assume that water isn't wet...." It wasn't till the foundation of modern aerodynamics that realistic models of lift based on the boundary layer were developed.
In fact, PFT plus Kutta doesn't even account for the boundary layer, and by definition doesn't allow for turbulence. So, it doesn't allow for the laminar flow region, the turbulent boundary layer region, nor for separated flow.
Therefore, taken by itself PFT is useless for explaining the lift of a wing with a thick trailing edge (where the flow involves turbulence and separation of the boundary layer behind the thick trailing edge).
It's sometimes used in a sub-sonic hybrid model, where a virtual wing boundary is imagined, and all the viscous effects occur within the boundary. In this case, it may be a reasonable approximation to the flow around the wings you refer to.
But nowdays, fast computers allow solutions based on Napier-Stokes and other equations that make more realistic physical assumptions. (talk) 19:27, 16 February 2009 (UTC)
My Kutta condition comment was in reference to the often stated "thin trailing edge" as a "requirement" for lift, when it seems that the real purpose of a thin trailing edge would be reduction of drag. Jeffareid (talk) 00:34, 17 February 2009 (UTC)
Ah, ok, my bad. Please then see if we agree on this, which is pretty much what you said about the real reason, but with some detail added :
To over-simplify: the real purposes of a thin trailing edge are:
(a) to make a low drag section with no lift (a fairing, in other words). The flow will generally be smoother at the trailing end, reducing drag due to turbulence.

(b) to make a low drag section with lift. Altering the angle of attack will then powerfully and efficiently control circulation (lift) up to a certain point (approaching stall). If the angle of attack is such that the trailing edge is exactly where the zero-circulation stagnation point is located, lift will be zero. As the wing is rotated clockwise (air coming from the left), the leading stagnation point will rotate counterclockwise and the aft stagnation point will rotate clockwise. Circulation, and thus lift, will therefore increase. A non-sharp trailing edge wouldn't JUST create more turbulent friction. It would also allow the aft stagnation point to slide around as angle of attack is increased, unlike sharp edge which holds onto stagnation point firmly. Stagnation point would slide to the spot on the rear area of the wing until there was so much friction that it couldn't slide any further. Lift still, but at a higher cost.
In order to make a low drag section with lift that doesn't stall till a higher angle of attack, make a cambered wing. Boundary layer separation (stall) will occur at a higher angle, and max lift coefficient will therefore be greater. I mention that this is the real reason for cambered wing because all three of the fallacious theories assume that camber somehow is involved in the creation of lift (talk) 01:25, 17 February 2009 (UTC)
Why is it called "stagnation" point? Only a small amount of air in the boudary layer isn't moving with respect to the wing. Seems like separation point and rejoin point would be better terms. I always thought cambered airfoils were cambered so that the surfaces follow the induced air flow (as well as contributing to the induced flow), which has an increasing downwards component of velocity as the air travels from leading edge to trailing edge (with respect to a wing).
Is there a tradeoff on the trailing edge between producing lift and minimizing an induced vortice from the differening flow above and below the trailing edge, or restated designing the trailing edge so that the air flows above and below the trailing edge are nearly the same (speed, direction, and pressure)? Jeffareid (talk) 04:55, 17 February 2009 (UTC)
Note: I tend to write about scientific subjects in the form of logical syllogisms, often without adding the courteous "I think". But every fact, and every bit of logic, is only my best thought at the moment, and all are subject to debate and correction. Hope my habit of speech doesn't offend. My wife always tells me I've got to change; I plan to, tomorrow.
Why "stagnation point?" I'm not sure how they chose that term. I think the terms you mention would be clearer.
Only a small amount of air in the boudary layer isn't moving with respect to the wing. Argument against this: "Stagnation line" or point is used also in potential flow theory. There is no boundary layer in potential flow theory. In that theory, the speed of the air as one approaches the stagnation point from any direction goes to a limit of zero--it truly is stagnant, even in a model where there is zero friction.
I always thought cambered airfoils were cambered so that the surfaces follow the induced air flow... Here is an argument against. The direction of flow at the trailing edge, which is the direction of the trailing stagnation line there, is always intermediate between the tangents to the upper and lower surfaces there, regardless of camber. So this could not be the reason for using camber.
(as well as contributing to the induced flow),... Here is an argument against. In any wing, regardless of camber, there is downwash. So this could not be the reason.
induced flow, which has an increasing downwards component of velocity as the air travels from leading edge to trailing edge (with respect to a wing) Yes. To be more detailed, if we think of a very simplified 3D vortex flow model, the downward component is positive inside the vortex loop and negative outside of it. Since the region just aft of the trailing edge is inside the loop, the downward component there is positive.
Is there a tradeoff on the trailing edge between producing lift and minimizing an induced vortice from the differening flow above and below the trailing edge, or restated designing the trailing edge so that the air flows above and below the trailing edge are nearly the same (speed, direction, and pressure)?
The induced vortex is caused by circulation, to speak mathematically, and by the difference in pressure between the upper and lower surfaces at the wingtips, to speak concretely. Not by the difference in directions of upper and lower flows at the trailing edge far from the wingtip. So no, this would not be a reason to minimize the designed trailing edge angle. The induced losses caused by generating the trailing vortex are minimized by the designers by high aspect ratio, and by optimizing the distribution of circulation along the wing (an elliptical distribution of circulation is optimal.) But even with a perfect distribution of circulation, if there is lift, there is still circulation. Therefore there is always induced drag, always a trailing (talk) 12:17, 17 February 2009 (UTC)
I didn't mean minimize the trailing edge angle, but instead optimizing it for minimum drag, and was wondering if the optimum angle might be the one that results in near equal pressure above and below the trailing edge. (Part of this equalization would be due to the lower pressure flow from above drawing some of the higher pressure below into the air flow aft of the trailing edge). Jeffareid (talk) 14:11, 17 February 2009 (UTC)
Interesting question, but I don't know enough detail yet to think about it. Say that we are comparing two different designs, similar except the for trailing edge angles of intersection of the upper and lower surfaces. Assume the flow is smooth in both cases (no turbulence). Is this a good the starting point? (talk) 18:30, 17 February 2009 (UTC)
Note that the diagrams of pressure versus chord position on aifoils at the trailing edge usually end with the pressures converging to a point (becoming equal), but I don't know if this is aft of the trailing edge. Naca_0012.svg Jeffareid (talk) 20:44, 17 February 2009 (UTC)
In a pressure vs. chord position diagram, the curves must always intersect at the trailing edge, by the definition of pressure. Reason: at the intersection of the two curves, the chart is not showing the individual pressures at two different points, but the single pressure at a single point. Aft of the trailing edge, I don't understand your question about two pressures converging or not. What two pressures? (talk) 14:09, 19 February 2009 (UTC)
The curves could intersect aft of the airfoil, but for many airfoils the curves smoothly join and follow the same line very near the end of an airfoil, as shown in that graph. Two pressures the graph is inverted, negative (below ambient) pressure above, positive below. The upper curve is for the pressure along the upper surface of an airfoil, the lower curve is for the pressure along the lower surface. These are the two pressures (upper and lower surface related) that I was referring to. Jeffareid (talk) 22:10, 19 February 2009 (UTC)
Reset indent. The pressure at the end of the upper curve is the pressure at the trailing edge. The pressure at the end of lower curve is the pressure at the trailing edge. Same identical point in space, so, same pressure. After the end of the curves, ain't no curves, so there ain't nothin' to (talk) 22:47, 19 February 2009 (UTC)
For that naca0012 airfoil at 11 degrees AOA, the pressures converge and follow the same path for a small distance before the trailing edge of the air foil. With other airfoils, the pressures may not converge until at or a tiny bit past the trailing edge, which would increase the induced vortice at the trailing edge. Jeffareid (talk) 02:20, 20 February 2009 (UTC)
I don't understand. How could one measure the pressure on the upper surface at a point past the trailing edge? (talk) 12:19, 20 February 2009 (UTC)
I badly worded that. The pressure on the upper and lower surfaces wouldn't converge. The pressure in the air flow from above and below the wind would converge aft of the trailing edge, the higher pressure flow accelerating towards the lower pressure flow, increasing the induced vortice at the trailing edge as mentioned before. Jeffareid (talk) 14:03, 20 February 2009 (UTC)
Ah ok, sorry.
No, I don't see how moving that "point of equal pressure" forward would have any effect on induced drag, unless in so doing you reduced the lift (which defeats the purpose of the wing) or the distribution of lift in the transverse direction to make it more elliptical.
I was just pointing out an observation of airfoil diagrams I've seen. If I had to guess, perhaps since most of the lift is accomplished well in front of the trailing edge, then optimizing for reduced drag at the trailing edge improves performance, which is why I asked the original question. It's not a big deal, I was just curious. Jeffareid (talk) 04:18, 21 February 2009 (UTC)
You are right that if a wing were designed to create a lot of lift closer to the trailing edge, it would just create a lot of drag. But it wouldn't be induced drag. It would be due to turbulence or boundary layer separation. Boundary layer separation does involve vortices, as does induced drag. So maybe this is what you meant? (talk) 12:30, 21 February 2009 (UTC)
If you look at a top view of the wing, the flow above the wingtip is inward and the flow below the wingtip is outward. This difference in the sideways component of the velocity above and below is what causes the vortex. (talk) 18:57, 20 February 2009 (UTC)

