Every object on earth or in space can be classified as a solid, a liquid or a gas. Dynamics is the study of how these objects behave when there is a force (a push or a pull) acting on it.

Solid objects have well-behaved molecules and atoms. These molecules line up in an even pattern that gives the object a specific shape. A block of wood is a solid, so is a crystal of salt. The primary characteristic of a solid is that the shape stays fixed. If a round piece of wood is placed in a square container, its shape does not change to match the container. In dynamics, this is called a non-deformable body (no automatic shape changing). A secondary characteristic of a solid is that no matter how hard it is squeezed or pulled, the molecules do not move closer together or further apart. The object may break, but the molecules don't move. This is called an incompressible object.

The molecules in a liquid, however, are not so well-organized. An amount of fluid, when poured from a square container into a round one, will not retain its square shape. It will take the shape of the round container. A primary characterization of a liquid is that it will deform, or take the shape of its container. The liquid will not, however, expand to fill a larger space. It cannot be made smaller by squeezing or pulling. The molecules do not move closer or further apart. Liquid is incompressible.

Gases, like air, have even less-organized molecules. Gases not only will take the shape of their containers, but also will expand or contract to fill the container. When a person takes a breath of air, for example, the air rushes down the bronchial tubes and tries to fill all the spaces in the lungs. A big breath makes it easier to feel the lungs expand, but a small breath fills ALL of the lungs, too. A gas can be expanded or compressed. Another example is compressed air in a cylinder used by a diver. Another name for liquids and gases is "fluid". A fluid is deformable.

The study of dynamics, then, can be split into four specialties: Dynamics of solids, which will be discussed more in the structures chapter; how liquids behave (hydrodynamics); how air and other gases move (aerodynamics), and how high speed gases change (gas dynamics). Hydrodynamics, aerodynamics, and gas dynamics are all part of fluid dynamics, and each will be discussed in the next few pages.

Hydrodynamics is the study of how forces (pushes and pulls) affect liquids. Something, like a boat or submarine, may be in a liquid, like water. Liquids could also be moving through something like a pipe or hose, such as water or oil. Or they might be contained, like water behind a dam. In each case there are rules and laws for the behavior (actions, reactions) of the fluid or liquid. Engineers study and apply these rules and laws when they design boats, pipes, dams, or anything that uses a liquid.

The study of hydrodynamics is sometimes confused with aerodynamics, especially when people are designing boats. The behaviors, rules, and laws are very similar in both fields. That's why some design engineers call themselves aerodynamicists, even though they are working with liquids, rather than gases

How Air and other Gases Move - Aerodynamics

Aerodynamics is the study of forces acting on an object. These forces become active when an object moves through the air (or gases). It is important to understand these forces for the design of airplanes, sailboats, cars, and other objects moving quickly through the air. Buildings, bridges, and windmills are also affected by wind moving past them.

Most of the sections in this chapter are about the motions of air around objects, rather than other gases. When the motions and shape of an object are understood the aerodynamic forces can be figured. The flight possibilities of the object can, then, be discussed.

How High Speed Gases Change - Gas Dynamics

When air flows over an object at very high speeds, like over fighter aircraft, or goes through jet engines with very high temparatures, the normal rules of aerodynamics sometimes don't apply. For these special cases another area of study, gas dynamics, has been developed. Gas dynamics expands the rules and laws of aerodynamics to include high speed flows and high temperature flows.

Sometimes, if an aircraft flies so high up and so fast, even the rules of gas dynamics break down. At high altitudes the air molecules are very far apart. Also, the temperatures around the plane can be so high that they cause chemical reactions among the air molecules. This is often called the hypersonic region. Hypersonics is the study of the air motion in these conditions. The government is currently building a High Speed Civil Transport (HSCT) that would fly in this region!

Measurements

We know that an object moving through the air creates certain forces. We are most interested in aerodynamic forces sufficient to allow flight. Both the object and the forces created must be measured. We can measure mass, time, length, and temperature.

Units

Units are used to define measurements so that everyone knows exactly how much. Some examples of units are meter, foot, inch, centimeter or a mile. If a planner draws a bridge and says it is 1000 long and the builder looks at the plans and says it is one short, this is a problem! Are they talking about a meter, a foot or an inch?

So, units are very important! A measurement should always include 2 things: a number and a unit. Some examples everyone may know include things like: there are 20 minutes until recess; it takes 10 days to drive across the country; a desk top is 20 inches wide and 25 inches long; a recipe uses 2 cups of flour; it is 85 degrees outside today. Each of these measurements includes a number and a unit.

Mass

Everything, whether it is a solid, liquid, or a gas has mass. It is a measure of how much of the substance is there - how many molecules. Sometimes mass is expressed as weight, even though they are not the same. In the metric system, the units for mass are grams, kilograms (1000 grams) or milligrams (1/1000 grams). In the American unit (called the English system), the weight of the substance is used, in pounds or ounces. A pound is 16 ounces. Often abbreviations are used for the units: a gram is g, a kilogram is kg, a milligram is mg, a pound is lb. and an ounce is oz.

Time

The easiest way to think of time is how long it takes something to happen. It may take 10 minutes to drive to school; it may take an hour to eat dinner. The units for time are the same around the world: seconds, hours, days, years. In aerodynamics, a common time measurement is how long it takes an object to go from one point to another or from point A to point B.

