Fluid Mechanics, Sound, and the Atmosphere

5-26 reduction is in accordance with Boyle’s law. The pressure of the mixed gases is equal to the sum of the partial pressures. This fact was discovered by Dalton, an English physicist, and is set forth in Dalton’s law: “A mixture of several gases which do not react chemically exerts a pressure equal to the sum of the pressures which the several gases would exert separately if each were allowed to occupy the entire space alone at the given temperature.”

Fluid Mechanics

By definition, a fluid is any substance that is able to flow if it is not in some way confined or restricted. Liquids and gases are both classified as fluids, and often act in a very similar way. One significant difference comes into play when a force is applied to these fluids. In this case, liquids tend to be incompressible and gases are highly compressible. Many of the principles that aviation is based on, such as the theory of lift on a wing and the force generated by a hydraulic system, can be explained and quantified by using the laws of fluid mechanics. Buoyancy A solid body submerged in a liquid or a gas weighs less than when weighed in free space. This is because of the upward force, called buoyant force, which any fluid exerts on a body submerged in it. An object will float if this upward force of the fluid is greater than the weight of the object. Objects denser than the fluid, even though they sink readily, appear to lose a part of their weight when submerged. A person can lift a larger weight under water than they can possibly lift in the air.

The following experiment is illustrated in Figure 5-38. The overflow can is filled to the spout with water. The heavy metal cube is first weighed in still air and weighs 10 lb. It is then weighed while completely submerged in the water and it weighs 3 lb. The difference between the two weights is the buoyant force of the water. As the cube is lowered into the overflow can, the water is caught in the catch bucket. The volume of water which overflows equals the volume of the cube. The volume of irregular shaped objects can also be measured by using this method. If this experiment is performed carefully, the weight of the water displaced by the metal cube exactly equals the buoyant force of the water, which the scale shows to be 7 lb.

Archimedes (287–212 B.C.) performed similar experiments. As a result, he discovered that the buoyant force which a fluid exerts upon a submerged body is equal to the weight of the fluid the body displaces. This statement is referred to as Archimedes’ principle. This principle applies to all fluids, gases as well as liquids. Just as water exerts a buoyant force on submerged objects, air exerts a buoyant force on objects submerged in it. The amount of buoyant force available to an object can be calculated by using the following formula: Buoyant Force = V olume of Object × Density of Fluid Displaced If the buoyant force is more than the object weighs, the object will float. If the buoyant force is less than the object weighs, the object will sink. For the object that sinks, its measurable weight will be less by the weight of the displaced fluid.

Example: A 10-ft3 object weighing 700 lb is placed in pure water. Will the object float? If the object sinks, what is its measurable weight in the submerged condition? If the object floats, how many cubic feet of its volume is below the water line? Buoyant Force = V olume of Object × Density of Fluid Displaced = 10 (62.4) = 624 lb The object will sink because the buoyant force is less than the object weighs. The difference between the buoyant force and the object’s weight will be its measurable weight, or 76 lb. Two good examples of buoyancy are a helium filled airship and a seaplane on floats. An airship is able to float in the atmosphere and a seaplane is able to float on water.

That means both have more buoyant force than weight. gross takeoff weight of 12,500 lb. At a minimum, the floats on this airplane must be large enough to displace a weight in water equal to the airplane’s weight. According to Title 14 of the Code of Federal Regulations (14 CFR) part 23, the floats must be 80 percent larger than the minimum needed to support the airplane. For this airplane, the necessary size of the floats would be calculated as follows: Divide the airplane weight by the density of water. 12,500 ÷ 62.4 = 200.3 ft3 Multiply this volume by 80%. 200.3 × 80% = 160.2 ft3 Add the two volumes together to get the total volume of the floats.

200.3 + 160.2 = 360.5 ft3 By looking at the Twin Otter in Figure 5-39, it is obvious that much of the volume of the floats is out of the water. This is accomplished by making sure the floats have at least 80 percent more volume than the minimum necessary. Some of the large Goodyear airships have a volume of 230,000 ft 3. Since the fluid they are submerged in is air, 5-27 0.11 cu' 10 lb 3 7 0.11 cu' Overflow can Catch bucket to find the buoyant force of the airship, the volume of the airship is multiplied by the density of air (.07651 lb⁄ft3). For this Goodyear airship, the buoyant force is 17,597 lb. Figure 5-40 shows an inside view of the Goodyear airship.

