What Is The Coanda Effect

What Is The Coanda Effect?The flow of gases is subject to a great many "effects" which have been observed and documented over the years.

In many cases, the person responsible for making the first observations of a particular effect has their name attributed to it and then they become famous -- albeit only amongst those who are interested in such things.

One such effect is that observed and documented by a Romamanian by the name of Henri-Marie Coanda in the 1930s.

Coanda noted that a stream of fluid or gas will tend to hug a convex contour when directed at a tangent to that surface.

You can check this out for yourself by turning on a tap, so that there's a steady but gentle continuous stream of water flowing. Now bring the back of a spoon into slight contact with the stream and you'll find that the water will no longer fall straight down but actually stick to the curve of the spoon.

This rather unintuitive behavior is the Coanda effect in action.

It's pretty easy to understand why a flow would be deflected by a concave curve -- the curve will "push" the flow around the corner -- but isn't it odd that the flow seems to be pulled by a curved surface?

My own experiments indicate that a single curved surface will deflect a gasflow by a maximum of about 90 degrees -- after which the flow detaches itself from the curve and travels at a tangent to that curve.

How Can This Be Used In A Pulsejet?Like all seemingly unnatural behaviors, the Coanda effect has been put to good use in a number of applications.

Indeed, some of the gasflows within my X-Jet engine rely on the Coanda effect so I thought I'd have a think about how the same effect could be applied to more traditional pulsejet engines.

Here's what I've come up with:

The Combustion PhaseWhat we have here is a possible valveless pulsejet design using the Coanda effect to significantly reduce the tendency for combustion gases to travel up the intake tube.

When the air-fuel ignites, some of the hot gases travel out the tailpipe through the expected route -- but those which would be expected to travel out the intake tube (the left-most arrows) are subjected to the Coanda effect produced by the curved path at the mouth of that internal tube.

These gases are further coerced down the tailpipe by another of these great "effects" first observed by (and named after) Mr Bernoulli. Because the gases which enter the tailpipe through the outermost path are travelling very fast, they produce a low-pressure area at the right-hand end of that internal tube. The flow entering the front of the internal tube is thus further encouraged to exit through the rear of the engine thanks to this area of low-pressure.

Now, let's see what happens during the intake phase of the engine's operation.

The Intake PhaseThe incoming air is deflected towards the outside path by way of the diamond shape in the middle of the intake tube.

Note that the diamond shape has sharp edges, not curves. If we made this a nicely curved shape then the Coanda effect would work against us by pulling the incoming air back towards the center of the internal tube. By using a sharp edge, the flow will separate and virtually all of it will travel outwards and into the combustion area.

However, because a vortex will form on the back-side of this diamond, a small amount of the incoming air will travel into the internal tube -- but that's not going to be a problem because it will simply become extra mass for the engine to eject later.

The fuel will be injected at the point where the incoming air passes over the circle at the front of the combustion area.

When the fresh air-fuel mixture ignites, the whole cycle repeats again.

Will It Work?Now all this looks fine on paper (or a webpage) but will it work as planned?

To be honest -- I don't know, I haven't built it yet.

Based on my experience with the design of pulsejets I'd have to say that there's probably a devil in the detail.

The precise angles and radius of the curves involved need to be established by a little calculation and much empirical work, but I see no reason why the basic theory won't hold up.

Now this isn't going to stop all the hot gases from trying to exit through the intake tube -- no valveless system can actually do that but I hope that it could provide enough flow control to allow such an engine to provide a good measure of static thrust.

The advantage of not bending the engine in half and facing the intake in the same direction as the exhaust is that you can then take much more advantage of ram-effect to increase the power of such an engine when it is operating at high speed.

The "Coanda Effect"

History of The "Coanda Effect"

I came across this device recently and hope you find it interesting also

In 1910 a young Romanian born engineer named Henri Coanda tested a plane he had built powered by the worlds first jet engine of which he was the inventor. The engine was not a Turbo jet which was later invented by Frank Whittle and Von Ohain, but had a gasoline engine driven centrifugal compressor, a combustion chamber and nozzle.

Coanda placed metal plates between the hot jet gases and the plywood fuselage. However instead of deflecting the jet away it deflected it onto the plates, ran along them and set his plane alight. Fascinated, he failed to notice he was approaching a wall at high speed until the last second, pulled back on the stick, became airborne enough to clear the wall, crashed and was thrown clear to watch his plane go up in flames.

More than 20 years later he came to understand precisely the phenomenon which was named after him, the "Coanda Effect".

Coanda jets are generated by blowing a moderate to high pressure gas (such as air) or liquid through a narrow slot over a surface which in some cases may be convexly curved.

The jet runs tangent to the surface and can circulate around 180 bends. This we call the primary jet. Our patentable methods are able to cause the jet to recirculate around 360.

The Coanda jets are never laminar like the flow over an aircraft wing or fan blade. The jets are always highly turbulent. The jet is composed of myriads of localised eddy currents. The speed of the air in the swirling or rotating currents is far higher than the linear velocity of the whole jet stream itself.

Pressure is related to speed as you are now aware of. A round jet issuing from a nozzle entrains ambient air due to its high velocity lowering its pressure which attracts the ambient air by collision and entrapment of molecules.

