Questions

Answers

Radial Momentum

Mr. Seykota:

Brilliant work on radial momentum. One quick question though. On your overview page, you use the equation:

My current derivation gives 1/3 and not 1/18.  I am unable to find any derivations on my site that show 1/18. 

Perhaps the 1/6 factor is left over from some earlier work (the area for one side of the cube is 1/6 the area of all 6 sides).  I also recall seeing the 1/18 factor somewhere in the literature.

I do not use the formula in any other derivations, so I have no other checks and balances on it.

Tue, 20 Apr 2004

The active region has a radius of about 1/8 inch for each pinhole, so if the spacing between holes is, say 1 inch,  I'd guess your demo might work.

Tue, 20 Apr 2004

Stunning Photo Of Jet Breaking Sound Barrier

You wrote in the RM FAQ: "I'd like to get a url to such photos."

This has photos, details of how they were made, and videos...

Wilk4: Breaking the Sound Barrier
http://www.wilk4.com/

Thu, 09 Oct 2003

Pressure Drop in Moving Fluids


Hi. I just stumbled onto your site and found it quite interesting. I too have never quite understood how a "pressure drop" can occur, as it seems to violate the rules of "relativity" - why should a mass of fluid moving in a pipe have a different pressure to one that is stationary? What is special about this movement, from the fluid's point of view, that causes pressure to change in any way? If you stack a lot of parallel flows side by side, this lower pressure must still exist, so effects of the walls can be counted out. Pressure doesn't vary along the length of the flow if it's related to velocity, so you can completely enclose this fluid with 6 walls and the pressure in that box must still be the same. If you stop it, then the pressure rises again?

On the other hand, your description of the Bernoulli Principle is the first time I have had an understanding of what's going on.

It's pretty obvious, if you have a 2:1 reduction in the flow (say water), then for conservation of energy (valid if you can expand and reduce and expand it again for minimal pressure drop) then the pressure head must reduce by the kinetic energy added. If the end of the pipe is open, then the pressure added by the constriction will be that necessary to accelerate the water jet to the exit velocity (in fact this will always be the case).

I knew that, but that's a pressure gain not a pressure drop; there's no way you can "harness" the energy of this so called pressure drop, the only thing you can do is convert kinetic energy back into potential energy - by slowing down the flow. Slowing an incompressible flow means radial expansion. I guess this is what you're getting at (you can probably tell I'm still working it through as I write it!).

Re plane wings, I thought the "fast flow low pressure" thing had gone by the wayside years ago.

My understanding of it is that flow diverges at the top which lowers pressure - that's why the wing is tapered (maximum possible lift area) and not a "D" shape (as well as flow separation, which implies you're not getting divergent flow) - I've kind of also assumed that the pressure front generated by the thick leading edge pushes some of the flow that was destined for the top surface underneath, along with the angle of attack robbing the column of atmosphere above the wing of pressure by slicing it off and sending it underneath.

If the Bernoulli Principle simply relates to the conversion/conservation of energy , then I assume this will work just as well in the analysis, but the whole concept of a pressure "drop" is totally meaningless unless there is convergent or divergent flow.

Now I know how a carburetor venturi works. The motor provides the energy to accelerate the air, the atmosphere provides the pressure.

Well I knew that, but now I know where the pressure drop comes from and what it means. If there was no venturi, there would be only asmuch pressure drop present as is required to get the air moving that fast in the manifold (obviously), and that pressure drop comes from the "suck" end causing it to move, not the movement itself.

That's why a paper (or cloth) tube won't collapse, so long as there's a slight positive pressure feeding one end and it's already flowing, this provides all the energy needed to the air for it to move as fast as it does. The air experiences no pressure drop relative to the outside air.

The paper cone collapses because the air wants to keep travelling in a jet, at the same speed, same pressure, and same diameter. Flow separation will tend to drag any air that's around this jet away, collapsing the cone walls. (I say confidently, having just learnt what flow separation actually is some time last week.)

"Surely" the people who work with this really do understand what it means, and using the "fast flow low pressure" thing to explain wing lift is just an attempt to dumb it down for the masses - catching out many an unaware student along the way. The concepts and maths are too simple to end up going down different paths, aren't they?

Well, regardless of that, thanks for the explanations on your site and the opportunity to finally work out for myself another one of those simple but intriguing questions of basic physics.