The forward and aft ballonets are air chambers within the airship. Through the air scoop, air can be pumped into the ballonets or evacuated from the ballonets in order to control the weight of the airship. Controlling the weight of the airship controls how much positive or negative lift it has. Although the airship is classified as a lighter-than-air aircraft, it is in fact flown in a condition slightly heavier than air. Fluid Pressure The pressure exerted on the bottom of a container by a liquid is determined by the height of the liquid and not by the shape of the container. This can be seen in Figure 5-41, where three different shapes and sizes of containers are full of colored water. Even though they are different shapes and have different volumes of liquid, each one has a height of 231 inches. Each one would exert a pressure on the bottom of 8.34 psi because of this height. The container on the left, with a surface area of 1 in 2, contains a volume of 231 in 3 (one gallon). One gallon of water weighs 8.34 lb, which is why the pressure on the bottom is 8.34 psi.

Still thinking about Figure 5-41, if the pressure was measured half way down, it would be half of 8.34, or 4.17 psi. In other words, the pressure is adjustable by varying the height of the column. Pressure based on the column height of a fluid is known as static pressure. With liquids, such as gasoline, it is sometimes referred to as a head of pressure. For example, if a carburetor needs to have 2 psi supplied to its inlet, or head of pressure, this could be accomplished by having the fuel tank positioned the appropriate number of inches higher than the carburetor. As identified in the previous paragraph, pressure due to the height of a fluid column is known as static pressure. When a fluid is in motion, and its velocity is converted to pressure, that pressure is known as ram. When ram pressure and static pressure are added together, the result is known as total pressure. In the inlet of a gas turbine engine, for example, total pressure is often measured to provide a signal to the fuel metering device or to provide a signal to a gauge on the flight deck.

Pascal’s Law The foundations of modern hydraulics and pneumatics were established in 1653 when Pascal discovered that pressure set up in a fluid acts equally in all directions. This pressure acts at right angles to containing surfaces. When the pressure in the fluid is caused solely by the fluid’s height, the pressure against the walls of the container is equal at any given level, but it is not equal if the pressure at the bottom is compared to the pressure half way down. The concept of the pressure set up in a fluid, and how it relates to the force acting on the fluid and the surface area through which it acts, is Pascal’s law.

In Figure 5-41, if a piston is placed at the top of the cylinder and an external force pushes down on the piston, additional pressure will be created in the liquid. If the additional pressure is 100 psi, this 100 psi will act equally and undiminished from the top of the cylinder all the way to the bottom. The 5-28 Nose cone support Suspension cables Light sign Neoprene cover Control surfaces Aft balloonet Air scoops Engines Passenger car Air valves Forward balloonet Each pressure gauge reads 8.34 psi Each container is filled with colored water to a height of 231 inches. 100 in2 150 in21 in2 gauge at the bottom will now read 108.34 psi, and if a gauge were positioned half way down the cylinder, it would read 104.17 psi, which is found by adding 100 plus half of 8.34.

Pascal’s law, when dealing with the variables of force, pressure, and area, is dealt with by way of the following formula. Force = Pressure × Area In this formula, the force is in units of pounds, the pressure is in pounds per square inch (psi), and the area is in square inches. By transposing the original formula, we have two additional formulas, as follows: Pressure = Force ÷ Area and Area = Force ÷ Pressure An easy and convenient way to remember the formulas for Pascal’s law, and the relationship between the variables, is with the triangle shown in Figure 5-42. If the variable we want to solve for is covered up, the position of the remaining two variables shows the proper math relationship. For example, if the “A,” or area, is covered up, what remains is the “F” on the top and the “P” on the bottom, meaning force divided by pressure.

The simple hydraulic system in Figure 5-43 has 5 lb force acting on a piston with a 1⁄2-in2 surface area. Based on Pascal’s law, the pressure in the system would be equal to the force applied divided by the area of the piston, or 10 psi. As shown in Figure 5-43, the pressure of 10 psi is present everywhere in the fluid. The hydraulic system in Figure 5-44 is a little more complex than the one in Figure 5-43. In Figure 5-44, the input force of 5 lb is acting on a 1⁄2-in2 piston, creating a pressure of 10 psi. The input cylinder and piston is connected to a second cylinder, which contains a 5-in2 piston. The pressure of 10 psi created by the input piston pushes on the piston in the second cylinder, creating an output force of 50 pounds.

