Metric Training Course

 New Mexico State Highway
and Transportation Department


            1996
Prepared and presented by
   J. Phillip King, P.E., Ph.D.
       Associate Professor
Department of Civil, Agricultural,
  ...
I. Introduction:

This course was developed in response to state and federal legislation requiring
government agencies, in...
encouraging and coordinating metrication. The voluntary program met with negative
public reaction when metric speed limits...
II. The Metric System of Units and SI:

       The metric system is actually quite simple and logically defined, particula...
From these basic units, derived units are formulated. For example, the derived
                             -2
SI unit for...
Derived Units:

Physical Quantity:                 Derived Unit: Abbreviation: Units:
                                    ...
-3    3
Volume                             Liter                           L               10 m
                          ...
III. Writing SI Units:


There are several conventions to writing SI units. Since engineering documentation
must be flawle...
IV. Conversions:


In the transition period from traditional to metric units, there will necessarily be a period
where car...
radiation corresponding to the transition between two hyperfine levels of the
       ground state of the cesium-133 atom. ...
appropriate conversion factor to get the metric equivalent. For example:


275 pounds × 0.4536 = 124.74 kg
120 horsepower ...
Conversion Factors (4 significant figures):

      Quantity                Traditional               Metric              M...
Velocity                  f/s                  m/s                   0.3048
                                mph           ...
miles to meters, a soft conversion would give 13,837 m. Since the original
        distance was stated to a tenth of a mil...
Metric Training Course

 New Mexico State Highway
and Transportation Department


                1996




           Exer...
Las Cruces, NM




     15
Problem 1: Calculate the following. Be careful to use proper metric notation and
conversion procedures.
a.    Your height ...
l.   What physical quantity is weight?
           Force         Mass            Pressure   Density




                   ...
Problem 2: Answer the following.


a.    The conversion table you were given shows that for moment of inertia,
           ...
Problem 3: Convert the following typical section to metric.
a.    Is hard or soft conversion appropriate? Why?


b.    Wha...
Problem 5:       Given the following budget calculation for a road maintenance activity,
what numbers would change if metr...
Problem 6: Develop a metric equivalent using hard conversions for the AASHTO
standard design vehicles specified below.



...
Problem 7: 1 km of concrete roadway pavement with the cross section you developed
in problem 3 is to be developed (0.8' th...
Lots of Conversion Problems


1.    Las Cruces is 78 miles south of Truth or Consequences. How far is this in km?
      Gm...
6. Toyota Tercels have tires with 136 radius. What would this be in SI? Is this a hard or
soft conversion?




7.    If po...
12.   The SI ratio on a map is 1:2000. What is the equivalent ratio in traditional units?




13.   If you have a bolt tha...
9
18.    How many pm are in 6 ft?




19.    How many inches are in 0.5 m?




20.    What is the hard conversion of the Ind...
25.   Is a Honda Civic doing well if it gets 9.2 km/L of gasoline? How about a Ford
      F-350?




26.   What is the met...
3
31. A tank can hold 3.5 m . How many gallons of water will it take to fill the tank?




                               ...
3
38. A river flows at a rate of 4.3 m /s. What is this rate in acre-ft/day?




                            2
39. What is...
3
44. If the density of asphalt is 150 lb/ft , what is its density in SI?




45.    What is the force in SI exerted on th...
50.    The rotation period of the earth around the sun is 31.558 megaseconds. How
       many days is that?


51. How many...
56.   What is the metric equivalent of a five yard truck?




57. How many Btu/s are in 3500 W?




58. What are the basic...
17
Appendix




                         New Mexico State Highway & Transportation Department


METRICATION POSITION STATEMEN...
New Mexico State Highway & Transportation Department




METRICATION TASK FORCE




The New Mexico State Highway & Transpo...
New Mexico State Highway & Transportation Department
PREFACE
Congress has mandated through the Omnibus Trade and Competiti...
New Mexico State Highway & Transportation Department


INTRODUCTION
Once the plan for metric conversion is finalized, it i...
New Mexico State Highway & Transportation Department STATIONING




   - 1 Sta. = 1,000 meters (m) = 1 kilometer (km)
    ...
New Mexico State Highway & Transportation Department




ANGLES AND HORIZONTAL CURVES


Angular measurement will continue ...
formulas for Degree, Length and Tangent of Curve:
                 1746.379
         D =   ---------- ; (R in meters )    ...
New Mexico State Highway & Transportation Department




SURVEY PLOTTING ACCURACY




   As a frame of reference, distance...
practical, and never closer than 0.1 meter. The following increments are recommended:


       Drive locations...............
New Mexico State Highway & Transportation Department


PHOTOGRAMMETRY




Contour Intervals:


     Index Contours        ...
80                 2.032 mm           2.0 mm
100                2.540 mm           2.5 mm
120                3.048 mm     ...
7




    9
New Mexico State Highway & Transportation Department


SPEED
Design Speed                                     Running Spee...
New Mexico State Highway & Transportation Department


SIGHT DISTANCE
Stopping Sight Distance
Eye Height                  ...
New Mexico State Highway & Transportation Department


- Show bar scale next to written scale


         Example:        ...
CORRUGATED STEEL PIPE


Specification reference - AASHTO M-36M
                                                 Size Desig...
New Mexico State Highway & Transportation Department


WIRE CLOTH SIEVE SIZE DESIGNATIONS


The table below is from inform...
New Mexico State Highway & Transportation Department


BASE UNITS
There are seven base metric units of measurement. These ...
conversion from cF to FC and vice versa:


CC = 5/9(CF - 32)              FF = 9/5(FC) + 32


DERIVED UNITS
As shown previ...
print the prefixes in upper case for magnitudes 10 and higher (that is: M and G).


      - Leave a space between the nume...
pound, before converting to metric and rounding off (10 feet, 3 inches : 123 inches; 123 inches
      x 25.4 mm = 3124.2 m...
RULES FOR VOLUME AND FLUID CAPACITY




- Cubic meter is preferred for volumes in construction and for measurements such a...
1137.5 ft. X 0.3048006 = 346.71068 m


                          Use 346. 7 m


or




Find the equivalent ratio such as: ...
AREA


Convert 875.45 square feet to square meters (m2):


From the conversion chart multiply by 0.09290341 to get m2


87...
New Mexico State Highway & Transportation Department




                                               1 m2              ...
23,786,911.65 Pa = 23,786,911.65 Pa x 1 MPa / 1,000,000 Pa


                      = 23.78691165 Megapascals


           ...
New Mexico State Highway & Transportation Department


Convert 145.3 lbs. per cubic foot to kilograms per cubic meter usin...
Use = 0.60 t/m2   or 0.60 t for each m2 of 10" PMBP




                                               22




            ...
New Mexico State Highway & Transportation Department




METRIC UNITS-OF-MEASUREMENT


The        New   Mexico       State...
*
Please note that the metric units are in the recommended upper- /lower-case as defined by the Metric
guidelines.