What is induced drag?[edit]

The classic definition "drag related to producing lift" is almost meaningless, since this doesn't take into account the amount of mass of air affected by an airfoil. The larger the mass of air affected by a wing, the less the required deflection. Is there some theoretical limit for a given wingspan and chord for a wing? The overall drag is related to the more common term "form drag", and some skin friction (combined with viscosity) effect. It's never been clear to me how (or why) form drag is seperated into two components, induced and parasitic. Jeffareid (talk) 02:28, 22 February 2009 (UTC)

The classical definition you gave is so vague as to be meaningless.
Why are they held to be different?
If there is frictionless, incompressible 3D flow, and lift, will there be induced drag? Yes.
Will there be any other kind of form drag? No.
If there is viscous, incompressible 2D flow, and lift, will there be any induced drag? No.
Will there be any other form drag? Yes. Even in 2D, where induced drag is undefined, viscosity destroys the balance between the pressure at the back of the wing pushing the wing forward, and the pressure at the front pushing it backward.
So, in both cases, these are completely independent forms of drag. (talk) 04:08, 22 February 2009 (UTC)
Wiki has a reasonable definition: Lift-induced_drag, but the article states wing tip vortices as the cause, while the article links to Lifting-line theory which states vortex sheet from the trailing edge as the cause. As one AE explained it to me, the wing tips of a 747 would collapse if all of the induced drag was due to wingtip vortices. The definition makes more sense, the deflected air flow results in a change of momentum of the air in the forward direction, however part of the deflection is due to forward acceleration of air, so I'm guessing that the angle of deflection used to define induced drag is atan((downards component of deflected air velocity) / (air speed)), and that parasitic drag is related to the forwards component of deflected air velocity? (talk) 02:47, 23 February 2009 (UTC)
Good point. I don't get it either, how to put these two definitions together into a consistent definition. There is a great diagram in "The Symmetry of Sailing" which I just came back to today, and realized that I never fully understood it. I think it may be helpful to us but I don't have a way to copy it here. Can you find a copy of this book? Meanwhile, I will let you know if I come across a satisfactory explanation, and please do the same if you learn more. (talk) 03:18, 23 February 2009 (UTC)

Assumption of flow parallel to the wing surface[edit]

The direction of motion of a parcel at the surface is always parallel to that surface, unless the speed is zero relative to the wing at that point. If the direction were more toward the wing, the wing would be absorbing matter. If away, then the wing would be creating air. It is necessary to consider the direction of the parcel as the limit of the direction of some point in the parcel, such as the center of mass, as the parcel size approaches zero. If the speed of the parcel is increasing and the surface is flat, then according to Bernoulli's principle, the outer streamline will be approaching the surface as the parcel narrows, and the center of mass of the parcel will also be approaching the wing. But the smaller the parcel, the closer the direction of the center of mass comes to being parallel to the surface. In the limit, the direction is parallel (talk) 22:59, 22 February 2009 (UTC)

