Since our little airplanes operate in air, it is important for us to understand something about the mechanical properties of air. Scientific knowledge is derived from careful observation of natural phenomena. I will describe some activities that you can do at home or in a classroom to observe basic properties of air as they pertain to our little airplanes.

The first investigations of the subject were under the general heading of fluid mechanics, which included both air and water. The primary concern was the flow of water in rivers and channels for flood control and agricultural irrigation. At that time airplanes were unknown. Classical fluid mechanics was a matter of abstract mathematics based on reasonable postulates, similar to Euclidean geometry. It was believed that ideal fluids were continuous and frictionless. It turns out that air has several different properties that manifest differently at different scales. It was assumed that energy must be conserved in fluid flow. Unfortunately its conclusions did not often match observed phenomena.

Bernoulli’s principle has often been invoked to “explain” the lift on a wing, but it has absolutely nothing whatsoever to do with lift, as described elsewhere.

Prandtl proposed the circulation theory of flow around a wing, following observations by Rayleigh, Lanchester and Montgomery. This provided a theory of lift that was in fair agreement with observation at least for small angles of attack. It gave no explanation of how the circulation came into operation or what determined its strength. It was found that the circulation produced lift close to what was observed when the flow came evenly off the trailing edge, known as the Kutta condition. ([1] Chapter VI, Airfoil Theory.) It didn’t fully explain drag.

The flow around a wing and the resulting forces derive from the molecular nature of real fluids. Real fluids are made of molecules that jiggle around at random with what is known as Brownian motion. This random jiggling permits transfer of momentum within a fluid. It creates the shearing forces that create circulation. It is the physical condition of the forces around the sharp trailing edge that determine the Kutta condition that defines the circulation strength that produces lift. ([1] Fig. 42-55, pages 296-301.)

It wasn’t until fairly recently that a correct understanding of the nature of air was achieved. We now know that air is not continuous, it is made of discrete molecules of several gasses. It is not frictionless, it is viscous. There had been a debate since ancient Greek times about the nature of matter. One theory was that matter could be subdivided without limit, that it was continuous. Another theory was that matter could be subdivided only so far, that there would be an uncuttable minimum, atoms. There were several lines of evidence that matter might be atomic. The fact that chemical elements combined in small integer ratios was suggestive, the fact that a drop of oil on water would spread out to cover a certain area proportional to the volume of oil in the drop showed that it would thin only so far and no more. There was the kinetic theory of gasses which assumed small particles zooming around and bouncing off of each other at random. There was Robert Brown’s observation that very small particles observed under a microscope jiggled around at random. But none of this was conclusive. It wasn’t until Albert Einstein’s 1905 paper on Brownian motion that the physics community reached a consensus that matter was atomic. There was no other way to explain Brownian motion. It could not happen in the ideal fluid of classical fluid mechanics.

The kinetic theory of gasses is that gasses are made of very small molecules which zoom around bouncing off of each other at random. Think of a large Plexiglas cube about 1/4 full of ping pong balls that is being shaken. The balls will bounce off the walls and each other randomly.

Brownian motion is observed only on very small particles, smaller than about 1/20,000″ in size. It can be observed with any good student quality microscope with magnifying power of 400 X or more. Some things to look at are dilute watercolor paint, whole milk diluted one drop to five drops water, candle lampblack in dilute liquid soap solution. Brownian motion is due to the random collisions of molecules with the small particles we can see. We may observe that the smaller particles are more active. Above a certain size, the particles do not seem to be moving at all. This is because the particle is responding to the random collision impacts of the water molecules in the surrounding fluid. A very small particle will have many fewer molecules striking it, so the odds of an imbalance of the number striking it on one side are favored. A larger particle will have a more uniform distribution of collisions. The larger sample of collisions will more closely approximate the average of zero. There will be about the same number of collisions on all sides. This is consistent with Einstein’s equation.

This random jiggling allows molecules to diffuse and transfer momentum from one place to another in a fluid. When two bodies of fluid move against each other, molecules will diffuse across the boundary, colliding with molecules on the other side, transferring momentum. When a fluid moves along a solid body, also made of molecules, the fluid molecules strike the solid molecules and momentum is transferred into the fluid, producing friction and a velocity gradient. This shearing action produces a rotational action, with fluid moving in opposite directions on opposite sides of a point or surface.

It is this random jiggling that makes circulation possible and it is circulation that produces the lift on a wing.

