Module 2 Physics for Aircraft Maintenance PDF

Physics Student Handout This page intentionally left blank  CONTENTS Page Definitions 5 Study Resources 6 Introduction 7...

Physics Student Handout This page intentionally left blank  CONTENTS Page Definitions 5 Study Resources 6 Introduction 7 What is Physics? 11 Topic 2.1 Matter 19 Topic 2.2.1 Statics 25 Topic 2.2.2 Kinetics 43 Topic 2.2.3 Dynamics 51 Topic 2.2.4 Fluid Dynamics 61 Topic 2.3 Thermodynamics 67 Topic 2.4 Optics (Light) 87 Topic 2.5 Wave Motion and Sound 103 Page 3 of 114  This page intentionally left blank Page 4 of 114  DEFINITIONS Define  To describe the nature or basic qualities of.  To state the precise meaning of (a word or sense of a word). State  Specify in words or writing.  To set forth in words; declare. Identify  To establish the identity of. List  Itemise. Describe  Represent in words enabling hearer or reader to form an idea of an object or process.  To tell the facts, details, or particulars of something verbally or in writing. Explain  Make known in detail.  Offer reason for cause and effect. Page 5 of 114  STUDY RESOURCES Jeppesen General B-2 Student Handout Page 6 of 114  INTRODUCTION The purpose of this subject is to familiarise you with mathematics and physics associated with aircraft design, manufacture and maintenance. On completion of the following topics you will be able to: Topic 1 Matter Define the nature of matter regarding:  The chemical elements  Structure of atoms  Molecules. Define chemical compounds. Define matter in solid, liquid, and gaseous states. Identify changes between states of matter and define the process. Topic 2.1 Statics Describe forces, moments and couples and represent the interaction of these as a vector. Describe the centre-of-gravity of a mass. Describe the elements of theory of stress, strain and elasticity to the following:  Tension  Compression  Shear  Torsion. Describe the nature and properties of solids, fluids, and gases. Describe the action of pressure and buoyancy in liquids (barometers). Topic 2.2 Kinetics Describe the following aspects of linear movement:  Uniform motion in a straight line  Motion under constant acceleration (motion under gravity). Describe the uniform circular motion (centrifugal/centripetal forces) aspect of rotational movement Describe periodic motion and pendular movement. Describe simple theory of the following:  Vibration  Harmonics  Resonance. Describe velocity ratio, mechanical advantage and efficiency. Page 7 of 114 Topic 2.3 Dynamics Describe the following with regard to mass:  Mass  Force  Inertia  Work  Power  Energy (potential, kinetic and total)  Resultant force and equilibrium  Heat  Efficiency. Describe momentum and conservation of momentum. Describe impulse. Describe gyroscopic principles. Describe friction, its nature and effects, and the coefficient of friction (rolling resistance). Topic 2.4 Fluid Dynamics In relation to fluids describe the following:  Viscosity- fluid resistance  Effects of streamlining  Effects of compressibility on fluids. Describe the following types of pressure:  Static  Dynamic  Total. Define Bernoulli’s Theorem and describe the operation of a venturi Topic 3 Thermodynamics Describe temperature and the operation of thermometers. Describe the following temperature scales:  Celsius  Fahrenheit  Kelvin. Define specific heat and describe heat capacity Describe the following methods of heat transfer:  Convection  Radiation  Conduction Describe volumetric expansion State the first and second laws of thermodynamics Describe the following regarding gases:  Ideal gas laws  Specific heat at constant volume and constant pressure  Work done by expanding gas Page 8 of 114  Describe the following:  Isothermal expansion and compression  Adiabatic expansion and compression  Engine cycles  Constant volume and constant pressure  Refrigerators and heat pumps  Latent heats of fusion and evaporation  Thermal energy  Heat of combustion Topic 4 Optics (Light) Describe the nature of light and state the speed of light Describe the laws of reflection and refraction:  Reflection at plane surfaces  Reflection by spherical surfaces  Refraction of light through various media  The use of lenses Describe the nature and use of fibre optics. Topic 5 Wave Motion And Sound Describe the nature of wave motion:  Mechanical waves  Sinusoidal wave motion  Interference phenomena Describe the characteristics of sound:  Production  Intensity  Pitch  Quality State the speed of sound and describe factors that affect it Describe the Doppler Effect. Page 9 of 114  This page intentionally left blank Page 10 of 114  What is Physics? Ever since Humankind developed the ability to ponder its existence, questions have been asked concerning the nature of its environment. Latin, the language of the Roman Empire, contained the word ‘Physica’ for ‘Nature’, hence our use of ‘Physics’ as the overall name of the body of knowledge which attempts to describe the inanimate world. We have become adept at observing and measuring the phenomena that surround us. Certain individuals, e.g. Archimedes and Newton, through chance and circumstance, were able to develop the relationships, between elements of these events, which are now called the Laws of Physics. In many cases, the absolute truths still elude us, and the scientific community has only ‘models’ to offer. For example, the origin of the Universe, or the Structure of the Atom. Even so, we have now gained enough knowledge to create and control the technological environment in which we live. This course attempts to address the basics which serve to underpin most of the technical knowledge that an Aircraft Maintenance Engineer needs. For organisational purposes, Physics is divided up into a number of topics, however it is important to remember that nature works its various strands of magic simultaneously. The rest of this introduction endeavours to provide the reader with the absolute minimum of knowledge with which to attack these separate topics. Origins of the Universe Recent observations have given us the “Big Bang Theory”, which in its most basic form, tells us that the space in which you and I, and the rest of the 1050 kg of matter exist, began as a point source, and has expanded into what we call the Universe. The universe has clumped together into Galaxies, and within these are Planetary Systems associated with Stars. The most frequently asked question when faced with this concept is: Fig 1 “OK, what was there before the Big Bang?” Well, the simplest answer is “nothing” because time itself came into existence and there is can be no concept of “before.” See Fig 1. There are no time values for any universe size less than zero. For all intents and purposes, our concept of time as Page 11 of 114 a means by which we can measure the rate at which events occur will suffice, and our studies will concentrate on those topics which explain our everyday lives. Nature of the Universe Apart from its size, what are the other characteristics or properties of the Universe as we perceive it today? What does it contain? We have already mentioned one - the 1050 kg of matter. The other is energy. What is energy? The Greek word, “energos” - means “that by which activity is possible”, so in non-physics terms, it could be thought of as “that which causes change”. However, that is not measurable enough for physicists. We say that energy provides the “capability to change the state of motion, or matter” of some object or other, and exists in many forms in a fixed amount. For example, kinetic energy is the energy possessed by a moving mass capable of causing change, while potential energy is the energy within a compressed spring which could cause change. Energy used is always fully accounted for in terms of the activity produced. What is matter? The states of matter can be solid, liquid or gaseous, and each of these is related to the amount of internal energy possessed by the matter being under consideration. We can detect this internal energy, and call it heat. It was originally thought to be an invisible fluid called caloric, however, we now know it is bound up in the vibratory motion of the basic particles which make up matter, called atoms and molecules. The amount of heat present depends on the quantity of matter, but how hot it is doesn’t. We express “hotness” as “temperature” and it is measured in degrees. Our star, called the Sun, has radiated energy on to this planet all through its existence, and all changes of state or motion we experience today, are only possible because of this radiation, past and present. An exception to this, is the development and use of Atomic or Nuclear Energy, which involves the conversion of matter into energy, in a similar way to that process used by stars. Properties of Matter Amounts of matter are measured in units of mass of which the standard is the kilogram, and the presence of a mass affects space in two ways. Firstly, there is the amount of space occupied by a certain mass. This is represented by its size in three dimensions. The product of an object’s length, width, and height is called volume, and when all three dimensions are measured in metres, we get cubic metres. Page 12 of 114 Secondly, all masses in space attract each other to a certain degree, depending on their size and distance apart. It is this property of mass that gives all objects on the giant mass we call Planet Earth, (including us), weight. The Latin word meaning heavy was, “gravitas,” - hence the property is now called, “Gravity”. Because the effects of gravity extend outwards from a mass, the mass is said to have a “Gravitational Field” surrounding it. Density To compare different types of matter, let us see how much of each occupies each cubic metre of space, i.e. the number of kilograms of the substance per cubic metre. This derived property thus measures the density of a particular substance, and we get the first relationship between properties, i.e. our first Law of Physics: Density (d or ρ) = Mass m kg/m3 “kilograms per cubic metre” Volume V As mentioned, the units kilogram and metre, are standardised, and most countries maintain an organisation to ensure that they represent the same measurement at all times. In Australia, this is the National