Coanda jets are ejected from slots and then traverse a hard surface or wall. They are sometimes called a wall jet. This wall after the slot creates a non-symmetrical nozzle.

The velocity of the jet immediately evacuates the molecules between it and the wall. This low pressure region cannot be relieved by ambient inflow as ambient air is on the other side of the jet and so the jet quickly deflects toward and runs tangent to the wall. The average pressure across a Coanda jet is lower than the average pressure across an unbounded round jet.

This means that the average velocity at any point in the Coanda jet is higher than in a conventional jet at the same distance from the slot. It follows then that the pressure is lower at any comparable distance from the slot and the momentum and mass flow are higher at the same points.

Flow augmentation by entrainment of ambient air is also greater than with a conventional jet because of the pressure gradient caused by the proximity of the hard surface (the wall) tangent to the jet and this is a more efficient means of momentum transfer than mere molecular collision and entrapment as with conventional jets.

The Coanda Effect

The "Coanda Effect" is a fascinating, powerful phenomenon that has been lying almost unused for decades waiting to be exploited commercially. The new "Jet-Fan" now makes it possible to revive the effect in domestic and industrial applications.

Some good quality higher pressure fans and applications over which the new "Jet-Fan" gives superior performance are:-

Turbine compressors (as in jet engines),

Computer chip cooling fans.

Ducting for air-conditioning,

Vacuum Cleaners

Ventilation in buildings,

Superchargers for racing cars, aircraft and trucks.

Lift and drive fans for Hovercraft

Ducted fans for aircraft

Jet boats

Water pumps for industry, agriculture and automotive

Large mine and power station ventilation and cooling

Radiator fans

Exotic new devices impossible or impractical before the "Jet-Fan".

The main advantages of the "Jet-Fan" are:-

It is stall free.

It does not require a diffuser or stator blades to realise a pressure gain.

It is more efficient over a wider speed range.

It delivers relatively high pressure air at a high flow rate with high efficiency

with no surging and delivers it axially through a nozzle.

To achieve this the main differences are:-

The blades converge, unlike other fans (Average 6% to 10%)

The "Jet-Fan" does not rotate airfoil blades around but rather rotates convergent passageways ie. each two blades define a passageway.

It has far more blades than a conventional fan.

All blades overlap each other.

It has blades that are much shorter and angled to the axis of rotation.

The new "Jet-Fan" is an entirely new concept.

The gap created by the convergent blades can change during runs.

Each blade has a spigot which extends into a bore in the hub which is aimed at the imaginary dead centre of a sphere which the hub is sliced from. (It has a spherical hub and shroud.) Because high pressure fans tend to leak air back the wrong direction the "Jet-Fan" employs a spherical hub and the blade roots touch the hub for their full length preventing back-flow. The inside of the shroud also has the same spherical aspect which shares the same dead centre as the hub. In this way back-flow near the blade tips is prevented and as all blades overlap significantly any air return is minimised and in fact over almost all its speed and pressure range back-flow is prevented entirely.

When the blades change pitch during runs the blade roots always remain touching the hub and the infinitesimal gap between the blade tips and shroud is not altered.

The basic idea of the "Jet-Fan" is very simple.

Blade speed in all fans, especially the centrifugal fans compresses air to some extent. This compression is inevitable and is detrimental to performance as it can cause blade stall by air circulating around the trailing edges. In addition, the air must expand to the average low pressure as it joins the higher speed, lower pressure flow at the trailing edges, subsequently it must have its pressure raised again as it is decelerated through the diffuser or stators. These pressure fluctuations decrease efficiency.

The "Jet-Fan" relies on the fact that the air will be compressed by blade speed just as in all conventional fans but in the case of the "Jet-Fan" the pressure generated is retained without re-expansion.

Blade pitch is configured to maximise compression (with liquids the pressure rises but liquids do not compress).

The blade dynamic pressure on the air can tend to rise by the square as the air is swept further out and so the blades are given a decreasing radius toward the trailing edges to ease the pressure within the passageways. This is to prevent back-flow along the passageways.

In addition the decreasing radius converges the blades and therefore each passageway that each pair of blades define is reduced in volume.

There is therefore a step-down in volume between the blades.

Significant useful pressure is generated by blade speed. The pressure increases by the square of the blade speed increase.

The passageway therefore along its length merely progressively conforms to the lesser space the compressed air occupies and the air is discharged in a pressurised state.

In practice the pressure within the discharge apertures is found to be identical to that immediately aft of the blades and before the air straighteners.

This avoids the abrupt pressure fluctuations found with other fans, the pressure being generated once only and maintained and this avoids the use of a diffuser or stators.

As system resistance increases due to a variable choke in some applications such as ducted fans, or jet boats the fan speed is increased and blades are brought closer together to postpone the stall.

How the "Jet Fan" Solves the problem

The new "Jet-Fan" is able to produce the same high pressures required for all the applications listed but without the need for a diffuser or stators.

That pressure is delivered immediately from between the fan trailing edges. This feat is achieved by the blade convergence of the "Jet-Fan" which is unlike any other fan.

What all of this means is that the new "Jet-Fan" is able to perform all of the applications listed and many more, better than existing conventional fans.

