|BACKGROUND: Below is the original discourse between Larry Witherspoon and Richard Miller after they got reacquainted through the miracle of the e-mail system. As you can see it grew into a life of its own, but it needed more input in order to achieve the definitive results desired by Richard. Please feel free to read through it (approximately 25 pages) and write down your questions and comments. Then post them directly to TWITT's e-mail address so they can be added to the consolidated page or, pass them along through the Nurflugel mailing list so others can share your thoughts. We aren't sure how long this will go along, but hope it stimulates enough radical thinking to introduce new concepts or theories. (If this is more than you want, click here to return to the original, condensed version.)|
|Subject: AIRFOIL THEORY
December 3, 1998
From: "richard miller" <email@example.com>
A few days ago I had a lengthy telephone coversation with one Emil Kissel, a fellow member of the old Ames Soaring Club. He built an Olympia back 1940-45. He is now 80 and still full of wonder about life, reflected by the fact that he's teaching a 4th-grade class at a school in Los Gatos. His invitation to me to talk to the kiddies about lift theory got me thinking about it again with the result that it is clearer and simpler in my mind that heretofore. Very simple. This is what's on the top of my mind right now, steaming, so I'm sending it to you for consideration.
The airfoil is a magic shape. It redirects force through an angle of 90 degrees. Make that (1), a (1) you can refer to, along with the subsequent numbers, if you have any objections.
(2) Diagram One. A horizontal vector, left to right, with a value of 10 ends at the said airfoil. A vertical vector of equal value begins at the airfoil and extends upward along the gravity vector. A simple "L" (reversed) with equal arms.
(3) We hang another vector, value 10, downwards, representing the force of gravity, thus equilibrium flight. Then we remove it, for clairty, but we know it's there.
(4) We have incurred losses due to the mass and viscoty of the air, so add a small vector, value l, aft of the airfoil. To offset this we add a vector, = 1, to the front of the horizontal vector. So,10 units of the horizontal vector are redirected to the vertical for the process of sustentation, one (1) unit compensates for (airfoil) drag.
(5) The vertical (lift) vector still follows the gravity vector. Yes, the two are combined as a rule into a single vector with a rearward slant. I want to leave out the (1) retarding and the (1) compensating for it, along with the vector, value = 10, representing gravity, leaving only the reversed "L".
Are you with me?
(6) When Prandtl and Munk and vonKarman attacked the problem at Goettingen in the late teens and 20s of this century they had two systems to refer to, rely on, but were -my assumption- aware of only Newtonian classical mechanics and used that.
(7) It is my conviction that I can say all that needs be said about the N(ewtonian) C(lassical) M(echanics) - NCM - with examples demonstrated on the billiard table. Thus:
(8) The launch of the cue ball down the center of the table, lengthwise, is represented by a vector, value 10, ending at the center. In CASE ONE, the cue ball hits the One ball directly and transfers all its momentum to it. Thus momentum, value = 10, travels down the center of the table using two balls.
(9) In CASE TWO the cue ball strikes the Two ball which is one half a ball diameter off center, toward the upper side pocket. The Two ball moves off diagonally toward the upper cushion, the cue ball toward the lower.
(10) In CASE THREE the cue ball skims past - does it touch? does it not touch? - the Three ball which is one ball diameter removed from the table center, toward the upper side pocket.
STOP! Have I spoken sooth? Is there anything inaccurate or misrepresented in the 10 points stated? I need to know.
(11) We now reduce everything to two figures, a reversed "L" with equal arms, one horizontal, the other veritcal, and a "Y" rotated 90 degrees clockwise. The horizontal vector of the "L" and the stem of the "Y", now horizontal, represent the same thing, the system force, the vector with a value = 10, that which drives the system.
(12) The vertical vector, residue of the reversed "L" is now, in a sense, the slot into which the proposed tool is to be inserted. A screwdriver, for example, will do, a hammer will not. The proposed tool, derived from NCM, are the two splayed vectors that remain of the rotated "Y". They do not fit.
(13) The characteristics of the slot, the vertical vector, value 10, are UNITY, DIRECTION, & FORCE.
(A) UNITY The vector representing the lift force is a single unbroken entity, the entire stipulated system energy. In the proposed tool this unity is divided, split, bifurcated.
(B) DIRECTION The direction of the vector representing the lift force is coincident with the gravity vector in the slot. In the solution derived from NCM the vectors depart substantially from the vertical.
(C) FORCE All the force in the model represented by the slot acts vertically from the upper surface of the aifoil. In the solution, the hammer version, a sizeable proportion of this force is directed downward. There remains only a component of the upward-sloping vector to apply to the function of lift. I am making the assumption that this corresponds to the value derived from the application of Newton's sine-square law.
Could it be more simple? Could it be more obvious that classsical mechanical theory has a considerable shortfall?
December 3, 1998
Hey Richard, I'm not sure of what you mean by shortfall, but if it is a lack of ability for the "Y" or hammer to fit the slot that's because we started by reducing all the VOLUMINOUS forces involved into a singular vector, or two vectors at right angles.
If you wish to force fit the Y/hammer then it too must be reduced to a single vector, e.g., one direction. Back on the pool table, I apologize, billiard table, on a molecular level, we would probably never actually observe a true transference of all momentum from one ball to another, though it might appear so to a casual observer on the other side of the room.
We are casual observers on the other side of the room when we fit the forces acting on an airfoil into a two dimensional vectorial representation.
Or have I missed the direction of your argument?
December 4, 1998
I'm a bit confused about your comments on reducing VOLUMINOUS forces to vectors. Air is a ponderable, material entity and the relationship between the airfoil and the on-coming flow has been represented by vectors since time immemorial.
I do not wish to fit the slot residue of the inverted "L" with the angled arms of the rotated "Y". What I am intent on doing is showing that this cannot be done. Momentum theory, the theory that holds that lift results from an equal and opposite reaction between the relative wind and the airfoil, that the airfoil is sustained by a constant exchange of momentum, is what splits momentum.
How can you deflect a portion - half? - the total system force/energy/momentum downward and still have all of it providing lift. That's the issue.
December 5, 1998
OK Richard - that's a little easier for me to follow, and yes, in basic aero, we were taught about representing all the forces on a wing with a few vector representations. But later on we start getting into stuff like lift distribution, circulation theory, drag buckets, etc. Things start getting more complicated than those nice straight lines. Am I preaching to the choir? You with your discussions of diffuser tip theory were one of my earliest influences to look past the simplistic representations, and to examine areas usually ignored.
OK -- If we start talking about equal and opposite momentum reactions, that may be only part of the picture, and that part has its' own special considerations. Agreed we have no problem with that portion deflected downward as providing lift as an opposite reaction. But not all of it is providing lift. Some of it is providing drag. I guess you must be ignoring that as befitting a vector which is 90 degrees away from the lift vector, and as such does not contribute to or detract from the lift discussion.
However I believe there is also lift provided by that portion of relative
wind deflected (sucked?) upward and over the top of the airfoil due to
the differential pressure brought about by the decrease in density over
the top. This requires a different look at momentum theory than with
more simple equal and opposite reactions we think about resulting from
downward air deflection. It is here that your representation of a
"Y" and the straight line vectors that we have grown comfortable with can
lead us astray. The airfoil works because it is not straight nor
is the path all of air takes, the shape of one of those arms of the "Y".