Length

How long is it? How far is it? These are questions heard every day. Length is a quality used by many people to define an object. A pencil is 7 inches long. A student is 4 feet tall. A swimming pool is 2 meters deep. The most common units for the metric system are a centimeter, a meter (100 centimeters) and a kilometer (1000 meters). In the English system, that most Americans use, common units are the inch, a foot (12 inches), or a mile (5280 feet). These units may be abbreviated: centimeter as cm, meter as m, kilometer as km, inch as in, foot or feet as ft, and a mile as mi.

In addition to the length of an object, it is often useful to know the area or volume of the object in question. The area is how much room is on a surface like the floor of the classroom or the surface of a wing. Area is found by multiplying one length by another length. The result is called "square units". For example, if a room was 20 feet by 25 feet long you would multiply 20 X 25 = 500 square feet. Many common measurements in science and engineering include square feet or square meters. Another common measurement is an acre, 40,000 square feet.

The volume of an object can either be how much space is available inside an object, like a fuel tank or how much actual material is inside a specific place. Volume has three measurements, length, height and width (all of these can be called lengths). Multiplying these together equal volume. The result is cubed. For example, a 12 inch long section of a 2 by 4 board (2 X 4 X 12 inches) would have a volume of 96 cubic inches. Cubic feet, cubic meters, gallons, liters, and cubic centimeters (cc for short) are all common units for volume.

Temperature

The quality of temperature is a measure of how hot or cold something is. A thermometer is commonly used to determine the temperature of an object. Everything has a tempertature - the rocks, trees, people, air. The weather report in the newspaper usually gives the high and low temperatures of the air each day. The common units

for temperature are degrees Fahrenheit or degrees Celsius (what used to be Centigrade). In America, almost everyone uses the Fahrenheit scale. In science and engineering, however, temperatures can be reported using either scale. The way this is shown is either 85° F or 85° C.

Properties

The aerodynamic forces for flight occur in a fluid. The fluid is usually either air or water, although there are other fluids. Before flight can occur the fluid must be measured to understand the forces generated by a moving object. In the Measurements section, units were introduced to help understand the qualities of a fluid. In this section, these qualities, or properties, of a fluid are defined. The units (inches, pounds, grams, meters) will be used in the following definitions. In addition, several other factors (facts or parts) are defined to help further understanding of aerodynamics. These include weight and gravity, velocity and acceleration.

Temperature

The temperature of the fluid is an important part of how the fluid behaves. Hot oil, for example, flows faster than cold oil. Warm air rises and cold air drops in a room; house designers often place heat vents at the floor level because of this. Very cold water is lighter than cool water, so it rises to the top of a lake. That's why lakes freeze from the surface down. Sound travels farther on cold days than hot days. It is crucial (important) then, to know the temperature of the fluid when computing aerodynamic quantities. As mentioned in the Measurements section, temperature has units of degrees Fahrenheit or degrees Celsius.

Pressure

The pressure of a fluid is another important consideration in aerodynamic forces. When a fluid moves over or through an object, it gives small pushes on the surface of the object. These pushes, over the entire surface, are defined as pressure. Pressure is measured as force per unit area (square inches, square meters). In metric units, pressure is measured in Newtons per square meter. In the English system, pressure is usually measured in pounds per square inch. Example: The atmosphere (air) presses on your skin at 14.7 pounds per square inch (psi).

Pressure can be powerful. A small pressure, spread over a very large area, can add up to be a very large force. Air pressure decreases as the altitude increases; pressure also decreases when the speed of the fluid (air, water) increases. When the temperature of a fluid increases, so does the pressure. The pressures on an airplane directly affects its flight capabilities!

Density

Density is a measure of how much mass (the amount of molecules) is included in a given object or volume. Another way to think about it is how tightly the molecules are packed in a volume or object. When we talk about the density of fluid (volume), we

often refer to a specific volume, such as a cubic meter, a cubic foot or a slug. A slug is equal to 32.174 pounds mass.

A fluid with a lot of molecules tightly packed together has a high density; one that has fewer molecules would have a lower density. Water, for example, has a much higher density than air. A 10 gallon fish tank with water in it has much more mass in it than a 10 gallon tank with air in it. Since it has more mass, it will weigh more (more on that in a later section.) In addition, the density is used to define whether a fluid is incompressible or compressible. If the density of the fluid is fixed (constant), the fluid is incompressible; neither the mass or the volume can change. Water is an incompressible fluid. The amount of volume and mass will stay the same, even under pressure.

Gases (like air), are compressible, they will expand to fill a new volume. The mass doesn't change, but the volume increases, so the density of the gas decreases in the new volume.

An aerodynamicist must pay attention to all of the properties of a fluid (air, water) to define flow conditions. This is because all of the properties are linked together. If the pressure or the temperature of a fluid changes, its density will usually change, too. The density of air on a hot day is lower than the density of air on a cold day. At high altitudes, where the pressure is lower, the density is also lower.

Viscosity

This is one of the most difficult properties on this list to define. Viscosity is a measure of how much a fluid will resist flowing. If you spill water on an inclined board, it will run quickly down the board. However, if you spill honey on the same board, it will travel down the board much more slowly. Honey has a much higher viscosity than water. It is said that honey is a more viscous fluid than water.

When a fluid flows over a surface, it exerts a force (measured in Newtons, for example) on it. Scientists and engineers define viscosity by using units of mass/length/time. The more commonly used units are kilogram per meter second (kg/m s) for the metric system, and pounds mass per foot second (lbm/ft s) in the English system.

