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Origins Of Lift



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                                         The Origins of Lift
                                                             By Arvel Gentry
                                                              January 2006
     Abstract
         The fundamentals of lift generation are presented with emphasis on their usefulness for
     understanding the flow around sails on a sailboat. These same concepts are applicable to conventional
     airfoils for aircraft. Well known basic aerodynamic principles are used to illustrate the starting vortex
     and the formation of a circulation flow field about two-dimensional airfoils that leads to the generation
     of lift. Three-dimensional effects supply additional flow complications but are not     December
                                                                                                central to 1999
                                                                                                           the
     fundamental origins of lift. The generation of lift requires that the fluid have some viscosity. An
     experiment with a fluid without viscosity has been conducted to prove this point. Without viscosity
     there would be no lift; birds and aircraft would not fly, and sailboats would not sail.

     The wind is blowing nicely as I trim my sails and move
smoothly across the water. A glider pilot searches for thermals to
prolong his playtime in the air. The NASA space shuttle pilot
makes his final maneuvers to line up with the runway and flares
to make a nice landing. All of these situations have one thing in
common; they all are able to generate a force that we call lift. For
the sailor, lift is everything as long as the wind blows. For the
glider pilot, it is almost everything but he needs help to get aloft.
The shuttle pilot needs just enough lift to get back to the runway
safely.
     All of these vehicles are flying, and flight depends upon
generating enough lifting force to avoid falling like a rock or, in             Figure 1. Water channel photograph showing separated flow.
my case, being left drifting with the tidal currents when the wind
dies. But how is this lifting force generated? What is the                         3. Fluid flow without viscosity. Computed streamlines for
fundamental explanation for the generation of lift?                           the inviscid flow about a flat plate airfoil are shown in Figure 2.
                                                                              The flow is from left to right. Green streamlines that actually
      1. To understand the fundamentals of how lift is                        touch the surface are called stagnation streamlines. They divide
generated, it is best to start with a simple two-dimensional                  the flow that goes on the top of the airfoil from the lower surface
airfoil. This allows us to get at the real essence of the origins of          flow. In areas where the streamlines get closer together, the
lift. Three-dimensional effects are just additional complicating              air speeds up and the pressure goes down (Bernoulli's equation,
factors and are not central to what really causes lift. Although the          [Reference 1, page 226]). Where the streamlines get farther
primary purpose of this article is to help sailors understand how             apart, the air slows down and the pressure goes up. If you rotate
their sails work, the concepts presented are exactly the same as              this flow diagram 180 degrees, you will see that it looks the
for conventional airfoils used on aircraft. The emphasis here is              same. The pressure force on the top will, therefore, be the same
on understanding more of the details of the airflow than is taught            as the pressure force on the bottom giving zero lift and zero drag.
to the beginning pilot. The pilot has only minimal influence on               This is known as D'Alembert's paradox [2, p 225]. A flat plate
the shape of his wing (control surfaces and flaps up or down).                airfoil is used here to illustrate this. However, regardless of the
However, the sailor has rather complete control of the shape of               airfoil shape, without viscosity the resulting lift and drag always
his airfoils and frequently makes use of two or more flexible sails           turns out to be zero according to D'Alembert's paradox.
that must be constantly shaped to work together for best
performance. Sailing also sometimes requires knowledge of the
airflow patterns around boats in close proximity.
      2. Air and water are fluids that have a small amount of
viscosity. Viscosity effects are most apparent in the region of the
flow very near the airfoil surfaces. We call this region the
boundary layer. The boundary layer is responsible for creating
skin friction drag on a surface. For most low speed flows, the
fluid outside of the boundary layer (the external flow) may be
viewed as inviscid (zero viscosity). When the pressure in the
external flow near the boundary layer is increasing too rapidly,
the normally well-behaved viscous boundary layer will separate
from the surface. This leaves an unsteady chaotic region that
distorts the external flow, decreasing lift and increasing drag (see
Figure 1). Separation is a viscous effect.                                            Figure 2. Non-lifting flow around a flat plate.