Yes. A little thinking and some experimentation are very good additions to memorizing what you find in books, or, for that matter what you find on this site.

Wed, 8 Oct 2003

You can see some photos of a similar effect on the sound barrier link, above.

Fri, 25 Jul 2003

The curvature of your car at the point of your open window induces flow separation and reduces the presure.  You can sometimes feel this effect on your ears if you open a window while you are driving.

This low pressure area likely collects air that enters your car through the heater port near the passenger floor mat.  This flow from the floor to the window may blow the bag into the air.

Wed, 9 Jul 2003

Radial Momentum

Dear Ed,

Air pressure is dependent on volume and temperature as given in the general gas equation:

P1.V1/T1 = P2.V2/T2

Air molecules are not "paired" - they zip around at random evidenced by Brownian Motion. ( Atoms may well be paired to form the molecule- e.g. O2) but they do not break up in air flow. A decrease in volume will cause an increase in pressure because the same number of molecules impinge on each other more frequently and probably the force of repulsion between the molecules increases with decrease in distance between them.

An increase in temperature causes the air molecules to zip around more rapidly and hence impinge on each other and the container more frequently causing a pressure rise. At absolute zero the molecules are at rest and theoretically the pressure might be zero, but all gases liquefy at some temperature above absolute zero dependent on the pressure and which gas is involved.

If we assume that the temperature change is minimal at low air speeds, then volume and pressure are interdependent. Considering air flow over an aircraft wing, the volume can be considered infinite and therefore pressure is the only likely variable.

If the air over the top surface has further to go compared with the bottom surface due to the shape of the wing it may suffer more drag due to the greater solid surface area.

There is no real reason why the air should speed up. Intuitively I would think it would be slowed, because it has further to travel over the wing surface. Air does not speed up just because it has further to travel - the air molecules above and below the wing are completely independent of each other.

Your idea that the deflected air also undergoes side spread over the top of the wing may be correct. On various jet aircraft I see spoilers on the wing to prevent this happening - probably an admission of imperfect wing design.

Trust this is helpful.

With kindest regards,

Yes, the "longer path" theory somehow assumes that molecules somehow notice each other at the leading edge of the wing, remember their friends, and somehow speed up or slow down so they can join up with the same ones at the end of the trip.

Tue, 8 Jul 2003

Radial Momentum

Dear Ed,

I came across this interesting site www.howstuffworks.com  which discusses aerodynamic lift in the engineering section.

Kind regards,

Pretty good summary of the state-of-the-art thinking on the topic - it concedes there are problems with the Bernoulli and "longer path" models of lift.

Mon, 30 Jun 2003

Radial Momentum


Dear Ed,

Is this correct.

Yes. The separation point, just behind the crest of the wind has relatively low pressure and attracts flow from the trailing edge of the wing.

Mon, 30 Jun 2003

Radial Momentum


Dear Ed,

I am imagining what is happening as I study the picture of the wing a tornado and some of your experiments.

Please correct me so I can picture the movement of the molecules in a more precise manner.

My imagination seems to think that velocity is causing a compression then expansion as well as a spinning motion on the molecules which causes some centrifugal forced radial expansion as well as upward spinning on the back top of the wing.

The upward spinning could also be causing some of the lift on the downward sloping top left of the wing where the air hits the second time. If the air movement is left to right or wing movement is right to left.

For some reason centrifugal spinning forced radial expansion and then contraction seems to be involved when I think about it.

In the Bernoulli pictures I do not see an accounting for the suction or a vacuum around the back top second half of the wing from the wing displacing the air.

I am going to attempt sending a quick drawing so you can correct any misconceptions I may have as a layman.

These are some links that may help explain what I mean.

http://dictionary.reference.com/

search?q=centrifugal

http://www.bbc.co.uk/dna/hub/A427565

http://www.teikokupump.co.jp/english/

productpage.html

http://www.bbc.co.uk/dna/h2g2/

alabaster/A427565

Wing lift is a function on angle of attack. Wing shape facilitates lift by entraining the air into laminar flow, rather that turbulent flow.  This saves energy, so the whole operation becomes more efficient, and so does lift.

Just behind the crest in the top on the wing, you can find a point of separation, that has low pressure, and may actually attract a back-flow from the rear of the wing.

Thu, 26 Jun 2003

Love your website!