In addition to producing high pressure air or liquids the "Jet-Fan" has several extra features giving it even more advantages over other fans.

The new "Jet-Fan" has blades that are arranged about a hub that is a slice taken from a true sphere. The blades extend into bores aimed at the imaginary dead centre. This enables the degree of blade convergence (the blade pitch) to be changed during runs. This enables the fan to maintain high pressure and efficiency over a wider RPM range and pressure duty than conventional fans.

The new "Jet-Fan" is also able to do this in very small versions, an achievement not seen before. This means that the existing applications already listed can be performed better by "Jet-Fans" as they are more efficient with higher pressures in smaller diameters and do not require the excess baggage, (diffusers or stators).

Tiny "Jet-Fans" are more efficient than existing computer fans which are normally only around 1% to 5% efficient. Marine And Aviation Transportation

Hovercraft require high volume air flow at moderate pressures. The "Jet Fan" can provide higher pressure when needed such as in heavy seas as it does not stall due to fluctuating back pressure, and it also occupies less space.

To whom it may concern,

The LMB Company welcomes the partnership we sealed in January with the Australian JET FAN Technology Company. We are looking forward to developing further the JET FAN for our market in association with Mr Terry Day, and to help him produce specific prototypes for other markets as well.

We have started our JET FAN R & D eight month program and will be very pleased to reveal these results, graphics and prototypes during the next military EUROSTATORY International Expo in Paris in June 1996.

All genuine enquiries for fan production for the Defence and Avionics market (such as cooling systems and air-conditioning in cells, cockpits, shelters) and for Medical and Transportation market s (such as air-conditioning and air-renewal in buses, tramways, trains, subways, etc....) can be addressed to:

Mr Chapalain / LMB Director

36 Ave Curie - Malemort

FRANCE

Fax: 33 55 92 29 00

Currently, LMB on behalf of JET FAN Technology is developing a computer designing software package for these applications. The first JET FANS are expected to be in production in the second half of 1996.

LMB is happy to have this statement published in future JET FAN Technology brochures and will consider seriously any JET FAN production enquiries concerning our specific market.

If you need further information please let me know.

Rene Chapalain

Managing Director

Interview with Terry Day

Is it noisy?

No. Noise from a fan is due to air turbulence. The "Jet Fan" drives high pressure air into a high pressure area. This makes it much quieter than other fans.

Is It Expensive to buy?

No. It will be no more expensive than the present day conventional fans it replaces. It may be less expensive due to it's smaller size and not needing a diffuser.

Will electric motor manufacturers be resistant due to higher speed requirements?

No. Almost all applications require no motor changes at all. Only a very few situations where a brushless electric motor is required for noise considerations will a one stage gearbox be needed to increase fan speed.

Will manufacturers resist change due to expensive plant changes?

No. Although the "Jet Fan" is a vast improvement over todays conventional fans, it is still after all only a fan from a manufacturing viewpoint.

With spherical hubs, shrouds and moveable blades, surely it is more complex and therefore more difficult to produce?

No. The more complex versions are for more exotic, high stress or special situations, mainly transportational, where pressures and thrust requirements change from second to second.

90% of applications including household ones need no speed change. The blade convergence is matched to the fan speed and the blades are an integral part of the hub and are cast or moulded in one piece as with other fans.

Will it be expensive to run?

No. The "Jet Fan" gives higher efficiency than other fans of the same size. In other words it uses less electrical power or fuel than others to do the same job.

Is there a lot more research and development needed before the fan is ready to licence to manufacturers?

No. Most applications of the fan are ready now. The pressure versus flow rate, the pressure being developed between the blades and the high efficiency in very small sizes, have all been proven. The "Jet Fan" is ready for manufacturing now.

The more complex versions including multi-staging as a compressor need more development time. We believe this period will not be long.

Is its high speed dangerous or a disadvantage?

No. We have not run it as fast as many conventional domestic vacuum cleaner fans yet.

What is the reaction from the engineers to such a simple improvement?

We have had many fan engineers and other technical people witness our fan demonstration test runs. We have had no negativity and only great enthusiasm from all.

What does buying or using an appliance with the "Jet Fan" mean to the average consumer?

The consumers work will be more efficient thus saving time and money. It also means a reduction in the consumption of fossil fuels for the production of electricity to supply appliances. The reduction of fossil fuel consumption will have a positive effect on green house gas emissions and the environment.

MODEL AIRPLANES, THE BERNOULLI EQUATION, AND THE COANDA EFFECT 1994 by Jef Raskin

"In aerodynamics, theory is what makes the invisible plain. Trying to fly an airplane without theory is like getting into a fistfight with a poltergeist."--David Thornburg [1992]."That we have written an equation does not remove from the flow of fluids its charm or mystery or its surprise."--Richard Feynman [1964]INTRODUCTIONA sound theoretical understanding of lift had been achieved within two decades of the Wright brothers' first flight (Prandtl's work was most influential1), but the most common explanation of lift seen in elementary texts and popular articles today is

The common explanation, from The Way Things Work[Macaulay 1988]The reasoning--though incomplete--i s based on the Bernoulli effect, which correctly correlates the increased speed with which air moves over a surface and the lowered air pressure measured at that surface.In fact, most airplane wings do have considerably more curvature on the top than the bottom, lending credence to this explanation. But, even as a child, I found that it presented me with a puzzle: how can a plane fly inverted (upside down). When I

1Ludwig Prandtl (1875-1953), a German physicist, often called the "father of aerodynamics." His famous book on the theory of wings, Tragfl geltheorie, was published in 1918.