                                          Copyright C 2006 by Arvel Gentry All rights reserved
                                                                        -1-
     4. Formation of the starting vortex. However, air does
have some viscosity! As the wind is initially turned on or airfoil
movement is started, the flow on both the upper and lower
surfaces near the trailing edge have some difficult maneuvers to
make. As soon as the boundary layer develops, it will not be able
to negotiate these maneuvers. The flow will separate from the
surface and form the starting vortex as shown in the sketches in
Figure 3 [1, p 393]. The external flow and the boundary layer will
quickly adjust, and as stable flow is established, the starting
vortex will be swept downstream. The same phenomena will
also occur on a curved airfoil representing a sail and on a
conventional airfoil such as used on aircraft. The starting vortex
will eventually dissipate because of the fluid's viscosity.
                                                                                        Figure 5. Lifting flow about flat plate.

                                                                            lifting flow field and the circulation flow field are added
                                                                            together, you get the final lifting-flow streamlines shown in
                                                                            Figure 5. The circulation flow field is obviously the primary
                                                                            contributor to creating the upwash in front of the airfoil and the
                                                                            downwash behind the airfoil. The circulation flow field causes a
                                                                            large amount of air to flow on the top (lee side) of the airfoil.
                                                                                  The same amount of air is flowing between each pair of
                                                                            streamlines. The speed of the flow increases in areas where the
            Figure 3. Formation of the starting vortex.
                                                                            streamlines get closer together such as near the leading edge of
     5. The vortex theorems. A set of vortex theorems by                    the airfoil. Higher speeds mean lower pressures. Where the
Hermann von Helmholtz and William Thomson (Lord Kelvin)                     streamlines get farther apart such as on the lower surface, the
play key parts in aerodynamics [1, p523]. The most important                flow slows down and the pressures get higher. Lower pressures
one in this situation is Thomson's circulation theorem. The                 on top and higher pressures on the bottom mean that the airfoil
application of this theorem in the two-dimensional airfoil case             now has lift.
basically means that as the starting vortex is created in the flow                With the proper computer programs, we can prepare
field, there must be another vortex equal in strength and opposite          accurate streamline drawings such as shown here to help us
in direction [3, p168-169].                                                 understand how the air flows around our thin sails or
     In aerodynamic's terminology, this new vortex field is                 conventional airfoils. Again, the green streamlines are the
called "circulation" and it surrounds the airfoil. The circulation          stagnation streamlines and divide the flow that goes on top (lee
field emerges as the starting vortex is formed. This is a dynamic           side) from the flow on the lower windward side. Note that the
process that becomes stable when the starting vortex is swept               streamline just above the airfoil passes very close to the leading
downstream and the flow conditions at the trailing edge have                edge and then gets farther away as it nears the trailing edge. This
become smooth and stable. This happens when the flow on both                means that the flow will be the fastest right at the leading edge
sides of the trailing edge have equal speeds (and pressures). This          and then slow down as it approaches the trailing edge. The
is known as the Kutta condition. The circulation flow field is              slowing down of the flow means the pressure is increasing.
equal in strength to the staring vortex and rotating in a clockwise         Remember that in real flow with viscosity, too rapid of an
direction (opposite to the starting vortex) as shown by the                 increase in pressure tends to make the boundary layer separate.
streamline plot in Figure 4.                                                Much of our sail shaping efforts are devoted to decreasing flow
     Aerodynamics theory tells us that the airfoil lift is equal to         separation on our sails.
the overall strength of the circulation flow field. The circulation               Note the distance between the two streamlines on each side
flow field is the strongest near the surface of the airfoil and             of the green stagnation streamline right at the trailing edge in
decreases at farther distances from the airfoil. When the non-              Figure 5. The streamlines are equally spaced. This means we
                                                                            have equal speeds and pressures on both sides at the trailing edge
                                                                            so no new starting vortex will be formed. The Kutta condition
                                                                            has been satisfied.
                                                                                  At this stage in our analysis, we have ignored the sharp turn
                                                                            around the leading edge of the simple flat plate airfoil. In the case
                                                                            of a sail, we would bend the leading edge of the airfoil down into
                                                                            the flow in order to avoid flow separation. For an airfoil on an
                                                                            airplane, we would give the airfoil some thickness with a round
                                                                            leading edge and possibly give the airfoil some overall curvature
                                                                            (camber).
                                                                                  The streamlines shown in Figures 2, 4, and 5 were
                                                                            calculated using conformal transformations as devised
                                                                            originally by Joukowski [4, p46]. The calculations and display of
                                                                            streamlines in these figures were accomplished using Boeing's
                                                                            Aero Grid and Paneling System (AGPS), see [5, 6]. Figures
                                                                            similar to 2 and 5 above may be found in a number of other
               Figure 4. Circulation flow field.                            references [7, p174, & 3, p174 ].
                                                                      -2-
     6. The flow field around an airfoil is the combination of
two flow fields: The flow field without lift shown in Figure 2,
and the circulation field about the airfoil. This concept is at first
difficult to understand but a simple analogy might help. If you
ride a bicycle in a crosswind, you feel only one wind on your
face, the vector combination of the true wind plus a wind vector
representing the speed of the bicycle. The same analogy applies
to the sailor as he motors at an angle to the true wind. The new
wind that he actually feels on his face is called the "apparent"
wind. He only feels one wind, but he knows that it is a
combination of the true wind and the boatspeed wind ( Figure 6).