From what I've read, the boundary layer thickens and may become turbulent from leading edge to trailing edge above a wing. This boundary layer is wedge like so the air flow outside the boundary layer doesn't quite follow the upper surface, and what would be a "void" is filled in by the wedge shaped boundary layer. This effect is more pronounced at high Reynolds numbers. One way to demonstrate this is to use a gas with a low vicosity factor, in this case using a flame to heat up the gas flow which also lights up the airfoil. In this sequence of pictures, it's clear that the flow isn't parallel to upper surface (or attached), but still deflected. airflow_and_gas_flow_youtube
What I was getting at previously was that in a dynamic situation, using the air as a frame of reference the air from further above a wing is accelerating and flowing towards the upper surface of the wing, but the wing has passed by before the air from further above reaches the point where the upper surface formerly was. At speeds below mach .3, I've read that the downwards (and initially backwards) flow of air occurs well above and a bit in front of the wing, as air from all directions is accelerated towards the moving low pressure zone directly above the wing. Jeffareid (talk) 03:06, 23 February 2009 (UTC)

Note: We need to identify which model we are talking about, as we may be answering each other with two different pictures in mind but not know it.
In PFT, there is no boundary layer and no turbulence.
You are speaking of a model where there is viscosity and turbulence. Here are my comments, based on that model:
General: The speed at the wing surface is zero everywhere. In contrast, in PFT it's only zero at the stagnation point (or points, depending on the parameters).
"From what I've read, the boundary layer thickens and may become turbulent from leading edge to trailing edge above a wing.
Yes, this is also my understanding.
"This boundary layer is wedge like so the air flow outside the boundary layer doesn't quite follow the upper surface, and what would be a "void" is filled in by the wedge shaped boundary layer.
Yes. The direction of flow in the streamtube neighboring the boundary layer wherever it has non-zero speed is always tangent to the boundary layer, not generally to the wing surface. The boundary layer forms a sort of virtual wing and the flow outside (not counting a boundary separation region) acts like the inviscid fluid in Potential Flow Theory ("PFT").
"This effect is more pronounced at high Reynolds numbers.
Which effect? (a) Widening of the boundary layer, (b) turbulence in the boundary layer, or (c) something else? .
Both (a) and (b). This is getting beyond my knowledge based on what I've read. That link of the youtube photos, airflow_and_gas_flow_youtube, shows a low viscosity (the gas) case, which similates a higher speed situation, and the flame above the air foil isn't parallel to the upper sufrace of the air foil, but is still deflected downwards until the last few photos where the angle of attack produces a stall. In some wind tunnel testing, a low vicosity gas (helium?) is used to see the effects of high Reynolds numbers (faster air speed, longer wing chord) on small models for more accurate measurements. The widening of the boundary layer is also related to angle of attack and the airfoil shape as well as Reynolds number.
I looked up (b) in the sailing book to confirm that you are right (which of course, we knew ! :-) and to understand it again. I can't keep R number in my head for some reason. In my understanding the reason that tendency to turbulence increases with R is that turbulence is promoted by inertia (this part not clear) and opposed by viscosity (this part is clear...friction is always damping out motion) added. The part about inertia seems to require that one consider the flow as a sort of a harmonic oscillator, with some characteristic "resonant" frequencies. Turbulence, according to the book, starts in the laminar flow region as a random perturbation (butterfly flaps its wings in the Amazon) which has some frequency content. The resonator amplifies some of these, and the tiny turbulent region grows as it moves aft, retaining its shape. The other frequencies get damped out.
So I kind of understand why high inertial forces (the numerator of the Reynolds number) promote turbulence. Its like putting an organ pipe outside in the wind. If it has a high R (a big 16 foot bass pipe, say around two octaves below middle C) there will be plenty of energy at that pitch to cause it to make a loud sound in the wind. A pipe three octaves above middle C (tiny Reynolds number) can't find in the random wind flow enough energy near its resonant frequencies to overcome viscous damping, so it makes very little sound.
As for (a), I simply take your word for it that widening of the boundary layer is promoted by high R. I don't understand why the boundary layer widens to begin with, and I have no articles that explain it unless its somewhere in "The Symmetry of Sailing" that I haven't studied yet. (talk) 12:33, 24 February 2009 (UTC)

A side note, since we've been talking about understanding drag: the biggest factor by far in creating drag is neither (a) nor (b), I think. It's boundary layer separation. Dimples are added to a golf ball to reduce drag. They do this by increasing turbulence in the boundary layer. Even though turbulence increases drag. The reason is that a turbulent boundary layer is slightly less prone to boundary layer separation. A slight reduction in the size of the separation region swamps the effect of adding turbulence. (talk) 15:29, 23 February 2009 (UTC)
I've only read that dimples reduce the tendency for a golf ball to curve (Magnus Effect), the flow detachment points at the upspin and downspin surfaces are more "aligned" on a dimpled spinning ball than a non-dimpled spinning ball, so less tendency to curve. I only recall a few instances of aircraft that used dimpled surfaces, and don't recall the results. Jeffareid (talk) 08:09, 26 February 2009 (UTC)
I've read a number of times that dimples have been found experimentally to dramatically increase distance travelled by reducing drag, but I have no sources handy. What you read doesn't mention that important factor for why they're used, which seems odd but may be because the writer' subject was specifically about controlling tendency to curve. The text you wrote implies that dimples reduce lift, which surprises me but I don't know.
Re use of dimples in aircraft: same here. I know it's been tried but it's been many years since I've read about it. (talk) 12:39, 26 February 2009 (UTC)

Turbulent flow isn't always bad. It can follow a convex surface better than a laminar flow.

In the case of gliders, the laminar flow detaches, transitions to turbulent, and reattaches. The surface of the wings on a composite glider are "roughed" up with 600 grit sandpaper, or sometimes "turbulators" are used. turbulators.htm. On small model gliders in the 1.5 meter class, the Reynolds numbers are low and the laminar flow doesn't separate consistently, so they use turbulator strips.