You do not have a "Y" you have a "I", which splits and becomes a "(" and
a "/". The "(" curves up and over the airfoil and meets the "/" that
has been deflected downward, aft of the trailing edge with a whole bunch
of turbulence, and momentum is conserved. Both contribute to lift. I guess
if we measure that portion of lift produced by deflected air and that portion
produced by sucked air we could represent the total as one vector and
Comments, are of course invited.
December 5, 1998
Why, why, why is this so difficult to get across? There is a finite
amount of force/momentum/energy, however you want to think of it, in the
system. It is generated by the relative motion of the airfoil and
the on-coming flow. I have represented it as a horizontal vector
and given it a value = 10. There is more force/energy/momentum involved,
moving the mass of the air, overcoming viscosity, which, in time-honored
ALL that force must be applied to the function of lift. ALL OF IT1 This I represent as a vector, value = 10, rising vertically from the upper surface of the airfoil. This is what an airfoil does. It redirects the horizontal force to one that is vertical. The downwash contains none of this system energy. It cannot. There is none to spare. ALL THE SYSTEM ENERGY, ALL 10 UNITS, IS EMPLOYED IN SUSTENTATION.
The downwash is an exhaust process. Air goes up, = upwash, ahead of the aerodynamic center and goes downward, = downwash, behind it, by which time the lift process is complete. Going down aft the aerodynamic center is all the air can do. It has no direct association either with lift nor with drag. "Induced drag" is a fiction, but that's part of the larger picture.
I purchase 10 units of food. Say it's a bottle of milk, all of which I drink. I am nourished to the value of 10 units. Say it's potatoes and eggs and apples and coffee and I throw out parings and cores and shells and grounds and eat, value 6 or 7, what's left. Can I now claim being nourished 10 units worth? No. Pretty soon I die. Same with a system that deflects part of the system force/ energy/momentum, value = 3 or 4, downward.
Do you not see this?
In mild frustration,
December 10, 1998
Ok Richard, I have tried to go back to the beginning and start over to more clearly understand where you are heading. I think I have a slightly better handle on it but I'm not sure.
First of all, perhaps I am getting confused by your analogies, but I will try to work with them so you can maybe understand my thought processes and be able to guide me a little better along yours where I get lost.
You speak of purchasing 10 units of food, a bottle of milk, all of which you drink and claim to be nourished 10 units. You change that 10 units to eggs apples potatoes and coffee, you throw out parings cores shells and grounds and eat a value of 6 or 7 units, then die from malnutrition, as you suppose your system will if it is said to deflect part of the system force/energy/momentum value = 3 or 4 downward.
From my perspective, that 10 units you paid for the milk really only provided you with 9 units of nourishment cause the container cost 1 unit. If you truly were sold 10 units of milk then the cost would be 11, nothings free. That 1 unit would be analogous to that extra horizontal vector you added a few letters ago to offset drag.
Conversely, all that vegetable mass you threw out as inedible did have nutritional value. You chose not to employ or were unable to metabolize it. However it was real, not imaginary, and even so, 6 or 7 or 3 units may be all you need to sustain yourself. That sustenance requirement is dependent upon your system weight.
Likewise, your 10 units of force approaching the leading edge of an airfoil will be able to lift the airfoil if that fractional component which opposes its' weight is greater than that of the airfoil. If the relative wind is of insufficient strength to entirely offset the weight, the airfoil stays on the ground or if aloft, it descends.
If you arbitrarily set the airfoil weight at 10 and give the horizontal force approaching the airfoil as 10 you have the condition previously illuminated with the bottle of milk that cost 10 units. There's not really 10 units of nourishment there, there's not 10 units of force that is all going to be redirected as lift.
If you insist on a horizontal force strong enough to provide 10 units of lift, then you started with a horizontal force which was in excess of 10 units. You know some of those units are deflected downward, some of it up and over the top, and some of it ignored and thrown away.
Now are you representing to me that the air which was deflected over the top surface played no part in lifting the airfoil? That it too was part of the material thrown in the garbage as providing no nourishment? Maybe not as a function of your Newtonian Classical Mechanics action/reaction model, but surely you must concede that there is nutritional value in the gaseous mass being accelerated over the camber and creating a decreased pressure over the upper surface...surely.
Likewise, I just can't imagine you rejecting the validity of the airfoil lower surface pushing down against the atmosphere and the atmosphere getting mad and pushing back up against the airfoil by an equal amount which translates into a force at least partially opposing the airfoil weight.
If we need 10 units of force opposing that of gravity to accelerate the mass of the airfoil upward, the relative wind providing that force must contain more than 10 units. If we ignore the excess units and examine only those providing lift, part of it is provided by air deflected downward at the leading edge and part of it upward.
Where amongst all of this do you disagree with me?
Equally Frustrated, Larry
December 10, 1998
I'm glad you're still there. I was afraid I was beginning to sound
too much like a scold and had perhaps estranged you a little. Let
me say that this is a significant matter in my life. What I did not say
at the outset of our correspondence, and probably should have, is that
I was given this problem to cut my teeth on about a quarter century ago,
in the early 1970s, and I have devoted extravagant amounts of mental energy
to it. I have found, to sum it up, that the entire Lancaster-Prantl
theory is corrupt, every aspect of it. I did not, do not,
But oh! how frustrating it is, this based on how utterly simple it appears to me. So if I do sound scoldish, know 1) that's not my attitude, and 2) I'm not that was at all, hardly ever.
Let's go back to the reversed "L", one horizontal vector, input, value
= 10, and one vertical vector, output, value = 10. Next let us add,
then immediately take away, 3 more vectors. The first is the one
representing gravity, = 10, which is the reason we're generating the lift
vector, and which results in equilibrium flight. Then there's a drag
vector, value - 1, aft of the airfoil, headed rearward.That's for drag
resulting from air mass
The milk metaphor. Have we dealt with the cost-price of the carton to your satisfaction?
The milk metaphor, part 11. Once more, with feeling. ALL
THE SYSTEM ENERGY/FORCE/ MOMENTUM, all 10 units, must act vertically along
the gravity vector, upward from the airfoil. (Excuse the redundancies.)
None can go off at an angle, can be redirected rearwards, and above all
go downwards. We cannot abstract it into components, one of which
provides lift and the other of which does something else. It
YET AGAIN, WITH FEELING. NO SYSTEM ENERGY/FORCE/MOMENTUM can be directed downward, which is to say as downwash. Yes, the air passes downward, moves downward past the lower surface of the airfoil, and yes, there is a transfer of momentum between that air and the lower surface of the airfoil, (I don't deny it) but it is not as you and as all previous generations of observers have imagined. The vector representing this transfer is not at an angle, oblique, but - guess what? - vertical. There is an intermediate mechanism, as if one nailed a pivot to the center of the billiard table, except you can't nail the air and you can't see the mechanism: Neither the air nor the mecanism, which is what makes the problem so difficult.
