CDC SC02M0X Aerospace Maintenance Technician Volume 1. General Aerospace Core Knowledge ___________ (cid:52) Air Force Institute for Advanced Distributed Learning Air University Air Education and Training Command This material contains “For Official Use Only” information, which cannot be released to unauthorized persons. The provisions of DOD Regulation 5400.7/Air Force Supplement apply. For Official Use Only Author: MSgt Daryle K. Fry 20th Air Force AFSPC A4I UNK Warren Air Force Base, Wyoming, 82001 DSN: 481-5424 E-mail address: [email protected] Instructional Systems Specialist: R. Pete Anderson Editor: Debra H. Banker Air Force Institute for Advanced Distributed Learning Air University (AETC) Maxwell Air Force Base, Gunter Annex, Alabama 36118–5643 Material in this volume is reviewed annually for technical accuracy, adequacy, and currency. For SKT purposes the examinee should check the Weighted Airman Promotion System Catalog to determine the correct references to study. For Official Use Only Preface ________________________________________________________i THIS TWO-volume specialized course, SC02M0X, is designed to expand the knowledge of the aerospace technician in a manner that may contribute to successful SpaceTEC® aerospace certification. SpaceTEC® is a National Science Foundation sponsored National Center of Excellence established to serve as a focal point for aerospace technician training. Volume one provides basic math skills, introduction to aerospace systems, and general safety requirements technicians need to know. Volume two’s focus is on the more specific processes a technician will encounter. These processes range from material processes to working with electrical components. Code numbers on figures are for preparing agency identification only. The use of a name of any specific manufacturer, commercial product, commodity, or service in this publication does not imply endorsement by the Air Force. To get a response to your questions concerning subject matter in this course or to point out technical errors you find in the text, unit review exercises, or course examination, call or write the author using the contact information on the inside front cover of this volume. NOTE: Do not use the IDEA Program to submit corrections for printing or typographical errors. Consult your education officer, training officer, or NCOIC if you have questions on course enrollment or administration, Your Key to a Successful Course, and irregularities (possible scoring errors, printing errors, etc.) on the unit review exercises and course examination. Send questions these people cannot answer to AFIADL/DOI, 50 South Turner Blvd., Maxwell AFB, Gunter Annex AL 36118–5643, on our Form 17, Student Request for Assistance. You may choose to complete Form 17 on the Internet at this site: http://www.maxwell.af.mil/au/afiadl/registrar/download_fr.htm. This volume is valued at 27 hours and 9 points. For Official Use Only ii _______________________________________________________ Preface NOTE: In this volume, the subject matter is divided into self-contained units. A unit menu begins each unit, identifying the lesson headings and numbers. After reading the unit menu page and unit introduction, study the section, answer the self-test questions, and compare your answers with those given at the end of the unit. Then complete the unit review exercises. For Official Use Only Contents ______________________________________________________iii Page Unit 1. Mathematics.............................................................................................................1–1 1–1. Basic Math.................................................................................................................1–1 1–2. Advanced Math........................................................................................................1–16 Unit 2. Introduction to Aerospace and Safety...................................................................2–1 2–1. Introduction to Aerospace..........................................................................................2–1 2–2. Introduction to Launch Systems...............................................................................2–41 Unit 3. Safety........................................................................................................................3–1 3–1. Workplace Hazards....................................................................................................3–1 3–2. Aerospace Safety......................................................................................................3–41 Glossary.............................................................................................................................................G–1 For Official Use Only Please read the menu for unit 1 and begin. (cid:206) For Official Use Only Unit 1. Mathematics 1–1. Basic Math.................................................................................................................................1–1 001. Whole numbers..................................................................................................................................1–1 002. Fractions............................................................................................................................................1–3 003. Decimals............................................................................................................................................1–7 