Often, the purpose of a hydraulic system is to generate a large output force, with the input force being much less. In Figure 5-44, the input force is 5 lb and the output force is 50 lb, or 10 times greater. The relationship between the output force and the input force, as discussed earlier in this chapter, is known as mechanical advantage. The mechanical advantage in Figure 5-44 would be 50 divided by 5, or 10. The following formulas can be used to calculate mechanical advantage. Mechanical Advantage = Force Out ÷ Force In or Mechanical Advantage = Distance Out ÷ Distance In Earlier in this chapter when simple machines, such as levers and gears were discussed, it was identified that no machine allows us to gain work. The same statement holds true for a hydraulic system, that we get no more work out of a hydraulic system than we put in. Since work is equal to force times distance, if we gain force with a hydraulic system, we must lose distance. We only get the same work out, if the system is 100 percent efficient.

In order to think about the distance that the output piston will move in response to the movement of the input piston, the 5-29 F A P 10 psi Force = 5 lb 10 psi Piston area = ½ in2 Pressure = force ÷ area Pressure = 5 ÷ ½ Pressure = 10 psi 10 psi Force = 5 lb Force = 50 lb Piston area = ½ in2 Piston area = 5 in2 Force = pressure x area Force = 10 psi x5 in2 Force = 50 lb 50 lb volume of fluid displaced must be considered. In the study of geometry, one learns that the volume of a cylinder is equal to the cylinder’s surface area multiplied by its height. So, when a piston of 2 in2 moves down in a cylinder a distance of 10 in, it displaces a volume of fluid equal to 20 in 3 (2 in2 × 10 in). The 20 in3 displaced by the first piston is what moves over to the second cylinder and causes its piston to move.

In a simple two-piston hydraulic system, the relationship between the piston area and the distance moved is shown by the following formula. Input Piston Area (Distance Moved) = Output Piston Area (Distance Moved) This formula shows that the volume in is equal to the volume out. This concept is shown in Figure 5-45, where a small input piston moves a distance of 20 inches, and the larger output piston only moves a distance of 1 inch. Example: A two-piston hydraulic system, like that shown in an output piston with an area of 15 in 2. An input force of 50 lb is applied, and the input piston moves 30 inches. What is the pressure in the system, how much force is generated by the output piston, how far would the output piston move, and what is the mechanical advantage?

Pressure = Force ÷ Area = 50 ÷ 1⁄4 = 200 psi Force = Pressure × Area = 200 × 15 = 3,000 lb Mechanical Advantage = Force Out ÷ Force In = 3,000 ÷ 50 = 60 Input Piston Area (Distance Moved) = Output Piston Area (Distance Moved) 1⁄4 (30) = 15 (Distance Moved) 1⁄4 (30) ÷ 15 = Distance Moved Distance Moved = 1⁄2 in Part of understanding Pascal’s law and hydraulics involves utilizing formulas, and recognizing the relationship between the individual variables. Before the numbers are plugged into the formulas, it is often possible to analyze the variables in the system and come to a realization about what is happening. For example, look at the variables in larger than the input piston, 5 in 2 compared to 1⁄4 in2. That comparison tells us that the output force will be 20 times greater than the input force, and also that the output piston will only move 1⁄20 as far. Without doing any formula based calculations, we can conclude that the hydraulic system in question has a mechanical advantage of 20.

Bernoulli’s Principle Bernoulli’s principle was originally stated to explain the action of a liquid flowing through the varying cross-sectional 5-30 Distance moved = 20 in Distance moved = 1 in Input piston area = ¼ in2 Output piston area = 15 in2 Piston area (distance) = Piston area (distance) ¼ in 2 (20 in) = 5 in (distance) 5 ÷ 5 = Distance Distance = 1 in areas of tubes. In Figure 5-46 a tube is shown in which the cross-sectional area gradually decreases to a minimum diameter in its center section. A tube constructed in this manner is called a “venturi,” or “venturi tube.” Where the cross-sectional area is decreasing, the passageway is referred to as a converging duct. As the passageway starts to spread out, it is referred to as a diverging duct.