I'm going to close now, not having said everything by a long shot. I will say this, however, that the dynamics-mechanics of that air, the quantity or stream passing the lower surface, is enchanting. Boy is it ever enchanting, and did it ever take me a long time to figure it out. But please, for now, try to deal with the primary stuff, those 10 units of force and what MUST happen to them.
December 11, 1998
OK Richard, now we're back on track. Square one.
You and I agree that there is a force created by the relative motion of air past an airfoil which can be resolved into two vectors. We will ignore the horizontal component and concentrate on the vertical one which by our convention we have assigned a value of 10, which neutralizes the weight of the airfoil also 10.
The vector representing, representing, the transfer of momentum between the air and the airfoil is not an oblique angle but is vertical because that is the convention we agreed upon as the resolution of all the aerodynamic forces on the airfoil into one opposing weight, along with the other, a horizontal force, opposing thrust.
And that is proper because that simplifies our system into as few vectorial representations as is practical since they exactly counter the direction of the other two forces acting on the airfoil, weight and thrust. We could have as our convention, a single oblique vector representing all the aerodynamic forces if we wanted to, but then we would just wind up back at the same spot when we needed to show how that oblique vector counteracted weight and thrust. The point being we are talking about pictorial representations and I want to talk about the physical reality of the molecular activity experienced by the gaseous mass resulting from the passage of the airfoil, or if you will, the path of discrete air particles which pass over the upper surface, and which pass under the lower surface, and the effect on the airfoil due to their passage.
We know from smoke generators and wind tunnels how the air moves over and around a wing. It does not seem mysterious to me that lift is provided by this relative motion, but I have the impression that the 90 degree change in direction of force has made you uncomfortable because the airflow does not change direction through an angle of 90 degrees. Or at least it does not appear to. But that's because you are not looking closely enough. Go back to the billiard table.
Those balls are like molecules. Some strike the airfoil, or at
least strike other air molecules that the airfoil is dragging along with
it, right smack dab at the point on the leading edge, that causes them
to bounce straight back like the rail of the table. Some strike at
a location below that neutral point at an oblique angle and cause a number
of airfoil molecules to go careening upward at some angle which conserves
the tiny amount of momentum in their minuscule individual systems while
causing a corresponding minuscule amount of lift. Still others are
deflected upward and over a tremendous mountain range of camber, while
stretching out and accelerating rearward which causes fewer of them available
to pound and bounce down against the upper surface compared to those pounding
and bouncing up against the lower surface. Which again, results in
We can't see all this upheaval of activity while looking at a stream of smoke flowing leisurely past an airfoil, but those countless balls jammed right in next to the surface are changing direction like crazy through 90 degrees and everything else, resulting in your mysterious lift vector.
I await your reply
December 11, 1998
I have the sense we're closing in a little on the matter. I'll
take your current letter
No. 1 Looks like we're in agreement
No. 2 Lift is defined, as I understand it, as a force acting in opposition to gravity, thus upwards along the gravity vector. For tails it's different, but that's for wings.
No. 3 Just when I have your back to the wall you slip through my fingers again. So I am forced to abandon my initial intent, to FORCE you to admit that all 10 nits of system force must be charged to lift, and its concomitant, none can be directed to any other purpose, especially downwash, and move to the next level.
Nos 4 & 5. The molecules of the free-stream do not strike the (lower, for the time being) surface of the airfoil. It is assumed that they do. It has been assumed since several of Newton's followers extracted the sine-square formulation from Proposition 38 (was it?) of Vol 11 of the Principia. "Achilles wrath, the direful spring of woes unnumbered, Oh heavenly goddess sing."
If you know how, go to my web site and read that quote from von Karman's book.
Gedenkenexperiment. A rack, inclined at an angle (to the horizontal) of say 20, 30 degrees, drops a contiguous row of bb's onto a flat surface below it, same inclination. The bb's strike the surface simultaneously, bounce, and disperse.
The rack disgorges a second row of bb's. Same thing. On automatic the rack dispenses rows of bb's regularly, periodically, with spaces between each dropping row. That space, assume it to be five bb diameters, is sufficient to permit the dispersion of the bb's of the previous row.
We turn a dial that controls the distance between drops. At, say, three bb diameters there is no longer time for the previous row to get out of the way. Backscatter begins. Bbs back up. It's a whole new ball game. We're dealing with a new phenomenon, THE FIELD.
I spoke, did I not, of an intermediary mechanism being necessary in order to get around that 90-degree corner. The field is it.
Do you have Einstein's The World as I See It? which was also published under another title, which I forget. Read it (if it please you to do so) and see how he rhapsodizes about the field, and does so repeatedly. Here's how I see it.
In the beginning there was Newtonian physics. Then along came Boscovich, Oerstead, Faraday, Maxwell, and whatshis name. AE saw what they had done, and that it was good. He saw the Newtonian structure as a building a ground level, as field theory as the framing for a second floor. He climbed the stairs, was intrigued, moved his desk up there and went to work. Voila! Relativity and all like that.
Nobody - nobody that I can identify - followed his lead. At base
it's not this physical theory or that one. It's a matter of mentality.
So long as "science" is dominated by a Newtonian mentality, as it appears
(to me) to be, we are going to have Newtonian thinking and Newtonian representations.
Gary Zukov noted how "scientists" worked all day in the Einstein mode,
then closed the lab door and went back to their Newtonian
Lancaster and Prandtl and Munk and vonKarman had no suspicion - my assumption - that they had any choice but to solve the problem of lift using Newtonian/billiard table/trigonometric function methods. They made it work, which tome is one of the miracle of modern "science". They fitted the two splayed arms of the sideways "Y" to the vertical member of the reversed "L" and wrote it in a book, or maybe a paper. After that, to the uttermost generation, people fell into line, repeated what came down from on high. Ain't that one hell of a story?
December 12, 1998
Hi Richard -
I appreciated the BB example and can visualize well how at a certain frequency / wavelength / spacing, we start to get backscatter and build up a something. Maybe we can call it a field. This field might be analogous to those molecules pulled along with the airfoil which we attribute to viscous drag, and we do have evidence that a layer of air which is static relative to the airfoil surface exists.
My concept of a field, as in magnetic, electric, or gravitic, is somewhat different. They are fields of force, which I believe cannot be represented as a single vector, however they can cause changes in forces which can be represented by a vector. If you headed where I think you are with this then it requires the conceptualization of an unfamiliar something we could call an airfield.
Now you have to start getting pretty abstract here as it seems you are
becoming Einsteinien and causing an airfield to materialize due to the
presence of a moving airfoil. Is this a stretch beyond the belief that
a mass creates and causes the deformation of a gravitic field, and/or that
molecules moving through a conductor as electric current create a magnetic
field which has a force oriented in a direction dependent on the current
I am afraid this airfield effect is too much for me. I'm ok with the BB's and their analogy as air molecules piling up as the airfoil moves with increasing velocity with respect to the atmosphere. However, to reclassify this viscous activity as a force field so that we may enjoy the angular changes it produces in the airfoil direction is pulling my leg off. I can appreciate this if meant to be taken as an analogy but for now, I still believe the pool balls do a better job of explaining the result of airfoil motion with respect to the atmosphere than do the BB's. But then, you stopped right when you were getting good and went off about all those dead guys, who are only names to me without knowledge of their work so I could go no further than I did.
