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Dynamics of Flight

What is Air?

Air is a physical substance which has weight. It has molecules which are constantly moving. Air pressure is created by the molecules moving around. Moving air has a force that will lift kites and balloons up and down. Air is a mixture of different gases; oxygen, carbon dioxide and nitrogen. All things that fly need air. Air has power to push and pull on the birds, balloons, kites and planes.

In , Evagelista Torricelli discovered that air has weight. When experimenting with measuring mercury, he discovered that air put pressure on the mercury.

Francesco Lana used this discovery to begin to plan for an airship in the late s. He drew an airship on paper that used the idea that air has weight. The ship was a hollow sphere which would have the air taken out of it. Once the air was removed, the sphere would have less weight and would be able to float up into the air. Each of four spheres would be attached to a boat-like structure and then the whole machine would float. The actual design was never tried.

Hot air expands and spreads out and it becomes lighter than cool air. When a balloon is full of hot air it rises up because the hot air expands inside the balloon. When the hot air cools and is let out of the balloon the balloon comes back down.

How Wings Lift the Plane

Airplane wings are shaped to make air move faster over the top of the wing. When air moves faster, the pressure of the air decreases. So the pressure on the top of the wing is less than the pressure on the bottom of the wing. The difference in pressure creates a force on the wing that lifts the wing up into the air.

Here is a simple computer simulation that you can use to explore how wings make lift.

Laws of Motion

Sir Isaac Newton proposed three laws of motion in . These Laws of Motion help to explain how a planes flies.

1. If an object is not moving, it will not start moving by itself. If an object is moving, it will not stop or change direction unless something pushes it.

2. Objects will move farther and faster when they are pushed harder.

3. When an object is pushed in one direction, there is always a resistance of the same size in the opposite direction.

Forces of Flight

Four forces of flight

Lift - upward
Drag - backward
Weight - downward
Thrust - forward

Controlling the Flight of a Plane

How does a plane fly? Let's pretend that our arms are wings. If we place one wing down and one wing up we can use the roll to change the direction of the plane. We are helping to turn the plane by yawing toward one side. If we raise our nose, like a pilot can raise the nose of the plane, we are raising the pitch of the plane. All these dimensions together combine to control the flight of the plane. A pilot of a plane has special controls that can be used to fly the plane. There are levers and buttons that the pilot can push to change the yaw, pitch and roll of the plane.

To roll the plane to the right or left, the ailerons are raised on one wing and lowered on the other. The wing with the lowered aileron rises while the wing with the raised aileron drops.

Pitch makes a plane descend or climb. The pilot adjusts the elevators on the tail to make a plane descend or climb. Lowering the elevators caused the airplane's nose to drop, sending the plane into a down. Raising the elevators causes the airplane to climb.

Yaw is the turning of a plane. When the rudder is turned to one side, the airplane moves left or right. The airplane's nose is pointed in the same direction as the direction of the rudder. The rudder and the ailerons are used together to make a turn

How does a Pilot Control the Plane?

To control a plane a pilot uses several instruments...

The pilot controls the engine power using the throttle. Pushing the throttle increases power, and pulling it decreases power.

The ailerons raise and lower the wings. The pilot controls the roll of the plane by raising one aileron or the other with a control wheel. Turning the control wheel clockwise raises the right aileron and lowers the left aileron, which rolls the aircraft to the right.

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Picture of plane in roll

The rudder works to control the yaw of the plane. The pilot moves rudder left and right, with left and right pedals. Pressing the right rudder pedal moves the rudder to the right. This yaws the aircraft to the right. Used together, the rudder and the ailerons are used to turn the plane.

Picture of plane Yaw

The elevators which are on the tail section are used to control the pitch of the plane. A pilot uses a control wheel to raise and lower the elevators, by moving it forward to back ward. Lowering the elevators makes the plane nose go down and allows the plane to go down. By raising the elevators the pilot can make the plane go up.

Picture of Plane Pitch

The pilot of the plane pushes the top of the rudder pedals to use the brakes. The brakes are used when the plane is on the ground to slow down the plane and get ready for stopping it. The top of the left rudder controls the left brake and the top of the right pedal controls the right brake.

If you look at these motions together you can see that each type of motion helps control the direction and level of the plane when it is flying.

Sound Barrier

Sound is made up of molecules of air that move. They push together and gather together to form sound waves . Sound waves travel at the speed of about 750 mph at sea level. When a plane travels the speed of sound the air waves gather together and compress the air in front of the plane to keep it from moving forward. This compression causes a shockwave to form in front of the plane.

In order to travel faster than the speed of sound the plane needs to be able to break through the shock wave. When the airplane moves through the waves, it is makes the sound waves spread out and this creates a loud noise or sonic boom . The sonic boom is caused by a sudden change in the air pressure. When the plane travels faster than sound it is traveling at supersonic speed. A plane traveling at the speed of sound is traveling at Mach 1 or about 760 MPH. Mach 2 is twice the speed of sound.

