Precision Measurement

1. Precision Measurement Foundations of Engineering

2. Precision Measurement When measured quantities are reported, the last significant digit in a measurement is somewhat uncertain. ( Park, 1996) “…the last significant digit is a carefully considered estimate by the experimenter and represents the limit of his or her ability to measure, given the measuring instrument being used and the conditions under which the measurement is made. This uncertainty carries over into the result calculated from the measurements. Thus the number of significant figures in a quantity is the number of trustworthy figures in it, the last trustworthy figure being somewhat in doubt (but still useful), because it is based upon an estimation.” ( Park, 1996)

3. Precision Measurement • Therefore Precision Measurement must take into consideration: • Significant Digits • Units • Measuring Power & Energy

4. Precision Measurement • How many digits are significant? • Addition and Subtraction: • Any answer can be no more accurate as the LEAST accurate number that was used to calculate it • Therefore: • 2.200 kg + 1.2 kg = 3.4 kg • 2.25 kg + 1.2 kg = *3.5 kg * - see rules for rounding.

5. Precision Measurement • In multiplication and division you must count the digits. • The answer can have only have as many significant figures as the LEAST of the numbers used to get it. • Non-zero digits are always significant. • 523.7 has ____ significant figures • Any zeros between two significant digits are significant. • 23.07 has ____ significant figures • A final zero or trailing zeros in the decimal portion ONLY are significant. • 3.200 has ____ significant figures • 200 has ____ significant figures • 2.00 x 10^2 ____ significant figures

6. Precision Measurement • Does 1000 ml mean exactly 1000? Not necessarily. • 100, 100, 10, and 1 all have one significant digit. • If the engineer wanted to express exactly 1000, he/she would have to write 1.00 x 10^3.

7. Precision Measurement • Rounding • Example: 3.141592653589 (What number is this?)* • Look at the number to the immediate right of the place you are rounding to: • If it is greater than 5 (i.e., 6, 7, 8, or 9), round the place of interest up. • So π to 4 decimal places is __________ • If it is less than 5 (i.e., 0, 1, 2, 3, 4), leave the place of interest unchanged. • So π to 2 decimal places is __________ • If it is 5 (use the round-to-even rule): round up by one if there are any non-zero digits following the 5 • If there are only zeros following the 5, round up by one if the place of interest is odd, or else leave it unchanged if it is even. • So π to 3 decimal places is __________ • So π to 7 decimal places is __________

8. Precision Measurement • Units of Measure • Base Units SI and EES (English Eng. System) Quantity SI EES Length meter foot Mass kilogram lb. Time second second Electric current ampere Thermd temp kelvin fahrenheit Amount of Substance mole Luminous intensity candela

9. Precision Measurement • Units of Measure • Supplemental Units SI and EES (English Eng. System) Quantity SI EES Plane Angle radian Solid Angle steradian

10. Precision Measurement • Units of Measure • Derived Units and Common Derived Units • Unit Conversions • Several should be committed to memory. • Fahrenheit to Celsius • Millimeters to inches • Kilograms to pounds • Gallons to liters • Online Conversion Sources • www.onlineconversions.com or www.efunda.com

11. Precision Measurement • Using the Engineering Solution Layout Excel Spreadsheet, convert the following paying attention to significant digits. • Assignment 1: Conversion Worksheet

12. Measuring Power & Energy Vocabulary Power Mechanical Converter Torque Efficiency Horsepower BTU Calorie Force Gravity Metric System Pressure Speed Tachometer Weight Work Precision Measurement

13. Precision Measurement • Energy Defined • Most energy converters such as a diesel or gasoline engine are designed to accomplish one purpose: convert energy into useful work. • Energy: the ability to do work. • How does this take place in a gasoline engine? • Forceis any push or pull on an object. • Gravity is a force that pulls down on every object on earth. • To lift the object we must exert force greater than the weight…therefore weight is considered to be a force equal to the pull of gravity on an object.

14. 20 LBS. X 50 FT.= 1000 FT-LB. 20 LBS. Precision Measurement • Work Defined: • Work is defined as the result of applying a force to move a mass a certain distance. • This force is created by the combustion of a source of fuel, such as gasoline. • Work is produced when the force moves a certain mass a certain distance. • WORK = FORCE X DISTANCE • Problem 1: FORCE 50 FEET

15. Precision Measurement • Torque Defined: • Torque is the twisting force on a shaft. • Torque wrench produces a twisting force, measured in ft.-lb. • Torque = Force (lbs.) x radius (ft.) • Torque is also produced on the output shaft of engines because of the combustion of fuel/pushes pistons downward/causing crankshaft to spin. • This force (torque) causes other objects to rotate, turning transmissions and wheels, boat props, lawn mower blades, etc. • Problem 2: • A lug nut on a car tire is very tight. When repairinga flat tire, Jenny has a choice between a 12 inch and 18 inch wrench. Which wrench will produce more torque?

16. Precision Measurement • Power Defined: • A measure of the work being done in a given period of time: • P (Power) = W (Work) / t (time) or P=(d * m)/t • Power is the final output of an engine after it has converted the energy in the fuel into work. • A common term used to describe output power is horsepower. • Based on the premise of the amount of work that a horse can do in one minute. • One horsepower is equal to the energy needed to lift 33,000 pounds 1 foot in 1 minute. This is the same energy needed to lift 550 lbs. one foot in one second.