There is something else about your field I am uncomfortable with; its' effectiveness is dependent on the shape and orientation of the object moving thru it which created it. Maybe we shouldn't ask this airfield to behave like other fields we have knowledge of, but I feel like that dependence on airfoil shape argues more for the pool ball model.
You will have to pick it up again from here.
Pool Ball Witherspoon
December 12, 1998 Date:
Again I will reply paragraph by paragraph.
1. The boundary layer goes ahead doing it's thing field or not. It is a separate issue, and independent.
2. The field defined and vector analysis. There are numerous definitions of field. Mine is the: The continuous distribution of some quantity or quality; also its reverse, the absence of some quantity or quality. A big flat pan of homogenous yogurt = a uniform field of the quality white. A dollop of chocolate in the yogurt, mixing around the edges. A field of black and of grays, or of the quality of non-whiteness.
The free-stream velocity is all, each molecule, little horizontal vectors. Imagine each one an inch long maybe. These can be summed up as a single vector or as many as you please. (Note Euler's many-particle addendum to Newton's concept.) The uniform yogurt field was static, this one is dynamic.
We block the free-stream flow with anything, a wall, a tree, our hand. The flow CANNOT impinge directly on the exposed surface; CANNOT convey its momentum directly to that surface. CANNOT111 Got that? Backscattering happens. A field is formed.
That field, your airfield, is defined as the continuous distribution
of quantities, vector lengths and directions, OTHER THAN that of the free-stream
flow. Some will be shorter, some longer and ALL will diverge from
the horizontal. As we have done with the vectors representing the
free-stream, amalgamating them into one, so we can do with the multitude
of vectors in the field. They will have a single vectorial resolution
that can be
Pay attention now. The vertical component in both cases, that of the decelerated air - shortened vectors - below the airfoil and the accelerated air - lengthened vectors - above it, are equal to our value, the system force, of 10.
3. It is field v. field. Lift is a field phenomenon. The lift field, to put it fancifully, envelopes the airfoil and liberates or protects it from the gravitational field.
I remembered whatshisname in the evening: Hertz.
Your letter said had the word "abstract" in it. I hope my description(s) made the concept of the aerodynamic field less abstract. Also, it is an aerodynamic field that negates a/the gravitational field. Hmmm.
I read, long ago, in a work of AE's I think, how the combination of rotatory with translatory motion creates a field. Source forgotten, but I'm pretty sure it was him.) I'm pretty sure that Einstein was thinking/talking about spinning bodies - consider the gyroscope - and forces largely gravitational, and I think he would be intrigued by the concept of a lift field. He WAS INTRIGUED by the Magnus effect, and there, in the cut tennis or ping pong ball, you have the requisite conditions, translatory and rotatory motion.
You have it around the airfoil to. The Lancaster-Prandtl theory, those dead guys I kind of assumed you might know something about, claims that there is an absolute rotation, but it is only relative.(To solve the problem they took an imaginary Magnus tube and superposed it on the wing, thus lifting-line theory and the concept of - ugh! - induced drag.)
But see the airfoil pass! There is most obviously translatory motion, the forward progress of the airfoil; and there is the relative rotatory motion. If you have trouble seeing that try this.Three trains: One, speed 50 mph, same as the free-stream velocity, enters the front of the airfoil, follows the mean-aerodynamic chord, exits at the trailing edge. It paces the free-stream that is beyond the upper and lower extremities of the lift fields.
A 40 mph train represents the decelerated flow beneath the airfoil and a 60 mph train that above it. Can you see how, if you were a passenger on the middle train, you would sense rotatory motion?
Out of time,
December 14, 1998
Here is the reductio ad absurdam of the matter.
1. The function of an airfoil - what it does, the reason it exists - is the redirection of force from the horizontal to the vertical; by definition, through an angle of 90 degrees.
2. Newton's law of action and reaction between ponderable bodies, by direct contact, his second, and the trigonometric functions that apply to the resultant distribution of momentum, yield -
a) At zero angle of divergence between the active and the reactive bodies - the rectilinear case - there is a complete - 100% - transfer of momentum;
b) At a 90-degree angle of divergence between the active and (non)reactive bodies there is zero - 0% - transfer of momentum.
3. The second case above - 2b - was used to explain/rationalize the first.
With kind regard,
December 17, 1998
And here I reply to the past 3 (this included) Richard Miller communication(s)
And here I plunge home the sword into the heart of the venerable Miller argument, compelling though it may have been. For the very substance of the argument has given me the material to once and for all explain the mysterious forces allowing this "Once And Future Wing" the miracle of flight.
I carefully arranged all prior communications in this series of aeronautical jousts in chronological order and reread them all, thereby gaining additional perspective and understanding. While I lack the theory and familiarity with the many, nay most of the luminaries quoted and referenced by Mr. Miller, I believe I still hold the key to the treasure chest of truth, which all of this has been about.
Richard, you have asserted that a relative wind approaching an airfoil
creates a field of sorts and you have assisted me in the visualization
of same using the ingenious BB device. Yes, I admit there is something
created which we may term a field. That airfield, or atmosphield
is, if I understand you correctly, all those particle vectors affected
by the presence of the airfoil which differ from the freestream particles.
That phield would
OK, let's return once again to the table, and to Newtonian mechanics.
If the billiard table were frictionless, and of infinite proportion, and we were limited to only the cue ball and the 8-ball, we would have a problem. We under these fanciful circumstances would be very unlikely to produce a transfer of 100% of the cue ball energy to the 8-ball at an angle of 90 degrees to that of the cue ball initial velocity.
But I don't know of anybody that's been able to find such a table outside of a mathematical expression. Your 100% transfer of energy from the freestream direction into lift 90 degrees opposed is quite probably another mathematical expression ignoring the reality of my molecular model.
Don't Leave The Table. Let's look at the way a table exists in reality. We rack the balls first, creating a field that resembles an equilateral triangle. This field protects the 8-ball from direct contact by the freestream cue ball. However, given sufficient velocity, the cue ball can impact the field in a manner such that backscatter interference causes energy transfer amongst the field particles so that some of them end up moving at right angles and yes, even at angles greater than 90 degrees, back in the direction from which the force originated. If the shape of this field, rather than that of a triangle, is optimized, to suit our purpose, we end up with something that allows an experienced, or even inexperienced shooter, the ability to impart a velocity to the 8-ball in the direction we choose, including 90 degrees from our original direction, though the cue need never actually contact the 8.
And so this ladies and gentlemen, is how an airfoil works.
The shape of the atmosphield is dictated in part by the shape of the object moving through it. That shape may be optimized to produce backscatter interference in the atmosphere such that it, the backscatter, becomes a mechanism through which energy is transferred from the freestream molecules to the airfoil, the 8-ball if you like, in a resulting force directed at 90 degrees opposition from that of the freestream!
Hmmmm. Is this Newtonian or not? I still think so.