Measurement Laboratory, located within the CSIRO Division of Applied Physics in Sydney. The unit kg/m3 is a derived unit Time The measurement of space occupies three dimensions of the Universe, but is not sufficient for us to include the progress of an event in that measurement. For this we have the concept of time, often called the Fourth Dimension. Our ancestors observed the cycles of nature, the passage of the sun etc. which gave them the initial units of days and years. The basic unit of time, the second, s is now fundamental and standardised. Motion With the concept of time, we can measure how a mass may change its position in space. In other words, the idea of motion. An object, (a mass), can be in particular state of motion. At rest (not moving), zero metres per second, (0 m/s) Changing its position at a constant rate, (i.e. a certain number of m/s) Page 13 of 114  Or, that rate could itself be changing with time, giving us m/s per second. (m/s2) A constant rate of m/s is called speed or velocity A constant rate of m/s per s is called acceleration What is required to be able to change this State of motion? Energy and Force English scientist, Isaac Newton (1642 – 1727), observed that if you gave a mass a push or a pull, its state of motion changed. For example, just going from “at rest”, to, “moving” meant an acceleration must have taken place. Energy has been used in this process, but not used up. The energy used to propel the object still exists as the object’s motion, (and in other forms that will be discussed later.) The energy required to provide the push to change this state of motion was found to depend on the mass contained in the object and the amount of acceleration. More mass and/or more acceleration required more push. To quantify this push or pull, Newton took the product of the mass and acceleration required, and called it force, - that which is required to change motion state. Force = Mass x Acceleration This will give us another derived unit for force, the kg.m/s per s. Far too unwieldy, so appropriately enough 1 kg.m/s per s, is actually called 1 Newton. Forces are not always applied by direct contact with an object. Let us revisit gravity. Should you be unlucky enough to be unsupported by the ground or a floor in the Earth’s gravitation field, you will experience a change in motion state. (Fall!) Ignoring for the moment that we have an atmosphere which actually slows thing up a bit, it can be shown that we fall with an acceleration of 9.8 m/s per s. This is called the “acceleration due to gravity” for Earth, and has its own symbol - “g”. From above, Force = Mass x Acceleration, and when that acceleration is “g”, that force is called your weight. Page 14 of 114  Weight = Mass x g (in Newtons) To all intents and purposes, g is constant for all us Earth bound surface dwellers, so interchanging the words mass and weight does not lead to short measures! Pressure Pushing on a surface (or just allowing weight to act on the surface) creates pressure. It is defined as Force per unit area or: P = F/A N/m2 or Pascals (Pa) after Blaise Pascal (1623 - 1662) Work and Power Energy was used during our application of force, and to help quantify what happens to this energy, we take the product of the applied force and the distance moved during the change of position, and call it work. Work = Force x Distance moved The work done equals the energy used, including the energy used to overcome any resistance, e.g. friction and air resistance. Another derived unit appears, the Newton Metre, better known as the Joule after James Joule (1818 -1889), and can now be used as the standard unit for energy of any form. Power is simply a measurement of the rate at which work is done or energy is used. Power = Work done or energy used J/s time time Joules per second are called Watts, after James Watt (1736 – 1819), who experimented with the work done by horses as they pulled barges around the canals of England. 1 horse power = 746 W Initial Conclusions So, what is physics? The study of matter and the activity it gets up to with the energy available? Page 15 of 114 In its simplest form, the Universe can be said to be a collection of Matter and Energy, so that may be as good an answer as any, but to be sure we must now start investigating things further by in the more traditional manner topic by topic. Initially, we will take a closer look at the structure of matter, both in its everyday and smallest form. Then there will be more on how force can be put to good use and how different types of motion can be analysed. Different forms of energy are discussed, including Heat, Light, and Sound, to see how they create the various phenomena that occur. The relationships between the Matter and Energy could just as easily be called the Laws of Nature. Add Chance to the mix and maybe, just maybe, the picture is complete. PS What about Electricity? Try to imagine a world without electricity! Not easy, however there has been no mention of it so far in this introduction to Physics. The use of electricity is so important that it has its own Module, (B1-3). However, it too has its origins in nature, and will be briefly introduced when we look at the structure of matter in its smallest forms. (Atoms and molecules) Fundamental Units The System Internationale, (SI or Metric System) has been internationally agreed, but there are many examples of the British System still used. For example, psi for pressure. Property Metric (SI) British Conversion Mass Kilogram kg Slug 1 slug = 14.59 kg Length Metre m Foot ft 1 ft = 0.305 m Time Second Second N/A Force Newton N Pound lb 1 lb = 4.45 N Pressure Pascal Pa lb/sq in (psi) 1 Pa = 0.00015 psi Work/Energy Joule Foot Pound 1 J = 0.738 ft.lb Acceleration 9.81 m/s per s 32.2 ft/s per s N/A due to gravity Page 16 of 114 Order of Magnitude In the metric system, many prefixes are used to denote how many of any particular unit are being used. The following table will be useful. AMBIENT CONDITIONS 1. Atmospheric Pressure We live at the bottom of an atmosphere comprising of a mixture of gaseous elements and compounds called air. The weight of air acts over the surface of the planet causing it to be ‘under atmospheric pressure’, according to the rule P = F/A. Extending to 160,000 km, with a varying density depending on height, one atmosphere exerts an average pressure, at sea level of 101,320 N/m 2 i.e. 101,320 Pa, which is more commonly written as 1013.2 hPa (hectopascals) alternatively, 1 bar = 100,000 Pa, so I atmosphere is 1.0132 bar or 1013.2 mb In British units, 1 atmosphere is 14.7 lb/in2 One practical method of determining atmospheric pressure is to measure how high a column of liquid can be supported by this pressure. (A barometer.) It turns out to be 29.92 inches or 760 mm of mercury. We feel no ill effect from this pressure because we are permeable enough to allow the pressure inside us to equalise to this. Rapid ascents or descents through the atmosphere are a different story, and aircraft are engineered to cope with this. Page 17 of 114 2. Ambient Temperature The sun radiates its energy continuously on the planet and its atmosphere. Over time, this ocean of air has settled into a complex series of weather patterns, one element of which is the temperature at any given location. This changes from place to place, and with your height above sea level. The temperature is measuring the relative degree of hotness of one area over another and is constantly changing as the day proceeds and the weather patterns shift. At sea level, the temperature ranges from about -30 “degrees Celsius” to about +50°C. At the typical cruising height of a passenger jet, the temperature is just above -60°C. More in Topic 3. 3. International Standard Atmosphere The performance of any aircraft depends heavily on air density, and we’ve just seen that density varies from location to location and with height, as the atmospheric pressure changes with the time of day and weather experienced. To create a benchmark against which aircraft performance can be measured, an International Standard Atmosphere was defined. The essential features of the ISA are a sea level temperature of 15°C, and pressure equal to 1013.2 hPa. Should the conditions be different from these at a particular location, then important performance factors like take-off and landing distances can be easily calculated. Page 18 of 114  TOPIC 1: MATTER Matter refers to everything which occupies space, and has mass which exists in one of three physical states, solid, liquid and gaseous. The total mass of the Universe is conserved, this meaning it cannot be created or destroyed, only changed from one form to another. If you burn 1kg of wood, you finish with 1 kg of ash, smoke, and other gases. Before we can discuss the different properties of each state, let us look at how all forms of matter are put together. Matter itself is made up of small particles. The simplest forms of matter are the elements, whose constituent particles are called atoms, as modeled below. Atoms are largely space with a relatively dense nucleus made up of elementary particles, protons and neutrons, and one or more shells of electrons at certain fixed distances. Each shell represents an energy level within the atom. It requires some two hundred million of them side by side to form a line a centimeter long. Fig 1.1 Imagine the full stop at the end of this sentence. It is probably about 0.5 mm in diameter. If that represents the nucleus, then the electrons in the first shell would be about 50 meters away. Within the atom, there are four Fundamental Interactions which give rise to all other physical processes in the Universe. Simply described, and in order of increasing strength, they are: 1. Gravity. This is the same as already discussed, but very insignificant on the atomic scale. 2. The Weak Nuclear Interaction, which contributes to radio activity. 3. The Electromagnetic Interaction. Acts between the nucleus and electrons and is the source of electrical and magnetic energy. 