When a wing starts moving through air, some of it goes over the top of the wing and some goes under. The point where the division takes place is called the stagnation point. There is a hypothetical streamline that divides the streamlines going over and under the wing. This stagnation line stops at the surface, thus it is stagnant. There is another point and line at the back of the airfoil where the streamlines going over and under come together. At the start of motion the forward stagnation point is under the chin of the airfoil and the aft stagnation point is a little way forward of the trailing edge on top of the airfoil. However, this situation is not stable. The air going around the sharp trailing edge is circling tightly, forming the starting vortex which will be shed, theoretically reaching infinite velocity at the sharp trailing edge. These air molecules are experiencing a strong centrifugal force. This creates a vacuum at the trailing edge which pulls the rear stagnation line down to the trailing edge. This action sheds a trailing vortex into the downstream flow. ([1] Fig. 42-55, pages 296-301.) With the flow going smoothly off the trailing edge without a sharp circular motion, the flow pattern becomes stable. However, this produces a circulation which goes up in front of the airfoil, back over the top, down behind and forward underneath. In combination with the backward flow, this produces a pattern of flow which arches over the airfoil. Again, the curving flow implies a centrifugal force which invokes a pressure gradient, from atmospheric above the airfoil to less than atmospheric on the top surface and more than atmospheric on the bottom surface of the airfoil to atmospheric some distance below the airfoil.

You can demonstrate the lifting and trailing vortices with simple equipment. Not only can you demonstrate the presence of the trailing and lifting vortices, but if you look closely as you pull the wing model through the water you can learn some things about the distribution of pressure on an airfoil. Look at the depth of the water at the surface of the airfoil. Note that the depth of the water compared with the surrounding water depth correlates with the pressure. Higher depth indicates more pressure, lower depth indicates lower pressure. What can you conclude about the distribution of pressure on the model airfoil? What can you conclude about the center of pressure location on a similar wing? Because the water is rather shallow in the pan, what we are seeing approximates two dimensional flow. There is no wingtip, so no flow along the span and off the wingtip. The movement essentially all takes place in a two dimensional plane.

Some say the lift is a result of Newton’s laws, that the downwash behind the wing, from the wing pushing the air down, means there must be an equal and opposite reaction which pushes the wing up. This is incorrect because it ignores important features of the phenomenon. There is also an upwash ahead of the wing. The pattern of flow is a combination of two flow patterns. One is the translational flow, front to back, which is essentially symmetrical. The other is a circulation, going up in front, back over the top, down behind and forward underneath. This is also essentially symmetrical by itself. Neither by itself produces lift. The combination of the two results in a flow pattern which is curved, convex downward. Air moving along a curved path must experience a centrifugal force. For the flow pattern to be stable, there must be an opposing force. That force is in the form of a pressure gradient, higher toward the outside of the curve. The ambient pressure at some distance from the wing is the same above and below the wing. That means the pressure across the top must be lower than atmospheric and the pressure below must be greater. This is known as the Lanchester-Prandtl circulation theory of lift.

Airfoil theory postulates two dimensional flow; that is, a flow pattern that would be found on a wing of infinite span. The flow pattern at each cross section is identical. There is no flow along the span. That is approximated experimentally by a wing model that goes across a wind tunnel from wall to wall. Airplane wings are three dimensional. They have tips, their span is finite. Air flows along the span. On the bottom of the wing, there is a component of velocity going outward from the center to the tip. On the top of the wing there is a component of velocity going inward from the tip to the center. At the tip, the flow circulates upward from the high pressure area to the low pressure area. Where these flows come off the trailing edge they are at an angle to each other. This produces a circulation.

The circulation around a wing may be observed with a vortex wheel, something like a water wheel.

The vortex wheel is an instrument for detecting circulation or sheer in air. It consists of a 1/16″ x 1/8″ x 12″ medium hard balsa stick, a 1/2″ pin, a glass bead and four 1/4″ x 1/2″ pieces of paper, folded across their short center lines and glued together around the pin such that they are free to rotate as a unit. They are not twisted, so the wheel does not rotate in straight wind.

This is used to demonstrate wing tip vortices. Get out on an open field with a steady wind. The wing is held up facing into the wind at a slight attack angle. The pinhead is pointed into the wind and then moved around the tip and trailing edge of the wing. You will find a very rapid counter clockwise rotation off the right wingtip. As you move inward along the wing trailing edge in the vicinity of the trailing edge the spin gradually becomes much lower and stops completely at the center line. As you approach the left tip, it spins in a clockwise direction. Again, there is a very strong vortex just above and inside the left tip, going clockwise.

Science is not about telling plausible stories. It is about carefully observing and accurately describing natural phenomena.

Reference:

[1]   L. Prandtl and O. G. Tietjens, Applied Hydro- and Aeromechanics, Dover Publications, New York, 1934, 1957.