As a liquid, or fluid, flows through the venturi tube, the gauges at points “A,” “B,” and “C” are positioned to register the velocity and the static pressure of the liquid. The venturi in Figure 5-46 can be used to illustrate Bernoulli’s principle, which states that: The static pressure of a fluid, liquid or gas, decreases at points where the velocity of the fluid increases, provided no energy is added to nor taken away from the fluid. The velocity of the air is kinetic energy and the static pressure of the air is potential energy. In the wide section of the venturi (points A and C of high static pressure, as indicated by the pressure gauge. As the tube narrows in the center, it must contain the same volume of fluid as the two end areas. As indicated by the velocity gauge reading high and the pressure gauge reading low, in this narrow section, the liquid moves at a higher velocity, producing a lower pressure than that at points A and C. A good application for the use of the venturi principle is in a float-type carburetor. As the air flows through the carburetor on its way to the engine, it goes through a venturi, where the static pressure is reduced. The fuel in the carburetor, which is under a higher pressure, flows into the lower pressure venturi area and mixes with the air.

Bernoulli’s principle is extremely important in understanding how some of the systems used in aviation work, including how the wing of an airplane generates lift or why the inlet duct of a turbine engine on a subsonic airplane is diverging in shape. The wing on a slow-moving airplane has a curved top surface and a relatively flat bottom surface. The curved top surface acts like half of the converging shaped middle of a venturi. As the air flow over the top of the wing, the air speeds up, and its static pressure decreases. The static pressure on the bottom of the wing is now greater than the pressure on the top, and this pressure difference creates the lift on the wing. Bernoulli’s principle and the concept of lift on a wing are covered in greater depth in “Aircraft Theory of Flight” located in this chapter.

Sound

Sound has been defined as a series of disturbances in matter that the human ear can detect. This definition can also be applied to disturbances which are beyond the range of human hearing. There are three elements which are necessary for the transmission and reception of sound. These are the source, a medium for carrying the sound, and the detector. Anything which moves back and forth, or vibrates, and disturbs the medium around it may be considered a sound source. An example of the production and transmission of sound is the ring of a bell. When the bell is struck and begins to vibrate, the particles of the medium, or the surrounding air, in contact with the bell also vibrate. The vibrational disturbance is transmitted from one particle of the medium to the next, and the vibrations travel in a “wave” through the medium until they reach the ear. The eardrum, acting as detector, is set in motion by the vibrating particles of air, and the brain interprets the eardrum’s vibrations as the characteristic sound associated with a bell.

Wave Motion Since sound is a wave motion in matter, it can best be understood by first considering water waves, like a series of circular waves travel away from the disturbance of an object thrown into a pool. In Figure 5-47 such waves are seen from a top perspective, with the waves traveling out from the center. In the cross-section perspective in of crests and troughs. The wavelength is the distance from the crest of one wave to the crest of the next. Water waves are known as transverse waves because the motion of the water molecules is up and down, or at right angles to the direction in which the waves are traveling. This can be seen by observing a cork on the water, bobbing up and down as the waves pass by.

Sound travels through matter in the form of longitudinal wave motions. These waves are called longitudinal waves because the particles of the medium vibrate back and forth longitudinally in the direction of propagation. [Figure 5-48] When the tine of a tuning fork moves in an outward direction, the air immediately in front of the tine is compressed so that its 5-31

Pressure

PressureVelocityVelocity Velocity “A” “B” “C” Low High Low High Low High Low High Low High Low High Trough CrestCrest Pressure waves traveling outward Round object dropped into the water momentary pressure is raised above that at other points in the surrounding medium. Because air is elastic, this disturbance is transmitted progressively in an outward direction from the tine in the form of a compression wave. When the tine returns and moves in an inward direction, the air in front of the tine is rarefied so that its momentary pressure is reduced below that at other points in the surrounding medium. This disturbance is transmitted in the form of a rarefaction, or expansion, wave and follows the compression wave through the medium. The progress of any wave involves two distinct motions: (1) The wave itself moves forward with constant speed, and (2) simultaneously, the particles of the medium that convey the wave vibrate harmonically. Examples of harmonic motion are the motion of a clock pendulum, the balance wheel in a watch, and the piston in a reciprocating engine.