Regarding drag, I've always though that it is related to work being peformed on the air. The linear kinetic energy of air is changed via forward acceleration, and the angular kinetic energy of air is changed via angular acceleration (turbulent eddies). Jeffareid (talk) 01:25, 24 February 2009 (UTC)
You wrote
In the case of gliders, the laminar flow detaches, transitions to turbulent, and reattaches.
I think this is not correct--could you check it? According to Ross, the typical sequence is quite different.
Boundary layer with laminar flow
Boundary layer with transitional flow (unpredictable mixture of laminar and turbulence
Boundary layer - turbulent
Separation - no boundary layer
Boundary layer - Re-attachment.
I'm basing this on what I've read at a few web sites. Do a web search for "glider oil flow test", and you'll get a few hits.
You wrote
Regarding drag, I've always though that it is related to work being peformed on the air.
This is also what I've thought. Specifically I think it is
Work done on the air, per unit time, by the backward component of force on the wing
divided by
Speed of the wing (talk) 15:03, 24 February 2009 (UTC)
Power = force x speed.
You wrote
The linear kinetic energy of air is changed via forward acceleration
The linear kinetic energy of which air? Do you mean the total kinetic energy of all the air in the atmosphere?
Only the air affected by an aircraft passing through a volume of air.
If so, then this is also what I think.
When you say that the air is accelerated forward, 'which air' do you mean? Do you mean the acceleration of the center of mass of all the air in the atmosphere? If so, I'm not sure, I will have to think about it. If we could assume the flow is irrotational in the limit of small parcels, then I think your statement is probably not correct. This is at and beyond the limits of my knowledge so far, but I will need to understand it if I am to get a basic understanding of lift.
Are you excluding PFT model when you say the above? If not, I'm not sure that you are correct. It depends on what the answer is to my puzzle about whether induced drag occurs in PFT. (talk) 15:03, 24 February 2009 (UTC)
Yes, I'm excluding PFT in all my posts. Jeffareid (talk) 22:00, 24 February 2009 (UTC)

Why does the boundary layer get thicker as one moves along the wing?[edit]

This question has always bugged me, and I don't recall ever seeing an explanation of it. Until I understand this, I really don't feel that understand lift and drag at a basic layman's level, which is a long-term goal of mine. (talk) 15:29, 23 February 2009 (UTC)

I'm not sure it has to, but around convex surfaces there has to be some sort of stress versus strain deformation due to pressure differences and corresponding accelerations. Since the air has momentum, it can't quite follow a convex surface, depending on the amount of acceleration and pressure differential required to nearly follow the surface. At the surface of the wing, the air isn't moving, but futher away the air is moving. I'm not sure if this thin shear layer is considered as part of the boundary layer. I'm thinking you have a shear layer, with the inner edge not moving with respect to the surface of a wing, and with the outer edge transitioning into laminar or turbulent flow, "merging" with what ever flow there is just a bit further away. There may be yet another separate flow above the one just above the shear layer. Really you have a bunch of flows. Air from all directions is accelerated towards lower pressure zones and away from higher pressure zones, except that flow through the solid wing is prevented by the presence of the wing, which allows the wing to divert the air perpendicular to the direction of travel. Jeffareid (talk) 08:21, 26 February 2009 (UTC)

Is there induced drag in Potential Flow Theory?[edit]

I have supposed not. I thought that induced drag entered consideration only when the vortex line is considered. There is no vortex line in 2D.

But what about this? If induced drag is due to downwash, and downwash exists in PFT whenever there is lift (ie, whenever there is non-zero free flow plus non-zero circulation, then there is induced drag in PFT whenever there if there is circulation. Is there downwash in PFT? If not, then the downward component aft of trailing edge is not downwash. In that case, what is downwash? (talk) 17:10, 23 February 2009 (UTC)

I've never liked the concept of 2D flows or infinite span wings, specifically the idea based on generating finite lift with an infinite wingspan. To resolve this, assume some amount of mass per unit volume on the wing, and then take the limit of lift / drag as wingspan approaches infinity. Jeffareid (talk) 08:27, 26 February 2009 (UTC)
You have incorrectly assumed that the potential flow model is based on generating finite lift with an infinite wingspan. In fact, it is based on finding the lift per unit length of wingspan, and then calculating the lift as span times lift per unit length. Does this address your issue with it? (talk) 12:14, 26 February 2009 (UTC)
Possibly, the issue is that as wingspan approaches infinity, then so does it's weight and the required lift. Lift per unit of wingspan is where it should stop. Lift per unit wingspan times infinity is infinity, it doesn't tell you much. Lift / drag per unit of wing span as wing span approaches infinity is interesting. Jeffareid (talk) 15:15, 26 February 2009 (UTC)
PFT would indeed be ridiculous if it were trying to find the total lift of an infinite wingspan. But it is not. It is only trying to find the sectional lift. It is used to find an approximate value of the lift only of a finite wing. Actual length times sectional lift is the estimate of lift of the real wing.
It is the same as a simple introduction to electromagnetism or capacitance or kinetic theory of gases or acoustics. One always starts in an introductory text with just such a model, based on infinite extent, for simplicity. But one is not actually trying to calculate the capacitance of an infinitely large capacitor, or the energy contained in the magnetic field around an infinitely long wire.
Does this make sense? My philosophy has been this. If one doesn't first understand the case of a time-independent, infinitely long wing without friction, one will never understand a more difficult model which takes end effects, turbulence, and friction into account. First step has to be a baby step, and then build understanding on top of the simple physical principles, which remain valid for all models. (talk) 18:06, 26 February 2009 (UTC)
Yes, and I wasn't paying attention to the title, PFT. I was thinking about the limit of lift / drag per unit section of an infinite wingspan in real air, not PFT. Sorry, was half asleep when I posted that (now the other half is asleep). Jeffareid (talk) 21:14, 26 February 2009 (UTC)

The natural state of a particle, a rigid bodies, or a body of fluid[edit]

Newton discovered that the natural condition of an object is not rest at a low place, as science had said for the previous 2,000 years. Its true tendency had been masked by friction, and by unawareness of forces such as gravity.