             Figure 6. Apparent wind vectors.




                                                                                  Figure 8. Bathtub experiment showing circulation field.

                                                                               Whidden and Michael Levitt [9]. In this experiment, a thin airfoil
                                                                               representing a sail is slowly pulled through a two inch layer of
     Figure 7. Circulation vector at a point in the flow field.                water in a bathtub (see Figure 8). The airfoil should always be
                                                                               touching the bottom of the tub. Pepper sprinkled on the water
      The two-dimensional airfoil as discussed above also feels                surface helps visualize the movement of the water.
the combination of two winds, the non-lifting inviscid flow field                   At the start of movement, we will see the formation of the
plus the circulation flow field caused by the starting vortex as               starting vortex near the right end of the tub. It will be rotating in a
shown in Figure 7.                                                             counter-clockwise direction. Halfway down the tub, we can
      However, the merging of two different flow fields is more                observe how some of the water is adjusting to flow on the top
complicated than the simple boat apparent wind problem. Both                   side of the airfoil. As we near the left end of the tub, we quickly
the zero-lift speed vectors and the circulation vectors vary in                remove the airfoil from the water. What we see left near the end
speeds and direction all over the flow fields around the airfoil.              of the tub is a circulation of flow in a clockwise direction. This is
The example shown in Figure 7 is for a point on a streamline as it             the circulation flow field. It is real!
swings up toward the airfoil. In this example, the circulation                      In this experiment, it is important to use a thin curved airfoil
vector has only a small effect on the final speed vector, but the              at a relatively small angle of attack (about 5 to 10 degrees). Let
flow direction is changed significantly by the circulation vector              the water settle down with no movement before starting the
at that point as it redirects the air to flow up and over the airfoil.         experiment. Try to keep the speed of the airfoil constant from the
At a different location such as on top of the airfoil, the circulation         start until the end where it is quickly lifted out of the water. The
vector would point in the aft direction and added to the non-                  airfoil should still be moving as you lift it out of the water. Each
lifting flow field gives a much higher final local wind speed. The             test run should take about 5 seconds. A number of tests may be
circulation flow field effects get smaller as you get farther away             required so you can concentrate on a key part of the experiment
from the airfoil as noted previously.                                          each time: the starting vortex, the upwash in front of the airfoil,
      When the sails are raised and generating lift, the actual                the downwash behind the airfoil, and the circulation flow field.
measured wind at the masthead that we loosely call the apparent                You will have to wait between tests in order to let all water
wind is further complicated by the three-dimensional flow field                movement stop.
around the sails (bound vortex and trailing vortex systems).                        This experiment can be done with a conventional thick
      7. The bathtub experiment. The concept of circulation at                 airfoil to illustrate the starting vortex and the upwash flow.
first seems like mathematical trickery. However, the circulation               However, the view of the circulation itself will not be very good
flow field is real and there is an experiment that can be performed            with the thick airfoil because of the inrush of water to fill the
to visualize this whole process. This is described in one of my                volume space when the thick airfoil is removed. To do the
technical sailing papers, A Review of Modern Sail Theory, [8]                  experiment correctly, use a thin rectangular piece of metal or part
and also in the book, The Art and Science of Sails, by Tom                     of a milk carton for the airfoil.
                                                                         -3-
      8. The generation of lift. The resulting circulation flow                a tube. The superfluid was pulled through
