AERODYNAMICS & EPISTEMOLOGY
by RICHARD MILLER
The following theory was put forth by Richard Miller as a consolidated version of an on-going electronic conversation he was having with Larry Witherspoon over the past couple of months. The consolidated version is presented first since it can be read easily in one sitting and provides food for thought.  Once you feel you have a grasp of Richard's theory, you may want to starting reading through the original text between Larry and him which includes questions and further explanations by Richard.  This may help answer some of your questions OR it might just create more which is good.  If you do have questions or comments about this theory, please forward them to TWITT and we will add them to this document as well as forwarding them on to Richard for a return explanation (this is due to his limited on-line resources).  Richard is very interested in receiving the largest possible response from the aviation community.  Please do not hesitate to question any part of the presetation, offering your reasons for why it is in error and offering any possible counter theory/rationale, if you have one. (You can see some of the original by clicking here.)

FROM RICHARD:  There is one point of clarification about the aerodynamic presentation.  I do not (see myself as having) a radical nor revolutionary new theory of lift.  My intention is to demonstrate the shortcomings, I would call them absurdities, of the momentum theory, that based on classical Newtonian mechanics, and, as a concomitant, give a satisfactory description of the Bernoulli principle.  There has been a tendency from the theoretical-academic community to sideline Bernoulli, to have recourse to his principle, at best, to account for the reduced pressure on the upper surface of the airfoil, a problematic area for a system of mechanics based on the direct transmission of momentum, from one ponderable body to another; to allow the explanation a place in popular literature, kid's stuff so to speak, but not worthy of serious consideration.
     Moreover the recourse to The Principle was never - never to my knowledge, and I've looked - more than recourse to The Principle.  It can be described in mechanical terms, and that I have done, and if there is anything new or unique in my presentation it is that I have done it.
 

PROLOGUE

     What began for me as an excursion into physical theory has ended, at the conclusion of great labor, in the realms of psychology and philosophy.  In what follows the theory of lift is only a pretext, in both senses of the word.  The real issue, for those who have eyes to see and ears to hear, goes to the roots of epistemology: What are those assumptions we make in the evolution of our personal metaphysic, in setting our course in life, and in solving the problems we encounter, that lie so deep that they are never questioned? 
     Such an assumption was called by them of old time - the natural philosophers of the 17th and 18th centuries - an Intuition, although with sometimes ambiguous variations in meaning.  [See a dictionary of philosophy to satisfy yourself.] For present purposes the concept is perhaps best defined negatively, by the term counter intuitive: counter to what one would intuitively believe. Thus, we observe the airfoil with its positive inclination to the relative wind, confirm the downwash in its wake, invoke laws of motion consonant with a deeply ingrained sense of kinematics [kinesthetics], and with these rationalize the conclusion that the surface acts as a vane, deflecting air downward, deriving sustentation from an exchange of momentum between ponderable bodies. 
      In assuming the function of the wing-as-vane and the phenomenon of lift based on a direct exchange of momentum between the airfoil and the relative wind we ignore: 

   Observation - The fact that smoke-flow photographs clearly show an upwash ahead of the wing; 
   The Economics of Force - That momentum appropriated to the function of lift, that derived from the force generated by 
     the mass X acceleration of the wing and the relative airstream, cannot be expended other than vertically upwards; further 
     to which the equal and opposite reaction of Newtonian mechanics would reduce the maximum possible efficiency of the 
     wing to 50%. 
   The Conservation of Momentum - That the aerodynamic center, nominally at the 1/4-chord point, is the center of 
     aerodynamics; thus a kind of zero-sum game in which acceleration matches deceleration, phase diaphase, and upwash 
     downwash. 
   The Distribution of Pressure - The pressure profile across an airfoil, and the center of that pressure, differs from that of a 
     vane. 
   The Absence of Evidence - of an upwash at the trailing edge of the wing to compensate for the putative forcing down of 
     air by the lower surface. 