4. The Strong Nuclear Interaction. Holds the nuclei together. To help analyse interaction 3, we say the proton has a positive electric charge, and the electron, a negative electric charge, where charge is a fundamental property of matter at this level, (in a similar way to mass at all levels.) Page 19 of 114 (The words ‘electron’ and ‘electricity’ come from the Greek word for ‘amber’, the first substance investigated with some of the properties we now control so confidently today.) Elements are detailed in the Periodic Table. For example, pure copper is an element because it is comprised only of copper atoms (Cu). An atom is the smallest part of an element that retains the properties of that element. Fig 1.2 Electrons surround the nucleus in successive groups or shells – like spheres within spheres A Copper atom has 2 electrons in its first or K shell, 8 in the second or L shell, and 18 in the third or M shell, and one electron in its fourth (N) and final, outer shell. Whether the outer shell is relatively empty, half full, or nearly full determines some of the electrical properties of the element. All atoms follow this rule: Maximum number of electrons possible in each shell = 2n2 where n is the shell number. Page 20 of 114 The Periodic Table of Elements Each atom has an identifiable number of protons, neutrons, and electrons. In addition, every atom has its own atomic number, as well as its own atomic mass (as depicted in the periodic table above). Copper has an Atomic Number of 29, because it has 29 protons. Its Atomic Mass is 63.55 amu, a more complex calculation involving averaging the mass of the total number of protons and neutrons together. (Electron mass is 0.0005 times less than either a proton or a neutron, and considered insignificant.) I amu = 1.6 x10-27 kg or 1kg = 625,000,000,000,000,000,000,000,000 amu Ions Atoms which have lost or gained an electron during a process. An atom losing an electron will become positive, whilst an atom gaining an electron will become negative. Isotopes Atoms of the same element with different numbers of neutrons. The Atomic Number remains the same, but the Atomic Mass changes. Page 21 of 114 COMPOUNDS There are 109 known elements currently, however most of the matter around us has been formed by one or more elements combining in such a way to form completely new substances called compounds. This is called chemical bonding, and generally when atoms bond together, they share or transfer electrons and form molecules. Water is a compound because it is made up of hydrogen and oxygen atoms (H2O). The same is true of carbon dioxide (CO2) and common salt, sodium chloride (NaCl). In the example of H2O (water), the oxygen atom has six electrons in its outer, or valence shell. Because there is room for eight electrons in the valence shell, one oxygen atom can combine with two hydrogen atoms by sharing the single electron from each hydrogen atom. Fig 1.3 Water Molecule A compound is matter in which all the molecules are identical, but the molecules are comprised of different atoms in exact proportions. The two or more individual elements are chemically combined to form a separate substance whose characteristics may be completely different from the original element characteristics. A molecule can have: Just one atom (helium) Two atoms of the same element (oxygen – O2) Atoms of several different elements (water – H2O) Subscripts indicate number of particular atoms in the molecule Al2 O3 means two atoms of aluminium and three atoms of oxygen in each molecule of alumina Page 22 of 114 MIXTURES A mixture is a mingled mass of two or more substances where each substance retains it own individual characteristics. For example, Fig 1.4 is a representation of NaCl in H2O (salty water). Mixtures have varying ratios of ingredients that do not combine chemically as they do in a compound. Fig 1.4 Other examples of mixtures are, air (a mixture of oxygen, nitrogen, carbon dioxide and other gases) and metal alloys. Metal alloys sometimes change characteristics when the metals are merged. For example, aluminium becomes stronger and harder when alloyed with certain other metals. This is a physical rather than a chemical combination, occurring at a microscopic scale. Fig 1.5 is a microscopic cross-section of a metal alloy showing crystalline structure. Mixtures may be separated into the original substances Fig 1.5 STATES OF MATTER All atoms and molecules in matter are constantly in vibratory motion. The degree of motion i.e. the internal kinetic energy possessed by the matter, determines its physical state. This internal KE is what we know as heat. What we call ‘temperature’ is, in fact, only a measure of this molecular activity So, at the everyday scale of things, these elements, compounds and mixtures exist as solids liquids or gases, depending on their internal energy or heat content. Fig 1.6 The physical state of a compound has no affect on a compound’s chemical structure. Ice, water, and steam are all H2O. Solids Page 23 of 114 A solid has a definite volume and shape, and is independent of its container. For example, a rock that is put into a jar does not reshape itself to form to the jar. In a solid there is very little heat energy and, therefore, the molecules or atoms cannot move very far from their relative position. For this reason a solid is incompressible, that is, has constant density. Liquids When heat energy is added to solid matter, its molecular movement increases. This causes the molecules to overcome their rigid shape. When a material changes from a solid to a liquid, the material’s volume does not significantly change. However, the material conforms to the shape of the container its held in. Liquids have definite volume but not shape. An example of this is molten steel. Although the molecules of a liquid are farther apart than those of a solid, they are still not far enough apart to make compressing possible and liquids are also considered incompressible. In a liquid, the molecules still partially bond together. This bonding force is known as surface tension and prevents liquids from expanding and spreading out in all directions. Surface tension is evident when a container is filled. Gas As heat energy is continually added to a material, the molecular movement increases further until the liquid reaches a point where surface tension can no longer hold the molecules down. At this point the molecules escape, becoming gas or vapour. The amount of heat required to change a liquid to a gas varies with different liquids. Gases differ from solids and liquids in the fact that they have neither a definite shape nor volume. Chemically, the molecules in a gas are exactly the same as they were in their solid or liquid state. However, because the molecules in a gas are spread out, gasses are compressible. Flow The same property that allows liquids and gases to adopt the shape of their containers, also allows them to flow, and they can both be called fluids. Page 24 of 114  TOPIC 2.1: STATICS Forces A force can be described as that which can produce a change in a body’s state of motion. An application of force will:  start  stop  accelerate, or  decelerate, a mass If energy is available, then forces can be used to do work. Force is an example of a VECTOR quantity that need magnitude (size) and direction to be fully defined. Fig 2.1.1 Most quantities are SCALARS and are defined with size only. For example, temperature, length, and time. Scale drawings are a convenient way to represent vectors. Vector Addition Fig. 2.1.2 Activity Resolve a single force into horizontal and vertical components Page 25 of 114  Sometimes, forces act at different directions on a body. In cases such as these, forces must be resolved to calculate a resultant net force. When an object does not change its state of motion or rest, the resultant of all the forces acting on it is zero, and it is said to be in a state of equilibrium. Fig 2.1.3 For example, if a car is being pushed at one end by a person and opposed at the other end by a similar force, the car does not move. The sum of the positive and negative forces are zero. Activity. Why are the scales in the slide not in equilibrium? Moments and Levers Either side of the lever below, has a moment which is the force multiplied by the distance, from the fulcrum, or pivot, (called the arm) LOAD MOMENT (load x load arm) EFFORT MOMENT Load Effort (force x effort arm) arm arm Fig 2.1.4 The system is balanced when the load moment and the effort moment are equal. If the effort force is increased, the load will be raised. The smaller effort force moves through a larger arc to raise the heavier load a small distance. This is the principle behind “leverage” Page 26 of 114 A lever is an example of a Simple Machine, which is a device used to gain a Mechanical Advantage, MA, where MA = Load Effort In other words, the multiplication of a force by the use of leverage. The mechanical advantage of a first-class lever depends on the distance moved by effort compared to load. The purpose of a lever is to perform work, for a load (L) to be lifted by an effort (E), pivoting around a fulcrum (F). If the load moved is greater than the effort used, the machine has a positive MA. An example of a first-class lever is a CROWBAR E L F Fig 2.1.5 The fulcrum is situated between the load and the effort, and the load is greater than the effort. The lid only needs to be raised a short distance but your hand travels a larger distance Hence “leverage” Examples of a second-class lever include cockpit control levers, such as a throttle or thrust lever, and a simple wheelbarrow. E L F Fig 2.1.6 The load is situated between the fulcrum and the effort. The load is greater than the effort. Positive MA. Page 27 of 114 An example of a third-class lever is the retraction mechanism on an aircraft landing gear Fig 2.1.7 L F E The effort is between the fulcrum and the load. The effort is greater than the load, and moves through a smaller distance MA is less than 1 Velocity Ratio A Velocity Ratio is the direct ratio of two speeds that may be present in the same system. For example, consider a pulley system that uses an MA of 4. The operator will pull through a metre of rope to raise the load by 0.25m. Therefore, the rope moves 4 times as fast as the load is being raised. The velocity ratio is 4:1 So, MA = Distance Ratio = VR Fig 2.1.8 Page 28 of 114 COUPLES A ‘couple’ is a type of moment which is derived from two equal forces acting in parallel but opposite