But most of all, let's not get too carried away with this 100%, 90 degree thing. 100% of the energy transfer which opposes gravity is termed lift, but 100% of the system energy does not end up opposing gravity. We need to have a cue ball, the freestream, moving toward the phield in a direction, so that after all the varied transfers occur, we end up with a force vector, a fraction of which can be resolved into opposition with gravity. With sufficient initial velocity, that fraction is enough to overcome the gravitational field effect. Air pushes on air, pushes on airfoil. The toe bone is connected to the jawbone.
I believe all this can be explained, if we look closely enough at the dozens of molecules involved with "simple" Newtonian mechanics. I have to admit you really had me going, and you've given me a different perspective for which I am grateful.
Unless you have another explanation.
Larry Witherspoon ...for Isaac Newton
December 22, 1998
I have read your last communique (Dick & Jane Physics + Part 11) several times. I'm just not getting it.
Because of my diminished mental capacity, I think for us to communicate effectively we will need to avoid abstractions and try to stick with whatever the opposite must be like billiard balls, BB's, and molecules. I do not believe you have rejected my explanations of the way lift is generated using literal examples of how some air molecules pass over the camber of an airfoil and how some are deflected downwards from the lower surface, but I have also not received a wholehearted acceptance of those explanations either.
Please, no more beating around the bush of abstractions if it can be avoided. Please explain whether you;
a) reject fully the way I have explained how lift is created due to a partial vacuum over the top surface and deflection under the lower surface of an airfoil
b) accept in part my explanations, but believe there is some additional mechanism at work to create lift which is unaccounted for by my examples
c) accept in full my examples and agree completely that they fully explain how lift is created, but feel it can be also explained in other ways
When we write of a single ball represented by a single vector and the abstract problems with directional changes in force of 90 degrees, to me it ignores the real world for which your field so wonderfully provides truth.
The airfoil generates lift when it passes thru the air. It is the collection and concentration, or rarefaction of molecules interacting with each other and with the airfoil that enables this generation. If we take the airfoil high enough and there are an insufficient number of molecules to interact effectively as a field, lift is diminished.
As I stated earlier, I wish to know whether you believe this is the truth, the whole truth, or part of the truth so help you God. If you believe this is not the whole truth, can you put into words easily understood by laypersons the missing part?
There is a common belief that the ancient Egyptians built the Great
Pyramid at Giza. If we examine some particulars in and of the structure
we find that there are things such as alignment, parallelism, flatness
and so forth that are of a precision that is astonishing. There is accuracy
of the sort that our modern machine tools would have trouble duplicating.
Because of this information, I am forced to conclude that those ancient
All this to say that I believe the illustrations given for the action of air on an airfoil adequately explain its' behavior. Those actions can be demonstrated and duplicated in a laboratory. At the end of your last message you seem to indicate they are merely contenders and by so doing imply there are other challengers.
I have a problem with the Great Pyramid. I believe tools in use
by humans at the time were inadequate to produce the finished structure.
I believe an explanation that extraterrestrial biological entities were
responsible is of greater contention than that of humans acting alone.
No beating any bushes. I have a problem. An accepted theory
provides an inadequate explanation. I have an alternate theory.
No beating. NO
If you have a problem with current lift theory I am ready to hear it. To me current theory seems adequate. If not to you why not? Horizontal gas flow encounters a solid, experiences resistance, is compressed, is rarefied, causes reaction in solid. If you were a flying airfoil you would feel wind pushing you backward and pushing and pulling you upward. No fair isolating one vector to create an abstract problem.
The process is dynamic and dependent upon a continuous flow of many vectors doing many things with one resolvable end result being that of lift. I am not comfortable with isolating the lift vector and declaring that it can't have turned the corner from the horizontal as though through some mysterious undetectable or unexplained mechanism. We isolate it when we wish to illustrate the effect of the force involved and when we wish to simply calculations, but in the non-abstract real world it is not isolated. It has help we can explain does it not? Can we not? If not, have you an alternate?
Larry no more bushes Witherspoon
December 22, 1998
Welcome back Larry,
Once more from the top.
I am willing to range as far and as wide as you please in the matter of the generation of lift, the theories and explanations that have been put forward to account for it, and my criticisms to or emendations of those theories. However...
What I had hoped to do was to isolate one single, simple aspect of the matter, an analysis of the principle forces involved, represented by the abstractions inherent in force-and-vector diagrams. Somewhere between you and me, or me and you, this has broken down. I'm going back to it now, one more time, after which (once I get a copy of it) I will endeavor, point to point, to deal with the content of that communication.
I rent a room from Bob for $100/week. I am hired by his brother Charlie to pluck chickens for $100/week. I take the $100 I get from Charlie each week and give it to Bob. Input = $100, output = $100.Rent paid. Equilibrium.
I rent a room from Dan for $100/week. His brother Ed hires me for $100/week to stuff sand in rat holes. He takes $40(or whatever)/week to pay the arrears on child support I've been ignoring. The $60(or whatever)/week remaining are insufficient to pay my rent. I am out in the cold.
Does this possible have any relevance to airfoil theory? Indeed it does. The airfoil earns $100 in its horizontal advance, distance X, through the atmosphere. It expends this $100 in the generation of lift during that transit. That, I repeat again, is what an airfoil does. It redirects the system momentum, F, generated by thrust, through an angle of 90 degrees, to the vertical. In the instance given, input = output = equilibrium flight.
Can you not, ever, accede (is that the word, accept, concur?) to this? Is it arcane, abstruse, unclear, in some manner obfuscated or distorted when, it is my conviction, I have stated it as clearly as a human being can?
NEW: The Law (or Rule) of Disjunctive (or Split, Divided, Bifurcated, Partitioned, Fractured) Momentum (or Force. The interactions of free bodies, as pool balls on the surface of a billiard table, or an airfoil and a body of air. An initial or subject momentum is imparted, or identified as being inherent in body A. Body A strikes, impacts, interacts physically with, body B. Upon contact, impact, interaction, body A transmits PART OF its momentum/force to body B. The remainder remains; it stays with body A.
(Special Case/Exception: When the contact is direct, no angular deviation between the tracks of the two balls. The cue ball launched directly down the middle of the table, hitting a colored ball that continues down the middle of the table. No deviation from the rectilinear, hence of no interest or applicability in the description of the lift phenomenon.
Matching metaphor to theory. All the force - ALL - generated by thrust and represented by the horizontal vector, F=10, is, must be redirected to the function of providing lift. Only in this way is the rent paid and do we have the figurative roof over our heads. We CANNOT divide, nor split, nor bifurcate, nor partition that, as in deflecting it off the lower surface of the wing, send it on its way as downwash, OR DOING ANYTHING ELSE THAT DIRECTING IT ALL, VERTICALLY, UPWARDS.
His labors at an end, he rested.
Just one point before I close.The air that passes over the upper surface of a wing (at subsonic speeds, the sort of velocities you and I live with) is not attenuated in that transit. There is no change in intermolecular distance, to put it another way, top nor bottom. You are in the realm of static pressures. The pressures on which lift depend are dynamic. That's another of that dozen or so topics I am willing, yea eager, to get into in the fullness of time.
I'm not going to tell you that I'm a student of Pyramid history, have read Peter Tompkins book, among others, because I don't want to get further distracted.
