AMT Handbook - General # Chapter 5: Physics for Aviation Physical science, which is most often called [[physics]], is a very interesting and exciting topic. For an individual who likes technical things and is a hands-on type of person, physics is an invaluable tool. Physics allows us to explain how engines work, both piston and gas turbine; how airplanes and helicopters fly; and countless other things related to the field of aviation and aerospace. In addition to allowing us to explain the operation of the things around us, it also allows us to quantify them. For example, through the use of physics we can explain what the concept of [[thrust]] means for a[[ jet engine]], and then follow it up by mathematically calculating the pounds of thrust being created. Physics is the term applied to an area of knowledge regarding the basic and fundamental nature of [[matter]] and [[energy]]. It does not attempt to determine why matter and energy behave as they do in their relation to physical phenomena, but rather how they behave. The people who maintain and repair aircraft should have knowledge of basic physics, which is sometimes called the science of matter and energy. ## Matter [[Matter]] is the foundation, or the building blocks, for any discussion of [[physics]]. According to the dictionary, matter is what all things are made of; whatever occupies [[Space physics]], has [[mass]], and is perceptible to the senses in some way. According to the [[Law of Conservation]], matter cannot be created or destroyed, although it is possible to change its physical state. When liquid gasoline vaporizes and mixes with air, and then burns, it might seem that this piece of matter has disappeared and no longer exists. Although it no longer exists in the state of liquid gasoline, the matter still exists in the form of the gases given off by the burning fuel. ### Characteristics of Matter. #### Mass and Weight [[Mass]] is a measure of the quantity of [[matter]] in an object. In other words, how many [[molecules]] are in the object, how many [[atom|atoms]] are in the object, or to be more specific, how many [[proton|protons]], [[neutron|neutrons]], and [[electron|electrons]] are in the object. The mass of an object does not change regardless of where you take it in the universe, or with a change of state. The only way to change the mass of an object is to add or take away atoms. Mathematically, mass can be stated as follows: $\text{Mass} = \text{Weight} \div \text{Acceleration due to gravity}$ The [[acceleration due to gravity]] here on earth is 32.2 feet per second per second (32.2 fps/s). An object weighing 32.2 pounds (lb) here on earth is said to have a mass of 1 slug. A slug is a quantity of mass that will accelerate at a rate of 1 ft. /s2 when a force of 1 pound is applied. In other words, under [[standard atmospheric condition]], which is that gravity is equal to 32.2 fps/s, a mass of one slug would be equal to 32.2 lb. [[Weight]] is a measure of the pull from [[gravity]] acting on the mass of an object. The more mass an object has, the more it will weigh under the earth’s force of gravity. The only way for an object to be weightless is for gravity to go away, because it is not possible for the mass of an object to disappear. When we view astronauts on the space shuttle, it appears that they are weightless. Even though the shuttle is far from the surface of the earth, the force of gravity has not completely gone away, and the astronauts are not weightless. The astronauts and the space shuttle are actually in a state of free fall, so relative to the shuttle the astronauts appear to be weightless. Mathematically, weight can be stated as follows: $\text{Weight} = \text{Mass} \times \text{Gravity}$ #### Attraction [[Attraction]] is mutual [[force]] acting between particles of matter, which tends to draw them together. Sir Isaac Newton called this the “[[Law of Universal Gravitation]].” Newton showed how each particle of matter attracts every other particle, how people are bound to the earth, and how the planets are attracted in the solar system. #### Porosity [[Porosity]] means having pores or spaces where smaller particles may fit when a mixture takes place. This is sometimes referred to as granular—consisting or appearing to consist of small grains or granules. #### Impenetrability [[Impenetrability]] means that no two objects can occupy the same place at the same time. Thus, two portions of matter cannot at the same time occupy the same space. #### Density The [[density]] of a substance is its [[weight]] per unit [[volume]]. The unit volume selected for use in the English system of measurement is 1 cubic foot (ft3). In the [[metric system]], it is 1 cubic centimeter (cm3). Therefore, density is expressed in pounds per cubic foot (lb⁄ft3) or in grams per cubic centimeter (g⁄cm3). To find the density of a substance, its weight and volume must be known. Its weight is then divided by its volume to find the weight per unit volume. For example, the liquid which fills a certain container weighs 1,497.6 lb. The container is 4 ft long, 3 ft wide and 2 ft deep. Its volume is 24 ft3 (4 ft. × 3 ft. × 2 ft.). If 24 ft3 of liquid weighs 1,497.6 lb, then 1 ft3 weighs 1,497.6 ÷ 24, or 62.4 lb. Therefore, the density of the liquid is 62.4 lb/ft3. This is the density of water at 4 °C ([[Centigrade]]) and is usually used as the standard for comparing densities of other substances. In the metric system, the densityof water is 1 g⁄cm3. The standard temperature of 4 °C is used when measuring the density of [[liquid]]s and [[Solid]]s. Changes in [[Temperature]] will not change the weight of a substance, but will change the volume of the substance by expansion or contraction, thus changing its weight per unit volume. The procedure for finding density applies to all substances; however, it is necessary to consider the [[pressure]] when finding the density of gases. Pressure is more critical when measuring the density of gases than it is for other substances. The density of a [[gas]] increases in direct proportion to the pressure exerted on it. Standard conditions for the measurement of the densities of gases have been established at 0 °C for temperature and a pressure of 76 cm of mercury (Hg), which is the average pressure of the [[atmosphere]] at sea level. Density is computed based on these conditions for all gases. #### Specific Gravity It is often necessary to compare the density of one substance with another substance. For this purpose, a standard is needed. Water is the standard that physicists have chosen to use when comparing the densities of all liquids and solids. For gases, air is most commonly used, but [[hydrogen]] is also sometimes used as a standard for gases. In physics, the word “specific” implies a ratio. Thus, [[specific gravity]] is calculated by comparing the weight of a definite volume of the given substance with the weight of an equal volume of water. The terms “specific weight” or “specific density” are sometimes used to express this ratio. The following [[formula]]s are used to find the specific gravity of liquids and solids. $\begin{align*} \text{Specific Gravity} &= \frac{\text{Weight of the substance}}{\text{Weight of an equal volume of water}}\\ &\\ &\text{or}\\ &\\ \text{Specific Gravity} &= \frac{\text{Density