directions on two different points of a body. To explain this concept, consider an aircraft flying straight and level. If a control input is made to turn the aircraft to the left, a force is generated at both the left wing tip and the right wing tip through the ailerons. Fig 2.1.9 The forces are equal, but act in opposite direction. The forces produce a ‘torque’ or twisting force to the aircraft, causing it to turn. If the wing span of the aircraft is b metres, then the torque produced by this couple is given by: T = F x b Nm Other examples include taps and steering wheels. Activity Using the principle of moments, prove that T = F x b for an aeroplane of wingspan b. Page 29 of 114 Centre of Gravity (CG) The Centre of Gravity (‘CG’ or ‘C of G’) of a body is the point from where the weight appears to act, irrespective of the body’s position. The cg of regularly shaped bodies of uniform density is easy to find. It is simply the geometric centre of the bodies Fig 2.1.10 If an irregularly shaped solid is hung first from one point, and then from another point, its CG is the intersection of the verticals passing through these points. The entire weight of a body is considered to act down through the vertical passing through its CG. The body can be raised without toppling by an upward-acting force applied to the underside of the body where the vertical exactly leaves it. Application of the upward force at any other point would tend to tilt the body. Therefore sling or lift loads as near to the CG as possible. Fig 2.1.10 Fig 2.1.12 The cg of an aircraft shifts if passengers, baggage, or equipment in the cabin move, or if unequal amounts of fuel are used from tanks in opposite wings. There is a range of acceptable CG positions between a forward limit and an aft limit. This will ensure the aircraft remains controllable without becoming tail heavy or nose heavy. Page 30 of 114 Consider a perfectly circular disc of constant thickness and density with an axle through its centre. The disc will be balanced at all positions to which it may be rotated around its cg at the centre of the axle. But further to this, balance will be retained regardless of the number of weights that are added to the disc, providing they are paired off diametrically with equal and opposite moments. Fig 2.1.13 Balance of Rotating Components Even with an object of regular shape—a disc or wheel for instance—the thickness or other dimensions may vary slightly because of manufacturing tolerances, or because of wear or damage during use. Also the density may not be perfectly uniform throughout the material. These factors may mean the cg does not coincide with the geometric centre or axis of rotation. Fig 2.1.14 Page 31 of 114 The unbalanced condition will cause vibration during rotation. To rectify this problem the cg must be shifted to make it the same point as the centre of rotation. This can be done by adding small masses of material to the light side of the component, or by removing small masses of material from its heavy side until it balances. Fig 2.1.15 Image shows a propeller in a static balancing rig. The propeller’s supporting mandrel or spindle rolls freely on a pair of horizontal knife edges with very little friction. This kind of balancing is also called mass balancing. The heaviest blade moves downward. When perfectly balanced the propeller will remain stationary in any position to which it is turned. Care must be taken that even slight air movements do not cause wrong indication of balance or imbalance. Many other rotating components are balanced during manufacture. Examples include landing-gear wheel assemblies, helicopter rotors, compressors, turbines, fans, and the rotors in generators, magnetos, and gyroscopes. Some of these may require re-balancing during reconditioning procedures following wear, damage, or replacement of parts. For a component spinning at very high speed even a tiny amount of unbalance may produce excessive vibration. Page 32 of 114 Fig 2.1.16 A component that is in perfect static balance may not be in a balanced state when it is rotating. To illustrate this consider the cylindrical component in the accompanying illustration. At (a) accept that it is in perfect balance when static and when rotating. If, as at (b), two equal weights A and B are added to opposite ends of the cylinder at equal but opposite radii, the cylinder will still be in static balance. However, it will not be balanced when rotating because the weights produce centrifugal forces that act in opposite directions and in different planes of rotation. In (b) the opposing centrifugal forces produced by the weights cause a ccw couple acting in the plane of the paper. Half a revolution later, as in (c), the centrifugal forces produced by the weights cause a cw couple. Thus the couple shown in (b) and (c) tends to cause the axis of the cylinder to wobble during rotation. The imbalanced state caused by the couple shown in (b) and (c) can be corrected by eliminating the couple, or by creating an equal and opposite couple that cancels the effect of the original one. The original couple can be eliminated by removing the weights, or by placing them diametrically opposite each other so that they rotate in the same plane as in (d). A couple equal and opposite to the original one can be created by placing two further weights, equal to A and B, diametrically opposite the A & B weights, as shown in (e). A rotating component that is in balance is said to be in ‘dynamic balance’. When removing interchangeable critical parts from balanced assemblies, it is good practice to identify where they came from so that they can be refitted in their original locations. This decreases the chances of losing the original balance. Page 33 of 114 STRESS, STRAIN and ELASTICITY Stress is the force acting through a section of solid material and defined as force per unit area. Stress = Force Area Strain is the deformation of the material as a result of the stress. If the strain is less than the material’s elastic limit, the elasticity of the material will allow it to return to its natural length. Strain below the elastic limit is directly proportional to the applied stress (Hooke’s Law). Doubling stress will double the strain, (below the elastic limit) If the cross sectional area of the bar is 2 sq.m, Fig 2.1.17 then the stress will be 1000 x 9.8 = 4900 N/m2 2 If it was 0.5 m long and extends by 2 mm, what is the strain? Strain = 2 x 100 = 0.8% 500 Tension describes forces that tend to pull an object apart. Flexible steel cable used in aircraft control systems is an example of a component designed to withstand tension loads. Fig 2.1.18 Compression is the resistance to an external force that tries to push an object together. The weight of an aircraft causes compressive stress to the runway. Fig 2.1.19 Page 34 of 114 Aircraft riveting is performed using compressive forces. When compression loads are applied to the rivet head, the rivet shank will expand until it fills the hole and forms a butt to hold the materials together SHEAR STRESS Fig 2.1.20 Shear stresses occur when external forces distort a body so that adjacent layers of material tend to slide over one another. Shear stress tries to slice a body apart. Shear stress may also occur in fluids, for example a layer of oil or grease between two sliding metal surfaces. Some molecules of lubricant cling to each sliding surface. The subsequent layers of lubricant tend to slide over each other to reduce friction between the metal surfaces. An aeroplane wing or a helicopter rotor blade is very similar to a plank or board. Aerodynamic and gravitational forces try to bend the wing or blade upwards and downwards. Consequently, the top and bottom surfaces of the wing are under alternating compression and tensile stresses and must be constructed to withstand the fatigue that could develop from this situation. During operation, moving parts experience a variety of loadings, caused by vibration, changes of load, and temperature changes. Fig 2.1.21 Repeated applications of small loads may eventually result in fatigue failure. Fatigue failures are quite common in aircraft and motor cars, and are at least as common as overload failures. Page 35 of 114 TORSIONAL STRESS Torsion or torque is a form of shear stress. If a twisting force is applied to a rod that is fixed at one end, the twist will try and slide sections of material over each other. The result is that, in the direction of the twist, there is compression stress and in the direction opposite to the twist, tension stress develops. Fig 2.1.22 A crack can originate at the point of highest tensile stress in a part. Such a crack can grow progressively and the part’s strength is reduced so much that it suddenly breaks. Residual Stress (“Locked In Stress”) Abrupt or uneven temperature changes tend to cause internal stress. This often occurs when heat-treating metals. This effect often explains why a component fails in service even though its externally applied stress levels are low. Residual Stress can be beneficial. The controlled crazing of some car windscreens in a crash or when hit by a stone, is achieved by building residual stress into the glass when the windscreen is made. Page 36 of 114  PRESSURE and BUOYANCY Both liquids and gases are fluids, therefore the theory behind buoyancy and pressure in liquids, such as water, and gases, such as air, is similar. An important difference to remember, though, is that liquids are considered incompressible, that is, have a constant density, while gases are compressible. Pressure Fig 2.1.23 Pressure is defined as: Force per unit area Pressure = Force N/m2 Area Using g = 10 m/s per s Block A, P = 100 x 10 = 250 N/m2 4 Block B, P = 100 x 10 = 1000 N/m2 1 This explains why high heel shoes do more damage to wooden floors, and wide wheels distribute a car’s weight over the tarmac. Pressure in Fluids Pressure is still defined as Force per unit area, but in a fluid it is caused by the continual bombardment of the molecules against the inside of the container The pressure exerted by a column of liquid is determined by the vertical height of the column, gravity, and the density of the fluid. The pressure is not affected by the volume or shape of the liquid. P = pgh where p = density kg/m3 m = mass kg Fig 2.1.24 h = depth m Page 37 of 114 Density and Specific Gravity Density is defined as the mass per unit volume of a substance. A given volume of lead has many times the mass of the same volume of water. When the density of other liquids are compared to water, a table of comparative densities or specific gravities can be determined. (Jepp Gen p. 2-5) Gasoline has a specific gravity of 0.72, which means its weight is 72% of the same amount of water. Gases are compared to air to obtain an SG. Note The term Relative Density is used to compare the density of air at different altitudes to sea level The SG of aviation fuel varies due to a variety of factors such as: refining process; Fig 2.1.25 storage facilities; ambient conditions. The refueller or engineer must check the SG of the fuel supply, to calculate how many litres will provide the weight of fuel requested. Weight of fuel (kg) = Volume (litres) x SG Activity Fuelling Exercise Bouyancy Archimedes principle states that an item placed in fluid will displace a volume of fluid equal to its own volume. Furthermore, the object submerged in the fluid is supported by a force equal to the weight of the fluid displaced. This is the buoyancy force. Therefore if a body displaces more fluid than its own weight it will float. Fig 2.1.26 Page 38 of 114 Three bodies of the same volume but of different SG’s are shown either floating or submerged in water: Fig 2.1.27 Body A with SG of 0.25 – only ¼ submerged Body B with SG of 0.5 – only ½ submerged Body C with SG of 2 – will not float in water – weight is ½’d though If tank were filled with fluid with SG greater than 2 – Body A & B would float higher, & body C would also float – ships float higher in salt water than in fresh. Lower density materials float on higher density materials. For example, gasoline or oil will float on water; Water sinks to the bottom of a petrol tank. ice will float on water; lead will float on mercury but sink in water. Use of Pressure for MA Pascal’s law states ,that when pressure is applied to a confined liquid, the liquid exerts an equal pressure at right angles to the container that encloses it Fig 2.1.28 Pascal’s Law can be used to provide Mechanical Advantage, e.g. A Hydraulic Jack Page 39 of 114 The same volume of fluid is displaced at each end of the system Fig 2.1.29 The same volume of fluid is displaced at each end of the system, 1 psi spread over 10 square inches can support 10 lb so, MA = 10. Note that the large piston will only move up 1/10 of the distance the small piston moves in. If a piston such as the above is used to drive in both directions an interesting situation occurs. The same pressure provides different forces according to direction of travel due to the differing area available. This will also affect the speed at which the operation will occur Fig 2.1.30 Measurement of Pressure Atmospheric pressure at a location then depends on the weight of the column of air above that location. Typically 14.7 psi at sea level up to 4.4.psi at 29,000 ft. Gauge pressure reads pressure above (or below) atmospheric so Absolute Pressure is Gauge Pressure plus Atmospheric Pressure. Tyre pressure gauges read Gauge Pressure For passenger comfort, modern aircraft retain a cabin altitude equivalent to 8000’ or 11 psi. Cruising at 29,000 ft, the outside pressure is 4.4 psi. Therefore, the structure of the aircraft is experiencing a differential pressure of 11 - 4.4 = 6.6.psi This is a significant component of the total stress on the airframe Page 40 of 114 Properties of Solids, Liquids and Gases Solids have a definite shape and a definite volume which is independent of its container. In a solid the forces (bonds) that keep the atoms or molecules together are strong. Therefore, a solid does not require outside support to maintain its shape. Most metals are solids and as such are usually hard and strong and capable of being shaped mechanically, (malleable and ductile). Both liquids and gases are classified as fluids. At any point on the surface of a submerged object, the force exerted by a fluid is perpendicular to the surface of the object. The force exerted by the fluid on the walls of the container is perpendicular to the walls at all points. Although liquids and gases both share the common characteristics of fluids, they have distinctive qualities of their own. A liquid is regarded as incompressible, (fixed density) whereas a gas is comparatively easy to compress. A change in volume of a gas can easily be achieved by changes of temperature and/or pressure. A given mass of gas has no fixed volume and will expand continuously unless restrained by a containing vessel. Page 41 of 114  Intentionally Blank Page 42 of 114 TOPIC 2.2: KINETICS Kinetics is all about states of motion. We will look at how objects can transfer from place to place, and in some cases have a motion whilst not actually getting anywhere! Displacement and Distance Fig 2.2.1 The aircraft may travel a total distance of 2 km as it veers left and right, but its displacement, measured only as the difference between the start point and finish point, will be less. The displacement of the aircraft in an easterly direction only is less again Displacement refers to the position of an object relative to its point of origin. This is different to distance which is the total length travelled by an object from its point of origin. Displacement takes direction into consideration, but distance does not care about direction. Speed and Velocity A similar distinction can be made between speed and velocity. They both refer to the distance travelled per unit of time, for example, miles per hour, Fig 2.2.2 metres per second etc. However, velocity is a vector quantity, so direction is important. Speed is a scalar quantity, so direction is irrelevant. Average speed is distance travelled divided by time taken. Average velocity is the final displacement divided by the total time. Page 43 of 114 Acceleration When an object has an initial velocity then, after a period of time, that velocity has changed (increased or decreased), the object is said to have accelerated. Acceleration can be positive or negative. Negative acceleration is called deceleration. Acceleration is the rate of change in velocity. Average acceleration is found by dividing the change in velocity by the total time taken for this change to occur. A formula can be used to represent this: a=Δv Δt (acceleration equals change in velocity divided by change in time) or, a = (v-u) t where v = final velocity, u = initial velocity and t = time. Acceleration is a vector, so a change in direction even when undertaken at constant speed, is an acceleration. You will remember that force is defined as that which uses energy to produce a change in motion state. NEWTON explored this and formulated his three famous Laws. 1. A body will remain at rest or continue its uniform motion in a straight line until acted upon by an external net force This law is a statement about INERTIA which is the property of mass that resists changes in motion. 2. The acceleration of a body is directly proportional to the force applied to it and is inversely proportional to the mass of the body. This law is represented by the formula: F = ma (force equals mass multiplied by acceleration). Imagine an object at rest on a table. It will stay that way unless pushed. (Newton 1). It is pushed forward by an external force and accelerates. (Newton 2) Stop the force and if there was no further resistance it would continue for ever at its new speed. In fact, there is friction, which provides another external force and the object decelerates and stops. (Also Newton 2) Now imagine a spacecraft outside our atmosphere. A single push will accelerate it to a new velocity which it will maintain for ever, (or until it hits something!) Alternatively, if the same craft was given a continuous push by a motor, it would continue to accelerate reaching enormous velocities. Page 44 of 114 A special case of F = ma is W = mg, where g is the acceleration caused by the gravitational attraction between the mass m and the Earth, equalling 9.8 m/s per sec, and produces the force we call weight W. 3. For every action, there is an equal and opposite reaction. The upward thrust of a rocket is the reaction to the force propelling the mass of hot gas downward. Stand on a skate board and throw a large mass away from yourself, and you will roll in the opposite direction. Linear Motion Motion is said to be uniform if equal displacements occur in equal periods of time. In other words constant velocity. Consider a body moving in a straight line. We have several relationships we can use. Average velocity = displacement and Average speed = distance time time and a = (v-u) where v = final velocity, u = initial velocity and t = time. t However for linear motion, distance and displacement will be the same, and we can extend the above to include the following, where s = distance CIRCULAR MOTION In accordance with Newton’s First Law, the object would shoot off on a straight path unless a Centripetal Force is continually applied to keep it turning along the curve. Page 45 of 114 Newtons 3rd Law demands that there is a reaction the this force keeping the string in tension, the Centrifugal Force. The object is accelerated towards the centre of the orbit. An object travelling along a curved path tends, at all instants, to fly off on the straight line that forms a tangent to the curve of its path (if the string breaks, for example). Tangential direction Fig 2.2.3 Centripetal force is given by Newtons 2nd Law F = ma = mv2 or mw 2 r r where m is mass, v is velocity, w is angular velocity (rpm) and r is the radius. Therefore doubling the rpm, quadruples the centrifugal force, which in a grinding wheel, for example, is trying to pull it apart! Observe RPM limits! This is also one of the reasons a turbine blade ‘creeps’ or elongates during operation. Other aircraft components susceptible to centrifugal stresses are:  Propeller and Helicopter rotor blades  Wheels and tyres Orbits The Earth orbits the Sun and the Moon orbits the Earth. In both cases the orbiting body uses the centrifugal force created by their motion to balance the attraction of gravity. Page 46 of 114 