The resistance to flow (viscosity) is important information when designing an object (like a wing or boat hull) to move through air or water. Several math formulas are used to get the viscosity reading needed to design surfaces that will reduce aerodynamic drag.

Force

Forces have been defined as pushes or pulls on an object. To determine the units of force, scientists and engineers use Newton's second law of motion. The second law states that a force on a moving object is equal to the mass of the object times the acceleration (a measure of its motion) of the object. Various mathematical formulas are used to measure force.

An interesting point about the force is that in addition to a value and units, it also has a direction associated with it. In the figure above, the force is applied to the box to the right, therefore the motion is to the right. If the force were applied down on the top of the box, no motion would occur; since the box is already on the ground, it can't move any further. No matter how large the force was, there would be no motion. So, defining a direction for a force is very important.

Weight and Gravity

In other countries, objects are measured in terms of their mass, in grams or kilograms. In the United States, however, people use the terms for weight to also mean mass. This works okay near the earth's surface because gravity is constant, so the units of "weight and mass" stay the same. (the acceleration due to gravity is equal to 32.174 feet per second, at sea level) Because of gravity, weight is actually a force and not the true mass of an object. If an object is taken up high in the atmosphere, the force of gravity is less. Therefore, the "force" of weight is less. An object will weigh less, at high altitude, but the mass will remain the same.

Scientists must be able to separate weight and mass. Therefore, the units are: pounds mass or pounds force. Mass will not change. Pounds force will change with altitude. Acceleration of an object at high altitudes is less, due to gravity, therefore the weight of the object is less.

This is why an object on the moon weighs less than the same object on the earth. The gravitational attraction on the moon is less than that of earth, so the acceleration due to gravity is less (about 1/6th that of the earth). When an object is weighed on the moon, it will weigh about 1/6th as much as the same object on earth. Example: A 60 pound child would weigh 10 pounds on the moon!

Velocity

How fast an object moves is measured by its velocity. Velocity is calculated by dividing the distance traveled (a length) by the time it takes to travel the distance. The units of velocity are, for example, meters per second (m/s) or feet per minute (ft/min). If a person runs 10 kilometers in 1 hour, his or her velocity is 10 kilometers per hour (km/hr). If a car travels from Los Angeles, CA, to San Diego, CA , a distance of 120 miles, in 2 hours, its velocity is 60 miles per hour (mph)(120/2hrs=60 mph). One exception to these units is a term held over from sailing days, the knot. In aeronautics, the velocity of the air is often measured in knots. One knot is equal to about 1.7 feet per second (ft/s).

Rate and speed are two of the many terms used interchangeably with velocity. When engineers work with velocities, they must know the direction of the motion as well as the numerical value. They will sometimes call the numerical value the rate or speed, and then define a direction: the box was moved at a rate of 3 ft/s to the right, or the rocket traveled upwards at a speed of 120 m/s.

Acceleration

Acceleration is a measure of how the velocity of an object is changing over time. It can be found by computing the difference in velocities at first one time, then some time later, and dividing that by the difference in time. Example: A car is traveling at 60 mph at the first mile post. One mile (and one minute) later the car is traveling at 70 mph. 70 - 60=10 divided by 1/60 hr. = 600 mph (if acceleration continued at the same rate for the next 59 minutes).

Different Ways Air Moves

The following terms and definitions are used by aerodynamicists to define the way a fluid moves in or around an object. In order to get a good picture of what is happening about a wing, for example, the aerodynamicist must know the velocity of the plane, the altitude of the plane, the size and shape of the wing, and the properties of the air. He or she will use the terms and concepts discussed in this list to define fluid flow.

Speed of Sound

If a person is standing very far from an explosion, he or she will not hear it right away. It takes time for the sound waves to travel. This is because sound travels in invisible waves of changing pressure through a fluid (usually air, but sometimes liquid). A person standing closer to the explosion will hear it sooner. At sea level, on a typical day (not too hot, not too cold), the speed of sound (how fast the sound waves travel) is about 760 miles per hour (mph).

The speed of sound depends on the pressure and density of the fluid in question. Since the pressure and the density can change with temperature or altitude, the aerodynamicist must compute the speed of sound at the altitude, pressure, and density where the plane is flying. This means the speed of sound could be more or less than 760 mph under different conditions.

Mach Number

The numbers Mach 1, Mach 2, Mach 3...etc. are used to show the pilot's speed in comparison to the speed of sound. Mach 2 is two times the speed of sound, for example. Remember, the speed of sound can change according to conditions in the atmosphere. An airplane at a low altitude flying at Mach 0.8 will have the same airflow behavior over the wing as the same airplane flying at a high altitude at Mach 0.8. The speed of sound decreases as the altitude increases, so in order for the airplane at the higher altitude to be flying at Mach 0.8, its velocity will be slower than that of the plane flying at the lower altitude! The behavior of airflow over the wing, however, will be the same on both planes.

The Mach number is named for Ernst Mach (1838 -1916), who conducted the first meaningful experiments in supersonic flight at the University of Prague, Germany.

Air flow, over a wing, changes around Mach 1.0. Different mathematical procedures are used to compute flow behavior. Air flow under Mach 1.0 is called subsonic flow. Air flow over Mach 1.0 is called supersonic flow. If the Mach number is greater than 5.0, that regime (pattern) is called hypersonic flow. However, an airplane traveling between Mach 0.75 and Mach 1.20 will have surface areas that are experiencing both

subsonic and supersonic airflow; aerodynamicists have named it the transonic regime. Airflow calculations must be done carefully in this area.