field causes some of the fluid that would normally go below the                vertically. A normal fluid would have spun the
airfoil to be redirected to flow on the top side. This is most                 wings like a tiny propeller, but the superfluid
apparent out in front of the airfoil where the circulation vector is           refused to cause twisting. Instead it slipped
                                                                               frictionlessly past. In their search for lighter
in an upward direction. Some of the fluid in front of the airfoil              and lighter airfoils, the experimenters finally
starts changing direction so that it will pass on the top side (to the         killed some local flies, or so they claimed, and
lee side of a sail). In aerodynamics we call this "upwash".                    the investigation became known as the flies'-wings
      On the top side of the airfoil, the circulation vectors are in           experiment."
the same direction as the free stream direction, therefore causing                A quantum liquid may be pushing the definition
the flow to speed up. This increase in speed means lower                       of a "real fluid" a bit, but I have thought that
pressures (according to Bernoulli's equation). On the bottom                   this experiment might help illustrate the fact
side of the airfoil, the circulation vector is opposite the general            that a fluid's friction properties are responsible
                                                                               for the generation of lift. Without friction,
flow direction so the fluid tends to be slowed down resulting in
                                                                               there would be no Kutta condition at the trailing
increased pressure. The difference in pressure forces between                  edge of airfoils, and therefore no drag and no
the top and bottom sides of an airfoil are what gives us lift.                 lift. Birds could not fly, airplanes would not
      The concept of circulation not only helps explain how and                fly, and sailboats would not sail!
why the fluid flows about an airfoil as it does, but it turns out to
be a key concept in correctly explaining the "slot effect" between             From: Russell J Donnelly
the jib and the mainsail. With two sails, each airfoil has its own             Sent: Saturday, November 06, 1999 4:43 PM
circulation flow field. The two circulations appose each other in              To: Arvel_Gentry
                                                                               Subject: RE: Quantum Fluids
the slot between the sails and add to each other in the region to lee
of the jib. More air is caused to flow on the lee side of the jib.                You are right. You might consult my
                                                                                                                  book
Also, each airfoil has its own Kutta condition. The flow at the                "Experimental Superfluidity" for a
trailing edge of the mainsail nears free stream conditions. This is            discussion of some of these matters.
called the dumping velocity. The trailing edge of the jib,                           I obtained Russell Donnelly's book [11] and also studied
however, is under the influence of the flow around the mainsail                other references on superfluidity. One very enjoyable book was
and, therefore, does not return to near free stream conditions. Its            by E.L. Andronikashvili, Reflections on Liquid Helium [12]. It
Kutta condition is satisfied at a higher dumping velocity, thus                was interesting that the introduction in this book was by none
reducing the possibility of flow separation. This means that the               other than the same Russell J. Donnelly from the University of
flow on the jib is improved by the presence of the mainsail. The               Oregon.
jib helps the mainsail by reducing the peak suction pressure near                    It can be argued that the formation of the starting vortex at
the mast so the sail will not stall. These effects were first properly         the sharp trailing edge of an airfoil is a result of the very high
understood by visualizing the respective circulation flow fields.              velocities that would be necessary to flow around the airfoil and
For more details see The Aerodynamics of Sail Interaction [13].                not due to viscosity. However, even an airfoil with a thick and
      9. Three-dimensional effects. With our simple two-                       rounded trailing edge to avoid the high local velocities still has a
dimensional airfoils, if you draw flow streamlines starting way                starting vortex and generates lift under the definite influence of