      The reader can readily confirm all these observation for him or herself; none can be disputed on any reasonable basis, yet in every particular they contravene the inferences of The Intuition, that the wing is sustained by a direct transfer of momentum, and the theory based on that assumption.  That any intuition could hold against such an onslaught of self-evident and logical conclusions speaks forcibly for its power to delude.  Charlie Brown was deluded when he imagined he'd go across the playground to talk to the little red-headed girl.  Not one of us but understands that.  But for generations of adult human beings, among them, one presumes, the brightest and the best, to receive from their intellectual forbears, and pass to their heirs as the received wisdom, the curious congeries of notions that comprise the momentum theory of lift is a delusion of a higher order, one approaching sublimity.  With charity for all, we acknowledge its special power to enthrall the human mind. 
     It is curious in the extreme, and that in a subject abounding in extreme curiosities, that in the science we call aerodynamics so little attention has been paid to the dynamics of the air.  The gross effects of flow have been dealt with as if fluids behaved in coherent and predictable ways, comparable to solids - another misleading intuition, and the source of great confusion that the theoreticians dealt with as best they could.  All the absurdities with which classical theory abounds, all that was intractable and misconstrued, may be seen as these attempts to etch glass with a hammer.  Concepts applicable to rods and cranks, derived from the work of Galileo, Kepler and Newton, principally, were applied to fluid flow with the conviction that there were direct exchanges of momentum between ponderable bodies, as a moving atmosphere and a surface, and that the results of these exchanges could be quantified, analyzed in accordance with trigonometric functions, and expressed directly with vectors. 
      It was an ill fit.  The tool applied to the task was not simply inadequate; it was qualitatively different, and the workman, lacking any idea of the true nature of the problem, nor of the appropriate method to solve it, forced the conclusions to fit the means at hand, and begot monstrosities.  It was, in fact, a system of fluid mechanics, one that ignored the tendencies of fluids to deform and for fields to coalesce within flows.  Fluid dynamics lay inherent, potential, biding its time. 
      The first hit up 'long side da head for the science of fluid mechanics was the failure of the measured force on an inclined plane in a flow to conform to the sine-square formulation.  The derivation of vector quantities resolved by trigonometric functions from the conditions stated in the 33rd Proposition of Section 7, Book II, of The Principia, yielded a considerable disparity in values between theory and practice, a difference of as much as 30:1.  If a red flag went up and learned men convened to address the matter, and regroup, no trace remains in history, although a discrepancy of that magnitude might be 
expected to provoke some curiosity. 
      It was not until the early years of the present century, when heavier-than-air craft began actually to fly in appreciable numbers, that matters sorted themselves out.  By degrees, engineers, using engineering methods - real measurements in the real world - took over the serious work of airplane design, and the theoreticians, perpetually confounded by the unreliability of their methods, and the refusal of the phenomenal world to conform to their methodology, invented a new world.  In their 
wake, however, they left an unmistakable trail of fictive hypotheses - a phrase of Euler's, to which I have become attached - and preposterous constructs that have come down to our times unchallenged and unchanged. Whatever effort is required to disinthral oneself from the cloud of delusion surrounding airfoil theory in its classical form, to see the nature of the flimsy conceits and gratuitous constructs human being will accept, is, I deem, well worth one's while. 
      There was a lurking unindicted co-conspirator in The Intuition of the wing functioning as a vane.  For the direct flow to have impacted the wing's lower surface as is commonly imagined, something approximating discrete molecular impact must have occurred, a direct contact transfer of momentum between the flow and the surface, each molecule in turn, as 
it streams past the airfoil, transmitting its quantum of momentum, then going about its business - downwash.  The steam of water from a garden hose, deflected by a surface, provides a good example. 
     In fact such a situation is all but unimaginable.  Any resistance to a fluid flow is going to result in a process of backward stacking, from the source of resistance to the limits of the dynamic force, in which the momentum of those air particles following the initial one, aggregates. 
     Two falling BBs, aligned vertically, and contiguous, will impact a surface with a greater force than one, and a still greater force as more BBs are added to the stack.  Were the designated bodies inelastic the aggregate force would be the sum of the acceleration X all the masses, and the graphic representation a straight line. 
     The atmosphere, both in its constituent properties and by virtue of its fluid nature, is elastic.  Dynamical pressures within any atmospheric flow vary with the square of the fluid velocity.  As a consequence of the first of these facts the rate of stacking in a line of air particles falls off with the distance from the obstruction causing it; and of the second that the rate of decay or attenuation of the momentum along the stack, is exponential. 
     As fortune would have it, and if ever there were a more singular instance of the fortuitous we need to know about it, the exponent of this (aggregate) momentum is the same as that which obtains in gravitational fields.  Thus, the highest dynamic value at the obstructing surface followed by exponential decay in accordance with the inverse-square law to a point of attenuation at which dynamic pressure as such ceases; The defining point between the dynamic and static, or ambient fields. 
     In most things in the phenomenal world the negative instance is the more problematical, and to conceptualize and describe in a satisfactory manner the negative concomitant of aggregate-momentum stacking and transfer presents a special challenge that I am going to let pass for the moment.  One simple instance will suffice; the piece of paper that sticks to the bottom of a book when you pick it up. 
     It is now possible to define aerodynamics: 
     That momentum aggregates (and extenuates, the negative instance) along lines, sheets, fields, transverse to the ambient flow past the airfoil; that the inherent forces of aggregation and extenuation are reciprocals of the velocity changes within that flow; and that the aggregate and extenuate fields they form constitute the total designated lift force of the system; that aggregate momentum is transferred, at right angles to the flow, to the wing's lower surface, extenuate momentum extracted (?), at right angles to the flow, from the upper surface. 

(This is an addendum by Richard as of February 6, 1999.)