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pressed my 6th grade science teacher on this question, he just got mad, denied that planes could fly inverted and tried to continue his lecture. I was very frustrated and argued until he said, "Shut up, Raskin!" I will relate what happened next later in this essay.A few years later I carried out a calculation according to a naive interpretation of the common explanation of how a wing works. Using data from a model airplane I found that the calculated lift was only 2% of that needed to fly the model. [See Appendix 1 for the calculation]. Given that Bernoulli's equation is correct (indeed, it is a form of the law of conservation of energy), I was left with my original question unanswered: where does the lift come from?In the next few sections we look at attempts to explain two related phenomena--what makes a spinning ball curve and how a wing's shape influences lift--and see how the common explanation of lift has led a surprising number of scientists (including some famous ones) astray.THE SPINNING BALLThe path of a ball spinning around a vertical axis and moving forward through the air is deflected to the right or the left of a straight path. Experiment shows that this effect depends both on the fact it is spinning and that it is immersed in a fluid (air). Non-spinning balls or spinning balls in a vacuum go straight. You might, before going on, want to decide for yourself which way a ball spinning counterclockwise (when seen from above) will turn.Let's see what five books say about this problem. Three are by physicists, one is a standard reference work, and the last, just for kicks, is from a book by my son's soccer coach. We'll start with physicist James Trefil, who writes [Trefil 1984],

Before leaving the Bernoulli effect, I'd like to point out one more area where its consequences should be explored, and that is the somewhat unexpected activity of a baseball. Consider, if you will, the curve ball. This particular pitch is thrown so that the ball spins around an axis as it moves forward, as shown in the top in figure 11-4. Because the surface of the ball is rough, the effect of viscous forces is to create a thin layer of air which rotates with the surface. Looking at the diagram, we see that the air at the point labeled A will be moving faster than the the air at the point labeled B, because in the first case the motion of the ball's surface is added to the ball's overall velocity, while in the second it is subtracted. The effect, then is a 'lift' force, which tends to move the ball in the direction shown.2

2The surface roughness is not essential. The effect is observed no matter how smooth the ball.

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Trefil's figure 11-4. It does not agree with some other sources.

Baseball aficionadoswould say that the ball curves toward third base. Trefil then shows a diagram of a fast ball, shown as deflecting downward when spinning so that the bottom of the ball is rotating forward. It is the same phenomenon with the axis of rotation shifted 90 degrees.In The Physics of Baseball, Robert K. Adair [Adair 1990] imagines a ball thrown toward home plate, so that it rotates counterclockwise as seen from above--as in Trefil's diagram. To the left of the pitcher is first base, to his right is third base. Adair writes:We can then expect the air pressure on the third-baseside of the ball, which is travelling faster through theair, to be greater than the pressure on the on thefirst-base side, which is travelling more slowly, andthe ball will be deflected toward first base. This is exactly the opposite of Trefil's conclusion though they agree that the side spinning forward is moving faster through the air. We have learned from these two sources that going faster through the air either increases or decreases the pressure on that side. I won't take sides in this argument as yet.The Encyclopedia Brittanica[1979] gives an explanation which introduces the concept of drag into the discussion."The drag of the side of the ball turning into the air(into the direction the ball is travelling) retards theairflow, whereas on the other side the drag speeds upthe airflow. Greater pressure on the side where theairflow is slowed down forces the ball in the directionof the low-pressure region on the opposite side, where arelative increase in airflow occurs."Now we have read that spinning the ball causes the air to move either faster or slower past the side spinning forward, and that faster moving air increases or decreases the pressure, depending on the authority you choose to follow. Speaking of authority, it

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might be appropriate to turn to one of the giants of physics of this century, Richard Feynman. He takes the side of Trefil,and uses a cylinder rather than a sphere [Feynman et. al. 1964. Italics are theirs. The lift force referred to is shown pointing upwards.]:"The flow velocity is higher on the upper side of acylinder [shown rotating so that its top is moving inthe same direction as its forward travel] than on thelower side. The pressures are therefore loweron theupperside than on the lower side. So when we have acombination of a circulation around a cylinder and a nethorizontal flow, there is a net vertical forceon thecylinder--it is called a lift force."Now for my son's coach's book. The coach in this case is the world-class soccer player, George Lamptey. There is almost no theory given, but we can be reasonably sure that Lamptey has repeatedly tried the experiment and should therefore report the direction the ball turns correctly. He writes[Lamptey 1985]:"The banana kick is more or less an off-center instepdrive kick which adds a spin to the soccer ball. Kickoff center to the right, the soccer ball curves to theleft. Kick off center to the left, the soccer ballcurves to the right... The amount the soccer ball curvesdepends on the speed of the spin."