of substance}}{\text{Density of water}} \end{align*}$ ![[5-1.png|350]] The same formulas are used to find the density of gases by substituting air or hydrogen for water. Specific gravity is not expressed in units, but as pure numbers. For example, if a certain [[hydraulic fluid]] has a specific gravity of 0.8, $1 ft^3$ of the liquid weighs 0.8 times as much as $1 ft^3$ of water: 62.4 times 0.8, or 49.92 lb. Specific gravity and density are independent of the size of the sample under consideration and depend only upon the substance of which it is made. See *[[5-1.png|[Figure 5-1] ]]* for typical values of specific gravity for various substances. ![[5-2.png|350]] A device called a [[hydrometer]] is used for measuring specific gravity of liquids. This device consists of a tubular glass float contained in a larger glass tube. *[[5-2.png|[Figure 5-2] ]]* The larger glass tube provides the container for the liquid. A rubber suction bulb draws the liquid up into the container. There must be enough liquid raising the float to prevent it from touching the bottom. The float is weighted and has a vertically graduated scale. To determine specific gravity, the scale is read at the surface of the liquid in which the float is immersed. An indication of 1000 is read when the float is immersed in pure water. When immersed in a liquid of greater density, the float rises, indicating a greater specific gravity. For liquids of lesser density, the float sinks, indicating a lower specific gravity. An example of the use of the hydrometer is to determine the specific gravity of the electrolyte (battery liquid) in an aircraft battery. When a battery is discharged, the calibrated float immersed in the electrolyte will indicate approximately 1150. The indication of a charged battery is between 1275 and 1310. The values 1150, 1275, and 1310 represent 1.150, 1.275, and 1.310. The electrolyte in a discharged battery is 1.15 times denser than water, and in a charged battery 1.275 to 1.31 times denser than water. ## Energy [[Energy]] is typically defined as something that gives us the capacity to perform [[work]]. As individuals, saying that we feel full of energy is an indicator that we can perform a lot of work. Energy can be classified as one of two types: either as potential energy or kinetic energy. ### Potential Energy [[Potential energy]] is defined as being energy at rest, or energy that is stored. Potential energy may be classified into three groups: (1) energy due to position, (2) energy due to distortion of an elastic body, and (3) energy which produces work through chemical action. Examples of the first group are water in an elevated reservoir or an airplane raised off the ground with jacks; a stretched bungee cord on a Piper Tri-Pacer or compressed spring are examples of the second group; and energy in aviation gasoline, food, or storage batteries are examples of the third group. To calculate the potential energy of an object due to its position, as in height, the following formula is used: $\text{Potential Energy} = \text{Weight} \times \text{Height}$ A calculation based on this formula will produce an answer that has units of foot-pounds (ft-lb) or inch pounds (in-lb), which are the same units that apply to work. [[Work]], which is covered later in this chapter, is described as a [[force]] being applied over a measured [[distance]], with the force being pounds and the distance being feet or inches. Potential energy and work have a lot in common. Example: A Boeing 747 weighing 450,000 pounds needs to be raised 4 feet in the air so [[maintenance]] can be done on the landing gear. How much potential energy does the airplane possess because of this raised position? $\begin{align*} \text{Potential Energy} &= \text{Weight} \times \text{Height}\\ \text{PE} &= 450,000lb \times 4ft\\ \text{PE} &= 1,800,800 ft-lb \end{align*}$ As previously mentioned, aviation gasoline possesses potential energy because of its chemical nature. Gasoline has the potential to release heat energy, based on its British thermal unit ([[BTU]]) content. One pound of aviation gas contains 18,900 BTU of heat energy, and each BTU is capable of 778 ft-lb of work. So, when we multiply 778 by 18,900, we find that one pound of aviation gas is capable of 14,704,200 ft-lb of work. Imagine the potential energy in the completely serviced fuel tanks of an airplane. ### Kinetic Energy [[Kinetic energy]] is defined as being energy that is in motion. An airplane rolling down the runway or a rotating [[flywheel]] on an [[engine]] are both examples of kinetic energy. Kinetic energy has the same units as potential energy, namely foot-pounds or inch-pounds. To calculate the kinetic energy for something in motion, the following formula is used: $\text{Kinetic Energy} = \frac{1}{2} \text{Mass} \times \text{Velocity}^{2}$ To use the formula, we will show the mass as weight divided by gravity and the velocity of the object will be in feet per second. This is necessary to end up with units in foot-pounds. ![[5-3.png|350]] Example: An Airbus A380 weighing 600,000 lb is moving down the runway on its takeoff roll with a velocity of 200 fps. How many foot-pounds of kinetic energy does the airplane possess? *[[5-3.png|[Figure 5-3] ]]* $\begin{align*} \text{Kinetic Energy} &= \frac{1}{2} \text{Mass} \times \text{Velocity}^{2}\\ \text{Kinetic Energy} &= \frac{1}{2} \times 600,000 \div 32.2 \times 200^2\\ \text{KE} &= 372,670,000ft-lb\\ \end{align*}$ ## Force, Work, Power, and Torque ### Force Before the concept of [[work]], [[Power Physics|power]] , or [[torque]] can be discussed, we need to understand what [[force]] means. According to the dictionary, force is the intensity of an [[impetus]], or the intensity of an input. For example, if we apply a force to an object, the tendency will be for the object to move. Another way to look at it is that for work, power, or torque to exist, there must be a force that initiates the process. The unit for force in the English system of measurement is pounds, and in the metric system it is newtons. One pound of force is equal to 4.448 newtons. When we calculate the [[thrust]] of a turbine engine, we use the formula “Force = Mass × Acceleration,” and the thrust of the engine is expressed in pounds. The GE90-115 turbofan engine (power plant for the Boeing 777-300), for example, has 115,000 pounds of thrust. ### Work The study of machines, both simple and complex, can be seen as a study of the energy of mechanical [[work]]. This is true because all machines transfer input energy, or the work done on the machine, to output energy, or the work done by the machine. Work, in the mechanical sense of the term, is done when a resistance is overcome by force acting through a measurable distance. Two factors are involved: (1) force and (2) movement through a distance. As an example, suppose a small aircraft is stuck in the snow. Two men push against it for a period of time, but the aircraft does not move. According to the technical definition, no work had been done when the men were pushing against the aircraft. By definition, work is accomplished only when an object is displaced some distance against a resistive force. To calculate work, the following formula is used: $\text{Work} = \text{Force(F)} \times \text{Distance(D)}$ In the English system, the force will be identified in pounds and the distance either in feet or inches, so the units will be foot-pounds or inch-pounds. Notice these are the same units that were used for potential and kinetic energy. In the metric system, the force is identified in newtons (N) and the distance in meters, with the resultant units being joules. One pound of force is equal to 4.448 N and one meter is equal to 3.28 feet. One joule is equal to 1.36 ft-lb. ![[5-4.png|350]] Example: How much work is accomplished by jacking a 150,000-lb Airbus A-320 airplane a vertical height of 4 ft?