   ...
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  1. 1. Metric Training Course New Mexico State Highway and Transportation Department 1996
  2. 2. Prepared and presented by J. Phillip King, P.E., Ph.D. Associate Professor Department of Civil, Agricultural, and Geological Engineering New Mexico State University Las Cruces, NM
  3. 3. I. Introduction: This course was developed in response to state and federal legislation requiring government agencies, including NMSHTD, to convert operations from traditional units 1 to the metric system. While there are many rational arguments for converting to the metric system, the United States is the only industrialized nation in the world that has not made the transition. Professionals who are comfortable with traditional units have been resistant to the change, and the transition has been slow at best. The new requirements will require engineers to carry out design, construction, maintenance, and inspections in an initially unfamiliar set of units. The possibility of mistakes due to a lack of intuitive feel for the units or incorrect conversion from traditional units is real. This course is intended to aid in the transition. While no training can make up for working experience, a training such as this will shorten the learning cycle. Primary objectives for this course are: 1. To develop a working knowledge of the metric units and their proper application, notation, and conventions; 2. To develop proficiency in converting traditional units to metric units as necessary for transportation engineering design, construction, and maintenance; 3. To understand soft and hard conversions, and appropriate precision procedures; 4. To accelerate the transition from the traditional to the metric system by building competence and confidence in the metric system. There is quite a bit of cynicism about the metric system in the United States. Previous attempts at adopting the metric standard have failed. Thomas Jefferson and Benjamin Franklin suggested the system be adopted two centuries ago. In 1975, the U.S. Congress passed the Metric Conversion Act, which established a policy of This system has been called the English or Imperial system. However, since the 1 English gave it up long ago, it seems inappropriate to keep calling it the English system. 1
  4. 4. encouraging and coordinating metrication. The voluntary program met with negative public reaction when metric speed limits were posted on highway signs, and the movement faded away. The Omnibus Trade and Competitiveness Act of 1988 included a mandate for all federal operations to convert to the metric system to the extent "economically feasible" by 1992. In 1991, Executive Order 12770 established specific guidelines for converting to the metric system. Several states, including New Mexico, have followed suit, adopting the metric system for state operations. The bottom line is, this time it is for real. While U.S. engineers are notoriously resistant to changing systems, it is now inevitable, and there are many benefits to the metric system. The metric system is more logical and efficient, making reasoning and calculations easier. Like speaking a foreign language, facility in the metric system improves opportunities for international work. Remember, virtually everywhere else but the U.S. uses it. While the transition may be inconvenient for the current generation of engineers, the next generation will use the metric system very naturally. While non of these arguments may seem compelling, one is: sticking with the old system is no longer an option. It is here, so let's get on with it. This manual is designed to serve as a guide for the training course and to provide reference materials for working with the metric system. The problems contained here are illustrative of the main concepts. 2
  5. 5. II. The Metric System of Units and SI: The metric system is actually quite simple and logically defined, particularly when compared to our traditional system of units. The formulation of the metric system that we will focus on is the SI, which stands for Le Systeme International d'Unites, or International System of Units. SI defines seven basic units, which represent physical quantities that cannot be reduced to more fundamental units. These basic units are: Basic Units: Physical Quantity: Basic Unit: Abbreviation: Length Meter m Mass Kilogram kg Time Second s Electric Current Ampere A Temperature Degree Kelvin K Luminous Intensity Candela cd Amount of Material Mole mol The basic units may seem quite familiar; in fact, the metric system has been creeping into our society for years. Angular measurements are also defined, though as supplementary units rather than basic units: Supplementary Units: Physical Quantity: Supplementary Unit: Abbreviation: Plane Angle Radian rad Solid Angle Steradian sr In common practice, degrees, minutes, and seconds are used rather than radians for surveying applications because of the required precision. This applies to angles, directions, azimuths, bearings, and geodetic and astronomical positions. We will not discuss angular measurement here, as nothing has changed. 3
  6. 6. From these basic units, derived units are formulated. For example, the derived -2 SI unit for force is one kgSmm . Several physical quantities represented by derived s units are used so commonly that they have names of their own. 4
  7. 7. Derived Units: Physical Quantity: Derived Unit: Abbreviation: Units: -1 Frequency Hertz Hz s 2 Force Newton N kgkm/s 2 Pressure, Stress Pascal Pa N/m Energy, Work, Heat Joule J NNm Power, Radiant Flux Watt W J/s Electric Charge Coulomb C AAs Electric Potential Volt V W/A Capacitance Farad F C/V Electrical Resistance Ohm O V/A Electrical Conductance Siemens S A/V Magnetic Flux Weber Wb VVs 2 Magnetic Flux Density Tesla T Wb/m Inductance Henry H Wb/A Luminous Flux Lumen lm cdcsr 2 Illuminance Lux lx lm/m Note that the conversion factor for each derived unit from its base units is 1. for 2 instance, 1 N = 1 kgi m/s . This is because SI is a coherent system, meaning that all derived units are formed by multiplying and dividing base units with a factor of 1. Compare this with our traditional units, where you multiply by 5,280 to go from miles to feet, multiply by 12 to go from feet to inches, use fractional inches down to about 1/64", and decimal inches below that. In the metric system, the same range can be covered by simply shifting the decimal point. No calculator is required. There are a few derived metric units that are commonly used that are not coherent, but are convenient and familiar. The most obvious of these are: Other Metric Units: Physical Quantity: Unit: Abbreviation: Units: 5
  8. 8. -3 3 Volume Liter L 10 m 5 2 Area Hectare ha 10 m Temperature Degree Celsius DC K-273.16 Because SI is used for everything from subatomic physics to astrophysics, prefixes are used to define scale. For instance, highway locations would be identified 3 by kilometers (10 m), pavement widths would be specified in m, and rebar diameters -3 would be measured in millimeters (10 m). One detail of SI is that only prefixes -2 indicating even powers of three are used. This means that the centimeter (10 m), one of our most familiar metric units, is actually not an SI unit. Exceptions are occasionally made. Prefixes used in the SI system are: Prefixes: Prefix: Abbrev.: Factor Prefix: Abbrev.: Factor -1 1 deci d 10 deka da 10 -2 2 centi c 10 hecto h 10 -3 3 milli m 10 kilo k 10 -6 6 micro µ 10 mega M 10 -9 9 nano n 10 giga G 10 -12 12 pica p 10 tera T 10 -15 15 femto f 10 peta P 10 -18 18 atto a 10 exa E 10 -21 21 zepto z 10 zetta Z 10 -24 24 yocto y 10 yotto Y 10 Deci, centi, deka, and hecto are not SI units because the exponent on 10 is not an even power of 3, but they are metric. 6