DECONSTRUCTING NEWTON
PRINCIPIA - BOOK II
PART II 

     The figure of Newton has come down to us as The Great Magus, he who wrought wonders in the phenomenal world, explicated the inexplicable, revealed and elucidated the arcane and abstruse, cast light in dark corners.  Remember Pope. 
     In the 41st Proposition, Book II, Section VIII of the Principia, he is at the height of his powers.  Here he undertakes as his subject "The Motion Propagated Through Fluids", and that without a definition of fluids nor reference to motion.  It is to be a high-wire act without a net, in fact one without a wire, a truly spectacular performance.  For besides ignoring motion he makes no mention of force, which is to say accelerated masses, nor of momentum, nor does he have recourse to those 
several, relevant, eponymous laws on which much of his fame rests. 
     No serious student of physics, nor of th e history of science, should deprive him, or herself of the experience of reading Proposition 41, although apparently many have, why else would it have lain there so long, and no one raise a great cry of surprise and wonder, or fright and alarm, whichever seemed appropriate.  Thus, for the intellectually curious: 
     "A pressure is not propagated through a fluid in rectilinear direction," the introductory line of the Proposition says, "except where the particles of the fluid lie in a right line."  Thence, in the text that follows, to the active agent, that being "the pressure" that "may indeed be propagated from [particle] a to e."  The source of the pressure is not specified, nor why it should bear on -b, -b on -c and on to -e. 
     As readers we have only the unarticulated assumption based on our inference that pressure is a force, and force the product of an accelerated mass, that such mass, thus accelerated, proceeds in a rectilinear fashion, thus along the right line a-e.  Thus we are forced to concede motion, but it is motionless motion, and as magically as it emerged out of the nowhere into the here, it disappears, or at least the rectilinear propagation beyond -e does.  We may scratch our heads and ask ourselves what kind of motion that was, and why it now appears along the oblique lines f-h-l and g-k-m. 
      All else having failed we are left to conclude the existence of a pressure partial to particular particles, one that proceeds willy nilly, independent of those laws the author himself framed and, as said, of causality itself.  And also to conclude that Newton did not have the least idea of the mechanics nor dynamics of fluids. 

      (Note by Richard:  What you have now is the A & E theory which should be completely adequate for the inquiring minds to which such things matter.  Whatever is not clear can be taken care of in the chat-room correspondence.)

 (ed. note:  The original e-mail text of the exchange between Richard and Larry can be found by clicking here.  It is quite extensive, taking up approximately 25 pages if you were to print it out.  However, by scanning it you may find answers to your first thought questions or find reasons to proceed with providing a comment back into the discussion.)
 

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Below are the e-mail rebutals or agreements to the above theory.  We will continue to add to this section, including rebutals by Richard, as they come in through direct contact with TWITT, Richard or the Nurflugel mailing list.
Richard Miller, words, and equations 
Date: Fri, 29 Jan 1999 21:37:11 EST 
From: DepThought@aol.com 

     Richard Miller's observations are entirely in keeping with the observations of 17th century Scientist/Philospher Isaac Newton, who's second law of motion, otherwise known as the conservation of momentum, can account for all the 
phenomenae Mr. Miller claims contradict momentum considerations. 
     Newton's 2nd Law: 
         F = d(mv)/dt (Force equals the rate of change of momentum) 
     In the case of a fluid moving past an airfoil, the force must act in the direction of curvature of the foil, if the fluid is to follow the fluid's shape. Thus the pressure gradient normal to the foil surface must be directly related to the curvature of the surface. Thus, low pressures on convex surfaces, and high pressures on concave surfaces. Once the regions of low and high pressure are mapped out, it is easy to see the source of upwash and downwash, fast and slow flow, why lift has to act normal to the velocity vector, etc. 
     In short, if one takes the time to follow through on the basic equations of motion (DO THE MATH) then  one would realize that fluid mechanics has been well understood for centuries, and that while Mr. Miller's words are pretty, they only serve to disguise the truth, not illuminate it. 

Patrick King 
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From: Jack Lambie <jlambie@inet1.inetworld.net> 
Date: Wed, 17 Feb 1999 23:46:49 -0800 