*[[5-4.png|[Figure 5-4] ]]* $\begin{align*} \text{Work} &= \text{Force} \times \text{Distance}\\ &= 150,000lb \times 4ft\\ &= 600,000ft-lb \end{align*}$ Example: How much work is accomplished when a tow tractor is hooked up to a tow bar and a Boeing 737-800 airplane weighing 130,000 lb is pushed 80 ft. into the hangar? The force on the tow bar is 5,000 lb. $\begin{align*} \text{Work} &= \text{Force} \times \text{Distance}\\ &= 5,000lb \times 80ft\\ &= 400,000ft-lb \end{align*}$ In this last example, notice the force does not equal the weight of the airplane. This is because the airplane is being moved horizontally and not lifted vertically. In almost all cases, it takes less work to move something horizontally than it does to lift it vertically. Most people can push their car a short distance if it runs out of gas, but they cannot get under their car and lift it off the ground. ### Friction and Work ![[5-5.png|350]] In calculating work done, the actual resistance overcome is measured. This is not necessarily the weight of the object being moved. *[[5-5.png|[Figure 5-5] ]]* A 900-lb load is being pulled a distance of 200 ft. This does not mean that the work done (force × distance) is 180,000 ft-lb (900 lb × 200 ft). This is because the person pulling the load is not working against the total weight of the load, but rather against the rolling [[friction]] of the cart, which may be no more than 90 lb. Friction is an important aspect of work. Without friction, it would be impossible to walk. One would have to shove oneself from place to place, and would have to bump against some obstacle to stop at a destination. Yet friction is a liability as well as an asset, and requires consideration when dealing with any moving mechanism. In experiments relating to friction, measurement of the applied forces reveals that there are three kinds of friction. One force is required to start a body moving, while another is required to keep the body moving at constant speed. Also, after a body is in motion, a definitely larger force is required to keep it sliding than to keep it rolling. Thus, the three kinds of friction may be classified as: (1) starting or [[static friction]], (2) sliding friction, and (3) rolling friction. #### Static Friction When an attempt is made to slide a heavy object along a surface, the object must first be broken loose or started. Once in motion, it slides more easily. The “breaking loose” force is, of course, proportional to the weight of the body. The force necessary to start the body moving slowly is designated “F,” and “F'” is the normal force pressing the body against the surface which is usually its weight. Since the nature of the surfaces rubbing against each other is important, they must be considered. The nature of the surfaces is indicated by the coefficient of starting friction which is designated by the letter “k.” This coefficient can be established for various materials and is often published in tabular form. Thus, when the load (weight of the object) is known, starting friction can be calculated by using the following formula: $F = kF'$ For example, if the coefficient of sliding friction of a smooth iron block on a smooth, horizontal surface is 0.3, the force required to start a 10 lb block would be 3 lb; a 40-lb block, 12 lb. Starting friction for objects equipped with wheels and roller bearings is much smaller than that for sliding objects. For example, a locomotive would have difficulty getting a long train of cars in motion all at one time. Therefore, the couples between the cars are purposely made to have a few inches of play. When starting the train, the engineer backs the engine until all the cars are pushed together. Then, with a quick start forward the first car is set in motion. This technique is employed to overcome the [[static friction]] of each wheel as well as the inertia of each car. It would be impossible for the engine to start all of the cars at the same instant, for static friction, which is the resistance of being set in motion, would be greater than the force exerted by the engine. However, once the cars are in motion, the static friction is greatly reduced and a smaller force is required to keep the train in motion than was required to start it. #### Sliding Friction [[Sliding friction]] is the resistance to motion offered by an object sliding over a surface. It pertains to friction produced after the object has been set in motion, and is always less than starting friction. The amount of sliding resistance is dependent on the nature of the surface of the object, the surface over which it slides, and the normal force between the object and the surface. This resistive force may be computed by using the following formula: $F = nM$ In the formula above, “F” is the resistive force due to friction expressed in pounds; “N” is the force exerted on or by the object perpendicular (normal) to the surface over which it slides; and “m” (mu) is the coefficient of sliding friction. On a horizontal surface, N is equal to the weight of the object in pounds. The area of the sliding object exposed to the sliding surface has no effect on the results. A block of wood, for example, will not slide any easier on one of the broad sides than it will on a narrow side, assuming all sides have the same smoothness. Therefore, area does not enter into the equation above. #### Rolling Friction Resistance to motion is greatly reduced if an object is mounted on wheels or rollers. The force of friction for objects mounted on wheels or rollers is called rolling friction. This force may be computed by the same equation used in computing sliding friction, but the values of “m” will be much smaller. For example, the value of “m” for rubber tires on concrete or macadam is about 0.02. The value of “m” for roller bearings is very small, usually ranging from 0.001 to 0.003 and is often disregarded. Example: An aircraft with a gross weight of 79,600 lb is towed over a concrete ramp. What force must be exerted by the towing vehicle to keep the airplane rolling after once set in motion? $\begin{align*} \text{F} &= \text{nM}\\ &= 0.02mu \times 79,600lb\\ &= 1,592lb. \end{align*}$ ### Power The concept of [[Power Physics|power]] involves the previously discussed topic of [[work]], which was a [[force]] being applied over a [[Measurement|measure]] [[distance]], but adds one more consideration—time. In other words, how long it takes to accomplish the work. If someone asked the average person if he or she could lift one million pounds 5 feet off the ground, the answer most assuredly would be no. This person would probably assume that he or she is to lift it all at once. What if he or she is given 365 