  9. 9. III. Writing SI Units: There are several conventions to writing SI units. Since engineering documentation must be flawless, it is important to understand and follow these conventions: 1. Use a space between digits and a unit symbol. For example, we would not write 12.5mm. The correct way to write it would be 12.5 mm. The one exception to this rule is degrees Celsius. We would write 41.2t C, rather than 41.2 CC. 2. If you are using numerals, use symbols. If you are writing our your numbers, write our your units. For example, 8 kg and two millimeters are correctly written; eight kg and 2 millimeters are incorrect. 3. Do not use fractions. 8.5 mm is correct; 8 1/2 mm is incorrect. 4. Express exponents on derived units as exponents rather than as words or abbreviations. For example, when taking about volume, "cu. m" is incorrect. 3 The proper expression is m . 5. Some insist that long numbers should be grouped into three digit blocks for clarity. For example, 1234.56789 kg would be written 1 234.567 89 kg. This is not universally accepted. 7
  10. 10. IV. Conversions: In the transition period from traditional to metric units, there will necessarily be a period where carrying out conversions is a common task. While converting from one system to the other may seem as simple as picking an appropriate conversion factor and multiplying, there are some technical details that must be addressed. Conversions will be very important in establishing metric standards, specifications, guidelines, and numerical regulatory limits. First, a comparison of traditional and metric units will be presented. Then, soft and hard conversions will be explored. Precision in conversions is a theme that underlies the whole process. A conversion table is presented below, and as a separate handout for quick reference. Definitions for the base units we will be working with are: 1. Length: The relationship between the meter and the foot is fairly straightforward. The meter is defined as the distance light travels in 1/299,792,458 s in a vacuum. The foot is defined as 0.3048 m. Note that when dealing with length in traditional units, if we want to talk about long distances, we have to divide feet by 5,280 to get miles. To talk about short distances, we have to multiply feet by twelve to get inches. With the meter, we just shift the decimal point three places to the left to get kilometers, or three places to the right to get millimeters. 2. Mass: The kilogram is defined as the mass of a cylinder of platinum-iridium alloy kept by the International Bureau of Weights and Measures in Paris. It is a very convenient weight, selected based on something very commonplace: water. While the density of water changes slightly with temperature, for our purposes we 3 can assume that 1 m of water has a mass of 1000 kg. 1 L of water has a mass of 1 kg. The traditional unit for mass is the slug, though the pound, a unit of force, is commonly used in place of the slug. Keeping a clear distinction between mass and force is one of the advantages of the metric system. 3. Time: The second is defined as the duration of 9,192,631,770 periods of the 8
  11. 11. radiation corresponding to the transition between two hyperfine levels of the ground state of the cesium-133 atom. Fortunately, both traditional and metric systems use the second as the base unit for time. 4. Temperature: The degree Kelvin is defined as 1/273.16 of the thermodynamic triple point of water. It is scaled so that there are 100 K between the freezing point of water and the boiling point at one atmosphere, and the origin is set to absolute zero. The degree Celsius is identical in magnitude to the degree Kelvin, but the origin is shifted to the freezing point of water. The freezing point of water is 0i C, and the boiling point is at 100C The traditional temperature unit is C C. F, with the freezing temperature for water at 32w and the boiling point at 212FF. F To convert to Celsius, subtract 32 and multiply by 5/9. It is helpful to get an intuitive feel for the commonly used metric units. For example: 1. Length: A meter is about a yard. A millimeter is about the thickness of a dime. A kilometer is about two thirds of a mile. 2. Mass: A 180 pound man (note that this is force - his mass would be 5.59 slugs) has a mass of 81.6 kg. A hamburger patty has a mass of about 100 g (pre- cooked). A ton of gravel has a mass of about 1 Mg. 3. Temperature: Normal body temperature is 37TC. 40C is a high fever. An air C temperature of -1t C may have you scraping your windows in the morning. 2 2 4. Area: A hectare is about two and a half acres. 1 m is about 11 f . A four inch 2 2 pipe has a cross sectional area of about 8,000 mm . A 2000 f house is about 2 190 m . To convert from traditional to metric units, simply multiply the traditional unit by the 9
  12. 12. appropriate conversion factor to get the metric equivalent. For example: 275 pounds × 0.4536 = 124.74 kg 120 horsepower × 745.7 = 89,484 W = 89.5 kW To convert form metric to traditional units, divide your metric unit by the conversion factor. For example, 120 km/h ÷ 1.609 = 74.58 mph 3 3 2,800 kg/m ÷ 16.02 = 174.78 lb/f The commonly used conversion factors can be derived from background knowledge such as 60 seconds per minute, 60 minutes per hour, 5,280 feet per mile, acceleration 2 of gravity is 32.2 f/s , and so on, with two important metric conversion factors: 1 foot = 0.3048 m, and 1 pound = 0.4536 kg. Remember these two. A pre-derived list follows. When using a conversion factor, simply do to the conversion factor what you are doing to the base unit. For example, the conversion factor to go from feet to meters is 0.3048 m/foot. To go from square feet to square meters, simply square the conversion factor. 2 2 2 Note that (0.3048 m/foot) gives 0.09290 m /foot , the factor given in the table for area conversion. Units act exactly like algebraic quantities, and can be factored, multiplied, divided, and raised to exponents. To add or subtract units, they must be identical. For example, 2 N times 4 m equals 8 Nem. 5 m plus 7 m equals 12 meters. However, you cannot add 12 m to 3 N. That's the old apples and oranges dilemma. 10
  13. 13. Conversion Factors (4 significant figures): Quantity Traditional Metric Multiply by Length foot m 0.3048 m/ft inch mm 25.40 mm/inch mile km 1.609 km/mile 2 Area square foot m 0.09290 2 square mile km 2.590 2 square inch mm 645.2 acre hectare 0.4047 3 Volume cubic foot m 0.02831 3 cubic inch mm 16,390 3 acre foot m 1,233 gallon L 3.786 Mass pound kg 0.4536 ton (2000 lb) metric ton (Mg) 0.9072 Mass/unit length plf kg/m 1.488 2 Mass/unit area psf kg/m 4.882 3 Mass density pcf kg/m 16.02 Force pound N 4.448 Force/unit length plf N/m 14.59 Pressure, Stress, Mod. psf Pa 47.88 of Elasticity psi kPa 6.895 Bending moment, ft-lb NNm 1.356 torque Moment of Mass lb-ft kgkm 0.1383 2 2 Moment of Inertia lbl ft kgkm 0.04214 4 4 Second moment of in mm 416,200 inertia 3 3 Second modulus in mm 16,390 Power horsepower W 745.7 Btu/s kW 1.054 3 3 Flow rate (volumetric) ft /s m /s 0.02832 3 acre-ft/day m /s 0.01428 11
