The Bernoulli Ball

You may have seen beachballs balancing on vacuum cleaner exhaust hoses. You can make a smaller version by balancing a ping-pong ball on the stream of air from a blow dryer.

The toy we will make in this section uses the same principles as the beachball and the ping-pong ball. A small ball of balsa wood floats on a stream of air you blow through a bent tube. The ball has a small wire hook stuck through it. The object of the game is to hook the ball on a hoop attached to the tube.

The completed toy looks like this when made of clear plastic tubing:

The toy can be made of wood, with a large long hole drilled almost all the way through the length, and a smaller hole drilled near one end to meet the larger hole. In both versions, the idea is to make a tube that bends at a right angle, so the air coming from your mouth comes out vertically about six inches from your face.

The hoop is a loop of wire (I used brass because it looks nice) formed by bending the wire in half around a broomstick and then twisting the ends to form the handle of the loop. This handle is inserted into a hole drilled near the far end of the tube.

In the version shown in the photograph, I started with a clear plastic tube 1/2 inch in diameter. These can be found in hobby stores or hardware stores. I found mine in a specialty plastics store.

A smaller clear plastic tube about an inch high and 1/8 inch diameter is glued to the larger tube 1/2 inch from the end. It is glued over a hole drilled in the larger tube.

The far end of the tube is closed by a circle of plastic cut to fit the end of the tube and glued on.

The ball is made of balsa wood, but any lightweight material will do, such as a hollow plastic ball, or smooth styrofoam. It is a little bigger than half an inch in diameter, although the diameter is not critical.

A stiff wire hook is stuck through the ball, so that about an inch and a half sticks out the bottom, and an inch sticks out the top. After bending the top into a hook, it is about a half inch above the ball.

I made my hook out of stiff steel wire. It would be better to use something that doesn't rust, such as stainless steel, or brass. You can see the rust stains on the plastic tube in my version, caused by warm moist air.

To operate the toy, place the straight wire of the ball in the upright tube as shown in the first photograph. Take a very deep breath (you'll need all you can get). Blow through the open end of the large tube hard enough to raise the ball up to the level of the hoop.

The ball is now dancing around on top of the stream of air, and is very erratic. The trick is to control the height of the ball so when the hook is over the hoop, you can let the ball down gently, with the hook caught in the hoop. This is not easy, and usually takes several breaths. It is fun to watch the expressions on faces as people try to hook the loop on their last bit of air.

Why does it do that?

How can a ball balance on a stream of air? How can an airplane wing keep an airplane from falling? How can a sailboat sail into the wind? To explain these things, we have come up with elaborate physics and mathematical models such as the Navier-Stokes equations, and the Bernoulli principle.

These models use concepts such as pressure, velocity, density, and viscosity. They are not simple to explain or understand. However, all of the concepts used in these complicated models can be explained by thinking of interactions of molecules.

To explain what is happening with the balancing ball, it is useful to look at other, sometimes simpler experiments, and see what is going on there.

Some simple experiments

When you hold your hand out the window of a moving car, you can make the wind lift your hand by tilting your hand at an angle to the wind. Notice that the force you feel that lifts your hand seems to press on the bottom of your hand. If there is any force acting on the top of your hand trying to suck it upwards, it is definitely smaller than the force on the bottom of your hand pushing it upwards. [Try sucking on the back of your hand using your mouth. It is easy to detect even small amounts of suction. The amount needed to lift your hand would definitely be noticed.]

It is easy to picture the molecules of air hitting the bottom of your hand and lifting it up. It is also easy to determine that the air that is hitting your hand is bouncing off your hand and going downwards. You can hold your hand in such a way as to make the air bounce off your hand and hit your face. When you do this, your hand is pushed in a direction away from your face.

Whichever way your hand directs the air, the air pushes your hand in the opposite direction. The amount of force your hand feels depends on the amount of air that is pushed in the opposite direction. If you hold something larger than your hand out the window of the car, you will feel a larger force, since more air is being moved. The amount of force your hand feels also depends on the speed of the car. The faster the wind, the larger the force. Lastly, the density of the air affects the force you feel. If you put your hand in the water when you travel by boat, you feel a much larger force, even if the boat is going much slower than the car.

Lift and drag

Notice that you feel the largest lifting force on your hand when it is held at a 45 degree angle. This angle causes the wind to bounce off your hand straight down. But you also feel a force pushing your hand backwards, away from the direction of travel. This is because you are stopping the air molecules from travelling backward, and are making them go down instead. The backward force you feel is equal to the upward force.

The backward force (the force resisting forward motion) is called drag, and it is easy to see that we cannot get lift without drag. We cannot change the direction of the wind without feeling its resistance to change.

There is another type of drag that is important to understanding how the ball balances on the stream of air, or how airplanes fly, or how sailboats sail into the wind.

Let's look again at your hand moving through water. If your hand moves very slowly, it will not stir up the water very much behind it. If you move your hand more quickly, you will see little whirlpools form behind your hand. It takes force to cause all this water motion, and that force is felt as added resistance to the movement of your hand. If we could somehow streamline your hand to get the most movement of water in the direction we want, while causing the least stirring up of the water, we would have less drag for a given lift, and we would have a more efficient wing, or propeller, or sail.

Viscosity and drag

In water, we have to move very slowly to avoid causing whirlpools (also known as vortices). In air, we can move a little faster without stirring up the air in the same way (we can see this if we use smoke to make the vortices visible). In a jar of honey, we have to move very slowly. The difference is viscosity.

