### by Saulius Pakalnis

THE COANDA EFFECT Ref. Jef Raskin's Webpage Coanda Effect: Understanding Why Wings Work

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 effect and is easily demonstrated by holding the back of a spoon vertically under a thin stream of water from a faucet. If you hold the spoon so that it can swing, you will feel it being pulled toward the 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.

 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 air alongside a curved surface that bends away from it still tends to follow the curvature of the surface. This is the Coanda effect.

Another thing we don't have to wonder about is why the Coanda effect works, we can take it as an experimental fact. But I hope your curiosity is unsatisfied on this point and that you will seek further.

Coanda and Flight

Many scientists have recently begun using the COANDA EFFECT to at least partially explain how planes fly. Ref .

For a long time many people believed (and many people still do) that LIFT during flight is achieved due to something called the BERNOULLI effect. This theory suggest that air moving across a wing moves more quickly over the top than underneath. This creates an area of lower pressure on top of the wing in comparison to the underside of the wing. Thus, less pressure pushes down on the wing and more pressure pushes up and consequently LIFTS the craft into the air…

However, many scientists disagree with this explanation! Is it time to say good bye to Bernoulli's principle while speaking about a lift of wing? My interpretation can be find here.

Some scientists have suggested recently that due to the shape of a planes wing, air moving along it due to the COANDA EFFECT will be deflected downwards as it leaves the wing and thus push the craft up into the air (due to NEWTONS THIRD LAW OF MOTION) and consequently assist with LIFT

What is the Coanda effect?

 Soldiers and girl. Soldiers are marching forward in straight line. Each soldier holds hand of his neighbor. Suddenly outsider soldier caches a hand of a girl standing on a sidewalk. See what happens. This is simplest explanation of Coanda effect. Note: it is assumed, that "soldiers" are some fluid elements, not single molecules.

Very simply, the COANDA (or ‘wall attachment’) EFFECT is the tendency for a moving fluid (either liquid or gas) to attach itself to a surface and flow along it.

One way of explaining this effect is to understand that as a fluid moves across a surface, and certain amount of friction (called skin friction) occurs between the two surfaces (friction is that force that slows down or prevents two surfaces from moving across each other). This friction tends to slow down the fluid as it moves across the other surface. This resistance to the flow of the fluid will then pull the fluid towards the other surface, making it stick to it… even as it bends around corners! Ref .

Air layers in vicinity of a flat foil.
Note 1.
The is a fluid stream front
Note 2. There are 2 types of friction:
a) friction between the lowest air stream and the foil. The friction bends the layer front into foil surface. This results in "dynamic sticking to the surface".
b) friction between different layers of streams (dynamic viscosity). Lower layer of stream drags and bends down the upper neighboring layer.
Note 3. The stream layers have velocities gradient along the normal to foil surfaces.
Note 4. The figure is simplified, but the foil is not considered to be very thin, as  increased fluid pressure
pillow at front of  foil initialize dynamic sticking phenomenon - Canda effect.  Air flow is laminar. The stream bending (and little compression for air only) is exaggerated in order to show it.
Note 5. Coanda effect has a dynamic origin - it appears at nonzero relative fluid and foil speed.

Boundary Layer. Ref.

When the air hits the airfoil leading edge it will separate into the upper and lower airstream, which meets again at the trailing edge.

It is obvious that the air very close to the airfoil "rubs" against the solid surface and is slowed down. In other words, starting downstream of the impact point, the air loses some of its momentum, or velocity. And it loses more and more as we follow it along the path close to the solid airfoil. We can see that friction creates an area where there is less speed. The reduced speed area just outside of the airfoil becomes thicker and thicker as we follow it from the leading edge to the trailing edge. This area is called the boundary layer. Its thickness is increasing as described and is defined as the thickness at which the local free stream speed is finally reached. A typical boundary layer thickness is 1/2" near the trailing edge. The friction, which obviously, is a loss, results in the friction drag of the airfoil.

Ref. Glenn Research Center

Again the theory of fluid dynamics shows that there are two possible types of stable boundary layers Ref. : The first, to build up, is called 'laminar" because the flow is nice and steady and the friction drag is relatively low.
The second is called 'turbulent" because the flow is rather rough and the friction drag is higher.
The unfortunate thing is that the "laminar boundary layer" will automatically become turbulent (with associated higher drag) close to the leading edge of the airfoil unless very special precautions are taken. These precautions are:

A very smooth airfoil surface: Slight construction defects (or bugs as they stick to the airfoil leading edge) will change the laminar boundary layer into a turbulent one. Unless you have a perfect airfoil and keep it this way forget about the gain possible with a laminar flow!
A special shape of the airfoil: The pressure distribution on the airfoil is related to the airfoil shape. Today we can calculate (with high speed computers) airfoils which maximize the length of the laminar boundary layer. Still, what is mentioned in a) applies. But, do not get desperate. The friction drag of the airfoil with a laminar boundary layer is .08, whereas in turbulent flow it becomes .12. Sure, this is a 50% increase but only on the friction drag of the airfoil.

Lift force of airfoil
Lift depends on the density of the air, the square of the velocity, the air's viscosity and compressibility, the surface area over which the air flows, the shape of the body, and the body's inclination to the flow. In general, the dependence on body shape, inclination, air viscosity and compressibility is very complex.
One way to deal with complex dependencies is to characterize the dependence by a single variable. As for lift, this variable is called the lift coefficient, designated "Cy." The lift equation states that lift L is equal to the lift coefficient Cy times the density rho times half of the velocity V squared times the wing area A.

Lift force = 1/2· Cy·A·rho·v2

For given air conditions, shape and inclination of the object, we have to determine a value for Cy to determine the lift. For some simple flow conditions, geometries and low inclinations, aerodynamicists can determine the value of Cy mathematically. But, in general, this parameter is determined experimentally. The combination of terms "density times the square of the velocity divided by two" is called the dynamic pressure.

Actually, the coefficient Cy hides a mechanism of lift (also physics of aerodynamics), but this allows us to collect all the effects, simple and complex, into a single equation. The question, what kind of mechanisms convert the drag force into the lift one, still remains under discussion. More about that you can find in Weltner, Klaus and Ingelman-Sundberg, Martin paper "Physics of Flight".
Notes:
The amount of air diverted by a wing is proportional to the speed of the wing and the air density.
The vertical velocity of the diverted air is proportional to the speed of the wing and the angle of attack.
The lift is proportional to the amount of air diverted times the vertical velocity of the air.