days to lift it, and could lift small amounts of weight at a time? The work involved would be the same, regardless of how long it took to lift the weight, but the power required is different. If the weight is to be lifted in a shorter period of time, it will take more power. The formula for power is as follows: $\text{Power} = \text{Force} \times \text{Distance} \div \text{Time}$ The units for power will be [[foot-pounds per minute]], [[foot-pounds per second]], [[inch-pounds per minute]] or second, and possibly mile-pounds per hour. The units depend on how distance and time are measured. Many years ago, there was a desire to compare the power of the newly evolving steam engine to that of horses. People wanted to know how many horses the steam engine was equivalent to. The value we know currently as one horsepower (hp) was developed, and it is equal to 550 foot-pounds per second (ft-lb/s) because of this. It was found that the average horse could lift a weight of 550 lb, one foot off the ground, in one second. The values we use today, in order to convert power to horsepower, are as follows: $\begin{align*} 1hp &= 550ft-lb/s\\ 1hp &= 33,000ft-lb/min.\\ 1hp &= 550 \text{ mile pounds per hour (mi-lb/hr.)}\\ 1hp &= 746 \text{ watts (electricity conversion)}\\ \end{align*}$ To convert power to horsepower, divide the power by the appropriate conversion based on the units being used. Example: What power would be needed, and also horsepower, to raise the GE-90 turbofan engine into position to install it on a Boeing 777-300 airplane? The engine weighs 19,000 lb, and it must be lifted 4 ft in 2 minutes. $\begin{align*}\\ \text{Power} &= \text{Force} \times \text{Distance} \div \text{Time}\\ &= 19000lb \times 4ft \div 2min.\\ &= 38,000ft-lb/min.\\ \end{align*}$ $\begin{align*}\\ \text{Hp} &= 38,000ft-lb/min. \div 33,000ft-lb/min.\\ \text{Hp} &= 1.15 \end{align*}$ The hoist that will be used to raise this engine into position will need to be powered by an electric motor because the average person will not be able to generate 1.15 hp in their arms for the necessary 2 minutes. ### Torque Torque is a very interesting concept and occurrence, and it is definitely something that needs to be discussed in conjunction with work and power. Whereas work is described as force acting through a distance, torque is described as force acting along a distance. Torque is something that creates twisting and tries to make something rotate. If we push on an object with a force of 10 lb and it moves 10 inches in a straight line, we have done 100 in-lb of work. By comparison, if we have a wrench 10 inches long that is on a bolt, and we push down on it with a force of 10 lb, a torque of 100 lb-in is applied to the bolt. If the bolt was already tight and did not move as we pushed down on the wrench, the torque of 100 lb-in would still exist. The formula for torque is: $ \text{Torque} = \text{Force} \times \text{Distance}$ Even though this formula looks the same as the other formula for calculating work, recognize that the distance value in this formula is not the linear distance an object moves, but rather the distance along which the force is applied. Notice that with torque nothing had to move, because the force is being applied along a distance and not through a distance. Notice also that although the units of work and torque appear to be the same, they are not. The units of work were inch-pounds and the units of torque were pound-inches, and that is what differentiates the two. Torque is very important when thinking about how engines work, both piston engines and gas turbine engines. Both types of engines create torque in advance of being able to create work or power. With a piston engine, a force in pounds pushes down on the top of the piston and tries to make it move. The piston is attached to the connecting rod, which is attached to the crankshaft at an offset. That offset would be like the length of the wrench discussed earlier, and the force acting along that length is what creates torque.*[[5-6.png|[Figure 5-6] ]]* ![[5-6.png|350]] For the cylinder in *[[5-6.png|Figure 5-6]]*, there is a force of 500 lb pushing down on the top of the piston. The connecting rod attaches to the crankshaft at an offset distance of 4 in. The product of the force and the offset distance is the torque, in this case 2,000 lb-in. In a turbine engine, the turbine blades at the back of the engine extract energy from the high velocity exhaust gases. The energy extracted becomes a force in pounds pushing on the turbine blades, which happen to be a certain number of inches from the center of the shaft they are trying to make rotate. The number of inches from the turbine blades to the center of the shaft would be like the length of the wrench discussed earlier. Mathematically, there is a relationship between the horsepower of an engine and the torque of an engine. The formula that shows this relationship is as follows: $\text{Torque} = \text{Horsepower} \times 5,252 \div \text{rpm}$ Example: A Cessna 172R has a Lycoming IO-360 engine that creates 180 horsepower at 2,700 rpm. How many pound-feet of torque is the engine producing? $\begin{align*} \text{Torque} &= 180 \times 5,252 \div 2,700\\ &= 350ft-lb. \end{align*}$ ## Simple Machines A machine is any device with which work may be accomplished. For example, machines can be used for any of the following purposes, or combinations of these 5 purposes: 1. Machines are used to transform energy, as in the case of a generator transforming mechanical energy into electrical energy. 2. Machines are used to transfer energy from one place to another, as in the examples of the connecting rods, crankshaft, and reduction gears transferring energy from an aircraft’s engine to its propeller. 3. Machines are used to multiply force; for example, a system of pulleys may be used to lift a heavy load. The pulley system enables the load to be raised by exerting a force that is smaller than the weight of the load. 4. Machines can be used to multiply speed. A good example is the bicycle, by which speed can be gained by exerting a greater force. 5. Machines can be used to change the direction of a force. An example of this use is the flag hoist. A downward force on one side of the rope exerts an upward force on the other side, raising the flag toward the top of the pole. There are only six simple machines. They are the lever, the pulley, the wheel and axle, the inclined plane, the screw, and the gear. Physicists, however, recognize only two basic principles in machines: the lever and the inclined plane. The pulley (block and tackle), the wheel and axle, and gears operate on the machine principle of the lever. The wedge and the screw use the principle of the inclined plane. An understanding of the principles of simple machines provides a necessary foundation for the study of compound machines, which are combinations of two or more simple machines. ### Mechanical Advantage of Machines As identified in statements 3 and 4 under simple machines, a machine can be used to multiply force or to multiply speed. It cannot, however, multiply force and speed at the same time. In order to gain one force, it must lose the other force. To do otherwise would mean the machine has more power going out than coming in, and that is not