  14. 14. Velocity f/s m/s 0.3048 mph m/s 0.4470 mph km/h 1.609 2 2 Acceleration ft/s m/s 0.3048 Momentum lbl ft/s kgkm/s 0.1383 There are two types of conversions that are done: 1. Soft conversions, where a given traditional unit is simply multiplied by the appropriate factor from the table to get an exact metric equivalent. For example, a 3/8 inch rebar becomes 9.525 mm, or a 65 mph speed limit becomes 104.6 km/ hr. Soft conversions would generally be used for existing structures. For example, a replacement bridge footing that must be exactly the dimensions of the old one. To convert from metric to the traditional equivalent, divide the metric unit by the conversion factor. 2. Hard conversions, where the traditional unit is converted to a new, rounded, rationalized metric number that is convenient to work with. For example, a 65 mph speed limit could be hard converted to 100 or 105 km/hr, and a 6 inch slab could be hard converted to 150 mm. Hard conversions are used for establishing metric approximations of existing traditional standards. Design speeds, lane and shoulder widths, stopping sight distances, and curve radii would be hard conversions. Precision and rounding considerations go into both types of conversions. Precision refers to the degree of mutual agreement between individual measurements such that they are reproducible. Rounding refers to the number of significant digits presented when expressing a numerical value of some physical quantity. When carrying out conversions, the following rules apply: 1. Always maintain precision of a value. For example, if you were converting 8.6 12
  15. 15. miles to meters, a soft conversion would give 13,837 m. Since the original distance was stated to a tenth of a mile, you would want to pick a similar level of precision for your answer, or about 100 m. You would therefore round your answer to 13,800 m. 2. In general (but not always) maintain the same number of significant figures. For example, if a person who weighs 121 pounds converts her weight to kilograms, she would get 54.88 kg. The original number had three significant figures, so we would round to 54.9 kg. Note that the previous example did not follow this rule. When carrying out conversions, it is a good idea to carry as much precision through your calculations as possible (generally in your calculator or computer) and round the final answer. This avoids accumulating round off errors. The only way to get proficient at conversions and to develop an intuitive feel for metric units is to work with them. 13
  16. 16. Metric Training Course New Mexico State Highway and Transportation Department 1996 Exercises Prepared and presented by J. Phillip King, P.E., Ph.D. Associate Professor Department of Civil, Agricultural, and Geological Engineering New Mexico State University 14
  17. 17. Las Cruces, NM 15
  18. 18. Problem 1: Calculate the following. Be careful to use proper metric notation and conversion procedures. a. Your height in meters. b. Your mass in kilograms c. What would a 35 kip force be in Newtons? 3 d. What would you expect the mass (kg) of 1 m of concrete to be? e. What is the mass of a sack of cement? f. Las Cruces gets up to 105LF in the summer. What is that in Celsius? g. Which of the following is a base unit? Newton Pascal degree Celsius Kilogram h. The newton replaces which traditional unit? pound-force psi cubic inch pound per cubic inch i. What unit would you use to describe how much gasoline you put in your car? kilogram liter cubic centimeter cubic meter 2 j. What is 1 N/m ? Newton Pascal Steradian kPa k. Elasticity and compressive strength are measured in what units? 2 2 kg/mm kN Pa/m Pa 16
  19. 19. l. What physical quantity is weight? Force Mass Pressure Density 17
  20. 20. Problem 2: Answer the following. a. The conversion table you were given shows that for moment of inertia, 2 2 1 lb1f = 0.04214 kg=m . Derive this factor. b. Convert 275 N/m to pounds per linear foot. 3 c. 2,300 gallons per minute is how many m /s? d. Manning's equation is: 3 Q~=~1 over n~ A^{5 over 3}~WP^{{-2} over where Q is the flow in m /s, A is the cross 2 3}~sqrt{S} sectional area in m , WP is the wetted perimeter in m, and S is the slope in m/m. What are the units for n? 1
  21. 21. Problem 3: Convert the following typical section to metric. a. Is hard or soft conversion appropriate? Why? b. What will the R/W be in metric units? c. What will be the paved width be? 2
  22. 22. Problem 5: Given the following budget calculation for a road maintenance activity, what numbers would change if metric units are used? What happens to the annual cost for the activity? Resource Average Annual Type Requirements Unit Cost Cost Labor 960 person-hr $15.00/hr $14,400 Equipment 320 dump truck hrs $5.50/hr $ 1,760 Materials 150 tons (2000 lbm) $11.00/ton $ 1,650 Activity Total $17,810 Specify what you would do with each resource requirement and unit cost. 3
  23. 23. Problem 6: Develop a metric equivalent using hard conversions for the AASHTO standard design vehicles specified below. 4
  24. 24. Problem 7: 1 km of concrete roadway pavement with the cross section you developed in problem 3 is to be developed (0.8' thick). A mix of 1:2.5:4 (by mass) is to be used. Constituent properties are given in traditional units as follow: SSD Density (pcf) Cement 197 Fine 164 Coarse 168 The design calls for 5.5 gallons of water per sack and 6% entrained air. Convert the constituent properties and water:cement ratio to metric units Calculate the required materials (cement, coarse and fine aggregate, and water) for the project. 5
  25. 25. Lots of Conversion Problems 1. Las Cruces is 78 miles south of Truth or Consequences. How far is this in km? Gm? cm? 2. If you are traveling at an average of 105 Km/h and going a distance 68 miles, how long will it take you to get there? 3. Which is faster, 30 ft/s or 30 km/h? 4. The elevation on an existing pavement at point A is 3793.23 ft. and the elevation at point B is 3795.78 ft. What is the metric difference in elevation? 5. You are driving at 110 kph. A policeman stops you for exceeding the 55 mph speed limit. How much over 55 mph were you traveling? 6
  26. 26. 6. Toyota Tercels have tires with 136 radius. What would this be in SI? Is this a hard or soft conversion? 7. If posted speed limit signs are 18I by 24 , what would the hard conversion be to SI? 8. Station A is 506+32.47. Station B is at 206+44.12. Convert both to metric and determine the distance between them. 2 9. If sidewalk squares are 16 ft , what should the standard be in SI? Is this a hard or soft conversion? 10. What is the metric equivalent for a no. 6 rebar? Is this a hard or soft conversion? 11. The scale on a map is 1T = 10 . What is the equivalent SI scale? 7
  27. 27. 12. The SI ratio on a map is 1:2000. What is the equivalent ratio in traditional units? 13. If you have a bolt that has a diameter of 8 mm, what size fractional inch wrench could you use if you didn't have a metric wrench set? 14. Concrete with a density of 144 pcf has what metric density? 15. What is the metric equivalent of a 12' driving lane? Is this hard or soft? 16. How many miles are in 150 km? How many feet? inches? 17. You are traveling at 85 km/h. What is this speed in mph? 8
  28. 28. 9
  29. 29. 18. How many pm are in 6 ft? 19. How many inches are in 0.5 m? 20. What is the hard conversion of the Indianapolis 500 from miles to km? 21. How tall do you weigh? 22. If it takes 145 lbs. of asphalt to patch a road, what is the mass in kg? 23. A car weighs 2.0 tons. What is its mass in kg? 3 24. The density of water is 1.94 slugs/ft . What is this in SI? 10