It is interesting to see what happens to air flow regimes (patterns) as an airplane approaches Mach 1.0. At subsonic speeds the waves of changing pressure about the plane travel out in all directions at the speed of sound for that altitude.

As the plane flies faster and approaches the transonic regime (still below Mach 1.0), the waves in front of the plane don't travel that much faster than the plane itself.

At the sonic barrier, Mach = 1.0, the front of the sound waves and the plane are traveling at the same speed.

As the plane flies faster than the speed of sound (Mach number greater than 1.0), the waves compress into a cone-shaped envelope around the plane. the flow conditions of the air ahead of the plane remain unchanged until the plane flies past. Only the region inside the cone is affected by the plane. This conical compression is called a shock wave, and it will be discussed in greater detail in a later section.

Friction

Anything that moves against another object causes friction or resistance to motion between the two objects. If a person tries to push a box across the floor, he or she must push hard to overcome the resistance. If the person applies a push, or force that is stronger (larger) than the frictional force, the box will move. If the push isn't strong enough the box won't move.

The friction between two moving objects can be affected by the surfaces of the objects. For example, it is easier to push a heavy box across a smooth wood floor, or a sheet of ice, than it is to push it across thick, bumpy carpet. That means the frictional force between the box and the smooth floor or ice sheet is less than the frictional force between the box and the thick carpet, so it takes less of a push to get it moving.

When a fluid like air flows across a surface such as a wing, there is friction resisting the motion. How much friction is dependent on two factors, the viscosity of the fluid and the smoothness of the surface. A very viscous fluid like honey (a fluid with high viscosity) will resist flowing, even down a smooth surface. The friction force is very strong at the surface. Af fluid like water with much lower viscosity will travel much faster down a smooth surface; the frictional force between the water and the surface is much smaller. However, if water flows across a very rough surface, like carpet, it will travel down more slowly than on the smooth surface. Because the surface is rougher, the friction force is stronger, the velocity is slower.

Boundary Layer

Because of this friction force, when a fluid flows over a surface, an interesting pattern develops. The fluid actually stops; there is no velocity or movement at the surface. A new layer develops on top of the stopped flow. There is less friction on this new surface so there is some movement of the flow. New layers develop, each with less friction, until some distance away from the original surface, there is no effect of the

slowed flow, and the remaining layers of the fluid travel at the original velocity. The distance from the original surface to the layer of the flow traveling at the original velocity is called the boundary layer thickness.

In general, the boundary layer gets thicker as the flow moves along the surface. How fast and how big the boundary layer grows is a function of the smoothness of the surface, the shape of the surface, and how fast the flow is travelling.

Laminar Boundary Layer

For lower velocities, fluid flowing over a smooth surface that is relatively short and flat will only devleop a very thin boundary layer. The flow inside the boundary layer will be smooth and orderly, meaning that the layers will basically stay in layers, without mixing. This condition is called laminar boundary layer.

Unfortunately, nature tends towards disorder, so it is rare to be able to maintain a laminar boundary layer for very long.

Turbulent Boundary Layer

As a fluid moves over a long, relatively flat surface, the boundary layer will get thicker, and the layers will start to mix and swirl around each other.. This swirling, rolling layer is called a turbulent boundary layer. The mixing and swirling is called trubulence; if the swirling is regular and repeatable, it is called a vortex or an eddy.

Since most of the boundary layers over an airplane will be turbulent, aerodynamicist will try to design the surfaces to minimize the amount of turbulence or disorder.

Transition

The region in the boundary layer where the orderly laminar layers start to mix together, but before they really start swirling, is called the transition region. Most of the time it is a fairly small region. The aerodynamicist will design the surface to keep the turbulent region small.

Flow Separation

Sometimes a boundary layer will be forced to move away from the surface. When this happens the flow inside the boundary layer gets so mixed up it starts to circulate and flow back towards the front of the surface! The outside, original fluid will move over a large bubble created by the circulating layer. This is called flow separation. The front of the bubble, where the outside fluid turns sharply away from the surface, is called the point of separation; the back of the bubble, where the outside fluid turns back to follow the surface again, is called the point of reattachment. If the region of flow separation extends past the surface, this region is called a wake.

Pilots and engineers usually don't like it when the flow separates on a wing. This is a condition known as stall. When a wing stalls, the lift (a force that helps a plane to fly; see later section) decreases sharply. The plane loses altitude, and if the stall is not corrected, the plane will crash. To land a plane however, a pilot will wait until the

plane is close to the ground, then initate a slight, controlled stall to gently drop the plane to the runway.

Buoyancy

Buoyancy is a force that is directed upward, or opposite of weight (which is considered a downward force). There is always buoyancy in a fluid. The fluid may be moving or stationary. The Greek scientist Archimedes (287 - 212 B.C.) deduced that the buoyancy force was equal to the weight of the fluid displaced by the body.

If an object, dropped in water, weighs less than the water displaced (pushed away) then it will float; if it weighs more then it will sink.

The density of liquids is much higher than for gases, like air. Therefore the buoyancy force of a liquid is much higher than in a gas. Naval architects and ship designers must use the buoyancy forces in their calculations. The buoyancy forces for airplanes are so small that they are usually ignored (not used). Hot air balloons and blimps do use the buoyancy force to get afloat, but they displace such an extremely large volume of air that the computed buoyancy force exceeds their weight so that they can fly.

