The classic theory of airplane lift is all about wing curvature ... and that, according to Bernoulli's Principle, fast-flowing air has lower pressure.  In 1997, after pondering this matter for some twenty years, Ed Seykota concludes that lift has nothing at all to with Bernoulli's Principle ... rather, lift is a function of Radial Momentum ... the radial fanning out of a fluid lowers its  density ... and therefore, the pressure decreases with the distance from the center of radiation.

Seykota's 1/r Law

 For Expanding Rings For Spherical Expansion P = S / r P = Sv / r2 Pressure is inversely proportional to the radius. Pressure is inversely proportional to the square of the radius.

This website tells all about the Seykota Theory of Lift: Radial Momentum.

Some Early Experiments and Correspondence

1995 ...

I visit the San Francisco Exploratorium

In the Bernoulli Levitator at the San Francisco Exploratorium, air flows down through the ceiling of the device and onto a plywood disk (not shown) and makes the disk stick to the ceiling.

I feel the Exploratorium misapplies Bernoulli's Principle to explain the Levitator. I also claim that standard physics texts misapply Bernoulli's Law to explain many things that involve levitation in open air, such as airplane wings, balls hovering in jets of air, atomizers and carburetors.

1997 ...

I run lots of experiments. Ziz Seykota holds a levitator test disk.

February 23, 1997 ... I write to Dr. Paul Doherty, a prominent MIT physicist who looks over the Exploratorium.

Hi - I see in my MIT Club News that Paul Doherty is planning to host a day at the Exploratorium on March 15. This reminds me I have a question about one of your exhibits. Perhaps Paul Doherty or someone can give an answer. You have a rather cool exhibit in which air blows down through the top of a ceiling and makes a wooden disk stick to that ceiling. The explanation on the card states that the disk sticks to the ceiling because the pressure above the disk is lower than the air in the room. If that is so and the pressure is really less, above the disk than below it, then I wonder how come air flows from above the disk into the room and does not get sucked out of the room to where the pressure is, supposedly, less. Thanks for setting this matter straight.

He writes back to say, in part,

"Oh I see, you are after a fundamental physics explanation of the Bernoulli effect. I too have looked for a long time, and there isn't one. Very few books give the correct statement. They usually say something like: 'air flowing at high speeds exerts low pressures,' which is often incomplete. A more correct statement of Bernoulli would be 'Under certain conditions, as air speeds up its pressure drops.'"

March 23, 1997 ... I write again,

Dr. Paul Doherty - I have posted some formal 1/r math to my site to explain the levitation force operating on the disk in terms of pressures and radii.

Fw = Fu (1 - (Ph/Pa)(Rh/Rd)² - 2*(Rh/Rd)(1 - Rh/Rd))

This equation is quite young, and while it has little lab verification, it derives from standard physics, and passes tests for reasonableness. I am aware of no attempt at math based on Bernoulli. I would be happy for you or someone from the Exploratorium to set me straight on this matter, or, if you conclude I'm right about Bernoulli and 1/r, to set straight the Exploratorium's explanation on the Levitator.

March 4, 1997 ... While I'm judging a science fair, at Incline Elementary School, I run into John L. Sullivan. He has the equipment and the skill to build aerodynamic laboratory setups. I tell John about my conundrum and he agrees to build a working model of a levitator so I can check it out and see how it actually works; that is, to to find out what really makes the levitator levitate. Meanwhile, I have a hunch it has more to do with air fanning, than with air velocity, so I work out some of the math. I even make some predictions about disks with channels. My math correctly predicts several phenomena I notice by experimentation: square holes and square tiles don't work as well as round holes and round disks; disks with channels to keep the air flowing in a linear path don't work; levitators with small holes and powerful motors work best.

This is an early version of the levitator that John L. Sullivan builds. A variable speed motor blows air down through a hole in the ceiling. With the air blowing down, if you hold a cardboard disk up over the hole, it sticks to the ceiling. Note: round disks work better than square tiles; channels that prevent the the air from fanning out above the disk ruin the effect; the effect works better with a smaller air hole and a more powerful motor.

From Jack Edwards, 23-March-97:
Leapin' Levitators - I think Bernoulli turned over in his grave! Anything that happens, especially levitation, in the Bay Area is subject to question - different laws apply there (or maybe no laws at all). So the disk may be trying to "escape" through the aperture because it sees God, for all I know.