The Space Shuttle and other satellites do exactly the same. The further from the Earth the craft is, the slower the orbital speed needs to be. Eventually at a height of about 22,300 miles, we have a Geosynchronous orbit, that is, an orbit where the satellite speed matches the rotation of the Earth, and it stays over the same spot. The “weightlessness” experienced by an astronaut is a result of the same equilibrium. His or her weight, is balanced by centrifugal force. Fig 2.2.4 Activity: Add the forces to the diagram. Page 47 of 114 PERIODIC MOTION Periodic motion or simple harmonic motion refers to repeated motion, i.e. that which repeats over time. For example, the mass on a spring (below) or a pendulum. The simple pendulum consists of a weight hanging from a point by a string. If the weight is set swinging, the oscillations are termed periodic motion, and the oscillations are predictable. The energy contained in a body moving with SHM is called wave energy. Fig 2.2.5 Fig 2.2.6 SHM occurs around an equilibrium position when a mass is subject to a linear restoring force. A linear restoring force is one that gets proportionally larger with displacement from the equilibrium position. Fig 2.2.7 Elasticity is the property of an object or material which causes it to be restored to its original shape after distortion. It is said to be more elastic if it restores itself more precisely to its original configuration – a piano wire is MORE elastic than a rubber band. A mass on a spring is a good example – when stretched, it exerts a restoring force which tends to bring it back to its original length. Below the elastic limit, the restoring force is proportional to the amount of stretch. (Hooke's Law.) The motion is sinusoidal and demonstrates a single natural or resonant frequency. The amplitude is the maximum distance the mass moves from its equilibrium position. It moves as far on one side as it does on the other. Page 48 of 114 The time that it takes to make one complete repetition or cycle is called the period of the motion. We will usually measure the period in seconds. Frequency is the number of cycles per second that an oscillator goes through. Frequency is measured in "hertz" which means cycles per second. Period and frequency are closely connected; they contain the same information: T = 1/f or f = 1/T The key feature of SHM is that the period or frequency of the motion does not depend on the amplitude of the oscillation From a practical viewpoint, this effect was used to make the first accurate clocks – a pendulum takes the same time to make one oscillation, even though the amplitude of the oscillations damps with time – the period does not change. A pendulum ‘s period T is given by: T = 2π √[L/g] (where L is length) In reality, oscillations do not continue forever – they gradually decrease their motion as energy is lost to friction. You may want the sound caused by a piano or a guitar to continue in this way. But you want the oscillation of your car to stop immediately after going over a bump. Hence the dampers, (shock absorbers.) Vibration is a term normally reserved for high frequency periodic motion In an aircraft, rotating or reciprocal components such as engines and propellers produce vibration which can be annoying and destructive. Vibration experienced in an aircraft may originate from the engines, turbulence, or from flight control flutter due to worn hinges or linkage bearings. The constant vibration is annoying to flight crew and passengers. Also, the structure of the aircraft and other components can vibrate in sympathy and structural damage and component wear can occur. Metal fatigue is an example of such structural damage. RESONANCE Page 49 of 114 The natural or resonant frequency of an object is the frequency where that object vibrates naturally, or without an external force. If two objects have the same natural frequency and are joined to each other, when one of them vibrates, it can transfer its wave energy to the other object making it vibrate. This transfer of energy is known as resonance Fig 2.2.8 Because resonance can induce vibration it can exert destructive forces on an aircraft. For example, it is possible to have portions of an aircraft, such as the propeller, vibrate in resonance at certain engine speeds. HARMONICS Harmonics exist as multiples of an original, natural frequency. That is, if the natural frequency is 100 Hz: the 1st harmonic is at 200 Hz and the 2nd harmonic is at 300 Hz etc Fig 2.2.9 Harmonics can resonate as well as natural frequencies Page 50 of 114  TOPIC 2.3: DYNAMICS One of the fundamental properties of the Universe is that it contains energy, which in turn can be used to effect change. When that change is the state of motion of a mass, then a force has been created. Dynamics is the study of forces at work in motion, and the use of energy. The Difference between Mass and Weight The Earth is a large mass in space and there is a mutual attraction between it and everything on its surface. Because the Earth is so much bigger than everything else, it seems like the attraction is only one way. Newtons Laws tell us that F =ma so when that force is the result of the acceleration due to gravity, g, we re-write this as: W = mg weight N = kg x m/s per s So, why do we say our weight is 70 kg and not 70 x 9.8 ≈ 700 N? Well, we shouldn’t! It has only become acceptable because, if we all stay on the Earth, the error becomes constant. Go to the moon, whose mass I/6 that of the Earth, and your weight will not be the same. You will still have 70 kg of mass, but the weight reduces to 70 x 9.8 ≈ 114 Newtons 6 Our earthly muscles, used to supporting 700 N, can make our 114 N body jump much higher. Travel to Jupiter, (mass 2½ times Earth) and you will weigh 70 x 9.8 x 2.5 ≈ 1715 N The same muscles will collapse under the stress of trying to support this force. Page 51 of 114 Inertia Inertia is the property of a mass which causes it to resist any change in its state of motion Newton’s first law of motion states: A body will remain at rest or continue its uniform motion in a straight line until acted upon by an external net force. The larger the mass, the greater the inertia. Fig 2.3.1 WORK When a force acts on an object, overcomes inertia, and sets it in motion, work is done. Unless the object moves through a distance the work done is said to be zero. Work done is found by the formula W = Fs Where F = force, s = distance The unit of work in the SI system is the joule, which equals 1 Newton metre (Nm) Example: If an object is moved 10 metres by a force of 100 newtons, the work is calculated as: W = Fs W = 100 x 10 (Nm) W = 1 000 joules. In the Imperial system of measurement, a measure of work is the foot-pound, the effort of raising one pound of mass by one foot. POWER Power is the rate of doing work. When determining the amount of work done, the time required to do the work is not considered. Power on the other hand takes time into consideration. For example, if a person climbs a flight of stairs, they perform the same amount of work whether they walk up or run up. However, when the person runs up they are working at a faster rate and therefore using more power. P = W/t The unit SI unit of power is the watt. One watt is the power generated when one joule of work is done in one second. In the imperial system of measurement, power is expressed in foot/pounds per second and one horsepower is equivalent to 550 foot/pounds per second and 746 Watts Page 52 of 114 Because Work = Force x distance Power ac be written as Force x distance time but distance divided by time is velocity so Power = Force x Velocity P = Fv (N x m/s = Watts) Activity The drag (air resistance) of an aircraft is 1500 N. What power is required to fly at 360 km/hr (Ans in kW) What is implied if you have a 230 kW motor? ENERGY Energy provides the capacity for work to be done and effect change. The SI unit of energy is the joule. One joule of energy can do one joule of work assuming there have been no losses like friction. An important concept when thinking about energy is the law of the conservation of energy which states: Energy can neither be created nor destroyed. It can only be changed from one form to another. For example, a car turns the chemical energy found in petrol into mechanical energy, heat and sound. Potential Energy The potential energy in a body or of a body means stored energy, stored in the body because of its position, condition or chemical nature. Even though an object is not doing work, it can still be capable of doing work. For example, a mass held above the ground. While it is being held it has no motion, so it is not doing work. If it is then released, it will fall immediately, thus doing work. (PE = mgh). Mass (kg) x accn due to gravity (9.8 m/s2) x height (m) Hydro electric power uses the energy stored by a mass of water flowing downhill. Page 53 of 114  A drum of gasoline, a stick of explosive, or a chocolate bar all contain potential energy, because of their chemical composition. Fig 2.3.2 Kinetic Energy Kinetic energy is energy a body has because of its motion. If a body is held aloft and then released, as it starts to fall to ground the potential energy is converted to kinetic energy. The formula for calculating kinetic energy is: KE = ½ mv2. Joules, where m = mass (kg) and v velocity in m/s Total Energy In accordance with the law of conservation of energy, the total energy does not change, but potential energy can be transformed into kinetic energy and vice-versa. A falling mass has maximum potential energy at highest elevation (PE = mgh). Kinetic energy is zero because the body has no motion (KE = ½ mv2). Once the mass is released and starts falling, the potential energy starts to be converted to kinetic energy. Half way through its fall, the potential energy exactly equals the kinetic energy. Then, at the instant the body strikes the floor, the kinetic energy is maximum. It has no distance left to fall so potential energy is zero. FRICTION When objects move they usually roll or slide in contact with other objects or substances. Such sliding or rolling contacts have resistance to the force that causes the motion. This resistance is called friction. Fig 2.3.3 In most industrial applications the minimisation of friction is sought, with lubricant, yet friction between our shoes and the ground is necessary to be able to walk and run. Likewise, it is the friction between tyres and the road and between brake rotors and discs that helps slow down a vehicle. Page 54 of 114 The coefficient of friction refers to the differences in friction between various materials. The higher the coefficient of friction (μ), the greater the resistance between two surfaces. Lubrication reduces friction. There are three types of friction 1. Starting or Static - Overcoming initial resistance until breakaway occurs. 