Still, just barely, in a good humor.
December 22, 1998
if we can.
Merry Christmas. Thank you for bearing with me and for your forbearance. I will be away from my computer for a couple of days on Holiday with my family, but I have a couple of things to send/ask now that you may care to answer.
I appreciate the start from the top again and think maybe if we stop our complicated, long, wordy explanations we can understand each other with more ease.
If the cue ball does not strike the eight ball dead on, the cue is deflected off at an angle, let's say below the table centerline, and the eight is deflected off at an angle above the centerline. Draw that out as a vector diagram and turn the table on edge.
Do we not have a representation similar to that of the oncoming airflow which strikes the airfoil lower surface (or the atmosphield near the lower surface), causing an action-reaction effect? One ball goes up the other down. Airfoil up airflow down.
The angles involved do not have to be 90 degrees for this to work. Do you agree or not? It seems like you are maintaining that this is not the case and that's what's giving me so much trouble understanding your position. Please explain.
If the path over the upper surface is longer than the path under the lower surface how can there be no attenuation? Remember the little trick of blowing over the top of a strip of paper to make the strip rise. The air going over the top is moving faster than the air on the bottom so it has a lower pressure than that on the bottom, hence there is a force pushing the strip upward toward the lower pressure area.
It seems like something has caused you to reject these empirically observable, duplicable, processes, so like my Great Pyramid, I would like to know what has caused you to reject the traditional explanations and I would like to know whether you have an alternative which seems to better explain this activity.
Merry Christmas, yours truly
December 23, 1998
It suits me fine, to keep it uncomplicated. It is, as I see it, uncomplicated. So once again by the paragraphs of your letter.
1. Merry Christmas, happy time with your family n' like that.
3. Balls hitting and deflecting and turning the table on its side. That's my "Y" tilted 90 degrees clockwise. The central feature is
4. The division or bifurcation of the available system force. You cant do that.
5. The velocity of the air over the upper surface, or anywhere, is another matter. It is part of the topology - is that the right word? - or the physical description of what happens and is not germane to the treatment of force per se. I really do want to do it one step at a time.
Here's what I wrote as a follow on yesterday and this morning. It is a summation and a recapitulation and a restatement. We have PRACTICE, by which I mean what really happens, and we have THEORY, which is what some people have decided to say about the matter, the received wisdom.
In PRACTICE there is a simple (not compound), direct action. Input
and output match on a 1:1 basis. It is as if, as the airfoil moves
forward along the (horizontal) flight path it gobbles up $100 worth of
system force, F, which it expends, in that transit, to sustain itself.
It is like a liquid poured directly from one contain into another.
Imagine the area of mystery, a circle around the airfoil where the mystery
takes place, to be a pulley.
In THEORY there is division. That which enters the system as one
is divided and leaves it as two. The cue ball strikes the colored
ball and AT THAT POINT, DIVISION. (I'm tempted to get theological
here, like noting the derivation of the word Teufel from two.) You CAN'T
DO THAT. A nut is cracked and the meat is eaten and the shell
discarded. A missile flies to its target as the booster falls back to earth.
There is no allowance for any discard nor diversion of force or forces.
We are dealing with a defined quantum of
Once again I raise my arms to heaven and ask, could it be simpler than that? Is it not a black-and-white, a go-no go, a one or a zero case? Was I mistaken in assigning it to the Dick-and-Jane category? Could I be faulted for an occasional expression of pique or exasperation that I am not understood?
Try it this way. We can take, as observer, whatever position please us, thus we speak of relative wind. Take a middle position, with that relative wind coming from one side, value F/2, and the airfoil, ditto (F/2) coming from the other. They meet in midstream, right before our eyes. The airstream - the divisive devil - its half of the system force, F/2, to the airfoil, the airfoil likewise.(Note, I hasten to note, necessarily half and half, but two components that add up to the total.) So there is the airfoil with half (some portion, 30%, 80%, 64.87463%) of the total while the relative wind carries the rest away. See the airfoil fall out of the sky; gradually, of course, because it needs the 100% and only has part of it.
Three minutes to 11 o-clock.
December 30, 1998
Happy New Year almost Richard -
OK, permit me to explain to you this phenomenon once again, and let's see if I understand what you have been trying to get across.
The airflow near the airfoil is going all over the place, spanwise, chordwise, vortexing, circulating, and so forth.
The FORCE applied to the airfoil, however, is a separate entity from the airflow around and in the vicinity of the airfoil.
The FORCE applied to the airfoil is essentially experienced as two vectors; one opposing thrust, one opposing weight.
The one opposing thrust is easy to understand, the one opposing weight not so easy, it's seems to be at right angles to the direction of motion responsible for the force.
OK - so far so good? Good. Let's go back to the BB's
If we move our airfoil through the atmosphield quickly enough to cause backscatter and stackup we create a field capable of significant resistance to passage through it. It is this very resistance to velocity that we depend on to support us, to lift us, and to oppose our weight. We take advantage of this resistance by attacking the field with the airfoil at an angle which is such that forward progress is still possible, however, we find the path of least resistance is uphill through the field. The airfoil shape then is one which is optimized to take advantage of field particle backscatter so that resistance to forward progress is minimized while resistance to the downward force of gravity maximized through a range of attack angles. Adjustments to thrust and by extension airfoil velocity, causes atmosphield stackup and backscatter which permits or promotes our rise, fall, or stabilization within it.
Are we there yet?
December 31, 1998
Not quite yet.
Paragraph 2: Backscatter does not mean totally random motion. Any backscattering particle is still contributing its forward motion to the enterprise.
Try this imagery to (maybe) help. A circle, slightly to the right of center of your paper. Represents the trunk of a tree. On the left side of it draw a bubble. Through in a little field of vectors coming from the left to indicate the wind. The bubble is the field of backscattered particles. All those particles, still with some component in the direction of the tree, contribute to the strength of the field.
If the wind hit the tree directly, and it can't - you cannot move your hand in front of your face so slowly that you do not form a field - the force would be only a fraction of what it is as a consequence of the field. This is why the (Newton) sine-square formulation turned out to be so wide of the mark, why it predicted a considerably lesser force acting vertically on the incline plane than there really was; what they found by experiment.
This is a critical point. It demonstrates the fallacy in the belief that the air particles hit, impinge directly on the surface. They do not. They cannot.
If we vectorize the bubble on the upwind side of the tree we find a "T" shape (Rotated 90 degrees clockwise. The stem represents the total (wind) force against the tree and the arms, one up and one down, or right and left, whatever, the lateral component(s). The sum of these equals the sum of the force(s) in the wind, which is the same as to say there is no contrary - back against the wind - motion, no random motion.
There is another bubble on the backside of the tree. The same sort of thing applies, only backwards. (When you stand with your back to a strong wind you know about this in the slight difficulty you have breathing.) The force tending to blow the tree over is the total potential between the (+) force on the upwind and (-) force on the lee side of the tree.
What an airfoil does is put the (+) force field on the bottom and the (-) field on the top. The potential between the two fields, across the airfoil, is the lift (force) potential.