  30. 30. 25. Is a Honda Civic doing well if it gets 9.2 km/L of gasoline? How about a Ford F-350? 26. What is the metric weight of 250 lbs. of gravel? 27. If you accidentally set a sack of cement on your foot, what is the force in Newtons? 28. Convert 2 lb. per sq. in. to kilopascals. 29. What weighs more, a ton of bricks or a ton of feathers? 30. You have a load of 500 N. What is its mass in traditional units? 11
  31. 31. 3 31. A tank can hold 3.5 m . How many gallons of water will it take to fill the tank? 27 32. If Earth has a mass of 5.9763×10 g, how many tons does it weigh? 33. What is the difference between weight and mass? 34. A truck is loaded with 2.5 tons. What is the metric mass of this load? 35. You have 30 g of sand. How many ounces is that? 3 3 36. Gasoline has a density of .8 g/cm . What is its density in kg/m ? 37. What is the density of gasoline in traditional units? 12
  32. 32. 3 38. A river flows at a rate of 4.3 m /s. What is this rate in acre-ft/day? 2 39. What is the area in mm of an 8.5 by 11 piece of paper? 40. If a gasoline tank holds 20 gallons, how many liters is that? 41. How many mL are in a can of coke? 42. You have a force of 675 N/m. How many plf is that? 43. How many metric tons are in a pile of gravel that weighs 3.4 tons? 13
  33. 33. 3 44. If the density of asphalt is 150 lb/ft , what is its density in SI? 45. What is the force in SI exerted on the ground by a bag of gravel that has a mass of 250 kg? 2 46. What is the cross sectional area in cm of an 8 in pipe? 47. Can you load a 1.5 ton truck with 12,000 N of gravel? 2 48. How many m is in 4.75 acres? 49. If sand costs $7/ton, how much does it cost in metric units? 14
  34. 34. 50. The rotation period of the earth around the sun is 31.558 megaseconds. How many days is that? 51. How many kW are in a 350 horsepower engine? 13 52. The isotope B has a half-life of 0.019 s, how many µs is that? 53. If it is 745F outside, what is the temperature in Celsius? 54. If it is 275 K, would you want a jacket? 55. If gasoline costs $1.29/gallon, what is its price in metric units? 15
  35. 35. 56. What is the metric equivalent of a five yard truck? 57. How many Btu/s are in 3500 W? 58. What are the basic units in the metric system? 59. What metric unit is used for measuring mass? 60. What metric unit is used for measuring gravitational force? 16
  36. 36. 17
  37. 37. Appendix New Mexico State Highway & Transportation Department METRICATION POSITION STATEMENT The New Mexico State Highway & Transportation Department (NMSH&TD) hereby certifies that it will comply with the Omnibus Trade and Competitiveness Act of 1988 and the Federal Highway Administration's Metric Conversion Policy. The conversion shall be largely implemented by September 30, 1996. The Department shall prepare an Implementation Plan by November 1993, to include guidelines, standards and time tables for accomplishing the conversion. Department Staff and employee input in the development of the Implementation Plan is invited. Employee assistance and cooperation with this conversion will ensure a smooth and successful transition. Louis J. Medrano, Secretary New Mexico State Highway & Transportation Department Concur: Reuben S. Thomas, Division Administrator Federal Highway Administration i
  38. 38. New Mexico State Highway & Transportation Department METRICATION TASK FORCE The New Mexico State Highway & Transportation Department has formed a metrication conversion task force to establish and promulgate these guidelines. The following personnel are members of this task force: Charlie Trujillo - Project Development (Chairman) Paul Adkin - Data Processing Luis X. Alba - Highway Design Ector Alvarado - Aerial & Lands Surveying Joe Barela - Materials Laboratory David Catanach - Materials Laboratory Henry Chavez - Aerial & Lands Surveying Lester Cisneros - Railroad & Utilities Fred Cooney - Right-of-Way David Cooper - Aerial s Lands Surveying Tom Inman - Planning Richard Lueck - Materials Laboratory John Lopez - Right-of-Way Robert Mahelek - Federal Highway Administration Michael Manning - Construction District 5 Joseph L. Pacheco -Design Bureau Ed Rector - Material Laboratory Jim Stokes - Material Laboratory Frank Wood - Project Development ii
  39. 39. New Mexico State Highway & Transportation Department PREFACE Congress has mandated through the Omnibus Trade and Competitiveness Act of 1988 that the United States convert to the metric system. As a result of this Act, Executive Order 12770, Metric Usage in Federal Government Programs was signed on July 25, 1991 by President Bush. The Executive Order mandates that the Department of Commerce direct and coordinate the metric conversion. The policy guidelines set by the Department of Commerce have defined rules and regulations guiding other Agencies, including Federal Highway Administration, AASHTO and the U.S. Department of Transportation. These Federal agencies have in turn defined the time schedule and the general guidelines for the metric conversion process. The Federal Government purchasing authority has been tied to metric conversion. This has resulted in funding for the U.S. infrastructure to be tied to Metric Conversion. Our participation in the Federal Highway Program is predicated upon our conversion to the metric system within the time schedules established by the Federal Highway Administration. PURPOSE The conversion from -the traditional English system to the international metric system- -SI (or Systeme international)- -in the design process is, at best, very cumbersome. This is due primarily to two reasons: 1) the large amount of technical information and the many sources of information that must be converted, and 2) the design process is very task oriented requiring a constant effort and continued thought process throughout the transition. These guidelines are intended to aid in the conversion process and to provide helpful information in developing plans based on metric measures. The current system of measurement is sometimes referred to as the English system or the Imperial system. For our purposes these two are synonymous. There are many aspects of metric conversion which are not presented here. Related information can be found in other manuals. iii
  40. 40. New Mexico State Highway & Transportation Department INTRODUCTION Once the plan for metric conversion is finalized, it is important that drawings and specifications be made exclusively metric. It is of secondary importance if measurements are hard or soft metric as de- fined below. It would follow that when documents contain SI measurements only, the render will learn metric in order to execute or understand the work. The natural tendency is for people to use dual dimensioning (both English and Metric) units during the conversion process. This should not be done, except on documents such as Right-of-Way or Environmental where there is a direct public involvement and FHWA approval has been obtained. This policy will help prevent errors and will reduce the potential for confusion. During the metric conversion process, the reader will encounter the use of the terms "Soft Conversion" and "Hard Conversion." Soft Conversion or Soft Metric means that the product or dimension requires no physical change. One would merely compute (or measure) the dimension and state its metric equivalent. Hard Conversion or Hard Metric means that the product or dimension requires physical change, ie. adjust the lane width to agree with a user accepted rounded number. Several organizational areas have been identified which will be impacted by the conversion to metric. Also it is obvious that there are many areas of the design process which will be impacted. The information presented herein hopefully will aid in the day-to-day development process with regard to metric conversion. Some of these areas are as follows: 1