Speed of Sound In any uniform medium, under given physical conditions, the sound travels at a definite speed. In some substances, the velocity of sound is higher than in others. Even in the same medium under different conditions of temperature, pressure, and so forth, the velocity of sound varies. Density and elasticity of a medium are the two basic physical properties which govern the velocity of sound. In general, a difference in density between two substances is sufficient to indicate which one will be the faster transmission medium for sound. For example, sound travels faster through water than it does through air at the same temperature. However, there are some surprising exceptions to this rule of thumb. An outstanding example among these exceptions involves comparison of the speed of sound in lead and aluminum at the same temperature. Sound travels at 16,700 fps in aluminum at 20 °C, and only 4,030 fps in lead at 20 °C, despite the fact that lead is much denser than aluminum. The reason for such exceptions is found in the fact, mentioned above, that sound velocity depends on elasticity as well as density.

Using density as a rough indication of the speed of sound in a given substance, it can be stated as a general rule that sound travels fastest in solid materials, slower in liquids, and slowest in gases. The velocity of sound in air at 0 °C (32 °F) is 1,087 fps and increases by 2 fps for each Centigrade degree of temperature rise, or 1.1 fps for each degree Fahrenheit. Mach Number In the study of aircraft that fly at supersonic speeds, it is customary to discuss aircraft speed in relation to the velocity of sound, which is approximately 761 miles per hour (mph) at 59 °F. The term “Mach number” has been given to the ratio of the speed of an aircraft to the speed of sound, in honor of Ernst Mach, an Austrian scientist. If the speed of sound at sea level is 761 mph, an aircraft flying at a Mach number of 1.2 at sea level would be traveling at a speed of 761 mph × 1.2 = 913 mph.

Frequency of Sound The term “pitch” is used to describe the frequency of a sound. The outstanding recognizable difference between the tones produced by two different keys on a piano is a difference in pitch. The pitch of a tone is proportional to the number of compressions and rarefactions received per second, which in turn, is determined by the vibration frequency of the sounding source. A good example of frequency is the noise generated by a turbofan engine on a commercial airliner. The 5-32 Amplitude Rarefaction Compression Wave Tuning fork length high tip speeds of the fan in the front of the engine create a high frequency sound, and the hot exhaust creates a low frequency sound.

Loudness When a bell rings, the sound waves spread out in all directions and the sound is heard in all directions. When a bell is struck lightly, the vibrations are of small amplitude and the sound is weak. A stronger blow produces vibrations of greater amplitude in the bell, and the sound is louder. It is evident that the amplitude of the air vibrations is greater when the amplitude of the vibrations of the source is increased. Hence, the loudness of the sound depends on the amplitude of the vibrations of the sound waves. As the distance from the source increases, the energy in each wave spreads out, and the sound becomes weaker.

As the sound wave advances, variations in pressure occur at all points in the transmitting medium. The greater the pressure variations, the more intense the sound wave is. The intensity is proportional to the square of the pressure variation regardless of the frequency. Thus, by measuring pressure changes, the intensities of sounds having different frequencies can be compared directly. Measurement of Sound Intensity Sound intensity is measured in decibels, with a decibel being the ratio of one sound to another. One decibel (dB) is the smallest change in sound intensity the human ear can detect. A faint whisper would have an intensity of 20 dB, and a pneumatic drill would be 80 dB. The engine on a modern jetliner, at takeoff thrust, would have a sound intensity of 90 dB when heard by someone standing 150 ft. away. A 110 dB noise, by comparison, would sound twice as loud as the jetliner’s engine. Figure 5-49 shows the sound intensity from a variety of different sources.

Doppler Effect When sound is coming from a moving object, the object’s forward motion adds to the frequency as sensed from the front and takes away from the frequency as sensed from the rear. This change in frequency is known as the Doppler Effect, and it explains why the sound from an airplane seems different as it approaches compared to how it sounds as it flies overhead. As it approaches, it becomes both louder and higher pitched. As it flies away, the loudness and pitch both decrease noticeably. If an airplane is flying at or higher than the speed of sound, the sound energy cannot travel out ahead of the airplane, because the airplane catches up to it the instant it tries to leave. The sound energy being created by the airplane piles up, and attaches itself to the structure of the airplane. As the airplane approaches, a person standing on the ground will not be able to hear it until it gets past their position, because the sound energy is actually trailing behind the airplane. When the sound of the airplane is heard, it will be in the form of what is called a sonic boom.