Dear Ed Seykota,

I just wanted to say I read through your cool web-site today. The reason I found it is because I have had this interesting idea for a lifting-device for the last 25 years or so which I have been mulling over in my mind.

And recently I was thinking about it again and I realized that this stupid Bernoulli effect might put a damper on its effectiveness.

So I was thinking about the Bernoulli effect, and I was thinking this Bernoulli principal is total nonsense (anyway, I hoped so). Anyway I was looking through all these websites to see if they were right or not. Then I came upon yours which I initially took to be some screwy guy who goes to a science demo place and decides he knows better than the people who wrote the explanations.

But by the time I finished I was going, god, this guy is bright and I think he is correct. I am afraid I'm no physicist and couldn't really follow all your equations, though. Anyway, here is why I don't believe in Bernoulli.

Let's say you are in a car driving down the highway at 70MPH with your windows closed (I noticed you have a similar idea on your website called "The moving jar experiment") and let's say your car is totally airtight. According to this Bernoulli principal, the air rushing by outside of the car is now at a lower air pressure than inside the car. My idea for a test for this is ... well here's one.  Measure the air pressure outside before you start moving. Then bring the barometer into the car and as you are moving 70MPH, open the windows. If the pressure of the air streaming by is less, then the air-pressure in the car should immediately drop.

Another way to do this is, make a small circular hole in the window say on the passenger side, like about 1 to 2 inches in diameter. Cover it with rubber from a balloon. If the air pressure outside decreases as you move faster, the balloon should deflect to show it. I'm afraid I am not interested enough to actually do this experiment on my car :), but I think it would show that Bernoulli is bogus.

Another thought experiment I thought of. Say you get onto a train and that train then takes off going at a good clip. Lets say the windows were made of some flexible material. Then they should bulge out as you are moving, right? Well, this is basically the same as the last idea. But here's another angle with the train that I haven't worked out completely so that is shows the utter absurdity of Bernoulli. If you are on the train, the air outside is going by at the same speed you are moving, so its pressure according to Bernoulli is less than the pressure in the train.

Now lets say you are on the platform watching the train go by. THE AIR IN THE TRAIN IS MOVING, RIGHT, RELATIVE TO YOU, SO THE AIR PRESSURE IN THE TRAIN IS LESS THAT THE AMBIENT AIR PRESSURE. Seems kind of contradictory, doesn't it. The only problem with this is, I can't have a port between the train and the outside which isn't attached to the train. So the example from within the train is the only one that makes sense to think about. I mean of course we know that the air pressure in the train will be the ambient air pressure.

It's how it relates to air moving by that is the question. But lets say theoretically that we have a stream of air the shape of a train moving by at the speed of a train. Now the thing is, what is to say that the ambient stationary air is considered the frame of reference rather than the moving train-shaped air. As Einstein knew, all physics is relative. To someone moving along with the train-shaped air, that air is still and the ambient outside air is moving. So Bernoulli says that air is of lower pressure. But to someone standing still outside of the train-shaped air, the train-shaped air is moving and has lower pressure. Well, it can't be both ways! So doesn't that prove that the idea that moving air has less pressure than stationary air cannot be valid? The mere fact that either the moving air or the stationary (or less rapidly moving) air can be considered the frame of reference. The physics has to work regardless of which frame of reference you use. In your moving jar experiment, which I've copied here, you seem like you almost were going in the same direction as I have above.

The moving jar experiment

Take an empty jar and put the lid on it so as to seal in some air. Now get in a car and take the jar for a fast ride on the highway. Scientists say that Bernoulli's Principle predicts that fast moving air has lower pressure. Do you really think the pressure in the jar changes when you go
fast?

Your website mostly seems to say that Bernoulli principal does not explain flight and floating ping-pong balls etc. But you never seem to say what I want to say, and that is that the Bernoulli principal is simply wrong! But I guess you can't say that because under the strict limits you have set out, incompressible fluid, etc., then it does work. Oh well...

I really like people who try to go up against the wall of what is generally accepted as truth.

Good luck fighting the establishment!
And good luck getting your Radial Momentum theory published!


ps - it was damn difficult finding your web address, assuming the one I am sending this to is correct! Otherwise, it was impossible.

I do not claim that Bernoulli's Principle is incorrect ... it is simply an energy balance equation ... I claim that the standard application of the principle to lift phenomena is incorrect. 