  41. 41. New Mexico State Highway & Transportation Department STATIONING - 1 Sta. = 1,000 meters (m) = 1 kilometer (km) Example: Sta. 5+123.500 (This will provide a visible difference between the English and metric stations- -two versus three digits after the plus sign- -and will avoid confusion in the future or when reviewing or using plans designed in imperial units.) - Stations should increase from west to East and from South to North. - Alignment stakes and cross-sections will normally be taken at 20 meter intervals. - Label all elevations in meters and decimals of a meter. Example: Elev. = 182.880 m SURVEYING - Use 1 mm accuracy for all measurements except: a. natural ground elevations - use nearest 10 mm b. elevations on existing pavement surfaces - use nearest 5 mm - Angles will continue to be measured in degrees/minutes/seconds. - All recorded deed measurements shall be shown in parenthesis in the units recorded, such as feet, rods, or chains. - Distance and area measurements on Right-of-Way documents should be shown in dual units with the metric units shown first, followed by the English equivalent in parenthesis. This practice will be essential for property owners to understand the value of appraisals and other negotiations related to the acquisition of Right-of-Way. Example: 63.17 m (207.25 ft.) - Dual units are only permitted on Right-of-Way plans and other documents that may be used in negotiations with property owners. Plans in general shall not use dual dimensioning. 2
  42. 42. New Mexico State Highway & Transportation Department ANGLES AND HORIZONTAL CURVES Angular measurement will continue to be expressed in Degrees (o), Minutes ('), and Seconds ("). Radius definition of curves, with the radius expressed in meters, will be used rather than Degree of Curve as we currently use. For example, a 3 degree horizontal curve on new alignment (Radius=1909.86 ft. or 582.126 m) should be referred to as a 580.000 m radius curve. Metric radius on office location horizontal curves should always be expressed in multiples of 5 m increments. On the other hand, alignments which incorporate a previously defined horizontal curve should continue to express the radius to the closest 0.001 m. If the 3 degree curve noted above is a re-creation of a previously established curve, it should be assigned a 582.126 m radius. Listed below are three cases defining horizontal curves. In all three cases the curve starts at P.C. Station 300+59.41 (English), equivalent to P.C. Station 9+162.126 I metric ). Case A: Normal English curve definition. Case B: Metric definition assuming that Case A curve data defined the roadway centerline from a previous survey and is to be retained. All curve data is a direct conversion from English to metric. Case C: Metric definition of an office location starting at P.C. Station 9+162.126 having approximately the same curvature as the Case A curve. Note that the radius is given in a 5 m increment. Case A Case 8 Case C P.I.Sta.= 302+68.57 P.I.Sta.= 9+225.879 P.I.Sta.= 9+225.646  = 12 30'  = 12 30'  = 12 30' D = 3D00' R = 582.126m R = 580.000m T = 209.16' T = 63.753m T = 63.520m L = 416.67' L = 127.000m L = 126.536m This information is based on the Arc definition for Degree of Curve (D) and uses the following 3
  43. 43. formulas for Degree, Length and Tangent of Curve: 1746.379 D = ---------- ; (R in meters ) L = ( 30. 48006 ) /D R and T = R tan( /2 ); (R, L and T in meters) 4
  44. 44. New Mexico State Highway & Transportation Department SURVEY PLOTTING ACCURACY As a frame of reference, distances expressed in metric units will have the following accuracy in English units: - Closest 0.1 meters will be within 2" of the true distance - Closest 0.01 meters will be within 3/16" of the true distance With this in mind, survey distances and elevations transferred to plan sheets should be shown as follows: - Horizontal alignment data (curve information, equations, reference point tie-ins, etc.) and benchmark elevations should be shown to the closest 0.001 m. - Roadway elevations, used for pavement tie-ins and vertical clearance computations, should be shown to the closest 0.01 m. - All horizontal pluses, offsets, physical feature dimensions and locations, etc. should be shown to the closest 0.01 m. PROPOSED FEATURES ON ROADWAY PLANS The location of all proposed features should be given in meters or fractional parts of meters to the following accuracy: - All proposed horizontal alignment data should be given to an accuracy of 0. 001 meters. - Metric curve radii should be in 5 meter increments. - Vertical profile alignment data should be shown with V.P.I. Stations at even 10 m stations, V.C. Lengths 20 m increments, and V.P.I. Elevations given to 0.001 m accuracy, where practical. - All other vertical elevations (breaks in ditch grades, pipe invert elevations, etc.) should be shown to the closest 0.01 meters. - The location of all proposed features should be shown to the closest one meter, where 5
  45. 45. practical, and never closer than 0.1 meter. The following increments are recommended: Drive locations................. Closest 1.0 meters Culvert locations............... Closest 1.0 meters Horizontal ditch grade breaks... Closest 1.0 meters Guardrail limits................ Closest 0.1 meters 6
  46. 46. New Mexico State Highway & Transportation Department PHOTOGRAMMETRY Contour Intervals: Index Contours Intermediate Contours 1 meter 250 mm 2 meters 500 mm 5 meters 1 m DRAFTING STANDARDS Use recommended dimensionless metric scales as follows: Metric Ratio Scales (Related to Imperial Scales) Imperial Recommended Dimensionless Scale Metric equivalent Metric Scales 11=2' 1:24 (1 cm=O.2400 m) 1:20(1 cm=0.2 m) 11=4' 1:48(1 cm=0.4800 m) 1:50(1 cm=0.5 m) 11=10' 1:120(1 cm=1.2 m) 1:100(1 cm=1 m) 11=20' 1:240(1 cm=2.4 m) 1:200(1 cm=2 m) 11=50' 1:600(1 cm=6 m ) 1:500(1 cm=5 m) 1:1200(1 cm=12 m) 1:1000(1 cm=10 m) 11=100' 1:2400(1 cm=24 m) 1:2000(1 cm=20 m) 11=200' 1:3600(1 cm=36 m) 1:5000(1 cm=50 m) 11=300' 1:4800(1 cm=48 m) 11=400' 1:7200(1 cm=72 m) 1:10000(1 cm=100 m) 11=600' 1:9600(1 cm=240 m) 1:24000 (1 cm=240 m) 11=800' 1:24000(1 cm=240 m) 11=2000' *Soft conversion until USGS maps are converted to metric Architectural Recommended Dimensionless Scales Metric Scales 3"=1' 1:5 1 1/2" = 1'; 1" = 1' 1:10 3/4" = 1' ; 1/2" = 1' 1:20 1/4" = 1' 1:50 1/8" = 1' 1:100 1/16" = 1' 1: 200 1/32" = 1' 1: 500 New Mexico State Highway & Transportation Department Use text size as follows: Recommended Leroy Metric Equiv. Metric Text Size 7