Draw the bubble under the airfoil. The forces within it resolve into two vectors. Call the free-stream velocity vector, as we have, value = 10. The air mass as it approaches the airfoil, encounters resistance, is slowed. By the time this air is within the field, backscattering, this horizontal vector, F = 10, is now shortened, let's say to 8. This happened with the vector in the bubble on the upwind side of the tree. The difference in the case of the airfoil is that both legs of the "T" now go in one direction, upward, rather than around. That's the vertical component, derived from the horizontal, that results in lift.
Why should both legs go one way? Why just a shortened horizontal vector and a vertical vector resulting from the shortening? Because of the upwash. The flow does not come directly at the surface. It senses the approaching fields, (+) on the bottom, (-) on the top, and takes the path of least resistance, is lifted.
Now get this: The field force across the wing, F = 10, is broadcast to the on-coming flow which rises with F = 10, which gives the vertical component to the field, F = 10, that... And around and around and around we go.
Last day of 1998. Library. Me half sick. Time about up. Can you believe 1999?
I'll be in touch, God willing, sometime then.
January 2, 1999
After my last reply to you - and it was Attachments that came up as Downloads at this end - I realized that the concept of backscatter was inappropriate and misleading. Let us therefore segue from the contiguous rows and ranks of dropping BBs to tackle/blocking practice on a football field. One vertical stack of BBs now equals a row of say 12 half- and fullbacks, all in a line, hitting the tackle dummy as hard as they can.
CASE ONE; Big Joe fullback smacks into the object with everything he's got. The dummy gives way, but not much. Big Joe then gets out of the way instantaneously and Big Eddie halfback hits the dummy with pretty much the same result. So on down the line.
CASE TWO: Big Joe hits again, again with everything he's got, again budges the dummy X amount. But instantaniety eludes him. He's good, but he can't move that fast. So his body becomes the means by which the momentum of Big Eddie, just behind him, and diminishing proportions of the rest of the row, are transmitted to the dummy. Call this AGGREGATE(D) MOMENTUM in which all the involved elements are exerting some momentum in the flow direction. Not backscattering n' like that. Sorry Mea culpa.
We have two concepts now. One is THE INFERENCE OF DISCRETE MOLECULAR IMPACTS and it corresponds to CASE ONE above. It also corresponds to the Newtonian formulation, that of sine-square, and to that operative line in the vonKarman quotation. It also corresponds to an estimate, for the force conveyed to the inclined plane, as little as 1/30th of the true value.
That that does not work. It has been known for 2-300 years that it doesn't work. That it doesn't work has been rationalized in a variety of ways, but nobody - nobody so far as I know, and I've looked, believe me, I've looked - has ever come to terms with it.
What works is CASE TWO, Aggregated Momentum. We know that there must be AM (and its reverse, non-AM, above the airfoil) because the air slows down (and speeds up). Why would the air slow down if it weren't, in some sort of way, stacking up like Big Joe Fullback and his buddies? Answer me that.
Yet another illustrative metaphor. An open tray, say the size of a pool table. Across the near end, at hand, a spacer, and in the area between the spacer, the sides, and the far end (a field of) small (like) ping-pong balls. They have the characteristic of responding to the least deformation by changes of color. Some, a little, more, a lot.
One - you - move the space in a compressive kind of way. See the color of the balls nearest the spacer change to a glowing red! See those in the subsequent rows change color as well, but attenuated shades until, at the limits of the field, being undistorted, they remain white! Can you get that? This is what I mean by AM and by the field.
Thanks to you, to this correspondence, I have thought and thought and thought about how the sine-sq discrepancy has been ignored and rationalized, and I have been increasingly impressed that it has been, ignored, and the way it has been, rationalized. I want to try to impress that on you. It is a central, seminal fact of the entire matter. "Achilles wrath..."
I had a lovely inspiration on the first day of this year, yesterday. It involves a couple of pieces of paper, and sliding one juxtaposed to the other, and it's neat. Come Monday, if there is a Monday, and my temper hold, and the library is open, and I get a computer, and and and.
Best New Year's Wishes
January 3, 1999
Dear Richard "Sine Square" Miller
I sense a convergence of thought on this simple subject turned complex.
I was satisfied with your backscattered BBs, and thought we had come to terms with some workable phield theory, but see you have not been happy. Your previous transmission which made reference to (+) and (-) forces on the airfoil upper and lower surface, causing the flow to take the path of least resistance was kind of like my airfoil taking the path of least resistance through the atmosphield created.
Now in this transmission you have got this aggregate momentum example happening to help me better visualize, but I think more important now may be to help me visualize what you are convinced is not happening. Please provide a similar kind of explanation for the sine-square formulation that you dislike and how it relates to the force against the inclined plane so I don't have to go researching.
I am pleased that you have been able to present an alternate "contender" to the Newtonian action-reaction explanation. It, as a sort of field theory, does seem to be more complex than action-reaction, and I, like the universe, want to lean towards the less complex explanation, but maybe you're onto something. There was a time when a flat earth was a more simple explanation than a round one.
Do you believe this atmosphield effect is applicable only to gaseous reactions? Would the action-reaction theory be applicable to an airfoil flying in water?
Larry "almost a believer" Witherspoon
January 7, 1999
Here's the final, or maybe penultimate installment.
Lift is a process, not a condition nor a state, and we are a disadvantage
that sliding one piece of paper across another, giving a cross-section
in time, does not completely address. That process, lift, is one of simultaneous
corollaries and concomitant dynamics. Thus: Charging, by the affect
of the entrained field on the upwash occurs concurrently with Discharge,
the vertical transfer of momentum to the lower surface of the wing; this
There is finally, and certainly not of least importance, a simultaneous flow of momentum passing horizontally in the air beneath the wing, one identified with the downwash, visible and obvious, and another interior, vertical, unseen and largely unsuspected.
It is in an attempt to make that flow visible and comprehensible that we now slide the pressure form, B(+), across the page. Designate an alphabetic progression, of which the letter "l", indicating the maximum amplitude of the upwash, terminating at the leading edge of the wing, is in central or index position. Move the pressure form one 1/4" increment to the right. Transfer, sketch in, the momentum represented by the band k-l to that area of the airfoil between the mean aerodynamic chord and the lower surface. Realize that this discharge is offset by the fact that the incremental advance has now charged "k" to maximum strength, that the band j-k will encounter the leading edge of the airfoil with the same strength as the one proceeding it.
There is a second and more satisfactory way to visualize the process: That the band k-l lay a horizontal track in the lower portion of the airfoil, while the bands l-m, m-n, n-o, and the remainder, do likewise.
Either way makes the case.
There is a little more to come, Larry. The three parts above need a certain amount of reworking and refinement, which I'll do when I get around it to, but it's all there, and you're the first guy, imagine that, to ever read it.
January 13, 1999
Bet you thought I (Richard) was finished since it's been a while.
Actually Richard has been extremely prolific, and got that way right after we agreed to keep it as simple as possible. He has been sending stuff faster than I could read it and now after receiving parts II, III and IV, which might be the end, I am sending it all along to you even before I have responded to or even read it.
I hope you can appreciate this revolutionary theory of lift Richard is laying down. He seems to really be onto something, but my knowledge is such that I would appreciate an analysis by someone on his level who can maintain impartiality, without falling into the "contrary-to-established-therefore-incorrect" syndrome.