Resonance All types of matter, regardless of whether it is a solid, liquid, or gas, have a natural frequency at which the atoms within that matter vibrate. If two pieces of matter have the same natural frequency, and one of them starts to vibrate, it can transfer its wave energy to the other one and cause it to vibrate. This transfer of energy is known as resonance. Some piston engine powered airplanes have an rpm range that they are placarded to avoid, because spinning the prop at that rpm can cause vibration problems. The difficulty lies in the natural frequency of the metal in the prop, and the frequency of vibration that will be set up with a particular tip speed for the prop. At that particular rpm, stresses can be set up that could lead to the propeller coming apart.

The Atmosphere

Aviation is so dependent upon that category of fluids called gases and the effect of forces and pressures acting upon gases that a discussion of the subject of the atmosphere is important to the persons maintaining and repairing aircraft. Data available about the atmosphere may determine whether a flight will succeed, or whether it will even become airborne. The various components of the air around the earth, the changes in temperatures and pressures at different levels above the earth, the properties of weather encountered by aircraft in flight, and many other detailed data are considered in the preparation of flight plans.

5-33 180 160 140 130 120 110 100 90 80 70 60 50 40 30 20 10 0 THRESHOLD OF FEELINGTHRESHOLD OF AUDIBILITY Lethal level Turbojet engine at 50 ft 50 horsepower siren at 50 ft Turbojet engine at takeoff at 150 ft Automobile horn Riveting machine, as heard by operator An express train passing close by Modern turbo engine at takeoff at 150 ft Subway train at 20 ft (1/2 the loudness of 110 dB noise) Pneumatic drill at 50 ft Vacuum cleaner at 50 ft Nearby freeway auto traffic Private business office Residential area in the evening Soft whisper at 5 ft Radio studio Faint whisper Pascan and Torricelli have been credited with developing the barometer, an instrument for measuring atmospheric pressure. The results of their experiments are still used today with very little improvement in design or knowledge. They determined that air has weight which changes as altitude is changed with respect to sea level. Today scientists are also interested in how the atmosphere affects the performance of the aircraft and its equipment.

Composition of the Atmosphere The atmosphere is a complex and ever changing mixture. Its ingredients vary from place to place and from day to day. In addition to a number of gases, it contains quantities of foreign matter such as pollen, dust, bacteria, soot, volcanic ash, spores, and dust from outer space. The composition of the air remains almost constant from sea level up to its highest level, but its density diminishes rapidly with altitude. Six miles up, for example, it is too thin to support respiration, and 12 miles up, there is not enough oxygen to support combustion, except in some specially designed turbine engine powered airplanes. At a point several hundred miles above the earth, some gas particles spray out into space, some are dragged by gravity and fall back into the ocean of air below, while others never return. Physicists disagree as to the boundaries of the outer fringes of the atmosphere. Some think it begins 240 miles above the earth and extends to 400 miles; others place its lower edge at 600 miles and its upper boundary at 6,000 miles.

There are also certain nonconformities at various levels. Between 12 and 30 miles, high solar ultraviolet radiation reacts with oxygen molecules to produce a thin curtain of ozone, a very poisonous gas without which life on earth could not exist. This ozone filters out a portion of the sun’s lethal ultraviolet rays, allowing only enough coming through to give us sunburn, kill bacteria, and prevent rickets. At 50 to 65 miles up, most of the oxygen molecules begin to break down under solar radiation into free atoms, and to form hydroxyl ions (OH) from water vapor. Also in this region, all the atoms become ionized.

Studies of the atmosphere have revealed that the temperature does not decrease uniformly with increasing altitude; instead it gets steadily colder up to a height of about 7 miles, where the rate of temperature change slows down abruptly and remains almost constant at −55° Centigrade (218° Kelvin) up to about 20 miles. Then the temperature begins to rise to a peak value of 77° Centigrade (350° Kelvin) at the 55 mile level. Thereafter it climbs steadily, reaching 2,270° Centigrade (2,543° Kelvin) at a height of 250 to 400 miles. From the 50 mile level upward, a man or any other living creature, without the protective cover of the atmosphere, would be broiled on the side facing the sun and frozen on the other.