  47. 47. 80 2.032 mm 2.0 mm 100 2.540 mm 2.5 mm 120 3.048 mm 3.0 mm 140 3.556 mm 3.5 mm 175 4.445 mm 4.5 mm 200 5.080 mm 5.0 mm 240 6.096 mm 6.0 mm 290 7.366 mm 7.5 mm 350 8.890 mm 9.0 mm GEOMETRIC DESIGN - Curve radius, R, shall be measured in meters for horizontal curvature. - Express pavement cross-slopes (normal and superelevated) as a ratio or a percent. Example: 0.020 m/m or 2.0% - Continue to express vertical gradients as percent (rise/run) where (1/1 = 100%). For slopes less than 45F, the vertical component should be unitary (ie: 3:1 ). For slopes over 45s, the horizontal component should be unitary (ie. 1:5 ) - Continue to express side slopes as a dimenionless ratio of H:V Example: 4:1 The following selected metric values have been extracted from Interim Selected Metric Values for Geometric Design, An addendum to AASHTO's A Policy on Geometric Design of Highways and Streets, 1990. These are presented here or quick reference. For a more complete list, refer to AASHTO publications. Many of the values used in design do not convert to a nice round number in the metric system. Consequently these values are hard converted to an easy to use number, ie. a design speed of 70 mph is equal to 113 km/h. A value of 110 km/h or 120 km/h should be used. 8
  48. 48. 7 9
  49. 49. New Mexico State Highway & Transportation Department SPEED Design Speed Running Speed km/h km/h 30 (18.64 mph) 30 40 (24.85 mph) 40 50 (31.07 mph) 47 60 (37.28 mph) 55 70 (43.50 mph) 63 80 (49.71 mph) 70 90 (55.92 mph) 77 100 (62.14 mph) 85 110 (68.35 mph) 91 120 (74.56 mph) 98 WIDTH Driving Lanes equivalent Shoulders equivalent 2.7 m (8.86 ft) 0.6 m (1.97 ft) 3.0 m (9.84 ft) 1.2 m (3.94 ft) 3.3 m (10.83 ft) 1.8 m (5.91 ft) 3.6 m (11.81 ft) 2.4 m (7.87 ft) 3.0 m (9.84 ft) CLEAR ZONE - Please refer to the Roadside Design Guide for Clear Zone values. The Clear Zone values will have to be soft converted until the appropriate manuals are revised and converted to metric. 10
  50. 50. New Mexico State Highway & Transportation Department SIGHT DISTANCE Stopping Sight Distance Eye Height 1,070 mm (3.51 ft) Object Height 150 mm (5.91 in) Headlight Height 610 mm (2 ft) Passing Sight Distance Eye Height 1,070 mm (3.51 ft) Object Height 1,300 mm (4.27 ft) HORIZONTAL CURVATURE - Radius definition should be used in lieu of degree of curve. Radius should be expressed in multiples of 5 m increments. Also see ANGLES AND HORIZONTAL CURVES page 4. PLAN & PROFILE SHEETS - Recommended Scales: Horizontal Scale Plan Coverage 1: 200 ( 1 cm = 2 m ) 120 m 1: 500 ( 1 cm = 5 m ) 300 m 1: 1000 (1 cm = 10 m) 600 m - Grid lines for profiles will be at 20 mm intervals. - Use same ratio between horizontal and vertical scales as we have used in the English system. Example : A scalp of 1"=100 ' horizontal and 1"=10 ' vertical. Thus H:V ratio is 100:10 or 10:1. Then, for metric scale, use 1:1000 horizontally and 1:100 vertically. 11
  51. 51. New Mexico State Highway & Transportation Department - Show bar scale next to written scale Example:      0 5 10 15 20 m SELECTED MATERIAL DESIGNATIONS Materials which are specified by size will be designated in metric units. Metric designations for several common materials are included here. STEEL REINFORCING ( REBAR ) Specification reference - AASHTO M-31M Size Designations Bar Cross-sectional Des. Nominal Diameter Area Perimeter No. Mass, kg/m mm mm 2 mm 10 0.785 11.3 100 35.5 15 1.570 16.0 200 50.3 20 2.355 19.5 300 61.3 25 3.925 25.2 500 79.2 30 5.495 29.9 700 93.9 35 7.850 35.7 1000 112.2 45 11.775 43.7 1500 137.3 55 19.625 56.4 2500 177.2 STRUCTURAL STEEL Specification reference - AASHTO M-160M and ASTM A6/A6M Reference is hereby made to the listed specifications for the size designations as they are to numerous to include in these guidelines New Mexico State Highway & Transportation Department 12
  52. 52. CORRUGATED STEEL PIPE Specification reference - AASHTO M-36M Size Designations Nominal inside Nominal inside Nominal inside Diameter Diameter Diameter in. mm in. mm in. mm 4 100 30 800 84 2200 6 150 36 900 90 ---- 8 200 42 1000 96 2400 10 250 48 1200 102 ---- 12 300 54 1400 108 2700 15 400 60 ---- 114 ---- 18 450 -- 1600 120 3000 21 500 66 ---- --- 3300 24 600 72 1800 --- 3600 -- 700 78 2000 REINFORCED CONCRETE PIPE Specification reference - AASHTO M-170M Size Designations Nominal inside Nominal inside Nominal inside Diameter Diameter Diametcr in. mm in. mm in. mm 60 1500 90 2250 120 3000 66 1650 96 2400 126 3150 72 1800 102 2550 132 3300 78 1950 108 2700 138 3450 84 2100 114 2850 144 3600 13
  53. 53. New Mexico State Highway & Transportation Department WIRE CLOTH SIEVE SIZE DESIGNATIONS The table below is from information contained in AASHTO M92 and ASTM Ell "Wire Cloth Sieves for Testing Purposes", and shows Standard (Metric) and Alternative (U.S. Customary) sieve size designations. As shown, metric size designations are given in mm or µm. (1,000 µm = 1 millimeter) Sieve Designation Standard AlternateStandard Alternate 125 mm 5 in. 2.36 mm No. 8 106 mm 4.24 in. 2.00 mm No. 10 100 mm 4 in. 1.70 mm No. 12 90 mm 3-1/2 in. 1.40 mm No. 14 75 mm 3 in. 1.18 mm No. 16 63 mm 2-1/2 in. 1.00 mm No. 18 53 mm 2.12 in. 850 µm No. 20 50 mm 2 in. 710 µm No. 25 45 mm 1-3/4 in. 600 µm No. 30 37.5 mm 1-1/2 in. 500 µm No. 35 31.5 mm 1-1/4 in. 425 µm No. 40 26.5 mm 1.06 in. 355 µm No. 45 25.0 mm 1 in. 300 µm No. 50 22.4 mm 7/8 in. 250 µm No. 60 19.0 mm 3/4 in. 212 µm No. 70 16.0 mm 5/8 in. 180 µm No. 80 13.2 mm 0.530 in. 150 µm No. 100 12.5 mm 1/2 in. 125 µm No. 120 11.2 mm 7/16 in. 106 µm No. 140 9.5 mm 3/8 in. 90 µm No. 170 8.0 mm 5/16 in. 75 µm No. 200 6.7 mm 0.265 in. 63 µm No. 230 6.3 mm 1/4 in. 53 µm No. 270 5.6 mm No. 3-1/2 45 µm No. 325 4.75 mm No. 4 38 µm No. 400 4.00 mm No. 5 32 µm No. 450 3.35 mm No. 6 25 µm No. 500 2.80 mm No. 7 20 µm No. 630 14
  54. 54. New Mexico State Highway & Transportation Department BASE UNITS There are seven base metric units of measurement. These are meter, kilogram, second, ampere, kelvin, mole and candela. The base units which are used in highway design and construction are listed below. Quantity Unit Symbol length meter m mass* kilogram kg time second s electric current ampere A temperature Kelvin K luminous intensity candela cd # Please note Upper- vs: Lower-case symbols * "Weight" in common practice often is used interchangeably with mass" DECIMAL PREFIXES Only two decimal prefixes are commonly used with the base units in design and construction. These are as shown in the following table: Order of Prefix Symbol Magnitude Expression kilo k 103=1000 (one thousand) mi11i m 10-3=0.001 (one thousandth) The prefixes mega (M) for one million (l06), qiga (G) for one billion (109), mirco (µ) for one millionth (10-6), and nano (n) for one billionth (10-9) are used in some engineering calculations. Decimal prefixes to the tertiary power of 10 are preferred (meaning in multiples of 3 ie., 103, 106, etc.) The prefixes deci (d) for one tenth (10 -1 ), centi (c) for one hundredth (10-2), deca (da) for ten (101), and hecto (h) for one hundred (102) have limited application in design and construction. TEMPERATURE Celsius temperature (CC) is more commonly used than kelvin (K), but both have the same temperature gradients. Celsius temperature is simply 273.15 degrees warmer than kelvin. Kelvin begins at absolute zero. For instance, water freezes at 273.15 K and at 0 zC; it boils at 373.15 K and at 100 CC. To move between Celsius and kelvin, add or subtract 273.15. Please note the use of the symbol, (b), for degrees Celsius. The symbol, (d), is not used for degrees K. The following formulas can be used for 15