possible. In reference to machines, mechanical advantage is a comparison of the output force to the input force, or the output distance to the input distance. If there is a mechanical advantage in terms of force, there will be a fractional disadvantage in terms of distance. The following formulas can be used to calculate mechanical advantage. $\begin{align*} \text{Mechanical Advantage} &= \text{Force Out} \div \text{Force in}\\ \text{or}\\ \text{Mechanical Advantage} &= \text{Distance Out} \div \text{Distance In} \end{align*}$ ### The Lever The simplest machine, and perhaps the most familiar one, is the lever. A seesaw is a familiar example of a lever, with two people sitting on either end of a board and a pivoting point in the middle. There are three basic parts in all levers. They are the fulcrum “F,” a force or effort “E,” and a resistance “R.” Shown in *[[5-7.png|Figure 5-7]]* are the pivot point “F” (fulcrum), the effort “E” which is applied at a distance “L” from the fulcrum, and a resistance “R” which acts at a distance “l” from the fulcrum. Distances “L” and “l” are the lever arms. ![[5-7.png|350]] The concept of torque was discussed earlier in this chapter, and torque is very much involved in the operation of a lever. When a person sits on one end of a seesaw, that person applies a downward force in pounds which acts along the distance to the center of the seesaw. This combination of force and distance creates torque, which tries to cause rotation. #### First Class Lever In the first class lever, the fulcrum is located between the effort and the resistance. As mentioned earlier, the seesaw is a good example of a lever, and it happens to be a first class lever. The amount of weight and the distance from the fulcrum can be varied to suit the need. Increasing the distance from the applied effort to the fulcrum, compared to the distance from the fulcrum to the weight being moved, increases the advantage provided by the lever. Crowbars, shears, and pliers are common examples of this class of lever. The proper balance of an airplane is also a good example, with the center of lift on the wing being the pivot point, or fulcrum, and the weight fore and aft of this point being the effort and the resistance. When calculating how much effort is required to lift a specific weight, or how much weight can be lifted by a specific effort, the following formula can be used. Effort (E) × Effort Arm (L) = Resistance (R) × Resistance Arm (l) What this formula really shows is the input torque (effort × effort arm) equals the output torque (resistance × resistance arm). This formula and concept apply to all three classes of levers and to all simple machines in general. Example: A first class lever is to be used to lift a 500-lb weight. The distance from the weight to the fulcrum is 12 inches and from the fulcrum to the applied effort is 60 inches. How much force is required to lift the weight? $\begin{align*} \text{Effort (E)} \times \text{Effort Arm (L)} &= \text{Resistance (R)} \times \text{Resistance Arm (I)} \\ \text{E} \times 60in &= 500lb \times 12in\\ \text{E} &= 500lb \times 12in \div 60in\\ \text{E} &= 100lb\\ \end{align*}$ The mechanical advantage of the lever in this example would be: $\begin{align*} \text{Mechanical Advantage} &= \text{Force Out} \div \text{Force In}\\ &=500lb \div 100lb\\ &= 5, \text{ or } 5 \text{ to } 1. \end{align*}$ An interesting thing to note with this example lever is if the applied effort moved down 10 inches, the weight on the other end would only move up 2 inches. The weight being lifted would only move one-fifth as far. The reason for this is the concept of work. If it allows you to lift 5 times more weight, you will only move it 1⁄5 as far as you move the effort, because a lever cannot have more work output than input. #### Second Class Lever The second class lever has the fulcrum at one end and the effort is applied at the other end. The resistance is somewhere between these points. A wheelbarrow is a good example of a second class lever, with the wheel at one end being the fulcrum, the handles at the opposite end being the applied effort, and the bucket in the middle being where the weight or resistance is placed. *[[5-8.png|[Figure 5-8] ]]* ![[5-8.png|350]] Both first and second class levers are commonly used to help in overcoming big resistances with a relatively small effort. The first class lever, however, is more versatile. Depending on how close or how far away the weight is placed from the fulcrum, the first class lever can be made to gain force or gain distance, but not both at the same time. The second class lever can only be made to gain force. Example: The distance from the center of the wheel to the handles on a wheelbarrow is 60 inches. The weight in the bucket is 18 inches from the center of the wheel. If 300 lb is placed in the bucket, how much force must be applied at the handles to lift the wheelbarrow? $\begin{align*} \text{Effort (E)} \times \text{Effort Arm (L)} &= \text{Resistance (R)} \times \text{Resistance Arm (I)} \\ \text{E} \times 60in &= 300lb \times 18in\\ \text{E} &= 300lb \times 18in \div 60in\\ \text{E} &= 90lb\\ \end{align*}$ The mechanical advantage of the lever in this example would be: $\begin{align*} \text{Mechanical Advantage} &= \text{Force Out} \div \text{Force In}\\ &=300lb \div 90lb\\ &= 3.33, \text{ or } 3.33 \text{ to } 1. \end{align*}$ #### Third Class Lever There are occasions when it is desirable to speed up the movement of the resistance even though a large amount of effort must be used. Levers that help accomplish this are third class levers. As shown in *[[5-9.png|Figure 5-9]]*, the fulcrum is at one end of the lever and the weight or resistance to be overcome is at the other end, with the effort applied at some point between. Third class levers are easily recognized because the effort is applied between the fulcrum and the resistance. The retractable main landing gear on an airplane is a good example of a third class lever. The top of the landing gear, where it attaches to the airplane, is the pivot point. The wheel and brake assembly at the bottom of the landing gear is the resistance. The hydraulic actuator that makes the gear retract is attached somewhere in the middle, and that is the applied effort. ![[5-9.png|350]] ### The Pulley ![[5-10.png|350]] Pulleys are simple machines in the form of a wheel mounted on a fixed axis and supported by a frame. The wheel, or disk, is normally grooved to accommodate a rope. The wheel is sometimes referred to as a “sheave,” or sometimes “sheaf.” The frame that supports the wheel is called a block. A block and tackle consists of a pair of blocks. Each block contains one or more pulleys and a rope connecting the pulley(s) of each block. #### Single Fixed Pulley A single fixed pulley is really a first class lever with equal arms. In *[[5-10.png|Figure 5-10]]*, the arm from point “R” to point “F” is equal to the arm from point “F” to point “E,” with both distances being equal to the radius of the pulley. When a first class lever has equal arms, the mechanical advantage is 1. Thus, the force of the pull on the rope must be equal to the weight of the object being lifted. The only advantage of a single fixed pulley is to change the direction of the force, or pull on the