     Aerodynamics is a most intriguing field. I like it because it is so stimulating to think about what is really going on.  Just about anything said in that field can be  true and false depending on size of the object, the  speed and the purpose of the design.  For example: The teardrop shape has lowest drag at higher speeds but a sphere has lowest drag at very 
slow speed. 
     A raindrop is not tear-shaped but  is a wiggling flattened blob. 
     A rough surface has lower drag at slow speed but higher drag at high speed. 
     A flat airfoil has better lift going very slow but a thicker  curved airfoil wing has better lift a bit faster. 
     A airfoil curved on the bottom and almost flat on top is better for lift just below the speed of sound to delay shock waves and lower drag. 
     Highest lift is with an airfoil more deeply arched on both top and bottom. 
     Flying near speed of sound things are different. Sharp edges or swept wings  are used to delay drag  used that give very poor lift at slower speeds, unless you really fly slowly, like bugs and model planes. 
     Then they  too need sharp leading edges and almost flat airfoils.  Flies have little hits sticking out on their wing edges to make the air turbulent which, in a fly-sized creature, is very viscous, sticky. 
     Most interesting is the confusion and misinformation in describing lift and drag. 
     This article explains this most contentious aspect, lift,  correctly  so we can all  enjoy this most subtle of technical subjects.  But why is something that has successfully allowed us to fly for almost a hundred years still argued about? 
     Here is the  “standard” explanation of  lift, then  why  this approach has gradually created a chorus of detractors pointing out the many anomalies. I’ll discuss why is not “true” and give examples of confusion wrought by the Bernoulli Suction idea. The action explanation will be shown to be more simple,  descriptive what is actually happening more accurately and with   power and goodness aerodynamic experimenters. 
      The standard “An airplane flies” says the wing is shaped with a greater  curve on the top of the surface than the bottom.  The air flowing over the wing  must  travel farther over the top than the bottom so it must speed up to meet the air that went past from which it was divided. As Bernoulli pointed out in 1796 “When air speeds up the pressure drops.” Thus the reduced air pressure over the top of provides most of the lift. 
        Air does not rush over and airplane wing and does not rush over the top of an air foil faster than under the bottom. In real life the wing moves through still air. 
     The slight downwash behind the wing is not caused by the pressures around the wing. 
     An airplane flies through the air. The air is not going over or under the wings but is being deflected from its stationary position by the planes’ passage. The plane is the thing doing the rushing. As its body and wings go through the air subsonic of  course,  the air ahead of the the plane begins to move out of the way, Some goes up as the wing approaches and some is pushed down. The air has mass and inertia. It wants to stay where it is and, when moved, it makes an action exactly equal and opposite on the object that is moving it by... how else?  Pressure changes. 
     The pressure change is in response to deflecting.   Any deflection of the air  both the action and the pressure differences on the object doing it , such as a wing, are instant and simultaneous.   Because they happen at the same time, would that make them equal as cause? There is a compelling case to pick action, not pressure, as the “cause”of lift. 
     We define “caused by” with action. The wing is moving the air so it is the thing doing  something  that  causes  lift. The can be no pressure changes without motion. 
      The action to this cause results in pressure differences.  Just because the action and pressure change is simultaneous doesn’t make them equal when we talk about cause. 
       More important  using action describes how any object that deflects air sets up an equal and opposite action.  This action caused by motion of the airplane also explains  a wider  range of situations, not just those in fluids. The simplicity of action3Daction, plus its ability to be sensed easily by us humans gives the “true” cause, not changes in fluid pressure. 
     Action is the cause of pressure change. Action to deflecting (accelerating) the air is the PRIMARY cause and the changes in pressure is the SECONDARY EFFECT that transfers the action to the body. 
     In the NASM section “What makes a Wing Work” the explanation is confused by using the secondary effect to explain lift. 
     “A wing is shaped and tilted so the air moving over it moves faster than the air under it. As the air speeds up, the pressure goes down. So the faster moving air above exerts less pressure on the wing with the slower moving air below. The result is an upward push on the wing-lift.  It then talks about the amount of lift being affected by the size shape and angle it meets the oncoming air. 
     What's wrong with that? First the air is not oncoming. The plane is flying through it. Why the confusing, to students, change in reference?  It might be fine for aerodynamicists working with wind tunnels, but for the public, tell it like its really happening.  Well you say ,”Its easier to explain with the air moving over the wing, its all relative anyway. There is no difference if the wing moves or if the air moves. “ 
         Ok. If you want to do it that way, but you better explain to the student or beginning pilot that this explanation is not the the true state of affairs but aerodynamicist’s jargon and an “as if” one that you are using because you think its easier to explain that way, probably because that's the way you learned.   Try explaining everyhthing yhou know about aerodynamics from the point of view of the wing moving through stationary air and you will gain a great understanding of what is really happening. 
    Using Bernoulli is entirely passe.  He died long before anyone thought of an airplane wing lifted by his theory of pressure change with speed. 
    Of course there are pressure differences  over a wing or body as it moves through a fluid or a fluid moves over it. That is correct. But Dan Bernoulli’s theorem is really no explanation of anything. It is just a statement of the relationship between speed and pressure. 
       Pressure can be measured with gauges connected to  taps, little holes in the surface and offer great possibilities for mathematical description and computer prediction and analysis but they are not the primary cause. Think about it. There can be no pressure change without deflecting air.   The first cause is the air being deflected. 
       The New Smithsonian Air and Space Museum is a classic example of the confusion wrought by the “virus infection” of the Bernoulli explanation. 
      The Smithsonian’s “Bernoulli Brain Teasers” can better be described by action-action. It should be called “Newtonian Brain Teasers.” For example one exhibit text says: 
     “An airfoil seen from the side is curved on top and nearly flat on the bottom. As a wing moves through the air, the air divides to pass above and below the wing. Since the wing’s upper surface is curved, the air rushing over the top speeds up and stretches out. This decreases the air pressure above the wing. The air flowing below the wing in a  fairly straight line so its speed and air pressure remain the same.” 
     That description of lift is full of anomalies. 
     Training hang gliders have a single surface airfoil. Its the same distance over the bottom as over the top. How can it fly?  How does a plane fly upside down? How come model planes and insects with flat airfoils fly so well? 
     Since the airfoil shape has not changed why does lift increase as the angle of attack increases? 