Regimes of Flight

Sometimes called speeds of flight, each regime is a different level of flight speed.

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On a windy December morning in , two brothers from Dayton, Ohio, made history. In just 12 seconds, the dream of powered human flight became a reality.

Aeronautical science has advanced dramatically since the Wright brothers’ flight at Kitty Hawk. It’s tempting to assume we’ve solved the mysteries of flight.

But did you know that scientists still debate how a wing creates lift? There is yet to be a singular explanation for the force that keeps airplanes aloft.

In this article, we’ll explore how early aviators discovered the magic of lift. We’ll also find out why, despite decades of research, engineers still can’t agree on how wings do what they do.

Key Takeaways

• Bernoulli’s theorem describes how pressure differences on a wing create lift.
• Newton’s laws of motion describe how the downward deflection of air creates an upward lift force.
• Neither Newton’s laws nor Bernoulli’s theorem entirely explain how wings generate lift.

Inventing the Wing

You might wonder how the airplane wing came about, considering we don’t fully know how lift works.

Well, the short answer is that we copied the blueprint from nature.

In the early 19th century, British inventor Sir George Cayley translated the shape of a bird’s wing into the modern airfoil. An airfoil is a shape designed to create lift.

Cayley’s studies led him to discover the importance of camber. Camber is the curvature of a wing. Airfoils with a larger curve on top than the bottom have a positive camber. Symmetrical airfoils have the same curve above and below the chord line. The chord line is an imaginary line from the wing’s leading edge to its trailing edge.

Airfoil Camber

Cayley discovered that a wing with a positive camber created more lift than a symmetrical or flat wing. Cambered wings were also more resistant to stalling.

His investigations didn’t stop there. Cayley pinpointed the four forces of flight: lift, weight, thrust, and drag. He also wrote extensively on aircraft control and stability. Amazingly, Cayley did this about 100 years before the Wrights’ first powered flight. 

Many of Cayley’s insights hold up surprisingly well. In his paper “On Aerial Navigation,” he suggested that the upper camber “creates a slight vacuity.” In other words, the curved top of the wing creates a partial vacuum when air passes over it. This more than hints at one of the scientific theories of lift we’ll discuss later.

The Origins of Modern Aeronautics

The invention of the wind tunnel by Frank Wenham in was a turning point in our understanding of the physics of lift. A wind tunnel is a device that allows engineers to test an airfoil’s lift, drag, and pressure distribution. Finally, inventors could consistently test their wing designs.

The Wrights would put Wenham’s invention to good use 30 years later.

The Wind Tunnel: A Controlled Environment

During the - flying season, the Wright brothers struggled with their glider design. Their wing provided less lift than data from their late friend Otto Lilienthal said it would. 

So, in the autumn of , the Wrights built the second wind tunnel in the United States. Their wind tunnel was the key to their successful airfoils. And they didn’t even have to leave their bicycle shop to use it.

The Pressure Connection

George Cayley knew back in that air pressure was lower on the top of an airfoil than on the bottom.

The Wrights clearly understood the association between accelerated airflow on the top of the wing and lower pressure. They knew that the pressure difference between the top and bottom of the wing creates lift. But the Wrights never published any theories on why this might be.

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It turns out the explanation would come from an 18th-century Swiss mathematician.

Bernoulli’s Theorem

George Cayley and the Wright brothers never mentioned Daniel Bernoulli by name in their writings, but they indirectly echoed his discoveries.  

Bernoulli was born in into a family of mathematicians. Unsurprisingly, he became a mathematician as well. 

But at his father’s request, he also studied medicine. His exploration of blood pressure gave him insight into the physical properties of fluids.

Hydrodynamica

In his work Hydrodynamica, Bernoulli used the principle of conservation of energy to describe fluid dynamics.

Bernoulli’s theorem states that when the velocity of a fluid increases, the static pressure decreases, and vice versa. This relationship applies to any fluid in a streamline: liquid or gas.

Bernoulli never applied his theorem to the creation of lift in his lifetime. However, it explains what we see with airflow over a wing. 

The air on top of the wing moves faster, corresponding with an area of low pressure. The higher pressure under the wing pushes up toward the lower pressure over the wing. This pressure differential is the lift force.

Bernoulli’s theorem became a popular way to explain lift in the following decades. However, it fails to explain why the top of the wing accelerates the air in the first place. This confusion drove many incorrect explanations over the years.

Incorrect Applications of Bernoulli

One common misunderstanding of Bernoulli’s principle is the “equal transit-time” theory. 

The explanation goes something like this. 

When a parcel of air hits the airfoil’s leading edge, it “splits” in two. The curved top of the airfoil creates a longer path for air molecules to travel than the bottom. So, for the air molecules on the top to meet up with air molecules on the bottom at the trailing edge, they must go faster. This increase in velocity causes a decrease in pressure, creating lift.