The atmosphere is divided into concentric layers or levels. Transition through these layers is gradual and without sharply defined boundaries. However, one boundary, the tropopause, exists between the first and second layer. The tropopause is defined as the point in the atmosphere at which the decrease in temperature, with increasing altitude, abruptly ceases. The four atmosphere layers are the troposphere, stratosphere, ionosphere, and the exosphere. The upper portion of the stratosphere is often called the chemosphere or ozonosphere, and the exosphere is also known as the mesosphere. The troposphere extends from the earth’s surface to about 35,000 ft at middle latitudes, but varies from 28,000 ft at the poles to about 54,000 ft at the equator. The troposphere is characterized by large changes in temperature and humidity and by generally turbulent conditions. Nearly all cloud formations are within the troposphere. Approximately three-fourths of the total weight of the atmosphere is within the troposphere. The stratosphere extends from the upper limits of the troposphere and the tropopause to an average altitude of 60 miles.

The ionosphere ranges from the 50-mile level to a level of 300 to 600 miles. Little is known about the characteristics of the ionosphere, but it is thought that many electrical phenomena occur there. Basically, this layer is characterized by the presence of ions and free electrons, and the ionization 5-34 seems to increase with altitude and in successive layers. The exosphere, or mesosphere, is the outer layer of the atmosphere. It begins at an altitude of 600 miles and extends to the limits of the atmosphere. In this layer, the temperature is fairly constant at 2,500° Kelvin, and propagation of sound is thought to be impossible due to lack of molecular substance.

Atmospheric Pressure The human body is under pressure, since it exists at the bottom of a sea of air. This pressure is due to the weight of the atmosphere. On a standard day at sea level, if a 1-in2 column of air extending to the top of the atmosphere was weighed, it would weigh 14.7 lb. That is why standard day atmospheric pressure is said to be 14.7 pounds per square inch (14.7 psi). Since atmospheric pressure at any altitude is due to the weight of air above it, pressure decreases with increased altitude. Obviously, the total weight of air above an area at 15,000 ft would be less than the total weight of the air above an area at 10,000 ft.

Atmospheric pressure is often measured by a mercury barometer. A glass tube somewhat over 30 inches in length is sealed at one end and then filled with mercury. It is then inverted and the open end placed in a dish of mercury. Immediately, the mercury level in the inverted tube will drop a short distance, leaving a small volume of mercury vapor at nearly zero absolute pressure in the tube just above the top of the liquid mercury column. Gravity acting on the mercury in the tube will try to make the mercury run out. Atmospheric pressure pushing down on the mercury in the open container tries to make the mercury stay in the tube. At some point these two forces (gravity and atmospheric pressure) will equilibrate out and the mercury will stabilize at a certain height in the tube. Under standard day atmospheric conditions, the air in a 1 square inch column extending to the top of the atmosphere would weigh 14.7 lb. A 1-in2 column of mercury, 29.92 inches tall, would also weigh 14.7 lb. That is why 14.7 psi is equal to 29.92 "Hg. Figure 5-50 demonstrates this point.

A second means of measuring atmospheric pressure is with an aneroid barometer. This mechanical instrument is a much better choice than a mercury barometer for use on airplanes. Aneroid barometers, or altimeters, are used to indicate altitude in flight. The calibrations are made in thousands of feet rather than in psi or inches of mercury. For example, the standard pressure at sea level is 29.92 "Hg, or 14.7 psi. At 10,000 feet above sea level, standard pressure is 20.58 "Hg, or 10.10 psi. Altimeters are calibrated so that if the pressure exerted by the atmosphere is 10.10 psi, the altimeter will point to 10,000 ft. [Figure 5-51] Atmospheric Density Since both temperature and pressure decrease with altitude, it might appear that the density of the atmosphere would remain fairly constant with increased altitude. This is not true, however, because pressure drops more rapidly with increased altitude than does the temperature. The result is that density decreases with increased altitude.