That is, it's a good tool ... just doesn't fit the problem. 

If you open a hole in a very flat surface of your vehicle, parallel to the air flow, you experience no pressure phenomenon.

If you open a driver seat window just a crack, up near the point where the windshield radially deflects the oncoming wind, you can feel the decrease in pressure in the car.

If you build an air scoop and stick it out the window to collect air and deflect it into the car, you can get an increase in pressure.

Sat, 21 Jun 2003

Radial Momentum


Dear Ed,

One more part to my question I just sent you on the tornadoes. I don't know if you know this or even care but here I go.

Where is the greatest suction on the disk in your experiments ? If the tube was bigger would the greatest suction be in the middle or a side or the outer rim of the tube or is the greatest suction somewhere on the disk away from the tube? Just thinking about tornadoes as air approaches the Earth.

I will try a paper disk or possibly a wet cloth to try to figure this out.

The minimum pressure between the disks occurs in the "active region," slightly past the input tube. See Model.

Sat, 21 Jun 2003

Radial Momentum


Dear Ed,

This site on Radial Momentum is very interesting. Please excuse me for not being a Super scientist or Mathematician but I have some questions.

I always hear about how tornados are such a mystery. Could Radial Momentum be the explanation? Could this be why there are videos of air sucking up 18 wheel trucks hundreds of feet into the air. Is there some kind of compression and expansion occurring in the upper atmosphere?

snrs.unl.edu/amet351/lippman/

why-occur.html

movies.warnerbros.com/twister/

You raise some interesting questions.  You can observe a cavitation ring by using water in the levitator.

I do not at this time have extensions of Radial Momentum Theory for hot air balloons or tornadoes.

Sat, 21 Jun 2003

More about expansion chambers and radial momentum

Hello Ed,

I had an hour free today so I looked on the net to see if I could find any useful articles that might help you with your theory validation. I used to know a fellow who made expansion chambers professionally for racing bikes. I remember him telling me about a man he knew who worked for Lotus, he remarked that this man was a genius, which coming from him was a bold statement considering his intelligence level was very high.
If you want to look into this area and need to talk to a professor type about how the pressure behaved inside the expansion chamber, I can try and find out his contact details for you.

Maybe refer him to this site.

One thing that stuck in my mind, was that when noise restrictions were introduced in UK, my friend explained that the method he used for reducing noise was to "double skin the pipe" meaning it was made of two pipes with one tightly fitting inside the other.

I could readily understand why the pipe would make less noise, but not why this reduced the power output by around 5-10%.

The pipes were made from steel sheet approx .030"-.035" thick, and after looking at your cone collapsing experiment, I think the reason for the power loss was caused by the secondary skin, restricting the movement of the inner pipe, because it had created a vacuum between the skins.

Correct me if I am wrong but this seems to indicate that the pipes were actually expanding and collapsing slightly as the pressure pulses ran through them? If pressure pulses can deform steel sheet, then surely this helps to prove your theory on radial momentum.

You can observe this phenomenon with a strobe lamp.

When I was deeply involved in this subject, the manufacturers who had the best expansion chamber designs were Suzuki, Yamaha and Rotax. If you were to contact them, I am sure you would find someone to help you.

Here's a link to a website that shows a very simple diagram of how these work.
www.stannakajak.com/skalmanmc/

My comments in red.

The cone-shape for exhaust takes advantage of some of the properties of radial-expansion induction of pressure drop.

Perhaps the efficiency increase has to do with reclaiming some of the exhaust energy ... as intake compression for the next stroke. (Just a hunch.)

Sat, 21 Jun 2003

Radial momentum & exhaust pipes

Hello Ed,

I was reading your experiments on radial momentum and some ideas came to mind, while looking at your cone experiment that made the cone collapse.

If you were to take a look at the design of the exhaust pipe of a two stroke racing engine, known as an expansion chamber, you would see it consists basically of two cones, one expanding away from the exhaust port and one contracting, the effect of this is to create a PARTIAL VACUUM as low as 6 psi, which aids the suction of fuel air mixture up from the crankcase through the transfer ports and into the cylinder.

I am not certain about this, but I think it may add some weight to your theory.

I'd like to see a diagram of the apparatus, with pressure profiles.