While this argument is tempting, it doesn’t stand up to scrutiny.

First, there is no reason why the air on top must simultaneously meet back up with the air on the bottom. The molecules are not “bound” to each other in any way.

Second, the air on top accelerates to a faster speed than this explanation requires. A parcel of air above the wing reaches the trailing edge before its below-wing equivalent.

As it turns out, a cambered wing is not required for lift production. Symmetrical airfoils work just fine. 

Stranger still, even a flat plate generates lift.

Flying the Barn Door

There’s an old saying in aviation that goes, “with a big enough engine, you can fly a barn door.”

And as silly as it sounds, there’s some truth to that. As un-aerodynamic as a barn door is, it can produce lift.

But how?

One key aspect of lift generation is the wing’s angle of attack. The angle of attack is the angle between the chord line of the wing and the relative wind. The relative wind is the direction the wing “feels’ the air is coming from. For an airplane, the relative wind is always opposite the direction of travel.

As the angle of attack increases, the pressure difference between the top and bottom of the wing increases. This differential causes lift to increase. Up to a point, anyway.

Once the wing reaches the critical angle of attack, any further increase in angle causes the airflow to separate from the wing’s surface. At this point, the wing stalls, and lift is significantly reduced.

A flat-plate wing creates extremely turbulent airflow at a higher angle of attack. The wing stalls quickly. But at a very low angle of attack, a flat wing works much like an airfoil, just not very efficiently. (A smooth shape resists stalling.) Airflow splits in two, and the top side has a lower pressure than the bottom, creating lift.

If that’s hard to believe, try it for yourself using NASA’s interactive airfoil simulation.

Similarly, a symmetrical airfoil works just fine to create lift. At zero angle of attack, the top and bottom pressures are equal, so there is no lift. But when the angle of attack increases, we see similar pressure patterns as with positively cambered airfoils.

Symmetrical airfoils are perfect for aerobatic airplanes that frequently fly inverted. But cambered airfoils can fly upside down as well. This feat simply requires a higher angle of attack.

So, not only is camber unnecessary to generate lift, but its lift-enhancing effects can be “overpowered” by angle of attack.

If lift doesn’t require a curved airfoil, how do we explain what creates the low pressure on top of a wing?

Enter Newton.

Newton’s Laws of Motion

Isaac Newton’s masterwork Principia took the scientific world by storm. For the first time,  science could mathematically explain the physical motion of bodies. 

Newton’s second law of motion states that any time a mass is accelerated, it imposes a net force. By acceleration, we mean a change in the speed or direction of the mass.

Although we don’t often think of air as particularly “heavy,” it has mass. When an airfoil slices through the air, its shape and angle of attack cause the airflow to accelerate and deflect downward. This “downwash” follows the airfoil’s contour, imparting a downward force.

And here’s where Newton’s third law comes in. This law states that for every action, there is an equal and opposite reaction. That is the conservation of momentum. So, when the airfoil accelerates the air downwards, an equal and opposite force accelerates the airfoil upwards.

This upward force is another way to explain lift.

Newton’s laws are not in opposition to Bernoulli’s theorem. They both describe the same lift force through different means. In fact, you can derive Bernoulli’s theorem directly from Newton’s second law.

Describing Lift is not Explaining Lift

You may have guessed that this is where the explanation of lift takes a complicated turn. Neither Bernoulli’s theorem nor Newton’s laws explain why an airfoil creates lift in the first place. And neither directly explains why the airfoil turns the air downward. They only describe the manifestations of lift.

We can think of lift as a relationship between four elements: an increase in airflow speed over the wing, a decrease in pressure over the wing, an increase in pressure under the wing, and a downward turning of the airflow. 

The missing piece of the puzzle is what ties these elements together. 

How do we create a complete theory of lift? Unfortunately, there is no easy solution to this predicament.

A Unified Theory of Lift?

Do you plan on diving deeper into the origins of lift? Be ready to come face-to-face with several complicated theories and models. 

There are pressure and velocity fields around the airfoil to consider. Don’t forget the Navier-Stokes equations. And then there’s the impact of viscosity to study. 

The Coandă effect seems promising to explain why air follows the airfoil’s curve. However, its direct application to the explanation of lift is controversial.

The Kutta-Joukowski theorem describes circulatory airflow around an airfoil. It’s a common explanation for how lift starts on a wing. However, it only mathematically expresses the circulation. It doesn’t provide a physical cause.

Even in , scientists are still working on new theories of lift. But one singular, clear explanation of lift has yet to satisfy all the requirements.

We may be waiting quite a while for a Unified Theory of Lift.

Conclusion

Aeronautical science has come a long way since those primitive years of wooden wind tunnels and hand-plotted graphs.

Today, we can design aircraft with a level of precision early aviators only dreamed of. Modern aircraft are faster, more efficient, and safer than ever before. But even with our sophisticated computer models, we still cannot provide a universal explanation for lift.

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