Perhaps by doing a thought experiment in which friction didn't exist, Newton discovered that the natural state of a particle is

motion in a straight line.

From this, it follows that the natural state of a rigid body is

motion in a straight line, OR
rotation about the center of mass, OR
a linear combination of these two.

From this, it follows that the natural state of a body of fluid in the vicinity of an obstruction is

a translational motion analogous to motion in a straight line; OR
circulation, which is analogous to rotation about the center of mass; OR
a combination of these two.

If the obscuring effect of friction is removed in a thought experiment, then the flow around a wing is one of the natural states of a body of fluid: a combination of translation (airspeed of the craft) and circulation.

In the case of a particle, the natural state is one with

no forces

For a rigid body, the natural state is one with

no forces EXCEPT
internal tensile forces which result from inertia

For a body of fluid translating or circulating, the natural state is one with

no forces, EXCEPT
internal compressive forces which result from inertia.

In all cases, the natural state which Newton discovered is a theoretical abstraction, not "natural" in the usual sense, because friction is everywhere in nature. (talk) 12:33, 24 February 2009 (UTC)

Fluid dynamics task force[edit]

Hello Mark. The former WikiProject Fluid Dynamics has been revived as the "Fluid Dynamics Taskforce" to the WikiProject Physics. Support is welcome, and if you like to join, you can do so at WP:FDTF. See also the talk page at WT:FDTF. Regards, Crowsnest (talk) 18:27, 10 April 2009 (UTC)

Lift Article-Talk pages, Momentum Transfer++[edit]

Hi Mark,

I just posted the following on the Lift-Talk page. This will probably be deleted very quickly from there, so I am also posting it here for you to read.

(Zapletal Writes ->) Mark, the main problem here is that you are dealing with religious zealots. Steelpillow and Burninthruthesky are true believers of an unsupportable ideology that "Lift is due to downwash". They are also both, unquestionably, dilletantes in this field. (Note that "dilletante = a person whose interest in a subject is superficial rather than professional".) Because of their lack of technical knowledge the only way that S and B can support their ideology is by continually hiding other people's posts (such as your's above, or mine at bottom of Talk-Archive-8), or by outright deleting them, or by threatening to block all contrary views in any way they can (again, see your hidden section above).

There was ONE expert editor here recently, namely Doug McLean, a lifetime Boeing employee and "Boeing Technical Fellow" before he retired. Over the last year or so Doug worked very hard to improve this article. But Steelpillow and Burninthruthesky mounted a relentless campaign of, frankly, pathetic arguments that resulted in the ""Lift <=> downwash" claim being shouted loud and proud at the top of the article. Burninthruthesky even stooped to the deplorable tactic of accusing Doug of unacceptable Wiki conduct on "Administrators Noticeboard - Incidents", page 872 #59. You only have to read through the archived Talk pages 7 and 8 to see the extreme HYPOCRISY of S and B in accusing Doug of "Incivility", "Not Listening", "Not Being Balanced", "Pushing own PoV", etc.

The end result of S and B's efforts is that the one person BEST qualified to edit this article is now gone. A disgraceful example of two inadequate nobodies gaming the system in order to boost their self-esteem!

At the moment Mr Swordfish is somewhere in the middle. For a while he was supporting Doug in Doug's attempts to remove "The Statement". But when S and B applied a little pressure Mr Swordfish folded. And while Mr S didn't directly accuse Doug of any unacceptabe Wiki conduct, he also did NOTHING to point out that S and B were, in fact, the ones engaging in exactly that sort of unacceptable conduct!

Anyway, the bottom line here is that THE LUNATICS HAVE TAKEN OVER THE ASYLUM. In particular, Steelpillow seems to have dedicated all his efforts to SUPPRESSING all views that are contrary to his own. He does this while making NO efforts to put forward well-reasoned arguments in support of his views. At the moment the only support for "TS" comes from a tiny number of UNreliable sources (or RSs taken OUT of context), while the great ocean of RSs all disagree with it.

Mark, I am encouraged to see that there are still some people out there who are trying to think these things through in a rational way. But, like Doug, I have no interest in spending excessive time helping the majority of lunatics here hasten our society's descent into The Next Dark Ages. I wish you the best of luck!

(PS. Please browse Lift-Talk pages 7 & 8, and also the User-Talk pages of S, B, Doug, Mr S, etc., for background.) (End Zapletal) (talk) 01:35, 19 February 2015 (UTC)

Thanks very much for this background and kind words, Zapletal. It is very discouraging to see Wikipedia abused in this way by the people you mention, and so many generous and knowledgeable writers pushed out. We all learn a lot from Wikipedia, but we could learn so much more, and acquire so much less misinformation, if it were not for this irresponsible, rather hateful behavior. I also feel that I could contribute to the editing effort, in those ways that a curious layman with some verbal and critical thinking skill often can.
I had hoped that a kind word might turn away wrath from the offenders. I thought that the pattern of giving only non-rational replies might be worn down by patient re-asking of questions until a rational response was received. Maybe not in this case.
Concerning the question of the role of momentum, which has frustrated and baffled me for decades, I still hope to cheat Wikipedia a little and at least learn the answers (perhaps using user talk pages?) even if abusers will not permit me to do any editing. I can convince myself that I am collaborating in developing improvements "offline" against the day when (wiki) wars shall cease. (talk) 15:12, 19 February 2015 (UTC)
Mark, I'm sorry you have been caught in the crossfire of this dispute, which has been going on at least since last August, was apparently settled, and now appears to be flaring up again. The dispute has been repeatedly presented as a misconception about the physics in those who wish to include The Statement by those who seek its removal. I won't try to explain in my own words. You can find a good explanation of the physics in section 112 of Lanchester: [1]
Hope this helps. Burninthruthesky (talk) 07:35, 20 February 2015 (UTC)
Thanks for your kind thoughts. And for the link! I will check it out.
It was disappointing to be harassed into leaving such an interesting Wiki subject, but not a big deal. I felt like a guest volunteer worker in Afghanistan who was allowed to leave when the Taliban took over, with only a minor public thrashing. The user community lost very little in any future contributions I might have made.
In contrast, it seems they lost everything when Doug McClean left, apparently hounded out. I just viewed a video presentation he made on Lift at U of M Engineering (wow!), and heard of his book on the subject. He is apparently one of the leading authorities in the country if not the world on this subject, and seems to be a real gentleman with a sense of humor as well. I would give a lot to have his expertise again at hand. (talk) 17:03, 20 February 2015 (UTC)

(Zapletal Writes - >) Mark, I noticed you just removed your 13 questions? Nevertheless, I prepared some answers, so I will give them here in the hope they are helpful to your understanding of Fluid Dynamic Lift.