By use of the general gas law, studied earlier, it can be shown that for a particular gas, pressure and temperature determine the density. Since standard pressure and temperatures have been associated with each altitude, the density of the air at these standard temperatures and pressures must also be considered standard. Thus, a particular atmospheric density is associated with each altitude. This gives rise to the expression “density altitude,” symbolized “Hd.” A density altitude of 15,000 ft is the altitude at which the density is the same as that considered standard for 15,000 ft. Remember, however, that density altitude is not necessarily true altitude. For example, on a day when the atmospheric pressure is higher than standard and the temperature is lower than standard, the density which is standard at 10,000 ft might occur at 12,000 ft. In this case, at an actual altitude of 12,000 ft, we have air that has the same density as standard air at 10,000 ft.

Density altitude is a calculated altitude obtained by correcting pressure altitude for temperature. Water Content of the Atmosphere In the troposphere, the air is rarely completely dry. It contains water vapor in one of two forms: (1) fog or (2) water vapor. Fog consists of minute droplets of water held in suspension by the air. Clouds are composed of fog. The height to which some clouds extend is a good indication of the presence of water in the atmosphere almost up to the stratosphere. The presence of water vapor in the air is quite evident in Figure 5-52, with a military F-18 doing a high-speed fly-by at nearly Mach 1. The temperature and pressure changes that occur as the airplane approaches supersonic flight cause the water vapor in the air to condense and form the vapor cloud that is visible.

As a result of evaporation, the atmosphere always contains some moisture in the form of water vapor. The moisture in the air is called the humidity of the air. Moisture does not consist of tiny particles of liquid held in suspension in the air as in the case of fog, but is an invisible vapor truly as gaseous as the air with which it mixes. Fog and humidity both affect the performance of an aircraft. In flight, at cruising power, the effects are small and receive no consideration. During takeoff, however, humidity has important effects. Two things are done to compensate for the effects of humidity on takeoff performance. Since humid air is less dense than dry air, the allowable takeoff gross weight of an aircraft is generally reduced for operation in areas that are consistently humid.

5-35 Vacuum 14.7 psi Atmospheric pressure 760 mm 29.92 in 30.029.929.8 I00 FEET I 456 7 9 2 0 8 3 ALT Second, because the power output of reciprocating engines is decreased by humidity, the manifold pressure may need to be increased above that recommended for takeoff in dry air in order to obtain the same power output. Engine power output is calculated on dry air. Since water vapor is incombustible, its pressure in the atmosphere is a total loss as far as contributing to power output. The mixture of water vapor and air is drawn through the carburetor, and fuel is metered into it as though it were all air. This mixture of water vapor, air, and fuel enters the combustion chamber where it is ignited. Since the water vapor will not burn, the effective air-fuel ratio is enriched and the engine operates as though it were on an excessively rich mixture. The resulting horsepower loss under humid conditions can therefore be attributed to the loss in volumetric efficiency due to displaced air, and the incomplete combustion due to an excessively rich fuel and air mixture.

The reduction in power that can be expected from humidity is usually given in charts in the flight manual. There are several types of charts in use. Some merely show the expected reduction in power due to humidity; others show the boost in manifold pressure necessary to restore full takeoff power. The effect of fog on the performance of an engine is very noticeable, particularly on engines with high compression ratios. Normally, some detonation will occur during acceleration, due to the high BMEP, which stands for brake mean effective pressures, developed. However, on a foggy day it is difficult to cause detonation to occur. The explanation of this lies in the fact that fog consists of particles of water that have not vaporized. When these particles enter the cylinders, they absorb a tremendous amount of heat energy in the process of vaporizing. The temperature is thus lowered, and the decrease is sufficient to prevent detonation.

Fog will generally cause a decrease in horsepower output. However, with a supercharged engine, it will be possible to use higher manifold pressures without danger of detonation. Absolute Humidity Absolute humidity is the actual amount of the water vapor in a mixture of air and water. It is expressed either in grams per cubic meter or pounds per cubic foot. The amount of water vapor that can be present in the air is dependent upon the temperature and pressure. The higher the temperatures, the more water vapor the air is capable of holding, assuming constant pressure. When air has all the water vapor it can hold at the prevailing temperature and pressure, it is said to be saturated.

Relative Humidity Relative humidity is the ratio of the amount of water vapor actually present in the atmosphere to the amount that would be present if the air were saturated at the prevailing temperature and pressure. This ratio is usually multiplied by 100 and expressed as a percentage. Suppose, for example, that a weather report includes the information that the temperature is 75 °F and the relative humidity is 56 percent. This indicates that the air holds 56 percent of the water vapor required to