rope. #### Single Movable Pulley ![[5-11.png#sideleft]] A single pulley can be used to magnify the force exerted. In *[[5-11.png|Figure 5-11]]*, the pulley is movable, and both ropes extending up from the pulley are sharing in the support of the weight. This single, movable pulley will act like a second class lever. The effort arm (EF) being the diameter of this pulley and the resistance arm (FR) being the radius of this pulley. This type of pulley would have a mechanical advantage of two because the diameter of the pulley is double the radius of the pulley. In use, if someone pulled in 4 ft of the effort rope, the weight would only rise off the floor 2 ft. If the weight was 100 lb, the effort applied would only need to be 50 lb. With this type of pulley, the effort will always be one-half of the weight being lifted. #### Block and Tackle ![[5-12.png|350]] A block and tackle is made up of multiple pulleys, some of them fixed and some movable. In *[[5-12.png|Figure 5-12]]*, the block and tackle is made up of four pulleys, the top two being fixed and the bottom two being movable. Viewing the figure from right to left, notice there are four ropes supporting the weight and a fifth rope where the effort is applied. The number of weight supporting ropes determines the mechanical advantage of a block and tackle, so in this case the mechanical advantage is four. If the weight was 200 lb, it would require a 50 lb effort to lift it. ### The Gear Two gears with teeth on their outer edges, as shown in *[[5-13.png|Figure 5-13]]*, act like a first class lever when one gear drives the other. The gear with the input force is called the drive gear, and the other is called the driven gear. The effort arm is the diameter of the driven gear, and the resistance arm is the diameter of the drive gear. ![[5-13.png#sideleft]] Notice that the two gears turn in opposite directions: the bottom one clockwise and the top one counterclockwise. The gear on top is 9 inches in diameter and has 45 teeth, and the gear on the bottom is 12 inches in diameter and has 60 teeth. Imagine that the blue gear is driving the yellow one, which makes the blue the drive and the yellow the driven. The mechanical advantage in terms of force would be the effort arm divided by the resistance arm, or 9 ÷ 12, which is 0.75. This would actually be called a fractional disadvantage, because there would be less force out than force in. The mechanical advantage in terms of distance, in rpm in this case, would be 12 ÷ 9, or 1.33. This analysis tells us that when a large gear drives a small one, the small one turns faster and has less available force. In order to be a force gaining machine, the small gear needs to turn the large one. When the terminology reduction gearbox is used, such as a propeller reduction gearbox, it means that there is more rpm going in than is coming out. The end result is an increase in force, and ultimately torque. ![[5-14.png|350]] Bevel gears are used to change the plane of rotation, so that a shaft turning horizontally can make a vertical shaft rotate. The size of the gears and their number of teeth determine the mechanical advantage, and whether force is being increased or rpm is being increased. If each gear has the same number of teeth, there would be no change in force or rpm. *[[5-14.png|[Figure 5-14] ]]* ![[5-15.png#sideleft]] The worm gear has an extremely high mechanical advantage. The input force goes into the spiral worm gear, which drives the spur gear. One complete revolution of the worm gear only makes the spur gear move an amount equal to one tooth. The mechanical advantage is equal to the number of teeth on the spur gear, which in this case there are 25. This is a force gaining machine, to the tune of 25 times more output force. *[[5-15.png|[Figure 5-15] ]]* ![[5-16.png|350]] The planetary sun gear system is typical of what would be found in a propeller reduction gearbox. The power output shaft of the engine would drive the sun gear in the middle, which rotates the planetary gears and ultimately the ring gear. In this example, the sun gear has 28 teeth, each planet gear has 22 teeth, and the ring gear has 82 teeth. To figure how much gear reduction is taking place, the number of teeth on the ring gear is divided by the number of teeth on the sun gear. In this case, the gear reduction is 2.93, meaning the engine has an rpm 2.93 times greater than the propeller. *[[5-16.png|[Figure 5-16] ]]* ### Inclined Plane ![[5-17.png|350]] The inclined plane is a simple machine that facilitates the raising or lowering of heavy objects by application of a small force over a relatively long distance. Some familiar examples of the inclined plane are mountain highways and a loading ramp on the back of a moving truck. When weighing a small airplane, like a Cessna 172, an inclined plane, or ramp, can be used to get the airplane on the scales by pushing it, rather than jacking it. A ramp can be seen in *[[5-17.png|Figure 5-17]]*, where a Cessna 172 right main gear is sitting on an electronic scale. The airplane was pushed up the ramps to get it on the scales. With an inclined plane, the length of the incline is the effort arm and the vertical height of the incline is the resistance arm. If the length of the incline is five times greater than the height, there will be a force advantage, or mechanical advantage, of five. The Mooney M20 in *[[5-17.png|Figure 5-17]]* weighed 1,600 lb on the day of the weighting. The ramp it is sitting on is 6 inches tall, which is the resistance arm, and the length of the ramp is 24 inches, which is the effort arm. To calculate the force needed to push the airplane up the ramps, use the same formula introduced earlier when levers were discussed, as follows: $\begin{align*} \text{Effort (E)} \times \text{Effort Arm (L)} &= \text{Resistance (R)} \times \text{Resistance Arm (I)} \\ E \times 24in &= 1600lb \times 6in\\ E &= 1600lb \times 6in \div 24in \\ E &= 400lb\\ \end{align*}$ ![[5-18.png|350]] Bolts, screws, and wedges are also examples of devices that operate on the principle of the inclined plane. A bolt, for example, has a spiral thread that runs around its circumference. As the thread winds around the bolt’s circumference, it moves a vertical distance equal to the space between the threads. The circumference of the bolt is the effort arm and the distance between the threads is the resistance arm. *[[5-18.png|[Figure 5-18] ]]* Based on this analysis, a fine threaded bolt, which has more threads per inch, has a greater mechanical advantage than a coarse threaded bolt. A chisel is a good example of a wedge. A chisel might be 8 inches long and only 1⁄2 inch wide, with a sharp tip and tapered sides. The 8-inch length is the effort arm and the 1⁄2- inch width is the resistance arm. This chisel would provide a force advantage, or mechanical advantage, of 16. ## Stress Whenever a machine is in operation, be it a simple machine like a lever or a screw, or a more complex machine like an aircraft piston engine or a hydraulically operated landing gear, the parts and pieces of that machine will experience something called stress. Whenever an external force is applied to an object, like a weight pushing on the end of a lever, a reaction will occur inside the object which is known as stress. Stress is