Lamptey, like Adair, has the high pressure on the side moving into the air. I will not relate more accounts, some having the ball swerve one way, some the other. Some explanations depend on the author's interpretation of the Bernoulli effect, some on viscosity, some on drag, some on turbulence.We will return to the subject of spinning balls, but we are not yet finished finding problems with the common explanation of lift.OTHER PARADOXESThecommon explanation of how a wing works leads us to conclude, for example, that a wing which is somewhat concave on the bottom, often called an "undercambered" wing, will always generate lesslift (under otherwise fixed conditions) than a flat

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bottomed one. This conclusion is wrong.

We then have to ask how a flat wing like that of a paper airplane, with no curves anywhere, can generate lift. Note that the flat wing has been drawn at a tilt, this tilt is called "angle of attack" and is necessary for the flat wing to generate lift. The topic of angle of attack will be returned to presently.

A flat wing can generate lift. This is a bit difficult to explaingiven the traditional mental model.The cross-sectional shapes of wings,like those illustrated here, are called "airfoils." A very efficient airfoil for small, slow-flying models is an arched piece of thin sheet material, but it is not clear at all from the common explanation how it can generate lift at all since the top and bottom of the airfoil are the same length.

If the common explanation is all there were to it, then we should be making the tops of wings even curvier than they now are. Then the air would have to go even faster, and we'd get more lift. In this diagram the wiggliness is exaggerated. More realistic lumpy examples will be encountered in a few moments.

If we make the top of the wing like this, the air on top has alot longer path to follow, so the air will go even faster thanwith a conventional wing. You might conclude that this kindof airfoil should have lots of lift. In fact, it is a disaster.Enough examples. While Bernoulli's equations are correct, their proper application to aerodynamic lift proceeds quite differently than the common explanation. Applied properly or not, the equations result in no convenient visualization that links the

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shape of an airfoil with its lift, and reveal nothing about drag. This lack of a readily-visualized mental model, combined with the prevalence of the plausible-sounding common explanation, is probably why even some excellent physicists have been misled.

ALBERT EINSTEIN'S WINGMy friend Yesso, who works for the aircraft industry (though not as a designer), came up with a proposed improved airfoil. Reasoning along the lines of the common explanation he suggested that you should get more lift from an airfoil if you restarted the top's curve part of the way along:

An extra lump for extra lift?This is just a "reasonable" version of the lumpy airfoil that I presented above. Yesso's idea was, of course, based on the concept that a longer upper surface should give more lift. I was about to tell Yesso why his foil idea wouldn't work when I happened to talk to J rgen Skogh3. He told me of a humped airfoil Albert Einstein4 designed during WWI that was based on much the same reasoning Yesso had used [Grosz 1988].

Albert Einstein's airfoil. It had noaerodynamic virtues.This meant that instead of telling Yesso merely that his idea wouldn't work, I could tell him that he had created a modernized version of Einstein's error! Einstein later noted, with chagrin, that he had goofed5. [Skogh 1993]

EVIDENCE FROM EXPERIMENTSIf it were the case that airfoils generate lift solely because the airflow across a surface lowers the pressure on that

3Mr. Skogh worked on aircraft design for Saab in Sweden and for Lockheed in the United States.4Albert Einstein [1879-1955], a German-American physicist, was one of the greatest scientists of all time. His small error in wing design does not detract from the massive revolution his thinking brought about in physics.5J rgen Skogh writes, "During the First World War Albert Einstein was for a time hired by the LVG (Luft-Verkehrs-Gesellshaft) as a consultant. At LVG he designed an airfoil with a pronounced mid-chord hump, an innovation intended to enhance lift. The airfoil was tested in the G ttingen wind tunnel and also on an actual aircraft and found, in both cases, to be a flop." In 1954 Einstein wrote "Although it is probably true that the principle of flight can be most simply explained in this [Bernoullian] way it by no means is wise to construct a wing in such a manner!" See [Grosz, 1988] for the full text.

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surface then, if the surface is curved, it does not matter whether it is straight,concave, or convex; the common explanation depends only on flow parallel to the surface. Here are some experiments that you can easily reproduce to test this idea.1. Make a strip of writing paper about 5 cm X 25 cm. Hold it in front of your lips so that it hangs out and down making a convex upward surface. When you blow across the top of the paper, it rises. Many books attribute this to the lowering of the air pressure on top solely to the Bernoulli effect.

blow air

Now use your fingers to form the paper into a curve that it is slightly concave upward along its whole length and again blow along the top of this strip. The paper now bends downward.2. As per the diagrams below, build a box of thin plywood or cardboard with a balsa airfoil held in place with pins that allow it to flap freely up and down. Air is introduced with a soda straw. That's one of the nice things about science. You don't have to take anybody's word for a claim, you can try it yourself!6In this wind tunnel the air flows only across the top of the shape. A student friend of mine made another where a leaf blower blew on both top and bottom and he got the same results, but that design takes more effort to build and the airfoil models require leading and trailing edge refinement. Incidentally, I tried to convince a company that makes science demonstrators to include this in their offerings. They weren't interested in it because "it didn't give the right results.""Then how does it work?" I asked. "I don't know," said the head designer.An experiment may be difficult to interpret but, unless it is fraudulent, it cannot give the wrong results.