Hope to hear from somebody.
Larry Ssspoon Witherspoon
January 13, 1999
Part 4 of 4
Please let me know if anybody else can follow these ideas. I have been trying to keep an open mind because knowledge changes and I have always believed I could accept new concepts even if contrary to established ones. Easier said than done sometimes, I guess, but I'm trying.
January 13, 1999
The second, or is it the third recursion.
Since the still more, below, yet more, an Addendum.
Still more: --- THE THEORY OF LIFT - PART IV ---
Our Intuition is that the wing acts as a vane, that it deflects the passing airstream downwards, deriving lift from the resultant exchange of momentum as this happens. This Intuition is confirmed for us by the existence of the downwash beneath the wing, and it is rationalized by familiar and established laws of motion.
That such is not the case, that the wing in fact turns the on-coming air upward, and that the observed downwash is devoid of any force that could contribute to the lift process is, by definition, counter intuitive.
The Intuition has a singular power, one that makes it all but immune to common-sense physical requirements, as well as observation, and it has beguiled generations of men. A century ago Otto Lilienthal referred to the upwash ahead of the wing as "die tragende Luftwelle", the carrying lift wave, and simple observation confirms his insight. Furthermore, the exigencies of the lift process, the requirement to accord with the conservation of momentum as it applies to aerodynamics, dictate such motion.
Ye have heard it said by them of old time, yadda, yadda, yadda, but I say unto you that there is a Law of Lift, that it subsumes all others, and obviates, or appears to, those of the received wisdom.
IN ALL PHASES OF THE LIFT PROCESS, WHETHER IN THE FORM OF THAT POTENTIAL
ACROSS THE WING UPON WHICH SUSTENTATION DEPENDS, OR ACTIVELY, AS THE INDUCED
MOMENTUM OF THE UPWASH, THE DESIGNATE FORCE, DERIVED FROM THRUST BY THE
RELATIVE MOMENTUM X ACCELERATION OF THE AIRFOIL AND THE RELATIVE WIND -
F/s, OR FORCE/system - MUST ACT UPWARD, VERTICALLY, ALONG THE
THE DESIGNATED FORCE, THAT DERIVED FROM THE MOMENTUM X ACCELERATION
OF THE WING VIS-A-VIS THE RELATIVE WIND; THE PRODUCT OF THRUST; HEREINAFTER
F/s, MUST, IN ALL PHASES OF THE LIFT PROCESS - SPECIFICALLY AS THAT PRESSURE
POTENTIAL BETWEEN THE POSITIVE AND NEGATIVE FIELDS ACROSS THE WING UPON
WHICH SUSTENTATION DEPENDS, AND IN THE INDUCED MOMENTUM THAT GIVES
IF, ONE THE ONE HAND, WE HAVE A PROCESS - THE HORIZONTAL PASSAGE OF
THE WING THROUGH THE AIR - THAT EXTRACTS A SPECIFIC, FINITE QUANTA OF TRANSVERSE
FORCE, = 100, IN ITS TRANSIT, AND, ON THE OTHER, A PROCESS OF SUSTENTATION
THAT DEPENDS ON THE CONVEYANCE TO THE WING [AND FROM IT] OF A LIKE FORCE,
= 100, ACTING VERTICALLY UPWARD ALONG THE GRAVITY VECTOR, IT IS AN ALL
BUT INESCAPABLE CONCLUSION THAT THE WING IN MOTION, BEING CENTRAL TO BOTH
PROCESSES, THAT IT IS THE SAME 100 UNITS OF MOMENTUM; THAT THE EXTRACTED
MOMENTUM, IN ITS TOTALITY, WAS ORIENTED UPWARDS; THAT THERE WAS NO SURPLUS
NOR EXTRANEOUS MOMENTUM, NONE THAT COULD BE DIRECTED OTHER THAN VERTICALLY,
UPWARDS, ALONG THE GRAVITY VECTOR, AND CERTAINLY
The reader is invited to contemplate this Law - so-called - to contravene or contradict it if he can, and once he grasps its import to apply it rigorously to the dynamics of the lift process, and see, as a consequence, what can and cannot happen.
Thus, the conclusions from simple observation and from accord with The
Law, given, apply as well to the downwash. Were the downwash an active
phase, which is to say the result of air being deflected downward, it would
be followed by a reactive phase, something comparable to the roostertail
of a fast boat, observable in the wake of the wing. The downwash is in
fact a reactive phase, what happens as a mirroring of the dynamics
And we know - The Law dictates - that one-half of the system energy
- F/s/2 - MUST BE transmitted to the lower surface of the airfoil, vertically
upwards, along the gravity vector, and that half that - F/s/4 - vertically
upward, along the gravity vector, to the area between the aerodynamic center
and the trailing edge.
It is a mysterious and confounding segment of air, that which flows beneath the wing between the center of pressure and the trailing edge of the airfoil. To discern its mysteries - well, that's for some future time, and besides, the wench is dead.
Or - Addendum
It is a mysterious and confounding segment of air, that downward flow beneath the wing aft of the aerodynamic center. Given the extent of its potential, as we perceive it, to mislead and delude us, it is necessary to analyse what happens within it with extreme care, to hew to The Law and by that means determine what MUST HAPPEN.
There are two dynamics, each with a reciprocal on the upwind side of the center of pressure, and themselves reciprocal, one set contradictory, so to speak, the other complementary. The flow in question, that past the under surface, is the resolution of all these.
The wave crests to a height determined by the system force, F/s. The peak of that crest is the dividing line between the reciprocal process of concomitant changes in velocity and amplitude. It is ebb and flow, systole and diastole, inhalation and exhalation. Thus this subject segment of air can do nothing else but subside, and as it does, accelerate, assuming its original undisturbed free-stream velocity. No sane man can ... yadda yadda yadda...
The reciprocal to that is neither so obvious nor easy to rationalize. The pressure form, in its extension phase - as it accelerates - draws in its sides, in this case one side, the upper, and the physical requirement here - p + v = 1 - would be for the extraction of momentum from an adjacent surface. Yet we know this: We know that the subject area of surface, that between the aerodynamic center and the trailing edge, IS SUSTAINED by the transfer of momentum, vertically upward, against it - F/s/4 - which force exactly matches the residual momentum, acting vertically, of the airmass passing beneath it; that, despite our Intuition, a cause and effect relationship between the two phenomena is highly likely.
What is curious is that the reduction of the force represented by the vertical vector does not appear to be in direct response to the extension, to its original length, of the horizontal one. It is doing its own thing, responding to its own exigencies, and coincidental to the process of pressure recovery. There is no contestation nor any reciprocal, zero-sum relationship, simply mutual convenience - the needs of one exactly accommodating those of the other - which almost seems contrived to clean up the scattered pieces of a process that couldn't come out right otherwise.
It is, finally, an abstruse and confounding play of abstract forces within an invisible medium, and contrary to some deep Intuition, deserving capitalization, that we have about the way things should happen, only to be discerned by careful conformity to the exigencies of The Law, of what must happen.
The End, sort of, I guess.
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