2. Sliding - Resistance during steady motion. 3. Rolling - Single point contact resistance is less than sliding. Still need some friction otherwise the wheel will not grip. The amount of sliding friction can be calculated from the relationship” F = μN where N is the reaction to the weight of the object from the surface on which it is sliding. Fig 2.3.4 From above it can be seen why pulling a box with a slight upward angle is easier that pushing when your force may be slightly down on the box. Consider an aircraft landing. Just after touchdown the wings are still supporting some of the weight, and the friction between the wheels and the surface will be small and braking will be inefficient. F = μN L but N = W - L F = μ (W –L) The greater the lift, the smaller the Page 55 of 114 W  friction Airflow spoilers are used to dump this lift and allow the pilot to begin braking earlier Fig 2.3.5 Some example of μ are: Steel on steel 0.09 Rubber tyre on airport runway 0.7 (dry) and 0.5 (wet), Teflon on Teflon 0.04. Coefficients of rolling resistance are very small. For example: Rubber tyres on concrete 0.02 Roller bearings 0.001 Rolling one surface over another creates less friction than sliding one surface over another. Fig 2.3.6 HEAT Heat is one of the most useful forms of energy because of its direct relationship with work, and with the use of engines. Other types of energy can be transformed, in accordance with the law of conservation of energy, into heat. Page 56 of 114 Heat is also found as a consequence of friction. The heat produced by friction is usually unwanted. More in Topic 3 Fig 2.3.7 EFFICIENCY With any machinery, the efficiency is the ratio of work output to workor energy input. If 100 joules of work is put into a gear train and the output is 90 joules, the efficiency is said to be: Efficiency = W (out) x 100 W (in) = 90 x100 = efficiency = 90% 100 It is friction that primarily determines the efficiency of a machine, because the friction between moving parts creates heat, sound and sometimes light. All of these are classified as energy losses. Fig 2.3.8 Reducing friction is usually accomplished by lubrication or streamlining. Page 57 of 114 MOMENTUM Inertia has been defined as the tendency of a mass to resist changes in its state of motion. Momentum however is the product of this inertia and the motion it already has. There are two types of momentum, linear and angular. Linear momentum is a measure of the tendency of a moving body to continue in motion along a straight line. Momentum is defined as the product of the mass and velocity of a body. Fig 2.3.9 M = mv. Momentum is conserved, so if two masses m1 and m2 travelling at v1 and v2 collide, sticking together, and continue as a single mass with new velocity v. then, m1v1 +m2v2 = (m1 +m2)v (V is a vector, so direction is important) Angular momentum is a measure of the tendency of a rotating body to continue to spin about an axis. M = mw where w is the rpm or angular velocity. A spinning skater can vary her RPM by moving her arms in and out, changing the resistance to her rotation Extending her arms places their mass further from the axis of rotation and the resistance to spin increases, reducing the rpm. Bringing them in brings their mass closer to the axis and the rpm increases. That she somehow speeds up, seemingly gaining energy from somewhere, is an illusion. It is actually due to the Conservation of Angular Momentum. Fig 2.3.10 Page 58 of 114 IMPULSE If a force is applied to a moving body, that body’s state of motion is altered. The momentum of the body is changed by an amount called the Impulse. Impulse I = Ft Force multiplied by time A spacecraft’s “burn” i.e. applying thrust for a number of seconds is an example of an Impulse Fig 2.3.11 Activity Consider a mass m acted on by a force F for t seconds. It changes velocity from u to v. Show that the Impulse = Ft is equivalent to a change in momentum mu to mv. A SIMPLE GYROSCOPE A gyroscope is any rotating mass. A useful example is the type consisting of a rotor mounted on gimbals, so that its supporting platform or case can be turned in one or more planes around the rotor without changing the rotor’s plane of rotation. Like all rotating masses, the gyroscope has two fundamental characteristics. These are gyroscopic inertia (rigidity in space) and precession. Fig 2.3.12 Gyroscopic rigidity This the natural property of any rotating mass to resist changes to its plane of rotation unless an external force causes a change. This is the reason a spinning top or coin remains upright until it runs down. If the rotor is in a case securely fitted to the airframe, it will show changes of aircraft attitude. This is the basis for the instrument called the Artificial Horizon or Attitude Indicator. Page 59 of 114 Precession This the change of the plane of rotation caused by an external force. If a force is applied to the rotating mass, overcoming the natural rigidity, then its plane of rotation will deflect 900 in the direction of rotation. Pushing the nose of this aircraft down causes the prop to swing the whole airframe left. If the rotor is aligned nose to tail it will deflect when the aircraft is turned, and measure Rate of Turn Try these with the bike wheel!! Fig 2.3.13 Page 60 of 114  TOPIC 2.4: FLUID DYNAMICS Although liquids & gasses behave in much the same way and share many similar characteristics, they also possess distinct characteristics of their own, specifically: A liquid is difficult to compress and often regarded as being incompressible A gas is easily to compress and usually treated as such - it changes volume with pressure Fig 2.4.1  A given mass of liquid occupies a given volume and will occupy the container it is in and form a free surface  A gas has no fixed volume, it changes volume to expand to fill its containing – it will completely fill the vessel, so no free surface is formed VISCOSITY When a force is applied to a fluid it flows and the fluid deforms permanently. Some fluids flow more readily, than others, and the term viscosity refers to the ‘stiffness’ of a fluid and is defined as the resistance of a fluid to flow. Fig 2.4.2 Thick oil is more resistant to flow than light sewing machine oil, so is more viscous. Page 61 of 114 Air must possess a small amount of viscosity, otherwise there would be no resistance to airflow to provide aerodynamic force. Fig 2.4.3 Viscosity Index The viscosity index of a fluid is a measure of the change in the viscosity of a fluid with a change in its temperature. For most liquids, viscosity decreases with increasing temperature. The molecules are less tightly bound at higher temperatures, so the friction between them is less. For lubricating oils used in aircraft, a low viscosity index is good because this means the properties of the oil will not change much over a wide range of operating temperatures. Molecules of gasses are only weakly kept in position by molecular cohesion – as they are so far apart As adjacent layers move by each other there is a continuous exchange of molecules So, if temperature of a gas increases the momentum exchange between layers will increase, thus increasing viscosity Properties of Fluid Flow A fluid can turn reasonable corners, as shown around this balloon, and this is the Coanda Effect. Because the air is deflected down, the balloon is lifted up. (Newton 3) Right down at the surface of the balloon, individual air molecules are being slowed by friction. The lowest layer of flow is practically stopped and each subsequent layer gets faster until the normal speed is reached a few mm above the surface. The region of flow in which the speed is reduced is called the Boundary Layer. Fig 2.4.4 The shape of an object in airflow is crucial. If the curvature is low enough, the Coanda effect can occur and the flow remains attached. If not, the flow separates and air resistance or drag is high. Page 62 of 114 STREAMLINING Streamlines AIR RESISTANCE OR “DRAG” 100% All three objects have the same sectional area Separated flow 50% However, using an external skin to allow the air to flow more easily 20% around the body will reduce the air resistance due to viscosity. Attached flow Fig 2.4.5 The flow remains attached longer.. This is called streamlining Remember, there has to be some resistance otherwise there would be no flight! STATIC, DYNAMIC AND TOTAL PRESSURE During aircraft flight, the plane travels through a fluid (air) which has a certain Atmospheric or Static pressure, (P), due to the weight of the atmosphere above it. The aeroplane also has forward, dynamic, motion which means that it is striking air molecules at a rate proportional to its speed. creating a dynamic pressure. DP or q = ½pV2 p is air density and V is velocity. Fig 2.4.6 Page 63 of 114 The Dynamic Pressure is caused by the air molecules giving up some of their KE as they meet the object in the airflow. However the Static Pressure is still acting everywhere at the same time. To measure q, a tubular probe is placed pointing into the airflow. It will detect static pressure and dynamic pressure, so a second probe (a hole) is placed out of the airflow at right angles to the flow or on the side of the tube. This hole will measure static pressure only and mechanism is used to subtract the static reading from the total reading. ½pV2 = Total Pressure - P Total probe RAF Static probe Fig 2.4.7 Sealed Capsule Case Total pressure is fed to the inside of the sealed capsule As the static pressure varies in the case, the sealed capsule expands or contracts. This is equivalent to: Fig 2.4.8 ½pV2 = Total Pressure – P A suitable link can moves an indicator as required. Dynamic pressure is expressed as Indicated