6In some fields, e.g. the study of sub-atomic particles, you might need megabucks and a staff of thousands to build an accelerator to do an independent check, but the principle is still there.

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CROSS SECTION

SIDE VIEW

AIRFOIL DEMONSTRATOR. These drawings are full size, but the exact size and shape aren't important. I made a number of airfoils to test. Here are drawings of the ones I made:

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NORMALCONCAVE

RECURVED FLAT

FLAT WITH DOWNTURN

FLAT WITH UPTURNEXPERIMENTAL RESULTSWhen the straw is blown into, the normal airfoil promptly lifts off the bottom and floats up. When the blowing stops, it goes back down. This is exactly what everybody expects. Now consider theconcave shape; the curve is exactly the same as the first airfoil , though turned upside down. If the common explanation were true, then, since the length along the curve is the same as with the "normal" example, you'd expect this one to rise, too. After all, the airflow along the surface must be lowering the pressure, allowing the normal ambient air pressure below to push it up. Nonetheless, the concave airfoil stays firmly down; if you hold the apparatus vertically, it will be seen to move awayfrom the airflow.In other words, an often-cited experiment which is usually taken as demonstrating the common explanation of lift does not do so; another effect is far stronger. The rest of the airfoils are for fun--try to anticipate the direction each will move before you put them in the apparatus. It has been noted that "progress in science comes when experiments contradict theory" [Gleick 1992] although in this case the science has been long known, and the experiment contradicts not aerodynamic theory, but the often- taught common interpretation. Nonetheless, even if science does not progress in this case, an individual's understanding of it may. Another simple experiment will lead us toward an explanation that may help to give a better feel for these aerodynamic effects.

THE COANDA EFFECT9

If a stream of water is flowing along a solid surface which is curved slightly away from the stream, the water will tend to follow the surface. This is an example of the Coanda effect7and is easily demonstrated by holding the back of a spoon vertically under a thin stream of water froma faucet. If you hold the spoon so that it can swing, you will feel it being pulled towardthe stream of water. The effect has limits: if you use a sphere instead of a spoon, you will find that the water will only follow a part of the way around. Further, if the surface is too sharply curved, the water will not follow but will just bend a bit and break away from the surface.

The Coanda effect works with any of our usual fluids, such as air at usual temperatures, pressures, and speeds. I make these qualifications because (to give a few examples) liquid helium, gasses at extremes of low or high pressure or temperature, and fluids at supersonic speeds often behave rather differently. Fortunately, we don't have to worry about all of those extremes with model planes.

7In the 1930's the Romanian aerodynamicist Henri-Marie Coanda(1885-1972) observed that a stream of air (or other fluid) emerging from a nozzle tends to follow a nearby curved or flat surface, if the curvature of the surface or angle the surface makes with the stream is not too sharp.

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A stream of air, such as what you'd get if you blow through a straw, goes in a straight line

A stream of air alongside a straight surface still goes in a straight line

A stream of air alongside a curved surface tends to follow the curvature of the surface. Seems natural enough.

Strangely, a stream of airalongside a curved surfacethat bends away from it stilltends to follow the curvatureof the surface. This is theCoanda effect.Another thing we don't haveto wonder about is why the Coanda effect works, we can take it as an experimentally given fact. But I hope your curiosity is unsatisfied on this point and that you will seek further.A word often used to describe the Coanda effect is to say that the airstream is "entrained" by the surface. One advantage of discussing lift and drag in terms of the Coanda effect is that we can visualize the forces involved in a rather straightforward way. The common explanation (and the methods used in serious texts on aerodynamics) are anything but clear in showing how the motion of the air is physically coupled to the wing. This is partly because much of the approach taken in the 1920s was shaped by the need for the resulting differential equations (mostly based on the Kutta- Joukowski theorem8) to have closed-form solutions or to yield useful numerical results with paper-and-pencil methods. Modern approaches use computers and are based on only slightly more intuitive constructs. We will now develop an alternative way of visualizing lift that makes predicting the basic phenomena associated with it easier.

8Discovered independently by the German mathematician M. Wilheim Kutta (1867- 1944) and the Russian physicist Nikolai Joukowski (1847-1921).

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A MENTAL MODEL OF HOW A WING GENERATES LIFT AND DRAGAs is typical of physicists, I have often spoken of the air moving past the wing. In aircraft wings usually move through the air. It makes no real difference, as flying a slow plane into the wind so that the plane's ground speed is zero demonstrates. So I will speak of the airplane moving or the wind moving whichever makes the point more clearly at the time.In the next illustration , it becomes convenient to look at

the air molecules, attracted to thesurface, are pulled down.Think of the wing moving to the left, with the air standing still. The air moves toward the wing much as if it was attached to the wing with invisible rubber bands. It is often helpful to think of lift as the action of the rubber bands that are pulling the wing up.Another detail is important: the air gets pulled along in the direction of the wing's motion as well. So the action is really more like the following picture.

