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Radial Momentum

An Alternate Theory of Lift

(c) August 19, 2014 by Ed Seykota

The Standard Textbook Model of Lift
doesn't make sense.

You may recall noticing a feeling of confusion looking at this diagram, during your high school physics classes. Something doesn't make sense. My alternative theory, Radial Momentum, does make sense, as I go on to demonstrate, below.

Below, I present some simple demonstrations, including a levitator, a paper cone and some fancy squirt guns - that show how lift really works.

You can recreate all these experiments at home.

The Simple Levitator

You can make a levitator from a spool of thread and a business card.

When you blow air down through the spool onto the card, the card sticks to the bottom of the spool!


This diagram shows how the air flows down the tube and out across the card.

High school and college science books try to explain how this curious device works by using Bernoulli's Equation. They say that fast-moving air above the card has low pressure - and that the higher pressure air below the card pushes the card upward.

I claim that  Bernoulli says nothing of the kind.


For example, if fast air always has lower pressure, then you could take a big old pickle jar full of air, put a pressure meter in the jar, screw on the top, take the jar out for a fast ride in your car, and watch the pressure in the jar drop.

Similarly you might conclude that if you ride in a jet airplane, the pressure of the air in your lungs would drop way down, something you might readily notice.

Simple thought experiments such as these show reductio ad absurdum or hogwash.

So much for all the theory. Let's see some demonstrations.

The Cone and Tube Demonstration

If you blow air through a tube and a cone, the cone collapses and the sides stick together. The tube does not collapse.  This shows that fast air, by itself does not explain lift.  Only the cone, that allows radial expansion of the air, collapses.

The Levitator Table

To get some more precise measurements, I build a levitator table, complete with instruments to measure air pressure and air flow. More about this, below.
Cavitation Ring Demonstration

I also run some tests with water and predict the existence of a cavitation ring around the levitator exit orifice and sure enough, I find one. More about this, below.

This site presents the case
that levitation has to do with Radial Momentum,
not with fluid velocity.


Some High School Physics


If you look in high school physics text books

you may find a couple standard diagrams



Airplane Wing Cross Section


This diagram supports the theory

that since air flows faster over the top of the wing

and slower under the bottom of the wing.

the pressure on the top falls

and therefore the wing rises.


You may recall seeing this diagram in high school.

You may also recall a feeling of confusion

and having trouble connecting all the dots.



Large to Narrow Pipe Diagram


In the same books, we find the large-to-narrow pipe diagram

along with a "proof" that high velocity and low pressure go together.


You can see the math at Note 1, below.

I Take Issue With This Piece of Physics


the math above holds only for self-containing systems.
so you can only use this math
for a self-containing hollow donut containing air.
This math does not apply to a wing sailing through the sky.

the math holds only for constant density.
However, with the constant-density restriction,
we have no way to motivate the air to move
and this implies zero velocity.


for cases involving air that actually moves around,

attempts to use Bernoulli's Principle

to show that fast air goes with low pressure
violate the basic assumptions you need
in order to apply the principle.


And By the Way,

the Bernoulli Theory requirement about constant density,
misses the main point
since density change explains the levitator.



Radial Momentum Offers a Better Explanation


The Radial Momentum Explanation:

as the air fans out radially from the center of the device

it expands into larger and larger volumes

and so it gets less and less dense.


This lower density explains the lower pressure.

There, you have it.

To test my Theory of Radial Momentum,
I design the Tube and Cone Experiment .


The cone collapses and the tube does not collapse.

This indicates that air fanning out goes with pressure drop

and that fast or slow air makes little difference.



The Cone Collapses


The Tube does not Collapse


To further test this out, I construct a more formal levitator table

from a big piece of see-through plastic

with which I can measure the air flow and pressure.



Fancy Levitator Table


See the flow meter on the left

and the pressure meter on the right.




View from Underneath


The air flows through a 1/8" orifice in the table.


I try my levitator table with various kinds of playing cards
since you can get lots of them near Reno, Nevada.

I find they all stick to the bottom of the table

when I blow air down the hole onto the cards.

Incidentally, I do not notice any difference
in the stickiness of the cards
that relates to their suit or rank.

I figure a real scientist
would think about stuff like that.

Next, I try my levitator table with smooth plastic disks.

The smooth plastic disks stick too.



Special Disks



Then, to test a hunch, I construct some special disks - ones with channels.



Channel Disks


The channels can force the air

to flow in different ways.



Detail of the Hourglass-Channel Disk


I then try these disks with my levitator

to see what happens.


All the disks stick to the levitator

when I put the smooth side up.


When I put the channel sides up,

all of them stick - except for one of them.


The one that does not stick

has the parallel channel.


This one, and only this one, does not allow

radial expansion of the air.


This further substantiates my theory

that Radial Momentum, not air speed

explains lift.



The Professor and His Business Card


I show my results to a professor from a nearby college.

He specializes in fluid dynamics and he says he thinks I'm crazy.


He says my theory goes up against 300 years of science

and that there is no way I can have it right.


Furthermore, he shows me a pile of final exam papers

from his graduating college seniors.

The exam question has to do with, of all things, the levitator.


I point out the errors in the exams,
searching rather unsuccessfully for a tactful way to do this

since these errors trace directly back to his teaching.


As I proceed, I notice, he appears to consider me
somewhere between a mild irritant and total idiot.


He tells me, with impatience and disdain,
that he has a simple way to prove he is right

about high velocity going with low pressure.


He suggests I build a table with a slit, rather than a hole.

The slit would broadcast air in a linear ribbon

that does not expand radially.