Several years ago I was developed a healthy obsession for the tuning of two stroke engines, and every time I got a new motorbike, I would immediately begin to take the engine apart and try to “think how the gases would behave” while flying around inside the air-box, carburetors, inlet manifolds, reed/disc valves, crankcase, transfer, boost and exhaust ports and EASILY THE MOST INFLUENTIAL COMPONENT, the expansion chamber.

Einstein also also liked to perform such "Gedanken" or thought experiments.

Changes in the dimensions of the expansion chamber yield drastic differences in engine characteristics, such as horsepower, torque, power band width, maximum rpms.

Reducing the length of the header pipe (the first part of the pipe to leave the cylinder) would normally cause the engine to

1. Produce more horsepower
2. Make its peak horse power output at approx 1000 rpm higher.
3. Reach peak volumetric efficiency at approx 1000 rpm higher (the point of maximum torque, and where the engine makes its most beautiful wasp like noise, also the best rpm to get wheelies)

Increasing the large end diameter of the cones (Therefore increasing its angle) would increase torque and reduce horsepower. It might be interesting to see if there is a direct correlation between these types of forces/powers/energies and the "rate of collapse" of the cones in your tests. What I mean by this is the ratios between :

1. The wall thickness of the cones
2. The angle of the cones
3 .The psi needed to collapse the cones.

Decreasing the diameter and/or increasing the length of the tailpipe (the final tube that the exhaust gases leave the expansion chamber from) would cause the engine to make more power (up to a point) at the expense of running hotter (constricting the outlet of hot gases, and increasing internal pressure)

If the tailpipe was simply joined at the end of the last cone the noise level would be very high.

If the same length/ diameter tailpipe was pushed INSIDE the last cone into its widest point, the power level would remain the same but the noise would be reduced by approximately 30-50% because the tailpipe end was in a low pressure area.

Oval-ising of the cones impedes engine performance.

If you would like to read some literature on this subject I can recommend a book entitled Performance tuning in theory and practice: Two strokes by Graham A. Bell

Published by Haynes books. Its a very good read and extremely well explained, as are your experiments. (See chapter 4, The exhaust)

I think you would have already tested this Ed, but if you haven't, it might be an idea to suspend weights underneath the plastic discs, to see which pattern of disc can hold the most weight.

I have suspended weights and measured inter-plate gaps as one of the ways to obtain confirming metrics for my model.  The experimental results confirm the theory. See: Model

My guess is that the plain flat one would be the winner, as it has no two dimensional restrictions to the expansion of radial airflow.

I concur.

Did you observe that increasing the air or water pressure increased or decreased the holding force of the discs? I would expect a greater psi would increase the weight they could hold.

I concur.

Also I was also curious as the whether or not a slightly convex (such as a magnifying glass lens) shape or even concave disc would adhere to the levitator.

Concave does not work ... acts like a balloon ... no initial creation of radial flow. Convex is similar to flat, since the active region in very close to the center.

One part of my brain has an inkling that a completely spherical object like a table tennis ball, would allow 3D expansion of the air/water and therefore hold the most weight, but another part tells me that it would not hold in place at all.

My comments in red.

Tue, 17 Jun 2003

A University Physicist Responds

Dear Ed,

Thanks for your letter.

Indeed, we have fundamental disagreements; I have seen them before our meeting, and tried to smooth them. First, let us exclude use of words "radial expansion". It comprises two things: radial flow, and expansion of liquid/gas with decrease of density. These are quite different things. 

Both things actually occur … that is one of my concepts … I am open to hearing any scientific arguments about the concepts that proceed from basic physics. Your attempt to restrict language is not really a scientific argument. 

As you mentioned to me, all conventional scientists thought that the compressibility of the liquid is not important. The correction compressibility introduces into velocity profile is proportional to (v/c)^2 - mathematically speaking. (v is typical speed of the liquid, c is the sound speed in the liquid). We got the same result - intuitively - that the correction to the velocity introduced by compressibility is very small. The velocity is measurable quantity; the correction is small; this is why nobody cares about that ... 

Some fluid mechanics solutions that derive from Navier Stokes traditionally use incompressibility to simplify the math. In this case, compressibility is at the heart of the phenomenon so the simplification is inappropriate. Your first sentence lacks context and may not apply to the situation at all.  You show no foundation for your assertion for a velocity profile correction.  You are unable to duplicate my profiles. You are unable to compute a correction term.  You are posting unnamed peoples’ feeling as a proxy for hard science.