The air is pulled forward as wellas down by the motion of thewing.If you were in a canoe and tried pulling someone in the water toward you with a rope, your canoe would move toward the person. It is classic action and reaction. You move a mass of air down and the wing moves up. This is a useful visualization of the lift generated by the top of the wing.As the diagram suggests, the wing has also spent some of its energy, necessarily, in moving the air forward. The imaginary rubber bands pull it back some. That's a way to think about the dragthat is caused by the lift the wing generates. Lift cannot be had without drag.The acceleration of the air around the sharper curvature near the front of the top of the wing also imparts a downward and forward component to the motion of the molecules of air (actually a slowing of their upward and backward motion, which is equivalent) and thus contributes to lift. The bottom of the wing is easier to understand, and an explanation is left to the reader.The experiments with the miniature wind tunnel described earlier are readily understood in terms of the Coanda effect: the downward-curved wing entrained the airflow to move downward, and a force upward is developed in reaction. The upward-curved (concave) airfoil entrained the airflow to move upwards, and a force downward was the result. The lumpy wing generates a lot of drag by moving air molecules up and down repeatedly. This eats up energy (by generating frictional heat) but doesn't create a net downward motion of the air and therefore doesn't create a net upward12

movement of the wing. It is easy, based on the Coanda effect, to visualize why angle of attack (the fore-and-aft tilt of the wing, as illustrated earlier) is crucially important to a symmetrical airfoil, why planes can fly inverted, why flat and thin wings work, and why Experiment 1 with its convex and concave strips of paper works as it does.What has been presented so far is by no means a physical account of lift and drag, but it does tend to give a good picture of the phenomena. We will now use this grasp to get a reasonable hold on the spinning ball problem.

WHY THE SPINNING BALL'S PATH CURVES, IN TERMS OF THE COANDA EFFECTThe Coanda effect tells us the air tends to follow the surface of the ball. Consider Trefil's side A which is rotating in the direction of flight. It is trying to entrain air with it as it spins, this action is opposed by the oncoming air. Thus, to entrain the air around the ball on this side, it must first decelerate it and then reaccelerate it in the opposite direction. On the B side, which is rotating opposite the direction of flight, the air is already moving (relative to the ball) in the same direction, and is thus more easily entrained. The air more readily follows the curvature of the B side around and acquires a velocity toward the A side. The ball therefore moves toward the B side by reaction.It is again time for a simple experiment. It is difficult to experiment with baseballs because their weight is large compared to the aerodynamic forces on them and it is very hard to control the magnitude and direction of the spin, so let us look at a case where the ball is lighter and aerodynamic effects easier to see. I use a cheap beach ball (expensive ones are made of heavier materials and show aerodynamic effects less). Thrown with enough bottom spin (bottom moving forward) such a ball will actuallyrise in a curve as it travels forward.The lift due to spin can be so strong that it is greater than the downward force of gravity! Soon, air resistance stops both the spin and the forward motion of the ball and it falls, but not before it has shown that Trefil's explanation of how spin affects the flight of a ballis wrong.The lift due to spinning while moving through the air is usually called the "Magnus9effect." Some books on aerodynamics also describe the "Flettner Rotor," which is a long-since abandoned attempt to use the Magnus effect to make an efficient boat sail. Many sources besides Trefil get the effect backwards including the usually reliable Hoerner [Hoerner 1965]. College- level texts tend to get it right [Kuethe and Chow 1976; Houghton and Carruthers 1982] but, as noted above, Feynman's Lectures on Physicshas the rotation backwards. I was relieved to see that the classicAerodynamics[von K rm n 1954] gets the lift force on a

9H. G. Magnus (1802-1870), a German physicist and chemist, demonstrated this effect in 1853.

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spinning ball in the correct direction though the reasoning seems a bit strained.I wish I could send this essay to the 6th grade science teacher who could not take the time to listen to my reasoning. Here's what happened: he sent me to the principal's office when I came in the next day with a balsa model plane with dead flat wings. It would fly with either side up depending on how an aluminum foil elevator adjustment was set. I used it to demonstrate that the explanation the class had been given must have been wrong, somehow. The principal, however, was informed that my offense was "flying paper airplanes in class" as though done with disruptive intent. After being warned that I was to improve my behavior, I went to my beloved math teacher who suggested that I go to the library to find out how airplanes fly--only to discover that all the books agreed with my science teacher! It was a shock to realize that my teacher and even the library books could be wrong. And it was a revelation that I could trust my own thinking in the face of such concerted opposition. My playing with model airplanes had led me to take a major step toward intellectual independence--and a spirit of innovation that later led me to create the Macintosh computer project (and other, less-well-known inventions) as an adult.

APPENDIX 1A QUANTITATIVE APPLICATION OF THE COMMON (INCORRECT) EXPLANATIONIf the pressure, in Newtons per square meter (Nm-2 = kgm-1s- 2), on the top of a wing is notatedptop , the pressure on the bottompbottom , the velocity (ms-1) on the top of the wing v, and the velocity on thebottomvbottom,andwhere__ is thetop