typically measured in pounds per square foot or pounds per square inch (psi). External force acting on an object causes the stress to manifest itself in one of five forms, or combination of those five. The five forms are tension, compression, torsion, bending, and shear. ### Tension ![[5-19.png|350]] Tension is a force that tries to pull an object apart. In the block and tackle system discussed earlier in this chapter, the upper block that housed the two fixed pulleys was secured to an overhead beam. The movable lower block and its two pulleys were hanging by ropes, and the weight was hanging below the entire assembly. The weight being lifted would cause the ropes and the blocks to be under tension. The weight is literally trying to pull the rope apart, and ultimately would cause the rope to break if the weight was too great. ### Compression Compression is a force that tries to crush an object. An excellent example of compression is when a sheet metal airplane is assembled using the fastener known as a rivet. The rivet passes through a hole drilled in the pieces of aluminum, and then a rivet gun on one side and a bucking bar on the other apply a force. This applied force tries to crush the rivet and makes it expand to fill the hole and securely hold the aluminum pieces together. *[[5-19.png|[Figure 5-19] ]]* ### Torsion ![[5-20.png|350]] Torsion is the stress an object experiences when it is twisted, which is what happens when torque is applied to a shaft. Torsion is made up of two other stresses: tension and compression. When a shaft is twisted, tension is experienced at a diagonal to the shaft and compression acts 90 degrees to the tension. *[[5-20.png|[Figure 5-20] ]]* ![[5-21.png#sideleft]] The turbine shaft on a turbofan engine, which connects to the compressor in order to drive it, is under a torsion stress. The turbine blades extract energy from the high velocity air as a force in pounds. This force in pounds acts along the length from the blades to the center of the shaft, and creates the torque that causes rotation. *[[5-21.png|[Figure 5-21] ]]* $\\ $ ### Bending ![[5-22.png|350]] An airplane in flight experiences a bending force on the wing as aerodynamic lift tries to raise the wing. This force of lift causes the skin on the top of the wing to compress and the skin on the bottom of the wing to be under tension. When the airplane is on the ground sitting on is landing gear, the force of gravity tries to bend the wing downward, subjecting the bottom of the wing to compression and the top of the wing tension. *[[5-22.png|[Figure 5-22] ]]* During the testing that occurs prior to FAA certification, an airplane manufacturer intentionally bends the wing up and down to make sure it can take the stress without failing. ### Shear ![[5-23.png|350]] When a shear stress is applied to an object, the force trues to cut or slice through, like a knife cutting through butter. A clevis bolt, which is often used to secure a cable to a part of the airframe, has shear stress acting on it. As shown in *[[5-23.png|Figure 5-23]]*, a fork fitting is secured to the end of the cable, and the fork attaches to an eye on the airframe with the clevis bolt. When the cable is put under tension, the fork tries to slide off the eye by cutting through the clevis bolt. This bolt would be designed to take very high shear loads. ### Strain ![[5-24.png|350]] If the stress acting on an object is great enough, it can cause the object to change its shape or to become distorted. One characteristic of matter is that it tends to be elastic, meaning it can be forced out of shape when a force is applied and then return to its original shape when the force is removed. When an object becomes distorted by an applied force, the object is said to be strained. On turbine engine test cells, the thrust of the engine is typically measured by what are called strain gages. When the force, or thrust, of the engine is pulling out against the strain gages, the amount of distortion is measured and then translated into the appropriate thrust reading. A deflecting beam style of torque wrench uses the strain on the drive end of the wrench and the resulting distortion of the beam to indicate the amount of torque on a bolt or nut. *[[5-24.png|[Figure 5-24] ]]* ## Motion The study of the relationship between the motion of bodies or objects and the forces acting on them is often called the study of “force and motion.” In a more specific sense, the relationship between velocity, acceleration, and distance is known as kinematics. ### Uniform Motion Motion may be defined as a continuing change of position or place, or as the process in which a body undergoes displacement. When an object is at different points in space at different times, that object is said to be in motion, and if the distance the object moves remains the same for a given period of time, the motion may be described as uniform. Thus, an object in uniform motion always has a constant speed. ### Speed and Velocity In everyday conversation, speed and velocity are often used as if they mean the same thing. In physics, they have definite and distinct meanings. Speed refers to how fast an object is moving, or how far the object will travel in a specific time. The speed of an object tells nothing about the direction an object is moving. For example, if the information is supplied that an airplane leaves New York City and travels 8 hours at a speed of 150 mph, this information tells nothing about the direction in which the airplane is moving. At the end of 8 hours, it might be in Kansas City, or if it traveled in a circular route, it could be back in New York City. Velocity is that quantity in physics which denotes both the speed of an object and the direction in which the object moves. Velocity can be defined as the rate of motion in a particular direction. Velocity is also described as being a vector quantity, a vector being a line of specific length, having an arrow on one end or the other. The length of the line indicates the number value and the arrow indicates the direction in which that number is acting. ![[5-25.png|350]] Two velocity vectors, such as one representing the velocity of an airplane and one representing the velocity of the wind, can be added together in what is called vector analysis. *[[5-25.png|Figure 5-25]]* demonstrates this, with vectors “A” and “B” representing the velocity of the airplane and the wind, and vector “C” being the resultant. With no wind, the speed and direction of the airplane would be that shown by vector “A.” When accounting for the wind direction and speed, the airplane ends up flying at the speed and direction shown by vector “C.” Imagine that an airplane is flying in a circular pattern at a constant speed. The airplane is constantly changing direction because of the circular pattern, which means the airplane is constantly changing velocity. The reason for this is the fact that velocity includes direction. To calculate the speed of an object, the distance it travels is divided by the elapsed time. If the distance is measured in miles and the time in hours, the units of speed will be miles per hour (mph). If the distance is measured in feet and the time in seconds, the units of speed will be feet per second (fps). To convert mph to fps, divide by 