Streamlines and Flow Patterns

Aerodynamicists and other engineers like to know where the flow is going. A streamline traces out the path of an element or piece of fluid as it travels in space and time around or through an object. Streamlines are computed mathematically from the velocities in the flow region. Streamlines are usually plotted as smooth lines, and they sometimes have arrows on them to show the direction of the flow. They can be used to show how the air travels around an airfoil (the cross-section or slice of a wing), with some of the air flowing over the top of the airfoil, and the rest flowing below the airfoil. In a previous section, for example, streamlines were used to show how flow separation appears on a wing.

Shocks

As discussed in the Mach number section, when a plane flies faster than the speed of sound, a shock wave is created. This is the conical-shaped enveleope formed around the plane as it flies at supersonic speed. When a shock wave is formed, fluid properties such as pressure, density, temperature, and velocity change drastically and instantaneously through a shock wave.

Theoretically, once a shock wave is formed it will travel on to infinity. In nature, however, atmospheric winds cause the shock to weaken and disperse. When an aircraft flying at supersonic speeds is at a high altitude, the shock wave is diffused (scattered) long before it reaches the earth's surface. If a plane, flying at supersonic speed, flies too close to the ground, however, the shock will hit the earth's surface. It will be heard and felt by observers on the ground (it's called a sonic boom). If the shock is strong enough, it will cause buildings to shake and windows to break!

The space shuttle has a shock wave around it as it returns to earth through the atmosphere. There is a section of southwestern Georgia that is along the flight path of

the returning shuttle when it lands at Cape Canaveral. when the shuttle travels along this path, it is still slightly supersonic, and it is close enough that the people on the ground hear the sonic boom as it travels over head. The shuttle can't be seen, but it can be heard! Before the shuttle flies low enough for the shock wave to cause any damage, however, it has dropped its speed below Mach 1.0 and the shock is gone.

In the early days of flight, the aerodynamics of transonic and supersonic flight were not well understood. As pilots went faster and approached the sonic region (called the sound barrier, back then) their airplanes would begin to shake and even fall apart! Some people were sure that there was an invisible barrier and that humans were not intended to go faster than the speed of sound.

In the late 1940's, designers started to understand high speed aerodynamics and began to design aircraft to fly in the supersonic regime. On October 14, 1947, Captain Charles Yeager, flying the experimental aircraft Bell XS-1, flew the first successful supersonic flight. Today many pilots regularly fly faster than the speed of sound.

Perfect Gas Law

The perfect gas law establishes the relationship between the pressure, density, and temperature of a gas at any instant in time or space. Air is treated as a perfect gas, even though it is a mixture of gases; it is mostly nitrogen. Engineers regularly use the perfect gas law to compute air flow properties.

Bernoulli's Theorem

Daniel Bernoulli (1700 -1782) was the first to develop a mathematical formula and theory that showed the relationship between fluid velocity and pressure: when the velocity in the flow increases, the pressure decreases, and when the velocity decreases, the pressure increases. This was an important discovery. As more people began to experiment with flying they were able to use Bernoulli's theorem to design airfoils. The theorum shows how lift is created when an airstream goes over a wing. This was the vital information needed to make flight possible.

Forces in Flight

The flight of an airplane, a bird, or any other object involves four forces that may be measured and compared: lift, drag, thrust, and weight. As can be seen in the figure below for straight and level flight, these four forces are distributed with the 1) lift force pointing upward; 2) weight pushing downward; 3) thrust pointing forward in the direction of flight; 4) and the drag force opposing the thrust. In order for the plane to fly, the lift force must be greater than or equal to the weight. The thrust force must be greater than or equal to the drag force. The terms and concepts that were defined earlier in this chapter can now be used to compute each of these forces.

Direction of Forces in Straight and Level Flight

Weight

The weight of the aircraft, as discussed earlier in the chapter, is a measure of a natural force that pulls the plane down towards the earth (gravity). Therefore, the direction assigned to the weight is downward.

Lift

The force that pushes an object up against the weight is lift. On an airplane or a bird, the lift is created by the movement of the air around the wings (the lift created by the body or tail is small). The figure below shows two streamlines about a typical airfoil (or wing); one travels over the top of the airfoil, the other moves underneath it.

If two particles were released from the same point at the same time, one on each streamline, they would start out moving together. As they approach the front of the airfoil, however, their velocity will start to change. Due to the shape of the airfoil, the air moves faster over the top of the airfoil than it does on the lower surface. The faster air leads to a lower pressure (from Bernoulli's Law) on the upper surface.

A smaller force, on top, will be pointed downward, and a larger force (underneath) will be pointing upwards. When the two forces are combined, the net force is lift, which is directed upwards.

The shape of the airfoil (wing) is a very important part of lift, and airplane designers design these shapes very carefully. Most airfoils today have camber, meaning they have curved upper surfaces and flatter lower surfaces. These airfoils generate lift even when the flow is horizontal (flat). The Wright brothers used symmetric airfoils to build the wings on their airplane. Since the upper and lower surfaces were the same, the particles on the streamlines above and below the symmetric airfoil move at the exact same velocity. The pressures on either surface (top or bottom) are exactly the same, so the net combined force on the airfoil is zero! No lift is generated by a symmetric airfoil in horizontal flow (flat wings moving straight ahead cannot fly). How, then, did the Wright brothers get their airplane off the ground?