density of air (approximately 1.2 kgm-3), then the pressure difference across the wing is given by the first term of Bernoulli's equation:ptop- pbottom= 1/2 _ (vtop2 - vbottom2)A rectangular planform (top view) wing of one meter span was measured as having a length chordwise along the bottom of 0.1624 m while the length across the top was 0.1636 m. The ratio of the lengths is 1.0074. This ratio is typical for many model and full- size aircraft wings. According to the common explanation which has two adjacent molecules separated at the leading edge mysteriously meeting at the trailing edge, the average air velocities on the top and bottom are also in the ratio of 1.0074.A typical speed for a model plane of 1m span and 0.16m chord with a mass of 0.7 kg (a weight of 6.9 N) is 10 ms-1 is 10 ms-1, so vwhich makes vtop10.074 ms-1. Given these numbers, webottomfind a pressure difference from the equation of about 0.9 kgm-1 - 2. The area of the wing is 0.16 m2sgiving a total force of 0.14 N. This is not nearly enough--it misses lifting the weight of 6.9 N by a factor of about 50. We would need an air velocity difference of14

about 3 ms-1to lift the plane.The calculation is, of course, an approximation since Bernoulli's equation assumes nonviscous, incompressible flow and air is both viscous and compressible. But the viscosity is small and at the speeds we are speaking of air does not compress significantly. Accounting for these details changes the outcome at most a percent or so. This treatment also ignores the second term (not shown) of the Bernoulli equation--the static pressure difference between the top and bottom of the wing due to their trivially different altitudes. Its contribution to lift is even smaller than the effects already ignored. The use of an average velocity assumes a circular arc for the top of the wing. This is not optimal but it will fly. None of these details affect the conclusion that the common explanation of how a wing generates lift--with its na ve application of the Bernoulli equation--fails quantitatively.FURTHER READING: There are many fine books and articles on the subject of model airplane aerodynamics (and many more on aerodynamics in general). Commendably accurate and readable are books and articles for modelers by Professor Martin Simons [e.g. Simons 1987]. Much can be learned from Frank Zaic's delightful, if not terribly technical, series [Zaic 1936 to Zaic 1964] (Available from the Academy of Model Aeronautics in the United States), and no treatments are more professional or useful than those of Professor Michael Selig and his colleagues [e.g. Selig et. al. 1989]. All of these authors are also well-known modelers. The other references on aerodynamics, e.g. Kuethe and Chow [1976] and Houghton and Carruthers [1982] are graduate or upper-level undergraduate texts, they require a knowledge of physics and calculus including partial differential equations. Jones [1988] is an informal treatment by a master and Hoerner [1965] is a magnificent compendium of experimental results, but has little theory--practical designers find his work invaluable.

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REFERENCES* Adair, Robert K. The Physics of Baseball, Harper and Row, NY, 1990. pg. 13* Feynman, R. et. al. Lectures on Physics, Vol II, Addison-Wesley 1964 pg. 40-9, 40-10, 41-11* Gleick, J. Genius. Pantheon Books, NY 1992 pg. 234 * Grosz, Peter M. "Herr Dr Prof Albert Who? Einstein the Aerodynamicist, That's Who!" WWI Aero No. 118, Feb. 1988 pg. 42 ff * Hoerner, S.F. Fluid-Dynamic Drag, Hoerner Fluid Dynamics, 1965 pg. 7-11* Houghton and Carruthers.Aerodynamics for Engineering Students, Edward Arnold Publishers, Ltd. London, 1982* Jones, R.T. Modern Subsonic Aerodynamics. Aircraft Designs Inc., 1988. pg.36* Lamptey, George. The Ten Bridges to Professional Soccer, Book 1: Bridge of Kicking. AcademyPress, Santa Clara CA, 1985. * Levy, Steven. "Insanely Great." Popular Science, February, 1994. pg. 56 ff.* Linzmayer, Owen. The Mac Bathroom Reader, Sybex 1994 * Kuethe and Chow.Foundations of Aerodynamics, Wiley, 1976 * Macaulay, David. The Way Things Work. Houghton Mifflin Co. Boston, 1988. pg. 115* Selig, M. et. al. Airfoils at Low Speeds. Soartech 8. Herk Stokely, 1504 Horseshoe Circle, Virginia Beach VA 23451, 1989 * Simons, M. Model Aircraft Aerodynamics, 2nd ed.. Argus Books Ltd., London, 1987.* Skogh, J rgen. Einstein's Folly and The Area of a Rectangle, in publication* Thornburg, Dave. Do You Speak Model Airplane?Pony X Press, 5 Monticello Drive, Albuquerque NM 87123, 1992* Trefil, James S. A Scientist At The Seashore.Collier Books, Macmillan Publishing Co., 1984, pp 148-149* von K rm n, T. Aerodynamics. Oxford Univ. Press 1954 pg. 33 * Zaic, Frank. Model Aeronautic Yearbooks. Published from the 30's to the 60's* Zaic, Frank. Circular Airflow. Model Aeronautic Publications, 1964.

ACKNOWLEDGMENTS

I am very appreciative of the suggestions I have received from a number of careful readers, including Dr. Bill Aldridge, Professors

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Michael Selig, Steve Berry, and Vincent Panico, and Linda Blum. They have materially improved both the content and the exposition, but where I have foolishly not taken their advice my own errors may yet shine through.

AUTHOR'S BIOGRAPHYJef Raskin was a professor at the University of California at San Diego and originated the Macintosh computer at Apple Computer Inc [Levy 1994; Linzmayer 1994]. He is a widely-published writer, an avid model airplane builder and competitor, and an active musician and composer.

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