1–2. Advanced Math.......................................................................................................................1–16 004. Ratios...............................................................................................................................................1–16 005. Proportion........................................................................................................................................1–19 006. Positive and negative numbers........................................................................................................1–19 007. Powers and roots..............................................................................................................................1–20 008. Computing area................................................................................................................................1–24 009. Computing the volume of solids......................................................................................................1–32 010. Graphs and charts............................................................................................................................1–36 011. Measurement systems......................................................................................................................1–39 012. Functions of numbers......................................................................................................................1–43 T HE use of mathematics is so woven into every area of everyday life that seldom, if ever, does one fully realize how very helpless we would be in the performance of most of our daily work without the knowledge of even the simplest form of mathematics. Many persons have difficulty with relatively simple computations involving only elementary mathematics. Performing mathematical computations with success requires an understanding of the correct procedures and continued practice in the use of mathematical manipulations. 1–1. Basic Math A person entering the aerospace field will be required to perform with accuracy. The aerospace mechanic is often involved in tasks that require mathematical computations of some sort. Tolerances in aircraft and engine components are often critical, making it necessary to measure within a thousandth or ten-thousandth of an inch. Because of the close tolerances to which you must adhere, it’s important that you (the aerospace mechanic) be able to make accurate measurements and mathematical calculations. Mathematics may be thought of as a kit of tools, each mathematical operation being compared to the use of one of the tools in the solving of a problem. The basic operations of addition, subtraction, multiplication, and division are the tools available to aid in solving a particular problem. In this section, we’ll explore the following four subject areas as they apply to basic math: 1. Whole numbers. 2. Fractions. 3. Mixed numbers. 4. Decimals. 001. Whole numbers Whole numbers are the numbers beginning with 0, with each successive number greater than its predecessor by 1. There are four basic mathematical operations you can perform using whole numbers. They are as follows: 1. Addition of whole numbers. 2. Subtraction of whole numbers. For Official Use Only 1–2 3. Multiplication of whole numbers. 4. Division of whole numbers Addition of whole numbers The process of finding the combined amount of two or more numbers is called addition. The answer is called the sum. When you’re adding several whole numbers, such as 4567, 832, 93122, and 65, place them under each other with their digits in columns so that the last, or right hand, digits are in the same column. When you’re adding decimals such as 45.67, 8.32, 9.8122, and .65, place them under each other so that the decimal points are in a straight “up-and-down” line. To check addition, either add the figures again in the same order, or add them in reverse order. Subtraction of whole numbers Subtraction is the process of finding the difference between two numbers by taking the smaller from the larger of the two numbers. The number that’s subtracted is called the subtrahend, the other number is the minuend, and their difference is called the remainder. To find the remainder, write the subtrahend under the minuend, as in addition. Beginning at the right, subtract each figure in the subtrahend from the figure above it and write the individual remainder below in the same column. When the process is completed, the number below the subtrahend is the remainder. To check subtraction, add the remainder and the subtrahend together. The sum of the two should equal the minuend. Multiplication of whole numbers The process of finding the quantity obtained by repeating a given number a specified number of times is called multiplication. More simply stated, the process of multiplication is, in effect, a case of repeated addition in which all the numbers being added are identical. Thus, the sum of 6 + 6 + 6 + 6 = 24 can be expressed by multiplication as 6 × 4 = 24. The numbers 6 and 4 are known as the factors of the multiplication, and 24 as the product. In multiplication, the product is formed by multiplying the factors. When one of the factors is a single-digit integer (whole number), the product is formed by multiplying the single-digit integer with each digit of the other factor from right to left, carrying when necessary. When both factors