Airspeed and is a measure of the KE of the airflow that is used to create flight Page 64 of 114 BERNOULLI’S THEOREM The Swiss physicist, Daniel Bernoulli, studied the effects of moving fluids. He used a tube with a throat, the venturi, to experiment with changing static and dynamic pressures. At point A, the fluid has a certain amount of static pressure P, acting in all directions, and an amount of dynamic pressure, Q dependent on its speed in the direction of flow. P A B C Q Fig 2.4.9 As the fluid approaches the constriction at B, it has to speed up to maintain a constant rate of mass flow. (At low speeds air is assumed to be incompressible) Now, if more energy is used in forward motion there is less available to exert pressure against the sides of the tube at B. (Conservation of Energy) So the static pressure P reduces. As each molecule speeds up through the venturi it strikes the tube wall less often. At C, the flow is the same as at A. This reduction of static pressure through a constriction is called the Venturi Effect and is represented by the Bernoulli Theorem equation: Static Pressure + Dynamic Pressure = Constant (Total Pressure) THE VENTURI EFFECT Page 65 of 114 Venturis are found in many applications. The piston above forces air through the venturi, and the pressure at the throat drops. Atmospheric pressure in the round container (reservoir) is now greater, and the liquid (red) travels up the tube, joins the airstream, and is sprayed. Fig 2.4.10 An extension of Bernoulli’s Theorem is the basis of how some of the lift is generated by aircraft wings, propellers and helicopter rotor blades. Fig 2.4.11 The top of the wing roughly approximates to half of a venturi. The air passing over the top surface of the wing moves at a higher velocity. The higher velocity causes a decreased pressure there, and a pressure difference between upper and lower wing surfaces contributes to the force known as ‘lift’. Note: Leading edges” experience total pressure, not dynamic pressure only Page 66 of 114  TOPIC 3: THERMODYNAMICS Earlier energy was described as that property of the Universe which can cause change. Through the application of force, work is done. Every star radiates the energy it develops internally, and any associated planets at the appropriate distance can absorb and use this energy to evolve accordingly. Heat is one form of energy, and in many cases the production of heat and its subsequent release can do useful work. The Conservation of Energy states that energy cannot be created or destroyed, only converted from one form to another. Energy concerning the application, loss or transfer of heat is termed thermal energy. According to the law of conservation of energy, thermal energy cannot be created or destroyed, but it is converted from, and to, other forms of energy. For example, thermal energy may be created from electrical, chemical, mechanical or nuclear energy. It can be converted to mechanical or kinetic energy. The heat in a thermal process can also add energy to chemical reactions. Although all substances can absorb and radiate heat energy, it is the gases that can most easily turn this into useful work. The work done by an expanding gas is one of the basic principles behind propulsion. HEAT TRANSFER Conduction Conduction requires physical contact between a body having a high level of heat energy and a body having a lower level of heat energy. When a cold object comes into contact with a hotter object, the action of the molecules in the hot material transfers some of their energy to the molecules in the colder material. Similarly, if one part of a body is heated then the energy will be transferred internally molecule to molecule as they become more agitated. Eventually the activity of the molecules in the two materials becomes equalised and thus the temperatures also equalise, before falling as heat is lost to the surroundings. Page 67 of 114  An example of heat transfer by conduction is the removal of heat from an engine cylinder by cooling fins. The combustion of gasoline in the cylinder releases heat which is conducted to the cylinder head and cooling fins. The heat is then conducted to the cooler air and carried away. Fig 3.1 CONVECTION Convection is the process by which heat is transferred by bulk movement of a fluid. As fluid is heated by a heat source, it becomes less dense and rises, being replaced by cooler fluid. Heating water in a kettle, heating air in a house and the circulation of atmospheric heat are examples of convection. The handle of the saucepan is made from a material that does not conduct heat very well. Therefore the handle will stay relatively cool while the metallic saucepan becomes hot. Convection currents Fig 3.2 RADIATION Page 68 of 114 Electromagnetic Radiation refers to the emission of energy from the surface of most objects, and is related to the acceleration of charged particles. EMR is energy propagation by periodic variation of the electric E, and magnetic field M, strengths caused by the acceleration of charged particles. There are charged particles within the molecules that make up a substance. The nature of the motion possessed by these particles is acceleration because they constantly change direction. Fig 3.3 These are not mechanical waves, but they display similar behaviour, and are able to travel through vacuum. The M and E waves are perpendicular to each other. At a certain frequency of this wave motion, approx 1013 Hz, the energy is propagated as heat. (Actually called Infra-Red as it is just lower than red light) Fig 3.4 All the energy we receive from the sun has been radiated to us across 93 million miles of vacuum. There is no need for intermediate matter to transfer radiant energy. Only a small part of the energy we receive from the sun is light. Much of the rest is radiant heat. Conduction and convection take place relatively slowly while radiation takes place at the speed of light. Page 69 of 114 Kinetic Theory of Matter It was discovered that the smallest particles of most substances, molecules, are constantly in random motion. (For elements, read atoms.) Heat is described as the kinetic energy associated with this motion The more heat energy there is in a material, the faster its molecules move, and changes will occur to the substance. Initially solids will expand as their molecules take up more space with the movement. Railway tracks have expansion joints fitted to allow the track to move under hot sun. Expansion is calculated using the formula E = kL(T2 –T1) Fig 3.5 Where L is the original size, T2 -T1 is the temperature difference, and k is the Co- efficient of Linear Expansion for the material. Jeppesen Gen p. 2-18 Remember, if two dissimilar substances are joined and heated, they will expand at different rates and create stress in the structure. (Bi-metallic strip) The two metals in the bi-metallic strip expand different amounts with heating. Hence the strip bends with temperature changes. Fig 3.6 The bending operates the electrical contacts for thermostats, and keeps the clock wheel in balance for constant speed at differing temperatures. Change of State Eventually, as heat is added, the same molecules have become so far apart that the substance changes state to a liquid. Keep heating the material and it changes state again and becomes a gas. The molecules are so far apart now that they become independent of each other. Remember our goal is to understand the transfer of energy (as heat), to effect change by the application of force. It is fairly simple to see using incompressible substances such as solids, (hitting something with a hammer!), and liquids. (Hydraulic Systems) Page 70 of 114 For gasses, which are compressible, it is more complicated and we must investigate the behaviour of gasses as they absorb and release heat before we see how they help create propulsion. Firstly though, some terminology: UNITS OF HEAT Calorie (cal): one calorie is the quantity of heat required to raise the temperature of one gram of water by one degree Celsius. British thermal unit (Btu): one Btu is the quantity of heat required to raise the temperature of one pound of water by on degree Fahrenheit. Joule (J): the SI unit for all forms of energy. Energy provides the capacity for work to be done. Fig 3.7 One joule of energy can do one joule of work. The heat produced by burning one litre of gasoline is about 8 x 106 cal, 3 x 104 Btu, or 3 x 107 J (30 MJ). TEMPERATURE Temperature represents the degree of heat possessed by one mass over another. When heat flows from one body to another, the hotter is said to be at a higher temperature. However, a cup of water at 90°C contains less heat than a swimming pool at 20°C. For this reason we define two properties, one called the Specific Heat of a substance, and the other, the Heat Capacity. (Jeppesen General p. 2-30) Specific Heat and Heat Capacity The specific heat of a substance is the number of calories required to raise the temperature of 1 gram of the substance by 1°C. or, the number of Btu’s required to raise the temperature of 1 pound of the substance by 1°F. Water is used as the benchmark as it takes 1 calorie to raise 1 gram of water by 1°C. Other substances, notably metals, take very much less energy to raise their temperature. The high specific heat of water is why ocean temperature does not vary as much as land temperature. This allows the oceans and large lakes of the earth to act as heat sinks or temperature stabilisers. The heat capacity C of a substance is the amount of heat required to change its temperature by one degree, and has units of energy per degree. Page 71 of 114 Temperature Scales Temperature represents the average kinetic energy of molecules and is measured in degrees (°). There are four main temperature scales: degrees Celsius (°C), degrees Fahrenheit (°F), degrees Rankine (°R) and Kelvin (K). With the Kelvin scale, the unit ‘degrees’ and its symbol(°) is not used. It is said that water boils at 373 K. Thermometers are used to measure temperature and they are constructed using the fact that changes of state occur at a constant temperature. The heat added during change of state is not used to expand the substance so mercury in a thin glass tube will expand and contract between the temperature