My Reply: I see you think this web site is a joke. While the site does have an intentionally breezy design, I am actually quite serious about claiming the classic physics explanations for levitators, atomizers, carburetors, airfoils and such that are based on Bernoulli (for a couple hundred years now) are all quite wrong. If this is true, it would necessitate a revision of the explanation at the Exploratorium and perhaps even a recall of quite a few physics texts.

From John L. Sullivan, 23-March-97:
Don't take this the wrong way, but your 1/R experiments are "all wet". In fact, your whole theory for what you think you know about 1/R vs. Bernoulli is "completely under water". Your experimental basis is simply under water - cavorting with Davy Jones, as it were.

I reply: To prove my theory, I have some demonstrations of the 1/R effect working with water. Reply: The 1/r effect seems to work with most all fluids and gasses. Furthermore, ire hoses already come off the roll, flattened out. Pumping water through them does not collapse them tighter; it balloons them out. So the tube demo seems to work with water as well.

23-March-97, from Sara Chennault:
I don't understand how come a square tile doesn't work as well as a round disk.

I reply: As soon as the radius of an advancing air ring crosses an edge of a square tile, it "breaks the seal." The part of the tile outside the radius becomes "dead weight." A round disk loses each air ring all at once, so there is no "dead weight." A square hole doesn't work as well as a round one since, initially, a round aperture fans air out radially while a square hole tends to spill the air in four linear (non-expanding) strips.

25-March-97, From Sara Chennault: Was my question really not that dumb then? Sometimes I feel silly asking such basic questions because I really don't know a lot about science and certainly nothing about physics.

I Reply: The feeling of silly seems to stop people from asking the basic questions. For the first couple months, people thought I was very silly in questioning a 200 year old theory. According to the way science evolves, if I happen to be right, The next step is for them to try to ignore me. Then they get angry. Then they fight it. Then they have a grand "aha" experience. Then they say it's obvious. Then they claim they thought of it first.

25-March-97: From Sara Chennault: It would seem to me then, that if it is the Bernoulli principle at work at the Exploratorium, that any shaped object should work just as well as a disk?

Reply: Apparently. That disks work the best seems to be more evidence for 1/r.

April, 1997 ... At my request, John Mathews, a friend and a broker from Palo Alto sends a friend of his over the the Exploratorium to copy the exact words from their Explanation. At this time, I am claiming their Bernoulli explanation is largely inapplicable.

"In this exhibit, air blowing down keeps a plywood disc hovering. To do and notice: Lift plywood disc up under the air outlet until it stays there by itself. If the disc is already hovering, try pulling it down. What's going on? When you lift the plywood disc up towards the air outlet you constrict the space that the air can flow through. In order for the same amount of air to get through the increasingly narrow space, it has to go faster. As air moves faster its pressure drops. As you continue to raise the disc, there is a certain point where the air is going so fast that its pressure drops below the pressure of the normal surrounding air. This fast moving, low pressure air above the disc pulls the board up. This lifting force is counteracted by the air blowing down on the disc and at a certain point the two forces cancel each other out and the disc just hovers."

I don't think the Bernoulli's Effect has very much to do with the Levitator at all. First of all, the air in the Levitator is not in a closed circuit; it comes down through the hole in the ceiling and then travels across the top of the disk and then spills out into the room. Second, if only Bernoulli applied here, it would lead to the absurd: if there were merely low pressure above the disk (and no air momentum effect), then the Levitator would suck air out of the room, not pump it into the room. Third, Bernoulli's Law says pressure rises as pipe size widens; now, the Levitator's virtual "pipe" is the space above the disk, so the "pipe" would be narrowest at the aperture and widest at the outside rim. Bernoulli would therefore predict an increase, instead of a decrease, in pressure as the air traveled. Fourth, no one has been able to derive the force formulas using the Bernoulli formulas; I have been able to derive a set of force formulas which pass reasonability tests using just the 1/r formula.

I think something entirely different is going on. Namely, most all of the action occurs across the aperture (just below the rim of the air port). As air flows across through this aperture, it goes through a big static pressure drop, almost down to ambient room pressure. This pressure drop quickly accelerates the air to its maximum velocity. At this point, the air has a total head (static pressure plus dynamic pressure relative to the disk) approximately equal to the ambient pressure plus the kinetic energy induced by the pressure drop across the aperture. So far so good and so far no Bernoulli principle involved.