1. Air comprises many particles, which act as if they were independent of each other.

2. The foil-air interaction consists in collisions between particles and foil.

3. Air comprises many particles and acts as if it were a continuous fluid, with respective to macroscopic measurables.

4. The foil-air interaction consists in continuous forces between foil and deformable constant-density parcels.


All of the above are merely different HYPOTHETICAL MODELS that can help you understand how the real world works. The idea that "air" is made of many independent "particles" that bounce off each other like little billiard-balls is no more "true" here than the idea that it is a "continuum" of stuff that can be indefinitely subdivided.

For example, the best model we have these days for the behaviour of really small stuff, like the above particles, is Quantum Mechanics. But in QM the "small things" can be thought of equally as sometimes being "particles", and sometimes being "waves". And sometimes they are both? And, for a really accurate account of everything, we should consider the interaction of ALL of the wavefunctions of EVERYTHING, EVERYWHERE, for ALL TIME. This approach quickly becomes too complicated to be a "useful" model.

Here is some background for ways of thinking that IMO are useful.

In antiquity Plato had chiselled above the entrance to his Academy the words, "Let no one ignorant of geometry enter here." This was NOT because he wanted his students to know about triangles and such. But rather because he wanted them to be familiar with the way of THINKING about any subject that was epitomised in the ancient teaching of geometry. This approach was later exemplified in Euclid's "Elements", which became the one compulsory textbook all students had to have for the next 2,000+ years. (And, sadly, nowadays it is a book that almost no student has heard of!)

This ancient way of thinking is nowadays called "Axiomatic-Deductive" reasoning. A more accurate description is "DEFINITIONS + Axioms => Deductions". Note that while giving clear "Definitions" is perhaps the most crucial part of this system (eg. see first word, Book 1, Page 1, of "Elements"), such clear definitions are hardly ever given these days! After the Definitions come a short-as-possible list of "Postulates" and "Common Notions" (= Axioms nowadays). These are clear statements of what is NOT KNOWN for certain, but must be ASSUMED in order to make progress. These Definitions + Axioms make a clearly stated foundation for all that follows. And following are the many Propositions, which are deduced in an incontrovertible step-by-step manner from the D+As ONLY. (So no "wild leaps", as is common these days.) These Propositions are useful ideas, such as Pythagoras's Theorem, which are complicated enough that they would be difficult to trust in themselves, but are made completely trustworthy by their ironclad descent from the earlier very simple list of D+As.

Anyway, if you read Newton's "Principia...", you see a book modelled very closely on the "Elements". It starts with clear Definitions of important words. Then there are three "Axioms", nowadays called Newton's Laws. These are clear statements of what Newton COULD NOT PROVE, but which he nevertheless had to ASSUME to be true so he could make progress. Then follow the many useful Propositions where interesting Deductions are made, such as the "inverse square" relationship of gravitationl force, which Newton found to be the "best fit" to observed data. IMO it is because of this ancient approach to reasoning that Newton called his book "The MATHEMATICAL Principles of Natural Philosophy". That is, it is an "idealised model" of how the real world might work, albeit one based on a very clear and honest way of thinking.

So, bottom line here, none of your above models is any "truer" or "falser" than the others. But the most "preferable" model, IMO, is the one that is most clearly and honestly explained in the above "D+A=>D" way (ie. with CLEAR Definitions, and CLEAR statements of what is ASSUMED), and that also gives the most accurate predictions of real world observations.



5. If we measured the transfer of momentum across the interface, the result would be equal in magnitude to the Lift.

6. If we measured the transfer of momentum across the interface, the result would be zero.

7. If we assume (1) and Newton's Laws, then it can be proved that theoretically the transfer of momentum across the interface is equal in magnitude to the Lift.

8. If we assume (2) and Newton's Laws, then it can be proved that theoretically the transfer of momentum across the interface is zero.

9. Force does not equal rate of momentum transfer between two bodies, if the force is constant and there is another force on one of the bodies cancelling the first. (Principle of No Momentum, Lanchester p. 7)


To paraphrase Newton's Axioms I and II, "A force impressed on a body causes a change in the body's quantity of motion" . (For more accurate versions I recommend Motte's English translation 1729, because Newton's words are much corrupted these days.)

The important points here are:

1. Momentum (= Newton's "quantity of motion") is a quantity that belongs to a body.

2. In order for there to be "transfer of momentum" between bodies, there must first be "forces impressed" between the bodies.

Earlier on the Lift-Talk page I gave an analogy of an Aerofoil being "supported" above the Earth by a Ball bouncing between A and E. In this case A moved on a "mmm" path because the "impressed force" acting on it varied significantly over time. So, while only E's gravity force acted on A, A moved in a downward curved path gaining downward momentum. Then, for the short time that the Ball contacted A and gave it a net upwards impressed force (ie. = - F.grav), A moved in a upward curved path, gaining upward momentum.

BUT, (and all this is very metaphorical!!!), imagine N x Balls bouncing between A and E such that they each take turns contacting A. Furthermore, assume that while each ball is in contact with A (for 1/Nth the time) it exerts an upwards contact force EXACTLY equal to earth's downward gravity force. So the total (net) impressed force on A is ZERO and there is NO CHANGE TO A's MOMENTUM ... EVER. This is effectively what happens in the Kinetic Theory of Gases model, where a great many "balls" are continuosly supporting A with a steady Lift force, which exactly counteracts gravity.