     The answer to these questions are clear when lift is described as the result of deflecting air. Any shape can create lift at a positive angle of attack. 
          The wing is moving through the air, and,  below the speed of sound, the air senses the coming wing.  Air above  moves forward,  then up and back and below it is pushed forward and down. Some air  is pulled along by friction with the surface. That area is called the boundary layer. It is called a stagnant region and a stall is when lift dissappears because the air loses energy and separates from the airfoil.  In reality  the air gains energy because it is swept along with the wing. The air does not separate but clings to the wing in a great swirling mass being pulled along and accelerated from its quiet state before being 
moved by the wing. The great increase in the energy of the air, sppeding up and being pulled along, comes from the airplane.  The energy to pull tha air along in a stall is usually so great the  plane slows and the nose drops because of the forward of lift center balance point and the tail which losing its downforce. There is just as much lift just  past the stall angle as just before it. Even plate flat on has a lift coefficient over 1.17 which is better than most canards. A dethermalizer on a model glider takes advantage of the ability to drop straight down to  a reasonably soft landing. This has been tried in full sizxe gliders and works great but if it is allowed to go on down to the surface it would severly damage the airplane. 
     “Hold  piece of paper between your fingers  and blow over it. It pulls up. Why?” Air above and below the breath of wind is pulled from its position into the high speed flow. If air is  moved down the equal and opposite action is an up force.  This force is transferred to the paper by pressure which pulls it up. 
      “Take two balloons put a little water in them for steadiness then tie each with a foot of string and hang them a few inches apart  Blow between them. Newton would say they move toward each other because the air is deflected in a curve over the balloon’s surface. Its acceleration from its straight path and the resulting action is a pull on the balloon. 
       When you go around the curve in a car. You are pulled to the outside. So  also the air going around the balloons sets up a force opposite to the accelerations of the air that force makes the balloons move toward each other. 
     “A ping pong ball is put on a flexible straw tube and you blow in it with the ball balanced on top. The ball does not blow away but stays in place. Why?”  The Newtonian or action explanation is simply that the air going around the curve has the equal and opposite action to its change in direction, which creates an instantaneous force pulling on the ball from all sides.  If it starts to move to one side it is quickly self correcting because if the air is cut off from one side and increased on the other with its attendant increase in force pulling it back over the center of the tube.  The more air being moved the greater reactive force. 
       “Take a thimble, put a piece of light cardboard over it with tack through it extending into the hole . Blow into the thimble and the card stays in place instead of blowing away.”  My action explanation is that the air coming out of the hole goes around the  corner at the edge of the hole in the thimble and the cardboard. Its  direction is changed.  When it goes around the corner that deflection makes a pull on the edge of the object making the air turn . That pull holds the cardboard in place. 
     The “Did You Know” section shows an obstacle, it looks like a streamlined shape like a fairing  over the NDB antenna on an airplane.  It says, “When moving air encounters an obstacle ---its path narrows as it flows around the object-------Freely flowing air ---speeds up where its path narrows and slows back down where it widens.” 
       Any grade school student would look at that as say, “But Mr. Lambie the air flow widens as it goes around the object. It has to or it would have to go right through the object.  I would have to say,”An obvious observation.  “Good for you. You are a intelligent student to question an explanation that doesn’t make sense.” 
      Here’s how I would explain this example with the True description. 
     The air must widen, not narrow, to go around any object.  The object deflects the air, that is, causes  it to moved. This instantaneously sets up a action opposite to its deflection.  This, over the  curve, would be a pull .  The counter  action, of course,  is transferred to the object by a minus pressure. How else? 
      The primary cause of the pressure change is action due to the air being “widened” out as it moved around the object. 
     The “Did  You Know?”  Has a most confusing example. It shows a truck and a car passing and says that the sideward tug you feel on your car when you pass a large truck going in the opposite direction is caused by air pressure. The passing vehicles form a constriction that speeds up the flow of air, reducing the pressure between them (it makes no difference which is moving the air or vehicles. (Thjis by the way is the only statement in the whole exhibit ointing out the crucial liberty they re taking with reality..that it’s relative flow. The result is the same. The higher pressure on the other side of the car pushes it 
toward the truck during the split second they pass.” 
       But my observant student would say. “I looks to me that if only the air were moving the truck would have a tailwind and the car headwind so there would be no deflection on air by the truck at all.”  True my good student, but as poor as this example is, it would work somewhat because the car pushing the strong headwind out of the way would be deflecting the air causing an equal and opposite action which would give a pull. The pull action is transferred to the front corners of the car as a lower pressure which the truck would also feel as a pull. 
     I have done two education  TV shows on this and written about it in all  7 of my books. It seems radical. It would negate every aviation and bird book dealing with movement in air and water and  require rethinking for teachers. No more blind copying of the encyclopedia by magazines and newspapers. 
      Yet,  I have discussed this for years with aerodynamicists Dr. Bob LIebeck, Dr. Peter Lissaman, Dr. Paul Mac Cready, Barnaby Wainfain, Bruce Carmichael and my  friend Balan Menen. The are unanimous in agreement with this interpretation and description being correct. 
     How come  the  “Curved airfoil” fallacy and why is it  so often repeated?    Why the Bernoulli description has become the most used is a good question for research.  One teacher likened it to a computer virus that spreads and spreads. Bernoulli’s simple faster-lower pressure relationship ideas were picked up when people first began to fly. His faster-flow-low pressure idea was presented to explain how lift is created and , while not a true explanation, somehow  appealed to the pilots and aerodynamicists.  Why? 
     Most people then would not to think that a special shape, curved more on the top would be the secret of lift. Perhaps it gave a certain mystique and power to those involved with airplanes. We all like to think we have special knowledge and this was a perfect and subtle explanation of lift. 
     The general feeling I get is, perhaps excepting Paul MacCready, is that it doesn’t rate the time involved in changing a way of looking at something they  already know and understand. 
      I suppose it is like when I talk about legal language to lawyers.  They largely agree that legal verbiage is redundant, ambiguous, archaic that its almost illiterate. But they are accustomed to it and know what is being said so who cares. Its their job. Why make plain language law.  Then people wouldn’t hire lawyers. 