out in front of the airfoil and also extend them way downstream,               viscosity and flow separation. In the case of objects with blunt
you would find that at the extremes they are at about the same                 trailing edges, the resulting separated flow region may be
level. The circulation flow field causes some of the fluid to flow             thought of as a rough extension of the original airfoil, and a
up and around the airfoil and then return to the same condition                starting vortex will be formed and circulation developed. "The
downstream. With three-dimensional wings, the circulation and                  aerodynamic lift forces and most other contributors to the forces
lift changes along the span, and wing tip effects cause another set            and moments on aircraft and other bodies moving through fluids
of vortex systems that greatly complicate the picture and creates              do not exist in the absence of vortices" (McGraw-Hill
a trailing downwash flow field. Gliders have very long wings in                Encyclopedia of Science & Technology Online).
order to minimize the 3-D effects. However, 3-D effects are not                      11. Other theories. Note that in this entire discussion I have
central to understanding the basic origins of lift.                            not once mentioned anything about (1) the air having farther to
      10. Physical proof? If the fluid has no viscosity, our                   go on the top side of an airfoil, or (2) Newton's laws of motion, or
aerodynamic theories indicate that we would have no lift and no                (3) about getting lift by "deflecting the air downward".
drag. But is there any physical proof of that? Yes! There is a fluid                 In the first case, there is nothing in aerodynamics requiring
with zero viscosity, super-cooled helium [10]. I really got                    the top and bottom flows having to reach the trailing edge at the
excited when I learned of this for I had been saying for years that            same time. This idea is a completely erroneous explanation for
without viscosity we would have no lift. I did some research to                lift. The flow on top gets to the trailing edge long before the flow
learn more, then contacted an expert in superfluid helium at the               on the bottom because of the circulation flow field.
University of Oregon to get final verification:                                      As for Newton, his laws are included within the
To: Prof. Russell J. Donnelly                                                  aerodynamic theories discussed.
Sent: Thursday, November 04, 1999 10:14 AM                                           And on the "deflecting the air downward" idea, that is a
Subject: Quantum Fluids                                                        three-dimensional effect. In our 2-D case, the circulation flow
   I am a retired Boeing aerodynamics engineer. I am
                                                                               field causes the air out in front of the airfoil to be directed upward
searching for information on an experiment performed
a number of years ago at Caltech, called "the
                                                                               around the airfoil and then back down to about the same level as
flies'-wings experiment." I learned of this in the                             it started out in front. Yet due to viscous effects and resulting
book GENIUS, the Life and Science of Richard                                   circulation, lift is generated. Yes, we can't fly with a two-
Feynman, by James Gleick (page 302).                                           dimensional wing and, therefore, are influenced by three-
   In this experiment "Tiny wings, airfoils, were                              dimensional effects caused by a complex trailing vortex system.
attached to a thin quartz fiber hanging down through                           We can reduce these 3-D effects by using very long wings such as
                                                                         -4-
on gliders or the around the world aircraft design by Bert Ruttan.
On an infinitely long wing, the 3-D effects are gone and we are              References:
essentially back to looking at two-dimensional airfoil
aerodynamics. If we can reduce the 3-D effects, then "deflecting             1. Krishnamurty Karamcheti, Principles of Ideal-fluid
the air downward" is not essential to the origins of lift.                   Aerodynamics.
      12. Multi-element airfoils. My first technical paper on the
aerodynamics of sails was published in 1971, The Aerodynamics                2. Richard Von Mises, Theory of Flight.
of Sail Interaction [13]. The primary objective of that paper was,
for the first time, to properly describe how two sails, the jib and          3. L. Prandtl, & O.G. Tietjens, Applied Hydro- and