17. Precision Measurement • Horsepower is a measure of the work being done by a mechanical converter, such as a diesel engine. • Horsepower is described in many ways as it relates to the mechanical converters. • When comparing engines, brake horsepower is used. • When discussing efficiency, frictional and indicated horsepower are used. • When analyzing gasoline mileage, road horsepower is used. • POWER: Energy per unit of time or work accomplished in a given period of time. • Example…I climb stairs, weight x height determines work done. Same work regardless if you walk or run up the stairs…but more power is used to run up the stairs.

18. Precision Measurement • A watt(W) is a unit used to measure electrical power. • It is equal to one joule of electrical energy per second. • A toaster may use 800 watts of power. This means the toaster needs 800 joules per second to make the heating element red-hot. • The heating of the element is the work that is accomplished. • Relationship to Power? • Pwr = W ÷ Δt • Horsepower • 1 hp = 550 ft lb/s = 746 W • 1 Watt = 1J/s (Joule per second) • 1 kW = 1000 W • Problem 3: How much power is required for you to run up a flight of stairs 10.54 ft higher than where you start in 2.2 seconds, if your mass was 160.2 lbs? Be sure to apply the rule for significant digits and indicate your answer in Watts.

19. Precision Measurement • Pressure • Pressure is another measurement of force. • Pressure is determined by the area over which a force is applied. • Pressure is force per a unit of area. • Snow shoes example. • Therefore is area = length x width and we apply 100 pounds per square inch…less pressure is applied on a greater area. • A confined fluid under pressure exerts equal force on all enclosing surfaces. • The air in an inflated balloon pushes with a small amount of pressure in all directions…however it is an even amount all over the interior surface of the chamber.

20. Precision Measurement • We can determine the force produced by a certain amount of pressure. • We must multiply the pressure (force per unit area) by the total area. • Inside surface area = 100 sq. in., Pressure is 1/4 psi. • Force = Pressure x Area • Force = 1/4 psi x 100 sq. in. • Force = 25 pounds • The difference between pressure and force is important. • We must remember that pressure is a special measurement of force. • It is force per unit of area. • However, the total amount of force depends on the total amount of area. • Problem 4: Show Mathematical proof why a sharp knife cuts better than a dull knife.

21. Precision Measurement • Two pistons, different sizes: 1 square inch area and a large one, 10 square inch area. • The pressure above each is 50 pounds per sq.l in. • Each provides different amounts of force. • The large piston produces ten times the force of the smaller cylinder. • But if the same amount of air is applied to each, the larger only moves 1/10 the distance of the smaller.

22. Precision Measurement • Heat: • Heat energy is measured in British Thermal Units (BTU’s). • One BTU is equal to the amount of heat energy needed to raise the temperature of one pound (about 1 pint) of water 1 degree F. • BTU is a measurement of energy…not power. • Power requires the element of time. • But we can measure BTU’s per hour. • We can also convert heat into power with engines. • When this happens we lose most of the heat. • It is absorbed in air and metal of the engines. • In a typical gasoline engine only 1/5th of the available heat energy is converted into power.

23. Precision Measurement • Another common unit of measurement for heat is called a calorie. • Small calorie: amount of heat needed to raise the temperature of 1 cubic cm of water 1 degree Celsius. • 252 calories in a BTU. • Large calorie: measures the amount of heat energy available to us in the food we eat.

24. Precision Measurement • Converter Efficiency: • Several types of efficiency are used for mechanical converters. • Efficiency generally refers to how well a particular job can be done. • Efficiency is expressed in a ratio of input to output. OUTPUT INPUT En. Con. Efficiency

25. Precision Measurement • Efficiencies are expressed as percentages, which are always less than 100%. • The difference between the percent efficiency and 100% is due to the percent loss incurred during the process of converting power. • Efficiency is important because it shows how much energy is being wasted. • Mechanical Efficiency: relationship between the theoretical (mat calculated) amount of work to move the motorcycle, and the actual amount of work to move it. • Mech. Efficiency=(actual work/theoretical work) x 100. • Power Efficiency=(output power/input power) x 100 • Problem 5a. The total mass of an elevator is 1200kg. An electric motor raises the elevator three floors (1.5m) at a constant speed in 12 seconds. Problem5b. What is the power outage of the motor?

26. Precision Measurement BJ Furman SJSU MAE Beckwith, T. G., Marangoni, R. D., Lienhard, J. H., Mechanical Measurements, Addison-Wesley, Reading, MA, 1995. Histand, M. B., Alciatore, D. G., Introduction to Mechatronics and Measurement Systems 2nd ed., WCB/McGraw-Hill, Boston, 2003. Park, J. L., Rules for Rounding Off [Online]. Available at http://dbhs.wvusd.k12.ca.us/webdocs/SigFigs/SigFigs.html, 1996. NIST Guide to SI Units –Appendix B [Online]. Available at http://physics.nist.gov/Pubs/SP811/appenB.html#B.7 “See, I have a rhyme assisting my little brain its tasks sometime resisting” (the number of letters in each word gives pi to 12 decimal places)