Viscosity is a property of fluids (like air or water). It is the ability of the fluid to resist changes in its shape that do not change its volume.

Viscosity is caused by interactions between the molecules of the fluid. It is the transfer of momentum from one part of the fluid to another part.

In a gas like air, viscosity is caused almost entirely by collisions between molecules. The faster the molecules are moving, the more effective is the transfer of momentum. In a hot gas, the molecules are moving faster than in a cold gas, so the viscosity is higher. A small part of viscosity in air is caused by attractive forces between molecules. These forces are much larger in water and honey, and play a bigger part there. These forces are called Van Der Waals forces. In air these forces are small enough to ignore when explaining lift and drag.

It is useful to compare the momentum forces in a fluid to the viscous forces. The ratio of the two is called the Reynolds number. It is defined as the density times the velocity times the length (width of your hand) all divided by the viscosity.

If the viscosity is low, like it is in air, or the speed is slow, then your hand does not transfer momemtum to very much air. Almost all of the momentum that is transfered goes into moving the air downwards, and very little goes into stirring it up. As the speed increases, or the viscosity increases, then more of the momentum is transfered to the air above, below, and behind your hand, and is wasted as extra drag.

Curved surfaces and the Coanda effect

If we limit the angle that the fluid has to turn as it passes the wing, then we can limit the rotation of the fluid. The fluid won't spin around as much if we don't kick it very much. If we put a cylinder in the water, we will see a lot of vortices created as it moves. If we shape it like a fish or a teardrop, where the trailing edge gradually tapers to a point, then the water does not have to turn as sharply, and so it does not spin as much, and smaller vortices are produced.

Now we can see why some wings are curved on the top. By gradually letting the air fill the empty space behind the wing, we limit the amount of spin we impart to the vortices. This limits the drag on the wing.

The tendency of a fluid to follow a curved surface is called the Coanda effect.

Notice what is happening in the following photograph of smoke pulses flowing over an airplane wing. The air slows down as it gets close to the wing. The Bernoulli principle says that this slower moving air will appear to the wing to have a higher pressure that faster moving air. What keeps this high pressure from pushing the wing down is the fact that it happens on the bottom of the wing as well, and is balanced.

Note also that the air does not speed up as it moves over the curved top of the wing, but it does slow down as it encounters the tilted bottom of the wing. We can measure the pressures on the top of the wing and on the bottom, and the difference is lift. We get the same value for lift whether we look at the mass of air moving downwards, or the pressure difference between the top of the wing and the bottom, because they are two different ways of looking at the same thing.

Notice that the viscosity of the fluid causes it to follow the shape of the wing. In a gas, the viscosity is the result of collisions between molecules. The molecules above the wing are constantly bumping into one another. As the wing sweeps away the molecules in front of it and pushes them downwards, it leaves an empty space behind it. The air above this empty space expands into it, due to the collisions of the molecules.

Picture the wing as having two springs attached to it, one pushing down on the top of the wing, and one pushing up on the bottom of the wing. If we move the wing down, we compress the bottom spring, and the top spring expands because we are no longer pushing on it as hard as we were before. The springs are the air molecules bouncing against the wing and each other. We are moving two masses of air in the downward direction. The air above the wing moves down as well as the air under the wing.

Before the wing moved the air, the air on the bottom was holding up the air on the top. In order to do this, there must have been a force pushing upwards. The wing moving through the air must not only accelerate the molecules in a downward direction, but it must overcome this upward force that is holding up the air above the wing. We can think of this upward force as helping to hold up the wing now instead of holding up the air above the wing. It thus adds to the lift on the wing. The air above the wing now falls into the empty space behind the wing. It also falls past the wing as the wing moves out of the way, and we can measure the amount of air that is moving down and see that it matches the lift on the wing as expected.

Back to why the ball balances...

We are now finally ready to see why the ball balances on the stream of air.

To balance, the ball must see a force that tends to center it on the air stream when it strays. From our discussion above, we would expect to see two things happen if this force exists. We would see air moving in the opposite direction of the ball's motion. We would also expect to see a higher pressure on the side of the ball opposite the air stream, and a lower pressure on the side facing the air stream.

Picture the air stream grazing the ball on the left side. The curve of the ball s fairly gentle, and causes the air to follow the curve. As the air follows the curve, it moves away from the stream of air. If the air is moving away from the stream of air, whatever caused it to move (the ball) must feel a force towards the stream of air.

This air on the left side is moving faster than the air on the right side (which isn't moving). As the air moves past the ball, it sweeps aside air molecules that were moving towards the ball, and would have hit the ball if they had not been moved aside. The pressure on that side of the ball is thus lower.

On the right side of the ball the air is not moving, so the pressure has not changed. The pressure on the left is lower than the pressure on the right, so the ball moves towards the stream of air.

No matter which direction the ball is deflected, it is attracted to the center of the air stream, and stays balanced.

The Bernoulli principle states that the pressure the ball sees on the side towards the moving air is less than on the side where the air is still. This is why we call the toy the "Bernoulli Ball'. Notice that what actually moves the ball is the recoil of lots more tiny air molecules on the right side of the ball than on the left. We could call the toy the "Newton Ball", but that lacks alliteration. Looking at it another way, we see air moving away from the stream of air as it follows the curve of the ball. So we could also call the toy the "Coanda Ball", although I prefer to think of the Coanda effect as the result of lift, not the cause.

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Send mail to Simon Quellen Field via sfield@scitoys.com

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