In order to generate lift with a symmetric airfoil, the airfoil must be turned (tilted) with respect to the flow, so that the upper surface is "lengthened" and the lower surface is "shortened".

This "tilting against the airflow" is called angle of attack. It can be used for either cambered or symmetric wings. This is why an airplane rotates slightly at takeoff; the pilot is increasing the angle of attack to generate more lift. If the angle of attack is

doubled, the lift doubles. There is a limit to how much lift can be generated, however. The angle of attack can be increased to a point where the net lift force drops drastically.

Airflow deflection is another way to explain lift. To understand the deflection of air by an airfoil let's apply Newton's Third Law of Motion. The airfoil deflects the air going over the upper surface downward as it leaves the trailing edge of the wing. According to Newton's Third Law, for every action there is an equal, but opposite reaction. Therefore, if the airfoil deflects the air down, the resulting opposite reaction is an upward push. Deflection is an important source of lift. Planes with flat wings, rather than cambered, or curved wings must tilt their wings to get deflection.

Another way to increase lift on a wing is to extend the flaps downward. This again lengthens the upper surface and shortens the lower surface to generate more lift.

The velocity of the freestream air (actually of the airplane) is the most important element in producing lift. If the velocity of the ariplane is increased, the lift will increase dramatically. If the velocity is doubled, the lift will be four times as large.

The generation of lift can be found elsewhere. Race car designers use airfoil-like surfaces to generate negative lift, or downward-directed force. This force, combined with the weight of the race car, helps the driver maintain stability in the high-speed turns on the race track.

Thrust

Any force pushing an airplane (or bird) forward is called thrust. Thrust is generated by the engines of the airplane (or by the flapping of a bird's wings). The engines push fast moving air out behind the plane, by either propeller or jet. The fast moving air causes the plane to move forward.

Drag

The drag is the fourth of the major forces for flight. It is a resistance force. This force works to slow the forward motion of an object, including planes. There are four types of drag: friction drag, form drag, induced drag and wave drag. These drag types develop around the shape of the body, the smoothness of the surfaces, and the velocity of the plane. All four sum together for the total drag force. The drag forces are the opposite of thrust. If the thrust force is greater than the drag force, the plane goes forward, but if the drag force exceeds the thrust, the plane will slow down and stop.

The friction drag is sometimes also called the skin friction drag. It is the friction force at the surfaces of the plane caused by the movement of air over the whole plane. If a

person were to look at the furface of a wing, for example, he or she would see that all the sheets of metal join smoothly, and even the rivets are rounded over and are as flush with the surface as possible. This helps keep the friction drag at a minimum.

The form drag, or pressure drag as it is sometimes called, is directly related to the shape of the body of the airplane. A smooth, streamlined shape will generate less form drag than a blunted or flat body.

Any object that moves through a fluid (water/air) can get a decrease in form drag by streamlining. Automobiles are streamlined, which translates (allows) better gas mileage; there is less drag so less fuel is required to "push" the car forward. Buses, vans, and large trucks are less streamline, and this one reason why they use more fuel than smaller, streamlined cars (weight is another reason).

Form drag is easy to demonstrate using a hand out the window of a moving car. If the hand is held flat, like a wing, it is a streamlined object. The person only feels a small tug or drag. If he or she turns the hand so that the palm is facing forward, the drag force is greatly increased, and the hand is pulled backwards! It is no longer streamlined. There are two additional drag forces, the induced drag and wave drag.

Induced drag is sometimes called the drag due to lift. As the lift force is generated along a wing, a small amount of excess (lift) force can be generated in the opposite direction. This force acts like drag and slows the forward motion of the airplane. Aircraft designers try to design wings that lower induced drag.

The last of the four types of drag is the wave drag. This generally only happens when the airplane is flying faster than the speed of sound. Wave drag is caused by the interactions of the shock waves over the surfaces and the pressure losses due to the shocks. Wave drag can also occur at transonic speeds, where the velocity of the air is already supersonic, locally. Since most commercial jets today fly at transonic speeds, wave drag is an important part of the total drag.

Summary

Every pilot knows and uses these four basic forces of flight. Aerobatic pilots are constantly balancing these forces to design amazing stunts to delight the crowds watching them. They will deliberately stall the wings of the airplane to cause the plane to lose lift and drop suddenly. They very carefully fly upside down, balancing the new lift force with the weight of the plane. They will point the airplane straught up into the air and fly staight up as far as they can, let the plane hang there for a second, then let it fall back down its original path. After a few heartbreaking seconds, the pilot will turn the airplane back so the nose points downward into the direction of the air flow to again regain level flight. These stunts are possible because the pilots carefully balance the forces of weight, lift, drag and thrust.

When an object is immersed in water, it feels lighter. In a cylinder filled with water, the action of inserting a mass in the liquid causes it to displace upward. In 212 B.C., the Greek scientist Archimedes discovered the following principle: an

object is immersed in a fluid is buoyed up by a force equal to the weight of the fluid displaced by the object. This became known as Archimede's principle. The weight of the displaced fluid can be found mathematically. The

fluid displaced has a weight W = mg. The mass can now be expressed in terms of the density and its volume, m = pV. Hence, W = pVg.

It is important to note that the buoyant force does not depend on the weight or shape of the submerged object, only on the weight of the displaced fluid.