the main, worked together. It used circulation concepts to                   Aeromechanics.
discover how the circulation flow fields about multiple sails
interact causing even more air to flow on the lee side of the jib,           4. Frederick O. Smetana, Introductory Aerodynamics and
while at the same time helping prevent the mainsail from                     Hydrodynamics of Wings and Bodies: A Software-Based
stalling. The old "slot effect" theory was dead. That paper also             Approach.
made it clear that the old theories as to how slats and slots on the
leading edge of aircraft wings worked were also wrong.                       5. D.K. Snepp, & R.C. Pomeroy, A Geometry System for
      In 1974, A.M.O. Smith, the famous aerodynamicist at                    Aerodynamic Design, AIAA Paper 87-2902, Sept. 1987.
Douglas Aircraft and my boss at the time, published his Wright
Brothers Lecture, High-Lift Aerodynamics [14]. AMO's paper,                  6. Arvel E. Gentry, Requirements for a Geometry
Section 6.3 and subsequent sections, describes how previous                  Programming Language for CFD Applications, from
theories were wrong. They also provided more detail as to how                Proceedings, Software Systems for Surface Modeling and
circulation fields are important in properly understanding multi-            Grid Generation Workshop, NASA Langley Research Center,
element airfoils and, therefore, how our sails work. AMO's paper             April 28-32, 1992.
is also in the book, Legacy of a Gentle Genius, The Life of A.M.O.
Smith, edited by Tuncer Cebeci [15].                                         7. L. Prandtl, & O.G. Tietjens, Fundamentals of Hydro- and
      However, old ideas are slow to die. A recent book on how               Aeromechanics.
airplanes fly [16] contains a very old and incorrect explanation
for how slots and slats work ("The high-pressure air below the               8. Arvel Gentry, A Review of Modern Sail Theory,
wing is drawn up through the slot and flows over the top of the              Proceedings of the 11th AIAA Symposium on the
wing. This energizes the boundary on top of the wing.").                     Aero/Hydronautics of Sailing, September 12, 1981, Seattle,
Apparently, the authors of that book, which includes a college               Washington.
aerodynamics professor, have not seen AMO's 1974 paper!
Unfortunately, many of these old incorrect slot effect                       9. Tom Whidden, & Michael Levitt, The Art and Science of
explanations also still appear in the sailing literature when                Sails, Chapter 5.
discussing the flow about the jib and the mainsail combination.
      13. Conclusion: Fluid viscosity is the fundamental reason              10. James Gleick, Genius, The Life and Science of Richard
why birds and airplanes can fly and why sailboats are able to sail.          Feynman.
Fluid viscosity causes the formation of the starting vortex which
leads to the creation of the circulation flow field. Understanding           11. E.L. Andronikashvili, Reflections on Liquid Helium.
the characteristics of the flow about our sails (and keels) is
important in adjusting the airfoil shapes for maximum                        12. Russell J. Donnelly, Experimental Superfluidity.
performance.
                                                                             13. Arvel Gentry, The Aerodynamics of Sail Interaction,
                                                                             Proceedings of the 3rd AIAA Symposium on the
                                                                             Aero/Hydronautica of Sailing, November 20, 1971, Redondo
                                                                             Beach, California.

                                                                             14. A.M.O. Smith, Wright Brothers Lecture, High-Lift
                                                                             Aerodynamics, AIAA Paper No. 74-939, AIAA 6th Aircraft
                                                                             Design, Flight Test, and Operations Meeting, Los Angeles,
                                                                             California, August 12-14, 1974.

                                                                             15. Tuncer Cebeci, Legacy of a Gentle Genius, The Life of
                                                                             A.M.O. Smith.

                                                                             16. David F. Anderson & Scott Eberhardt, Understanding
                                                                             Flight.




                                                                       -5-


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