PO Box 1231 Morongo Valley, CA 92256 
 Phone and FAX 760 363 6806 
jlambie@mail.idt.net 
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From: Al Bowers <bowers@orville.dfrc.nasa.gov> 
Date: Thu, 18 Feb 1999 08:53:32 -0800 (PST) 

Well, I looked at it.  I wish that Richard didn't have to hide his idea with words that common people don't use.  This line of thinking has also been promulgated by Peter Lissaman in his "The Meaning of Lift" (AIAA 96-0161).  But Peter's work is only _slightly_ more readable.  There is some work like this by Arvel Gentry from the late 1970s, but I had some serious reservations with the logic behind some of Gentry's conclusions (I didn't fault the conclusions, just his logic for them). 
     Along these lines, and anecdote.  The closing dinner of the 1998 MIT Symposium of Low Speed and Motorless Flight was held in the Boston Museum of Science and Technology.  Along one wall on the ground floor is a wave machine, perhaps 120 feet long, about 8 feet deep and maybe 4 feet wide.  the waves are created by a machine on the left (south) side 
and the wave travel right to crash on an artificial "beach" at the far end.  It's mesmerizing to watch, and my family already has a strong connection to the sea (I'm the first in three generations on BOTH sides not to got to sea as a professional sailor at some point in my life).  I was near the machine end watchin the waves form.  Near the other end were Mark Drela and Paul MacCready discussing something, what I could not hear over the sound of the wave machine.  As I walked down to the end where Mark and Paul were standing, I picked up on the conversation.  It was one of those situations where I wanted to HEAR what they were saying, without appearing as though I were eve's dropping on them.  I needn't have bothered.  They were discussing the origin of lift.  About the time I had ascertained this (less than 20 seconds), Paul invited me over to arbitrate their dispute.  (!)  I don't recall the particulars of Mark's theory, but Paul's idea is simply _outstanding_ for it's simplicity, ease of understanding, and elegance.  Lissaman and Miller should let MacCready do their talking for them, in my humble opinion (IMHO). 
     Let me see if I can do justice to Paul's explanation.  MacCready's theory is that the air has no vorticity as it approaches an infinite span wing.  But the pressure field prior to the wing causes it to be drawn up towards the leading edge (upwash).  As it contacts the wing, the skin friction causes the boundary layer to establish vorticity along the surface of the upper and lower surfaces.  Because of the shape and pressure distribution of the airfoil, the upper surface gains more vorticity than the lower surface does.  At the end of the airfoil, both flows are imbued with this vorticity, and the upper surface's greater vorticity is 
exactly equal to the vorticity as described by Prantdl's lifting line theory (this assumes that the Kutta condition holds and the flow is not separated).  The flow field aft of the wing moves downwards so that the stagnation streamline from the leading edge of the wing exactly moves back to the same position as prior to the wing influencing the air.  The imbedded vorticity in the air (energy) is exactly equal to the profile drag of the airfoil. Note that the upwash exactly equals the downwash, so there is no momentum transfer (thinking of the wing as a "turning vane"). 
     Elegant and simple (better than Lissaman and Miller, and WAY better than Gentry, IMHO).  In general, all three agree on salient points, though I'm still shakey on Gentry. 
     A last note, downwash _only_ exists in greater amounts than upwash for _finite_ wings, and this "excess" downwash causes induced drag, rotation of the lift vector aft, and is the part of "lift" that can be described as a "turning vane" effect. 
     As for Reinhold's work on Prandtl and sin^3 span loads as having the minimum induced drag for a given wing root bending moment, all I can say is _excellent work_.  Given that it was published in 1933, I'm a little surprised that we (the USA) had not heard of it.  Indeed, as Doug pointed out, Robert T Jones (most folks call him "RT") did an independent derivation of this and came to the _exact_ same conclusions.  It was written up in Soaring magazine (R. T. Jones, Soaring 10/79, pg 26; also NASA TN D-8260).  But I failed to make the connection (DUH!). 
     As a further aside, the 1.22 longer span of the bell would require a heavier spar, though no stronger, than that of an elliptical.  If the additional material of the bell spar were used in the elliptical, what increase in span could we make on the elliptical?  We're playing the structures vs aero game again.  But I don't think the increased span elliptical could gain 
enough against the 0.89 induced drag of the bell.  I think the bell still wins.  I should do that integration and find the result... 
     I've run into a fascinating puzzle.  I mentioned I had been thinking about kayaks as of late.  One of the great innovations in the kayak world in the last 20 years is the "wing" paddle.  This blade develops lift in the forward direction because of the slight outward motion of the paddlers stroke.  There is a possible 20% increase in efficiency over conventional paddles.  The puzzle is that the blades are about 0.75 ft^2, and the best paddlers have a blade velocity (through the water) of about 6.4 ft/s, and produce about 90 lbf.  (!)  This implies a lift coefficient of about 3 from a single element, single surface airfoil.  My first 
reaction is "No way."  But if the force vectors are added up, and the accelerations and masses accounted for, plus the drag of the kayak, then the paddlers MUST be developing about 90 lbf.  Lift coefficients of 3.  "Way."  All I can come up with is dynamic vortex lift (shades of Kasper again), and in my own personal observations, indeed wing paddles do have a large entrained vortex that follows the blade (this is not the same as separation, the flow is fully attached).  Fascinating... 