But what about the "transfer of momentum" to the gas particles in KToG, or to the Balls in above analogy?

The KToG model, developed by Clausius, Maxwell, Boltzmann, and others in middle 1800s, is very useful for solving many problems. One thing it tells us is that for air at typical (sea-level) temperatures and pressures, the "mean-free-path-length" of the hypothetical "particles" is less than 1/10 of a micron (<10^-7 m), and they travel at about 500 m/s on average.

So after these particles, or the Balls in above analogy, bounce off the bottom of Aerofoil they travel downwards a tiny distance (0.1 micron), and about 1/10 of a nanosecond later (!!!) they bounce back up again off other particles/Balls below them. So these "supporting Balls" have alternately (ie. every 10^-10 s) upward and downward momentum that is almost equal in magnitude. But, because these momenta are of opposite direction, the average net momentum of this very thin layer, or "body", of air under the Aerofoil, taken over, say, a nanosecond, is practically ZERO.

Another way to think of this is that half of the "transfer of momentum" to the Bs at A's undersurface comes from stopping their upward velocity (the other half comes from A "throwing" the Bs downward). But the Bs only have this large upward velocity, which is significantly higher than in other regions of the air, because they earlier bounced upwards of the "air" below them. These upwards forces on this lower boundary of the thin layer, or "body" of air or bouncing Bs, and the consequent "transfers of momentum" there, should (MUST?) also be considered when calculating the net "transfer of momentum" to this thin "body" of air. End result is close to zero "transfer of momentum" to the thin "body" of air that supports A.

Importantly, this KToG model has so far only given a tiny part of the whole explanation. Namely, it only says that the particles in the very thin layer below the Aerofoil must have LARGER vertical velocities (both downward and UPWARD) than elsewhere in the flow field. But how do they get these larger UPWARD velocities? Well, digging deeper we find they get the increased upward velocity when they bounce off the particles under them, which are also quite fast moving. But why are these lower particles moving so abnormally fast...? And so on...

In more common Fluid Dynamic language these larger than normal velocities are simply described as greater fluid PRESSURE near A's undersurface, than elsewhere. For a really useful model we would like to know what the pressures are like everywhere in the fluid domain. And we would also like to know the average "drift" velocities of the particles/fluid everywhere. KToG model can do this (with considerable difficulty), but the Continuum model does it MUCH more easily, and just as accurately.



10. If (1) is true then (3) is false.

11. If (3) is true, then (1) is false.

12. The transfer of momentum across the interface is not a macroscopic measurable.

13. If (12) is true, then the fact that air acts as a continuous fluid with respect to macroscopic measurables is not inconsistent with (5) or (7).

ANSWERS 10-13:

Once again, none are truer or falser, but some models are easier understand, and more accurate to work with in practice, so are PREFERABLE.

Near the end of "Principia...", under "Rules of Reasoning in Philosophy", Newton has, "Rule 1. We are to admit no more causes of natural things than such as are both true and sufficient to explain their appearances." This is N's version of "Occam's Razor", which in a simple form states that "simple explanations are better".

So, while the above KToG model can certainly be used to model Lift in gases, it is much more complicated than the very much simpler Circulation Theory of Lift in the Continuum model. And, more importantly (!), the KToG model DOES NOT WORK for liquids. This is because liquids are hypothesized to be made up of many particles always in intimate contact. Since these particles exert forces on each other ALL the time, concepts such as "free kinetic motion" become redundant. So any use of KToG for liquids would be very contrary to the approach to thinking exemplified in the "Elements", because the Definitions and Axioms would no longer be valid, or honest.

On the other hand, the CToL Continuum-Model is a rather simple one. It works very well for low-speed (sub-sonic) gas flows, as well as for normal liquids, and also for the "ideal" superfluids (note that Lift has been observed in "frictionless liquids" such as supercooled Helium!). It was also developed (originally) in the same Axiomatic-Deductive way as the "Elements" and "Principe", so is very trustworthy in that way. (Sadly, most modern explanations don't explain it nearly so well.)

So CToL is the simpler model that covers the greater range of natural phenomena. So it is the preferable model for me.

You, of course, can choose any model you want. But I strongly suggest you think a lot more about the CLARITY OF THINKING that supports the particular model, before you consider the model itself. But that is just a suggestion... :)

Regards, Zapletal. (talk) 01:30, 24 February 2015 (UTC)