1.467. Velocity is calculated the same way, the only difference being it must be recalculated every time the direction changes. ### Acceleration Acceleration is defined as the rate of change of velocity. If the velocity of an object is increased from 20 mph to 30 mph, the object has been accelerated. If the increase in velocity is 10 mph in 5 seconds, the rate of change in velocity is 10 mph in 5 seconds, or 2 mph per second. If this were multiplied by 1.467, it could also be expressed as an acceleration of 2.93 feet per second per second (fps/s). By comparison, the [[acceleration due to gravity]] is 32.2 fps/s. To calculate acceleration, the following formula is used. $\text{Acceleration (A)} = \frac{\text{Velocity Final (Vf) - Velocity Initial (Vi)}} {\text{Time (t)}}$ Example: An Air Force F-15 fighter is cruising at 400 mph. The pilot advances the throttles to full afterburner and accelerates to 1,200 mph in 20 seconds. What is the average acceleration in mph/s and fps/s? $\begin{align*} A &= \frac {(Vf - Vi)}{t}\\ A &= \frac {(1200 - 400)}{20}\\ A &= 40 mph/s \text{, or multiplying by 1.467, 58.7} fps/s\\ \end{align*}$ In the example just shown, the acceleration was found to be 58.7 fps/s. Since 32.2 fps/s is equal to the [[acceleration due to gravity]], divide the F-15’s acceleration by 32.2 to find out how many G forces the pilot is experiencing. In this case, it would be 1.82 Gs. ### Newton’s Law of Motion #### First Law When a magician snatches a tablecloth from a table and leaves a full setting of dishes undisturbed, he is not displaying a mystic art; he is actually demonstrating the principle of inertia. Inertia is responsible for the discomfort felt when an airplane is brought to a sudden halt in the parking area and the passengers are thrown forward in their seats. Inertia is a property of matter. This property of matter is described by Newton’s first law of motion, which states: Objects at rest tend to remain at rest and objects in motion tend to remain in motion at the same speed and in the same direction, unless acted on by an external force. #### Second Law Bodies in motion have the property called momentum. A body that has great momentum has a strong tendency to remain in motion and is therefore hard to stop. For example, a train moving at even low velocity is difficult to stop because of its large mass. Newton’s second law applies to this property. It states: When a force acts upon a body, the momentum of that body is changed. The rate of change of momentum is proportional to the applied force. Based on Newton’s second law, the formula for calculating thrust is derived, which states that force equals mass times acceleration (F = MA). Earlier in this chapter, it was determined that mass equals weight divided by gravity, and acceleration equals velocity final minus velocity initial divided by time. Putting all these concepts together, the formula for thrust is: $\begin{align*} \text{Force} &= \frac{\text{Weight (Velocity final - Velocity initial)}}{\text{Gravity (Time)}}\\ \text{Force} &= \frac{W(Vf - Vi)}{Gt}\\ \end{align*}$ Example: A turbojet engine is moving 150 lb of air per second through the engine. The air enters going 100 fps and leaves going 1,200 fps. How much thrust, in pounds, is the engine creating? $\begin{align*} F &= \frac{W(Vf - Vi)}{Gt}\\ F &= \frac{150(1200 - 100)}{32.2(1)}\\ F& = 5,124lb \text{ of thrust} \end{align*}$ #### Third Law Newton’s third law of motion is often called the law of action and reaction. It states that for every action there is an equal and opposite reaction. This means that if a force is applied to an object, the object will supply a resistive force exactly equal to and in the opposite direction of the force applied. It is easy to see how this might apply to objects at rest. In application, as a man stands on the floor, the floor exerts a force against his feet exactly equal to his weight. This law is also applicable when a force is applied to an object in motion. Forces always occur in pairs. The term “acting force” means the force one body exerts on a second body, and reacting force means the force the second body exerts on the first. When an aircraft propeller pushes a stream of air backward with a force of 500 lb, the air pushes the blades forward with a force of 500 lb. This forward force causes the aircraft to move forward. A turbofan engine exerts a force on the air entering the inlet duct, causing it to accelerate out the fan duct and the tailpipe. The air accelerating to the rear is the action, and the force inside the engine that makes it happen is the reaction, also called thrust. ### Circular Motion ![[5-26.png|350]] Circular motion is the motion of an object along a curved path that has a constant radius. For example, if one end of a string is tied to an object and the other end is held in the hand, the object can be swung in a circle. The object is constantly deflected from a straight (linear) path by the pull exerted on the string, as shown in *[[5-26.png|Figure 5-26]]*. When the weight is atpoint A, due to inertia it wants to keep moving in a straight line and end up at point B. It is forced to move in a circular path and end up at point C because of the force being exerted on the string. The string exerts a centripetal force on the object, and the object exerts an equal but opposite force on the string, obeying Newton’s third law of motion. The force that is equal to centripetal force, but acting in an opposite direction, is called centrifugal force. Centripetal force is always directly proportional to the mass of the object in circular motion. Thus, if the mass of the object in *[[5-26.png|Figure 5-26]]* is doubled, the pull on the string must be doubled to keep the object in its circular path, provided the speed of the object remains constant. Centripetal force is inversely proportional to the radius of the circle in which an object travels. If the string in *[[5-26.png|Figure 5-26]]* is shortened and the speed remains constant, the pull on the string must be increased since the radius is decreased, and the string must pull the object from its linear path more rapidly. Using the same reasoning, the pull on the string must be increased if the object is swung more rapidly in its orbit. Centripetal force is thus directly proportional to the square of the velocity of the object. The formula for centripetal force is: $\text{Centripetal Force} = \text{Mass}(Velocity^2)\div \text{Radius}\\ $ For the formula above, mass would typically be converted to weight divided by gravity, velocity would be in feet per second, and the radius would be in feet. Example: What would the centripetal force be if a 10-pound weight was moving in a 3-ft radius circular path at a velocity of 500 fps? $\begin{align*} \text{Centripetal Force} &= \text{Mass}(Velocity^2)\div \text{Radius}\\ \text{Centripetal Force} &= 10(500^2)\div 32.2(3)\\ &= 25,880lb \end{align*}$ In the condition identified in the example, the object acts like it weighs 2,588 times more than it actually does. It can also be said that the object is experiencing 2,588 Gs, or force of gravity. The fan blades in a large turbofan engine, when the engine is operating at maximum rpm, are experiencing many thousands of Gs for the same reason. [[AMT General Handbook Ch5_2|➡️]]