Al Bowers  ...fluid dynamic puzzles... 

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From: "Don Stackhouse @ DJ Aerotech" <djarotec@bright.net> 
Date: Fri, 19 Feb 1999 08:38:18 

Al Bowers writes: 

>As a further aside, the 1.22 longer span of the bell would require a heavier spar, though no stronger, than that of an elliptical.  If the additional material of the bell spar were used in the elliptical, what increase in span could we make on the elliptical?  We're playing the structures vs aero game again.  But I don't think the increased span elliptical could gain 
enough against the 0.89 induced drag of the bell.  I think the bell still wins.  I should do that integration and find the result... < 
     The other question I have is what about whetted area, skin friction and profile drag? If the bell distribution has a longer span, then either it has more wing area (and more whetted area) or else it has less chord and lower Reynolds numbers. If the spar is to stay the same depth, then the lower chord also means airfoils with a greater % thickness, exactly what you DON'T want at lower Re's. Maybe on large full-scale aircraft this isn't as much of a problem, but on R/C sized models it's a MAJOR issue. I like the lower induced drag, but not if it means killing cruise and penetration to get it. Being able to thermal better because of an induced drag benefit does you no good if you can't reach the thermal because of the increased parasite drag. 
     Does this mean that the optimum lift distribution overall is somewhere BETWEEN the elliptical and the sin^3 bell distribution? 

Don Stackhouse @ DJ Aerotech 
djarotec@bright.net 
http://www.bright.net/~djwerks/ 
---------------------------------------------------------------------- 
From: Robert Osfield <robert@mve.com> 
Date: Fri, 19 Feb 1999 14:09:46 +0000 

Don Stackhouse @ DJ Aerotech wrote: 

> The other question I have is what about whetted area, skin friction and profile drag? ........... 

I was thinking along these lines too. 
     Off the top of my head I can add a futher two factors to the above is that increased span has with regard to thermalling performance : 

   1) Increased dynamic differential across the wing, however the bell shaped lift distribution will help reduce this effect. 

   2) Increased turn radius of the outer tip. Assuming a parabolic distribution of thermal strength across the thermal radius the outside tip will be in lower lift than the inside tip is in greater lift and consequently producing a lower overall experienced climb rate. 

     Also add in factors of non-planner wakes and you get a much more complicated picture than just elliptical and the sin^3 bell distribution. 
     The theoretical ideals are useful for illumiating areas of design, but when it comes down to optimizing a real wing for various different tasks which normally challenge it, life's much more complicated.  In this realm I expect accurate computer modelling to come into its own helping the designer iterate towards the optimum(s:-) for their paticular aircraft. 