Now, air molecules have momentum, and once they start moving, they keep moving until something stops them. So these air molecules, traveling at their "escape velocity" keep speeding out toward the edge of the disk.

Now, and here's the cool part, the part I call the One-Over-R Effect. The molecules spread out into larger and larger diameter rings. These rings have volume proportional to their radius, r. Therefore, as the air molecules fan out, the same number of them occupy a larger space and their static pressure drops off as 1/r, hence the vacuum above the disk and the name, the 1/r effect.

And there you have it, the 1/r effect is the explanation for the Levitator. So it's not really a Bernoulli Levitator at all; it's a One-Over-R Levitator.

Some Notes: The dynamic pressure aims horizontally outward, along the gap between the ceiling and the top of the disk, while the static pressure acts in all directions. The static pressure effects the levitation. The static pressure plus the kinetic energy (the total head) flows out radially to confront the ambient pressure in the room. The way these pressures balance determines the "virtual" radius of the disk, which may be greater or less than the radius of the physical disk. Very loosely speaking, air in motion has its static pressure operating in all directions and its kinetic pressure "polarized" in the direction of flow. I have no contention as to the veracity of the Bernoulli principle. I just think it does not apply to the levitator.

In case you may be, properly, a wee bit skeptical about me challenging the applicability of a theory that is in wide use since the 1700's, I have a simple demonstration to prove it is the 1/r Effect and not the Bernoulli Effect that makes the disk stick to the ceiling. I also have some math which derives from the 1/r assumption and seems to give reasonably accurate predictions. Note: I am not aware of any attempt to develop any numerical substantiation from Bernoulli's principle.

A Demonstration of the One-Over-R effect
The 1/r Effect depends upon air maintaining constant velocity, due to momentum, and then fanning out in such a way as to occupy greater volume and thus lower density and pressure. The Bernoulli Effect is sometimes misapplied to indicate that wherever air flows fast, its pressure is low. To differentiate between these two effects, I design the following experiment. First, I blow air through a soft paper tube that is slightly squeezed flat. I notice that the air acts to blow the soft paper tube open a bit. Next, I blow air through the small end of a soft paper cone that is slightly squeezed flat. I notice the air acts to squeeze the cone even flatter. I conclude that the Bernoulli Effect does not work to compress the tube any more than you can compress a drinking straw by blowing through it. On the other hand, the cone, that allows the air to fan out and become less dense toward the big end, does compress and support the 1/r theory. For a more rigorous treatment, see the math.

John L. Sullivan holds the paper tube at the end of the air hose while Ziz Seykota (right) prepares to turn on the air jet and Aziza Seykota (left) conducts simultaneous research into the taste of corn chips.

Left, the tube without air (one finger) and the tube with air flowing through it (two fingers). The tube with air flowing through it widens slightly, indicating the absence a Bernoulli, high-velocity-therefore-low-pressure effect. Right, The cone without air (one finger) and the cone with air flowing through it (two fingers). The cone with air flowing through it collapses noticeably, indicating the 1/r effect is alive and well. Note: you can easily reproduce this effect at home by making a soft paper cone and blowing into a hole in the small end.

Left, Blackie (SmartOnyx) checks out device to test levitation of linear flow. The white rails serve as guides to ensure the fluid does not fan out across the surface of the levitating disk. Right, Blackie looks through the fluid import tube. As predicted, the device fails to levitate a disk, or even a strip sized to fit up between the rails.

Left, modification of Levitator to demonstrate effect of partial fan out. The red plastic guides allow the water to fan out partially. Right, as predicted, partial fanning does indeed produce levitation.

Notes:

1. A small raised central area seems to keep a disk self-centered on the air pipe.

2. If you aim an air jet upward, you can balance a ball in it. If you then tip the air jet to the side, you can get the ball to suspend out at about a 45 degree angle. I think this has to do with 1/r again. The air fans out into a cone of low pressure, The ball, then, rests against a conical wall of higher pressure and the air jet keeps it aloft.

3. You can build a kind of a suction cup by attaching a high pressure air hose to a smooth disk with a small hole in the center. You can get an impressive amount of lift, and pick up fairly heavy flat objects. I feel this further confirms the 1/r theory.