Thanks, haven't had time to read it all but your first answer is very helpful in clarifying something about the nature of the debate about aerodynamics.
I will necessarily appear to be talking right past everything you say in your reply, since I've yet to study it. I risk that so that I can capture at least temporarily my first reaction to your first few sentences.
So. I am starting to think that there are two distinct systems of thought involved here, with fundamentally different assumptions about classical physics; some differences of opinion may be due to this initially hidden difference in assumptions. I don't know that this accounts for the prior controversy about "TS"; rather I think it applies to new difficulties, in my mind only, since my arrival, on a question about gross momentum transfers (not regional) that both sides in the earlier debates may agree on.
To simplify (for clarity, and just temporarily):
One camp holds that
the particle model (kinetic theory of gases) and continuum theory are on equal footing with respect to physical reality
continuum theory is more correct than the particle theory
eg, Lanchester contrasts the "theoretical" Newtonian medium of particles with the "actual" continuous fluid, and seems to state that Newtonian medium analysis gives results inconsistent with continuous theory and with experimental results not due merely to simplifying approximations in the analysis, but to a fundamental inapplicability of the Newtonian medium approach to some hydrodynamic problems.
each can give a materially different answers to the same question about physical reality with both being equally correct.
forces are transmitted from an object approaching a wall from a great distance through the fluid to the walls of a container instantaneously (instantaneous action at a distance.)
The other camp holds that kinetic theory of gases is a correct description of air-body-earth interaction (within the non-relativistic, non-quantum domain, and perhaps with other approximation assumptions as well, concerning low density, electrostatic interactions, etc.). For example, they believe that
--air particles have physical, experimentally verifiable existence
--air is verifiably not a continuous fluid
--the particles make detectable collisions with an object and with the walls of a container
--the physics of continuous fluids is no more and no less that an approximation of that model, which holds only in the domain of large numbers of particles and events.
--both models must give the same results for any macroscopic phenomena (within the limits of their respective approximations) which both in fact give a result for. (Other than predicting a value for momentum transfers, I don't know of any useful result about Lift that the particle theory can produce).
--in any case where the respective models give unequivocal and mutually exclusive predictions, the experiment must involve microscopic phenomena
--in those cases, kinetic gas theory is correct and continuum mechanics is incorrect
--the latter is incorrect in those cases precisely because it does not account for physically real microscopic phenomena, and introduces a fictional continuous force nowhere posited in Classical Mechanics as fundamental force
--the action on the walls resulting from actions at the boundary of the body is verifiably the result of a series of discrete collisions over time between air particle and object, and between intermediate air particles.
--the non-tangential velocities which account for momentum transfer are excluded A PRIORI by the continuum approximation, so the fact that the momentum exchange is predicted not to exist is not surprising, but cannot logically offer any evidence for the assumed non-existence.
--The question "is there a momentum exchange across the boundary" is an experimentally testable question about physical reality. It therefore is not valid to say that the question doesn't have meaning, nor that there can be two different answers, both correct.
--The continuum theory properly assumes the non-existence of particle motion and momentum transfer not because it denies physical reality, but because it is a useful approximation of reality for other (macroscopic) questions. In particular, it allows Analysis (2- and 3D Vector Calculus) to be brought to bear. Without calculus, no useful aerodynamics could be done. The CToL theory, which correctly accounts for Lift, would be impossible to derive using only the kinetic theory of gases approach.
From experience, I'm almost sure that this new conclusion of mine will prove to be wrong, but I think it likely that in the discovery of the error, I will again get closer to an understanding of the truth. (talk) 23:17, 24 February 2015 (UTC)
I've had time now to view your responses a little further. Here are my thoughts on your response to QUESTIONS 1-4:

|1. Air comprises many particles, which act as if they were independent of each other.

|2. The foil-air interaction consists in collisions between particles and foil.

|3. Air comprises many particles and acts as if it were a continuous fluid, with respective to macroscopic measurables.

|4. The foil-air interaction consists in continuous forces between foil and deformable constant-density parcels.


|All of the above are merely different HYPOTHETICAL MODELS that can help you understand how the real world works.

==> I think I understand your view, and we disagree on this.

==>Here is my view of science:

--A "hypothesis" is a testable set of definitions and propositions.
--Science advances within what Thomas Kuhn called the current "paradigm" when a new hypothesis that claims to explained something previously unexplained is (a) tested experimentally and validated and (b) found to be consistent with the paradigm and (c) found to be the simplest of those hypotheses meeting the other two criteria (Occam's Razor).
--Science advances in a revolutionary way when (1) a hypothesis failing only (b) is accepted; (2) a new paradigm is created; and (3) the last believer in the old paradigm dies.

==> An example of "simplest": if one hypothesis requires new ad hoc assumptions (Bohr theory with its arbitrary and unintuitive rule forbidding continuous changes in electron orbital energy, e.g.), that is viewed as a flaw--if another theory (e.g., quantum theory) can do the job without ad hoc assumptions, it is accepted because it is simpler.

==>My view of KToG is that it is not "merely [a] hypothetical model", as you state, but rather part of the accepted classical mechanics theory of science, according to the above understanding of how science advances, which in turn is a limit approximation of relativistic and quantum mechanics.

==>Since KToG is in my view settled science, CToL cannot be "merely [a} hypothetical model", as you believe. In my opinion, if it disagreed with KToL, it would have been rejected.

==>In my view, CToL introduces neither a new space-continuous fundamental form of matter (the continuous fluid), nor a new space- and time-continuous fundamental force (the force due to fluid pressure), as I think you are saying. I think that if it did introduce a new matter form or a new fundamental force not required by the paradigm, it would have been rejected on the principle of Occam's Razor. Rather, I think that pressure is a calculated measurable, calculable as the statistical time average of the surface integral of momentum due to the collisions of (in the case of gases) KToG. So, I think it is derived from and consistent with the rest of classical mechanics, not an ad hoc separate hypothesis, and that it is accepted science, not merely one of many hypothetical models as you believe.

| The idea that "air" is made of many independent "particles" that bounce off each other like little billiard-balls is no more "true" here than the idea that it is a "continuum" of stuff that can be indefinitely subdivided.

==>On this we disagree, same discussion as my previous applies. Whether or not particles and collisions exist is, according to my view of science, a question to be answered by experiment. If they can be detected and their experimental behavior agrees with the hypothesis, then science accepts the hypothesis according to the above process. In my opinion, the question of whether air is a continuous fluid is for a scientist a question to be solved by the same process.

| For example, the best model we have these days for the behaviour of really small stuff, like the above particles, is Quantum Mechanics. But in QM the "small things" can be thought of equally as sometimes being "particles", and sometimes being "waves". And sometimes they are both? And, for a really accurate account of everything, we should consider the interaction of ALL of the wavefunctions of EVERYTHING, EVERYWHERE, for ALL TIME. This approach quickly becomes too complicated to be a "useful" model.

==>Agree completely. (talk) 14:15, 25 February 2015 (UTC)

Zapletal, as I read further into your reply, I find that there is an unexpected difference in our points of view, one that doesn't allow further progress in mutual understanding because it is so profound. We each are looking for answers, but not according to a common tradition, a common set of assumptions and definitions and principles. What is for me a question to be answered by (what is for me) the educated scientific community, is for you an absurdity. What is an answer for you is for me likewise an absurdity: for you, to believe what I believe about the nature of science is to deny reason itself (to deny "axiomatic-deductive reasoning", in your words, and thus excuse oneself from the conversation of rational people).

I appreciate the time you took to try to help me understand this difficult subject.

Mark (talk) 00:52, 13 March 2015 (UTC)