Rising air, 

Robert Osfield, Software Development Manager, 
Midland Valley Exploration Ltd, 
14 Park Circus, Glasgow G3 6AX, Scotland. 
Phone: +44 (0)141 332 2681 Fax: +44 (0)141 332 6792 
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From: Al Bowers <bowers@orville.dfrc.nasa.gov> 
Date: Fri, 19 Feb 1999 11:02:02 -0800 (PST) 

> Al Bowers writes: 

>> As a further aside, the 1.22 longer span of the bell would require a heavier spar, though no stronger, than that of an elliptical.  If the additional material of the bell spar were used in the elliptical, what increase in span could we make on the elliptical?>> 

>Don Stackhouse writes:  The other question I have is what about whetted area, skin friction and profile drag? If the bell distribution has a longer span, then either it has more wing area (and more whetted area) or else it has less chord and lower Reynolds numbers...> 

Right, but there is a medium where you can gain in the induced drag without too large a penalty in profile drag and you _should_ come out ahead. 

> Does this mean that the optimum lift distribution overall is somewhere BETWEEN the elliptical and the sin^3 bell distribution?< 

     I think it does.  robert points out (correctly) that the more components you can understand (turning, cruise, distribution of the lift WRT the thermal, etc) the better the ultimate solution will be. 
     An example of "high tech" gone wrong is the the advent of carbon fiber spars in sailplanes.  Stronger spars meant thinner wings, but they were too stiff and lost energy in turbulence over the older flexible spars (thicker airfoils too!).  You goota think it through! 

Al Bowers 
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From: Gregg MacPherson <viz@nznet.gen.nz> 
Date: Sat, 20 Feb 1999 14:52:12 +1300 

Don, Al and all, 

At 08:38 AM 19/02/99, Don wrote: 
>Al Bowers writes:  As a further aside, the 1.22 longer span of the bell would require a heavier spar, though no stronger, than that of an elliptical...........> 
     Refering habitually to the R.T.Jones TN2249 "The Spanwise Dist. of Lift for Minimum Induced Drag of Wings Having a Given lift and a Given Bending moment" (sorry al I still haven't got the other papers that have been refered to): For those not up on all this, a variation on span is allowed, while keeping the above constraints. Various loading distributions are displayed in figure 5. A distribution with a *1.275 span is shown which looks like a sin^3 loading with bit less loading mid-semispan and a bit more loading at the root. Another dist. with *1.15 span is shown, which is similar but with more loading at the tip (convex curve on graph at tip). 
     Figure 4 shows CDi/(CDi of the elliptic) vs (semispan/semispanellipse). The *1.15 case above achieves max improvement of 15% of CDi with a 15% increase in span. Further increases in span (example the *1.275 case) yield no further reduction in CDi. 
     Now the *1.275 case is not an accurate sin^3 dist. so can't draw real conclusions from this, but, going out on a limb, it looks like the Horten distribution exploits_the_principle somewhat, but is unlikely to be the optomised case. Applogies to all, especially Reinhold if I'm wrong. I havent read all the stuff yet. 
     Al, does the spar definately have to be heavier ? 

>The other question I have is what about whetted area, skin friction and profile drag? If the bell distribution has a longer span, then either it has more wing area (and more whetted area) or else it has less chord and lower Reynolds numbers....> 

Wing area should be almost the same (comparisons are between wings generating the same lift). The lower Re outboard makes it difficult - if turbulent separation is starting earlier at lower Re, then there will be a bit less lift so need slightly more area? The Re outboard will tend to have a Cd penalty, and there won't be much compensating improvement on the bigger root chord, but remember that the outboard chord, hence area, is small which affects the actual CD contribution, and the Cl's are relatively low (looking at a better place on the 2D polar?). At the moment I also think it is possible to exploit the high taper when arranging the flap/elevon deflections for trim at min CD at speed. 

>If the spar is to stay the same depth, then the lower chord also means airfoils with a greater % thickness, exactly what you DON'T want at lower Re's. Maybe on large full-scale aircraft this isn't as much of a problem, but on R/C sized models it's a MAJOR issue. I like the lower induced drag, but not if it means killing cruise and penetration to get it. Being able to thermal better because of an induced drag benefit does you no good if you can't reach the thermal because of the increased parasite drag.> 

In the simplest case of the comparisons underlying this discussion, the foil % thickness would stay the same, and I don't think that presents a major problem for spar design on the "bell" dist. wing. However some variation on thickness could be possible. The kinds of % thickness that would make these ides work are fine for a full sized sailplane.  Full size, the thickness can increase OK at the root. (I know that Dr Boermans has this on some of his latest concepts). 

>Does this mean that the optimum lift distribution overall is somewhere BETWEEN the elliptical and the sin^3 bell distribution?> 

That's my guess. If someone has TN2249 and a scanner mabee they could put some of that data on Doug's site so people can get the gist of all this better. These are quite worthy  concepts. (whole paper is only 15pages) 
     Now, what about folding the tips of one of these idealised distributions up into a winglet (very roughly speaking). If we can retain a similar CDi then the winglet has some other usefull features that we can exploit. For the *1.15 distribution this looked possible, and led to the initial version of our sailplane. 

Regards 
Gregg. 
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