are multiple-digit integers, the product is formed by multiplying each digit in the multiplying factor with the other factor. Exercise care when you’re writing down the partial products formed. Be certain that the extreme right digit lines up under the multiplying digit. It’s then a matter of simple addition to find the final product. Example: Determine the cost of 18 spark plugs that cost $3.25 each. 3.25 ×18 2600 3250 58.50 When you’re multiplying a series of numbers together, the final product will be the same regardless of the order in which the numbers are arranged. For Official Use Only 1–3 Example: Multiply: (7) (3) (5) (2) = 210 7 21 105 7 3 25 ×3 ×5 ×2 or ×5 ×2 ×6 21 105 210 35 6 210 Division of whole numbers The process of finding how many times one number is contained in a second number is called division. The first number is called the divisor, the second the dividend, and the result is the quotient. Of the four basic operations with integers, division is the only one that involves trial and error in its solution. It’s necessary that you guess at the proper quotient digits, and through experience you’ll tend to lessen the number of trials; everyone will guess incorrectly at some time or another. Placing the decimal point correctly in the quotient quite often presents a problem. When you’re dividing a decimal by a decimal, an important step is to first remove the decimal from the divisor. Do this by shifting the decimal point to the right the number of places needed to eliminate it. Next, move the decimal point to the right as many places in the dividend as was necessary to move it in the divisor, and then proceed as in ordinary division. Example: 2.75 divided by .25 1. First, move the decimal point of the divisor two places to the right. 2. Then, move the decimal point of the dividend two places to the right. Order of operation when solving complex equations. When solving equations, many times more than one mathematical operation will be performed. For instance, two numbers may be added together and then divided by another. Brackets and parentheses are used to identify the necessary operations. These operations must be done in a certain order also. The operation within the parentheses is accomplished first and then the operation within the brackets is accomplished before solving the equation. Here is an example. Solve the equation. [(2–1) + (5×2)] Divided by 2 = ? Solve parentheses. [1+10] Divided by 2 = ? Solve brackets. 11 Divided by 2 = ? Solve equation. 11 divided (also represented by the symbol “/”) 2 = 5.5 002. Fractions A fraction is an indicated division that expresses one or more of the equal parts into which a unit is divided. For example, the fraction 2/3 indicates that the whole has been divided into 3 equal parts and that 2 of these parts are being used or considered. The number above the line is the numerator, and the number below the line is the denominator. If the numerator of a fraction is equal to or larger than the denominator, the fraction is known as an improper fraction. In the fraction 15/8; if the indicated division is performed, the improper fraction is changed to a mixed number, which is a whole number and a fraction: 15 7 =1 8 8 For Official Use Only 1–4 A complex fraction is one that contains one or more fractions or mixed numbers in either the numerator or denominator. The following fractions are examples: 1 5 3 1 3 2 8 4 2 ; ; ; ; 2 2 5 2 3 8 3 A decimal fraction is obtained by dividing the numerator of a fraction by the denominator and showing the quotient as a decimal. The fraction 5/8 equals 5 ÷ 8 = .625. A fraction doesn’t change its value if both numerator and denominator are multiplied or divided by the same number. 1 3 3 1 × = = 4 3 12 4 The same fundamental four operations (addition, subtraction, multiplication, and division) you performed with whole numbers can also be performed with fractions. Addition and subtraction of common fractions In order to add or subtract fractions, all the denominators must be alike. In working with fractions, as in whole numbers, the rule of likeness applies; that is, only like fractions may be added or subtracted. When you’re adding or subtracting fractions that have like denominators, it’s only necessary for you to add or subtract the numerators and express the result as the numerator of a fraction whose denominator is the common denominator. When the denominators are unlike, it’s necessary that you first reduce the fractions to a common denominator before proceeding with the addition or subtraction process. Examples: 1. A certain switch installation requires 5/8-inch plunger travel before switch actuation occurs. If 1/8-inch travel is required after actuation, what will be the total plunger travel? FIRST: Add the numerators. 5+1=6 NEXT: Express the result as the numerator of a fraction whose denominator is the common denominator. 5 1 6 + = 8 8 8 2. The total travel of a jackscrew is 13/16 of an inch. If the travel in one direction from the neutral position is 7/16 of an inch, what’s the travel in the opposite direction? FIRST: Subtract the numerators. 13−7=6 NEXT: Express the result as the numerator of a fraction whose denominator is the common denominator. 13 7 6 − = 16 16 16 3. Find the outside diameter of a section of tubing that has a 1/4-inch inside diameter and a combined wall thickness of 5/8 inch. 1 2 5 5 FIRST: Reduce the fractions to a common denominator. = = 4 8 8 8 For Official Use Only