For some reason, you want to multiply the correction on bulk modulus. Then, of course, you will get something of order 1. Why you want to multiply ? I don't know...

Bulk Modulus (ratio of pressure to change in volume) is the inverse of compressibility. Your previous argument is that compressibility does not matter since it is so small.  Actually, for very small compressibility, bulk modulus is very large and explains the effect. Since I am explaining a pressure change, high bulk modulus would predict a greater effect, as is true. Incidentally, and consistent with my theory, the effect is greater for water than for air. 

I understand it is not easy for you to accept the idea. Unfortunately, this is the way things are. Forget about me; say I am wrong. Is the correction substantial ? 

I do not see you proposing any ideas for me to either accept or reject. 

I am not saying that the small effect is non-existent. I am just saying that, being small, it is not very interesting, and this is why nobody cares (including me; then you also will join). On contrary, the cavitation is NOT a small effect, and this is why it is interesting.

The cavitation effect that I recall predicting and later noticing for water, is the direct result of radial momentum.  So far, I do not see you presenting any alternative explanations that account for the pressure and velocity profiles -- and that also have the correct interfaces at fluid entry and exit. 

Before anything could be done about cavitation, we should agree on principles. Otherwise, it will end not well. 

I base my argument on science, particularly basic physics.  Your arguments show a lack of connection to any scientific principles. 

You may think that this tendency to idealization and neglect of small features of the reality in the favor of clarity and simplicity is just my personal trait. First of all, this is indeed my trait, and I am happy about that. 

You do not say what features you are neglecting.  If you are choosing to ignore compressibility, or bulk modulus, you are, in effect simply ignoring the central thesis.

Second, this is the very essence of science. The scientist who can do this idealization and abstraction from non-essential features the best - is the best scientist (the same in trading).  This is not just my personal view, but, rather, I would think, view of scientific community (though you may argue with that). You may not like it, but this is the way things are; and I think this is right. 

You present no science, essential or otherwise, to which I can respond. 

Such idealization is not easy though since requires understanding, and deep penetration into subject, and ability to see the essence. 

You post no evidence of understanding or penetration into the subject matter – indeed, you do not mention the physics at all, other than in the context of your feelings. 

Believe me I understand how painful is to find that the problem on which you worked has been done. I know. But - it has been done. Cut the loss. Move further. Otherwise, you will stretch psychological loss too far. 

I see no such work.  I repeatedly ask you for a solution that explains the essential velocity, pressure and density profiles, so we may compare with my solutions. So far you fail to produce such.  I do not feel pain, so much as frustration and disappointment that a professor of physics would argue a point in physics without citing basic physics. 

And, by the way, I fully appreciate now your words about psychological compatibility with the trading model, and understanding of personal risk profile. This part of my personality has not been developed. I'll do a couple of things with that. I learned a lot from you. Thanks. I indeed sincerely grateful. 

The letter on the left is from a physicist who works at a well-known university ... my comments are in red. 

The interchange seems typical of others with the academic establishment.

The ceiling is one of the plates, so removing it changes the fundamental geometry.

You can run the test yourself with a thread spool and a playing card.

see: Overview

Mon, 21 Apr 2003


Ed,

Just found your web site on Trading Tribes from the TurtleTrader web site and saw your response to the FAQ dated April 14, 2003 (subj.: Lift Theory, in the Physics section) about URLs for the picture of the jet braking the sound barrier. If you haven't been to the StrangeCosmos www.strangecosmos.com/ web site they have a plethora of pictures (go to the PICTURES section) from all walks of life. There are a couple military sections. If you go through the pictures you might find what you're looking for.

Hope this helps you out.
PS - Great story in Market Wizards.

www.strangecosmos.com

Sat, 19 Apr 2003

Pressure Drop Prediction

Dear Ed,

I was wondering if you would be so kind and please help me. I was searching
the web and ran across an article that you had written and it seems to be
closely related to the problem I am trying to figure out. As seen in this diagram
attached, I am trying to predict the pressure drop between two orifices. One being a fixed size, the other being variable. I have found several formulas for
p-drop across a single orifice, but nothing for two.

Your problem is like trying to blow up a balloon with a hole in it - or trying to take living expenses out of your trading account.