He says that when I see the card sticking to the slit,

I would have to abandon my theory, develop some humility
and maybe apply for admission to his class
and start to learn some real physics.



The Business Card Levitator Experiment


I build the experiment according to his suggestion.



The Slit Levitator


The air enters through the fitting at the right

and emerges out of the slit that holds the card.


In operation, the card sits flat on the bed

between the "headboard and footboard."


To make it all the more dramatic,

I use one of the professor's own business cards

as the test pilot.


I turn on the pump and begin the experiment.


The card does not stick to the equipment.


This lends further evidence that Radial Momentum

and not air velocity correctly explains

lift in the levitator.


I call the professor with the good news

that he and all his students have it wrong.


He does not sound very happy to hear the news.


He does not want to discuss the matter further with me.


I do not know if he still teaches his seniors about the levitator.




Fun with Water


I run further experiments with water.


The results turn out much more vivid.


Parallel Channel Water Nozzle



Hourglass Channel Water Nozzle



The Hourglass Works as a Levitator


Again, the parallel channel does not levitate.


I get a much stronger effect with water

since water has less compressibility,

so pulling water molecules apart, even a little bit,
generates a much stronger pressure drop.



Some Theory: The Ring of Air


The Ring of Air



The Theory of Radial Momentum holds that fluid, once in motion,

expands out radially, by momentum,into larger and larger rings of air.


When the same mass of air occupies a larger volume

its density drops and the pressure goes down with density.



Computer Model


I build a computer model, using Radial Momentum as the organizing principle.


Computer Model Output


The model shows the pressure, velocity, density, mass and mass flux

running from the center of the disk (left) out to the edge (right).


The model shows the pressure drops right around the center

in a region I call the active zone.


The pressure reaches a minimum in a ring around the central orifice.

This low pressure also motivates the air to increase in velocity,

imparting additional radial momentum to the particles.


As the fluid particles continue radiating outward from the center,

the fluid becomes less dense and the pressure falls.


As the particles flow past the minimum pressure ring,

they experience back-pressure that tends to slow them further.


The velocity continues to fall until the Radial Momentum dissipates,

the pressure rises to slightly above ambient pressure

and the fluid gently drains out at the edge of the disk.



The Cavitation Ring


According to the model, the lift effect occurs

in a small active region around the center of the disk.


I begin searching for evidence of this ring.


I take the equipment outside into my back yard

where I can use water.



Portable Levitator with Water as the Fluid


The jet travels about 30 feet.

If you hold your hand in front of it, it deforms your hand

and feels painful.



Close-Up of the Portable Levitator


The water emerges through a small hole in the center of the disk.



Bringing the Disk up to the Levitator


The stream of water hits the disk and sprays everywhere.

The stream also pushes the disk away with considerable force.


Note: experimenters sometimes have to subject themselves

to back splash and other hardships in the pursuit of scientific knowledge.

Note: Truly passionate scientists sometimes grow their hair out, Einstein style,
to help keep their good thinking from leaking out.






When the disk comes flush with the levitator, the levitator suddenly "captures" it.

The disks stick together with several pounds of force.

Consistent with the Radial Momentum model,

the water gently emerges from around the edge of the disk.



Levitation, Another View


I use my left hand only to keep the disk from sliding to the side.

I apply little or no upward pressure on the disk.

The stream of water from the hose levitates the disk.




It Works Under Water


I test the effect under water,

and I find the effect still works.


Without the levitation effect holding the disk to the levitator,

the water jet from the hose would shoot back out of the dish.


Looking for the Ring


This Image Shows the Underside of the Levitator (see the orifice above thumb). 
The disk (lower right) has a handle on it.


I first run the test at low pressure, by crimping the hose.

I notice a faint white ring around the central orifice.


I figure this indicates tiny air bubbles,

emerging from the water as the low pressure sucks them out.



Turning up the Flow


I let the hose go a little bit, increasing the flow.

The cavitation ring becomes bigger and whiter.



Even More Flow


The ring gets bigger and whiter.



Maximum Flow


I let the hose go, full on.

The ring gets even bigger and whiter.



Other Rings


Water on the Back of a Dish


You can see a very thin low-lying layer of water

in the "active region" in the center of the dish

and a "hydraulic jump" a couple inches from the center.


This profile matches that of the levitator.



Jet Aircraft with Trailing Ring


According to the Theory of Radial Momentum
the nose of the craft (and the cockpit)

divert the air into a radially expanding pattern

that forms an expanding cone along the nose-to-tail axis.


This results in a decrease of pressure and temperature

in the active regions behind the cockpit and at the tail.

The lower temperature and humidity in the air

interact momentarily to generate a visible cloud.



Other Evidence


Flow Versus Pressure for a 3.9 oz. Disk Using Air


I take some actual measurements on the levitator table

to compile a flow-versus-pressure chart.


For low head pressure (from the pump)

I see a flow of about 2.5 standard cubic feet per minute.


As the pressure rises, the flow actually decreases!


This phenomenon has to do with the levitation effect

as the disk moves closer to the levitator

restricting the flow.

The standard Bernoulli explanation
does not account for this phenomenon.





Radial Momentum explains Levitator lift.


Fast or Slow air has little to do with it.


The Bernoulli Equation has to do with energy balance.


It does not apply to the levitator.




Save Our Children


Photo Source: http://www.savethechildren.ca/page.aspx?pid=385


Please Consider Saving Innocent Children from Bernoulli Abuse.

Give them Cones and Tubes.




Daniel Bernoulli (1700-1782)


"It would be better for the true physics

if there were no mathematicians on earth."

-- Daniel Bernoulli



Note 1. High-School Math





The End (for now).