Archimede's principle applies to object of all densities. If the density of the object is greater than that of the fluid, the object will sink. If the density of the object is equal to that of the fluid, the object will neither sink or float. If the density of the

object is less than that of the fluid, the object will float.

A light ray is a stream of light with the smallest possible cross-sectional area. (Rays are theoretical constructs.) The incident ray is defined as a ray approaching a surface. The

point of incidence is where the incident ray strikes a surface. The normal is a construction line drawn perpendicular to the surface at the point of incidence. The

reflected ray is the portion of the incident ray that leaves the surface at the point of incidence. The angle of incidence is the angle between the incident ray and the

normal. The angle of reflection is the angle between the normal and the reflected ray.

The Laws of reflection:

   - The angle of incidence is equal to the angle of reflection   - The incident ray, the normal, and the reflected ray are coplanar

Specular reflection (regular reflection) occurs when incident parallel rays are also reflected parallel from a smooth surface. If the surface is rough (on a microscopic level),

parallel incident rays are no longer parallel when reflected. This results in diffuse reflection (irregular reflection). The laws of reflection apply to diffuse reflection. The

irregular surface can be considered to be made up of a large number of small planar reflecting surfaces positioned at slightly different angles. Indirect (or diffuse) lighting

produces soft shadows. It produces less eye strain than harsher, direct lighting.

The applet below illustrates how reflection and refraction takes place in common substances such as water, vacuum, air, glass, and even diamond.

When a source generating waves moves relative to an observer, or when an observer moves relative to a source, there is an apparent shift in frequency. If the distance between the observer and the

source is increasing, the frequency apparently decreases, whereas the frequency apparently increases if the distance between the observer and the source is decreasing. This relationship is

called Doppler Effect (or Doppler Shift) after Austrian Physicist Christian Johann Doppler (1803-1853).

The relationship describing the Doppler Shift for a moving source is given by:

f2 = f1v / (v ± vs)

where f2 is the apparent frequency, f1 is the actual frequency emitted by the source, v is the speed of sound in the medium, vs is the speed of the source through the medium (the negative sign is used if

the source is moving towards the observer).

The relationship describing the Doppler Shift for a moving observer is given by:

fo = fs(v ± vo) / v

where fo is the observed frequency, fs is the source frequency, v is the speed of sound, vo is the speed of the observer (it is taken to be negative if the observer is receding from the source).

The Doppler Effect explains the apparent change in pitch of a passing automobile. Of course, the frequency of the sound emitted by a source remains unchanged, and so does the velocity of the sound in the transmitting medium. A similar effect (Doppler Shift for light) can also be used to

determine the speed of a star relative to the earth. The red shift of the star's spectrum indicates that the distance between an observed star and the earth may be increasing. The Doppler Shift for light

describes a change in wavelength, not a change in frequency as with sound. Short range radar devices use the Doppler Shift principle. A change in frequency between emitted and returning pulses

can be used to find the relative speed.

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Bernoulli's Principle and Airplane Aerodynamics

A Critical Analysis

The aerodynamic lift on the wing of an airplane (airfoil) is generally explained by the argument that the faster speed of the air along the top of the wing leads to reduced air pressure there and hence produces a lift (Bernoulli's Law). Using this argument, one should also expect a lift for a symmetric wing profile as shown in Fig.1.

  Fig.1 However, if one considers the problem from a microscopic point of view, one comes to a different conclusion: upward and downward forces should exactly cancel for a

symmetric wing profile. This is easy to see if one simplifies the situation and replaces the curved wing surface by two plane sections (Fig.2)

  Fig.2 If the wing is stationary, the pressure on all parts of the wing is identical, i.e. there is no lift. If the wing is moving in the indicated direction and assuming an inviscid gas, the front half of the upper wing surface experiences an increased pressure because of the increased speed and number of air molecules hitting it (due to the orientation of the surface, this creates a downward force). On the other hand, the rear half experiences a reduced pressure because the of the reduced speed and number of air molecules hitting it (creating a lift) (for a more detailed theoretical analysis of this see the page regarding aerodynamic drag and lift). Overall, there is consequently no lift, but only an anti-clockwise torque. It is obvious that an overall lift is only achieved if the rear section of the wing has a larger area than the front section, i.e. one would get the maximum lift for the following profile (Fig.3)

  Fig.3 and wing profiles are actually asymmetric in this sense (see for instance http://www.zenithair.com/kit-data/ht-87-6.html).On the other hand, the reverse situation (Fig.4) should lead to a downward force, although Bernoulli's Law would again predict a lift.

  Fig.4 Note: the above arguments assume that the lower surface of the wing is always parallel to the velocity vector, i.e. the pressure acting on it is unchanged; by varying the 'angle of attack' of the wing the amount of lift can of course be changed arbitrarily and one could even generate a lift for the bottom image (Fig.4). In any case, it is clear that an airflow parallel to a surface can not transfer any momentum to it and therefore not exert any force on it. This invalidates Bernoulli's equation as an explanation for the aerodynamic lift. The enhanced airflow speed around certain sections of the wing is not the cause of the aerodynamic lift, but both the lift and the speed enhancement are separate consequences of the pressure changes at the different wing sections caused by the motion of the wing in the viscous air.In this way one has also to interpret the frequently given example of blowing over a