In both cases, the less you withdraw, the better you float.  See FAQ page on www.tradingtribe.com. 

See Figures 1 and 2 at the bottom of this page. You can simplify your problem somewhat: assume for 100 psig, that flow is supersonic, and choked. Then flow is roughly proportional to the product of aperture and pressure drop. (for subsonic flow, it's proportional to the square root of the pressure drop)

F₁ = k * P₁ * A₁ and

F₂ = k * P₂ * A₂

also, the flows are equal so

F₁ = F₂

and from the problem,

P₁ +  P₂ = 100 psig

solving,

P₂ = 100 / (1 +  A₂/A₁)

Pressure Vs. Aperture

See Figures 1 & 2, below

Wed, 16 Apr 2003

Strips Stay Parallel

Hello,

Thank you for the quick response.
 

I did not know, that the lift is generated mainly near the entry orifice. If so, then everything looks fine. My curiosity overcame my laziness and I decided to perform the experiment I described before. It was not perfect, but I spent half an hour totally absorbed in the project and I enjoyed it.

I used two stripes of paper hinged on paper clips between the table and a plexiglass board parallel to the table.

The most stable position for the stripes is parallel. No mater what you do with them at the beginning, they tend to end up parallel If the free-moving ends are at the same distance as the hinged ones - after blowing air between the stripes, they remain parallel. If the free-moving ends are at a greater distance than the hinged ones- the air blown between the stripes brings them together to parallel.
If the free ends are closer than the hinged ones - the air flow opens them - to parallel.

If one of the stripes is curved to the outside, making a "bubbled" channel, the air brings it back, straightens it and the stripes stay parallel.

I did not try to curve the paper to the inside.

Tue, 15 Apr 2003

Radial Momentum

Hello,

I like your radial momentum model.

Although I did not educate myself in physics as much as many others, I enjoy thinking about different topics and analyzing. Like George Castanza put it during one of his job interviews , " I enjoy understanding". I will be happy, if I can contribute anything to the discussion.

Seems like radial expansion has something to do with the lift. The most convincing experiments seem to be the ones with the levitators. The tube and cone - the tube of a smaller diameter may be stiffer than the cone, even if made of the same material and thickness -as the radius of the cone increases, the surface becomes more and more flat, hence easier to fold it.

The flaw, that I see with the levitators is that the parallel channel has a smaller surface than the ones allowing for expansion. Whatever causes the difference in pressure, if is applied to a smaller surface will result in smaller force.

I have thought of an experiment. It is very simple and probably somebody has done it before. As you mentioned on your web site, if you blow air above a stripe of paper, the paper is being lifted. Also if you have two stripes of paper parallel to each other and blow air in between them, while holding the ends, the other ends will come closer.

But I do not know if it is because of velocity or air expansion. Both are happening at the same time. It would be nice to eliminate one of the factors , to see if the other has any effect.
We can limit the air flow to the sides ,thus eliminating the expansion, by two larger planes perpendicular to the surfaces of the paper stripes.

We will then have a channel with perpendicular walls, two opposite walls made of paper and two other of stiff material.

The stiff walls material is transparent, so we can see what is happening. The paper walls can move at the ends between the stiff walls. The other ends of paper are being held in place. Even better if we can replace the paper with a stiff , light , low friction material and fix it on pins going perpendicular to the stiff, immobile larger planes, so in it is hinged allowing the light boards to change angle.

You seem to have a good grasp of the theory.

Per your observation about surface area: see levitator table. The V plate adheres, although the area between the guides is about the same as the area between the guides on the parallel plate. The difference in lift is quite apparent. 

The V plate lifts and the parallel plate does not. 

Also: unrestricted plates with total area much smaller than the parallel area on the parallel plate show considerable lift.

The active lift region is relatively close to the entry orifice.

Your suggestion for a double strip paper experiment is similar to the long-slit experiment I ran, in which a business card rests against a smooth plastic plate.

Mon, 14 Apr 2003

Lift theory

This makes a great deal of intuitive sense if you've ever seen a picture of the Concorde landing. The curved delta wing of the aircraft generates twin vortices with the axes of rotation parallel to the
fuselage. Neat!

I'd like to get a url to such photos.

Condensation Ring

This ring is analogous to the cavitation ring in the liquid levitator. As the air expands radially, in a cone extending from the nose of the plane, the temperature drops and water drops precipitate.