piece of paper. In fact, if one puts a sheet of paper flat on a table, fixes it to the edge of the table and blows over it from the edge, the paper will not lift by one millimeter, despite the motion of the air which according to Bernoulli's law should cause an underpressure.The apparent attraction that is observed when blowing between two sheets of paper can be either explained by the fact that the sheets are in fact not exactly parallel to the airflow but bend away from it (hence reducing the pressure on the surface), or by the circumstance that the airflow does not cover the whole width of the paper (which leads to the stationary molecules being pulled into the airstream by means of friction (viscosity), which again reduces the pressure because molecules are removed from between the sheets; one can verify this by just using two narrow (1cm wide) strips of paper; these show no attraction but tend to stay parallel).Either of these two mechanism should indeed be responsible for many of the phenomena attributed to Bernoulli's Principle. It should therefore be obvious that Bernoulli's law is only a viable physical explanation in cases where the viscosity of the medium is instrumental for the considered effect. Contrary to some scientific misconceptions, this is neither the case for the aerodynamic lift associated with airplanes nor for the drag of objects moving through a medium (see my separate page regarding aerodynamic drag and lift for a more detailed theoretical analysis of these issues). Note 1: it is frequently claimed by other critics of Bernoulli's law in this context, that Newton's law of action and reaction in connection with the observed 'downwash' of air near the wing is the explanation for the lift force acting on an airplane (see Ref. 1, Ref. 2). This view has to be rejected as well: this is not a problem of an action at a distance, but the only way a force can be exerted on a wing is by an increase of the number and speed of air molecules hitting the wing surface. Everything else, including the 'downwash', is merely a consequence of this, not the cause (some people argue that this cause/effect issue would be merely a semantic problem, but a) it is worrying if physicists don't care any more about the correct chain of cause and effect and b) the above examples show clearly that this can indeed be of practical relevance). Note 2: In contrast to the usual aerodynamic lift, the well known Magnus effect due to the rotation of objects does however not exist in an inviscid gas and can only be explained in terms of Bernoulli's principle:consider a rotating ball that is moving through an inviscid gas (i.e. molecules interacting with the ball but not with each other): if the surface of the ball would be mathematically smooth, then the rotation would actually be without any effect at all because the air molecules would just bounce off like for a non-rotating sphere, but even for a realistic rough surface (obviously a surface can not be smoother than about 1 atomic radius), the overall effect still cancels to zero: the pressure on the side rotating against the airstream is higher at the front but smaller at the back (and the other way around for the co-rotating side) so overall there is no resultant force on the ball but merely a torque that slows down the rotation.Hydrodynamics arguments (i.e. Bernoulli's principle) are therefore required to explain the Magnus effect but not for the aerodynamic lift.

Supersonics

Supersonics is the branch of aerodynamics that concerns

phenomena arising when the speed of an object exceeds the speed of sound. The speed of sound is represented by a so-called Mach number Ernst Mach, which is the speed of the object divided by the speed of sound in the same substance under the same conditions. Mach numbers represent actual flight conditions more accurately than distance per hour.

Photographic studies of artillery projectiles in flight show the atmospheric disturbances encountered in supersonic flight. At subsonic speeds, the only atmospheric disturbance is turbulence in the projectile's wake. As the speed passes M-1 (Mach number 1), shock waves arise from the nose and tail and spread from the projectile in a cone.

This research has led designers to make modern high speed airplanes with wings that are swept back to avoid the shock wave from the nose of the plane. Research has identified other factors, such as the shape of the projectile, the rate of gas flow, and atmospheric pressure, that influence the efficiency of the projectile's flight. Aircraft designers have also used wind tunnels to test airplane models and airplane parts in air currents at supersonic speeds.

Drag and Aerodynamics

The shape of an object drastically affects the degree to which air resistance, or drag, impedes the object's motion. For example, a sphere, top, and especially a square, bottom, both force the air to redirect itself, slowing the objects down. An

airfoil, middle, minimally disturbs the air as it travels, so the airfoil experiences little drag.

 

An object that is falling through the atmosphere is subjected to two external forces. The first force is the gravitational force, expressed as the weight of the object, and the second force is the aerodynamic drag of the object. The weight equation defines the weight W to be equal to the mass m of the object times the gravitational acceleration g:

W = m * g

the value of g is 9.8 meters per square second on the surface of the earth. The gravitational acceleration decreases with the square of the distance from the center of the earth. But for most practical problems in the atmosphere, we can assume this factor is constant. If the object were falling in a vacuum, this would be the only force acting on the object. But in the atmosphere, the motion of a falling object is opposed by the aerodynamic drag. The drag equation tells us that drag D is equal to a drag coefficient Cd times one half the air density r times the velocity V squared times a reference area A on which the drag coefficient is based:

D = Cd * .5 * r * V^2 * A

The motion of any moving object can be described by Newton's second law of motion, force F equals mass m times acceleration a:

F = m * a

We can do a little algebra and solve for the acceleration of the object in terms of the net external force and the mass of the object:

a = F / m

Weight and drag are forces which are vector quantities. The net external force is then equal to the difference of the weight and the drag forces:

F = W - D

The acceleration of the object then becomes:

a = (W - D) / m

The drag force depends on the square of the velocity. So as the body accelerates its velocity and the drag increase. It quickly reaches a point where the drag is exactly equal to the weight. When drag is equal to weight, there is no net external force on the object, and the acceleration becomes zero. The object then falls at a constant velocity as described by Newton's first law of motion. The constant velocity is called the terminal velocity.