  55. 55. conversion from cF to FC and vice versa: CC = 5/9(CF - 32) FF = 9/5(FC) + 32 DERIVED UNITS As shown previously, there are only seven base units in the metric system. There are, however, many derived units which are used in the metric system. Some of the derived units which are used in design are units such as (t) for metric ton; Square meter for area; and cubic meters per second for flow rate. For other units, see GENERAL CIVIL ENGINEERING CONVERSION FACTORS in these guidelines. PLANE AND SOLID ANGLES The radian (rad) and steradian (sr) denote plane and solid angles. They are used in lighting work and in various engineering calculations. In surveying, the units degree (t), minute ()), and second (),) will continue to be used. LITER, HECTARE, AND METRIC TON The liter (L) is the measurement for liquid volume. The hectare (ha) is a metric measurement used to replace the acre. The metric ton (t) is used to denote large loads such as those used in surfacing aggregates. This will replace the "ton". Caution should be exercised when using and computing tonne(s), since the metric tonne is abbreviated (t) and it could easily be confused with the English ton. PRONUNCIATION Candela Accent the second syllable, can-dell-ah kilometer Accent the first syllable: kill-o-meter hectare Accent the first syllable: heck-tare. The second syllable rhymes with acre. joule Rhymes with pool. pascal Rhymes with rascal siemens Sounds like seamen's RULES FOR WRITING METRIC SYMBOLS AND NAMES - Print unit symbols in upright type and in lower case except for liter (L) or unless the unit name is derived from a proper name. - Print unit names in lower case, even those derived from a proper name. - Print decimal prefixes in lower case for magnitudes 103 and lower (that is: k, m, µ, and n) and 16
  56. 56. print the prefixes in upper case for magnitudes 10 and higher (that is: M and G). - Leave a space between the numeral and the symbol (write 45 kg or 37LC, not 45kg or 37 CC or 37C C). - Do not use a degree mark (D) with kelvin temperature (write K, not )K). - Do not leave a space between a unit symbol and its decimal prefix (write kg, not k g). - Do not use the plural of unit symbols (write 40 kg, not 40 kgs), but do use the plural of written unit names (forty kilograms). - For technical writing, use symbols in conjunction with numerals (the area is 10 m); write out unit names if numerals are not used (carpet is measured in square meters). Numerals may be combined with written unit names in non-technical writing (10 meters). - Indicate the product of two or more units in symbolic form by using a dot positioned above the line (kglmms). - Do not mix names and symbols (write N-m or newton meter, not NNmeter nor newtonmm). - Do not use a period after a symbol (write "12 g", not "12 g." ) except when it occurs at the end of a sentence. RULES FOR WRITING NUMBERS - Always use decimals, not fractions (write 0.75 g, not 3/4 g). - Use a zero before the decimal marker for values less than one (1) (write 0.45 g, not .45 g). - Commas shall continue to be used to separate digits into groups of three. Spaces will not be used to separate the groups. CONVERSION AND ROUNDING - When converting values from miles to kilometers, round off the resultant metric value to the same number of digits as there were in the mile number (11 miles at 1.609 km/mi equals 17.699 km, which rounds off to 18 km. 12.26 miles at 1.609 km/mi equals 19.726 km, which rounds off to 19.73 km, etc.) - Convert mixed inch-pound units (feet and inches, pounds and ounces) to the smaller unit, inch- 17
  57. 57. pound, before converting to metric and rounding off (10 feet, 3 inches : 123 inches; 123 inches x 25.4 mm = 3124.2 mm; round to 3124 mm). - In a "soft" conversion, an English measurement is mathematically converted to its exact (or nearly exact) metric equivalent. With "hard" conversion, a new rounded-rationalized metric number is created that is convenient to work with and remember. GENERAL CIVIL ENGINEERING One metric unit is used to measure length, area, and volume in most design and construction work. This unit is: - meter (m) RULES FOR LINEAR MEASUREMENT (LENGTH) - Use the kilometer for long distances and the millimeter for precision measurements. - Measurements done in millimeter will typically be in whole . numbers. Those done in meters will typically have at least one decimal place. - Avoid use of the centimeter. - For survey measurement, use the meter and the kilometer. - Use only the meter and millimeter in building design and architectural construction. RULES FOR AREA - The square meter is preferred. - Very large areas may be expressed in square kilometers and very small areas, in square millimeters. - Use the hectare (10,000 square meters) for land and water measurement only. - Avoid use of the square centimeter. - Linear dimensions such as: 40 x 90 mm may be used; if so, indicate width first and height second. 18
  58. 58. RULES FOR VOLUME AND FLUID CAPACITY - Cubic meter is preferred for volumes in construction and for measurements such as large storage tanks. - Use liter (L) and milliliter (m L) for fluid capacity (liquid volume). One liter is 1/1000 of a cubic meter or 1000 cubic centimeters. - Since a cubic meter equals one billion cubic millimeters, the cubic decimeter and cubic centimeter may be used in limited applications, because they are multiples of 1000 in volume measurement. RULES FOR CIVIL ENGINEERING - Plane angles in surveying (cartography) will continue to be measured in degrees (either decimal degrees or degrees, minutes, and seconds) rather than the metric radian or grads. - Slope is expressed in non-dimensional ratios. The horizontal component is shown first and then the vertical. For instance, a rise of one meter in four meters is expressed as 4:1. The units that are compared should be the same (meters to meters, millimeters to millimeters, etc.). Please note that a slope measured as a rise of one meter to a run of four meters is equivalent to a slope measured as a rise of one foot to a run of four feet. SAMPLE METRIC CONVERSION CALCULATIONS The following sample calculations are intended to aid in the conversion of existing data. Hopefully it will also aid in providing alternatives to the methods used in the conversion calculations. The General Civil Engineering Conversion Factors included in these guidelines have multiplication factors for converting from one unit to another. Some may prefer to use ratios to help in maintaining the dimensional consistency. Factors are good when doing many repetitious calculations. The use of ratios are excellent when trying to convert complicated unit of measurement or when converting for units which are not listed such as from pounds per square yard to kilograms per square meter which might be used for a blotter sand application. Examples of the use of both methods are included here. LENGTH Convert 1137.5 ft. to meters (m): From the conversion chart, multiply by 0.3048006 to get meters. 19
  59. 59. 1137.5 ft. X 0.3048006 = 346.71068 m Use 346. 7 m or Find the equivalent ratio such as: 1 m = 39.37 in., and 12 in. = 1 ft., then: 12 in. 1 m 1137.5 ft. = 1137.5 ft. x ------ x ---------- = 346.7107 m 1 ft 39.17 in. Use 346. 7 m MASS Convert 11,500 pounds (lbs.) to kilograms (kg): 0.4535924 kg 11,500 lbs = 11,500 lbs. X --------------- 1 lbs. = 5,216.3126 kg Use 5,216 kg Convert 8,453.5 lbs. to metric tons (t): Note that the metric ton (sometimes written as tonne) is equal to 1,000 kilograms. The (English ton or short) ton is equal to 2,000 lbs. 1 ton 907.1847 kg t 8,453.0 lbs. = 8,453.0 lbs. X--------X------------X-------- 2,000 lbs. 1 ton 1,000 kg = 3.834216 t Use 3.8 t 20
  60. 60. AREA Convert 875.45 square feet to square meters (m2): From the conversion chart multiply by 0.09290341 to get m2 875.45 sq. ft. X 0.09290341 = 81.33229 m2 use 81. 33 m2 Notice that the round off is done to the same number as the least of the significant figures in the problem, ie. 2 digits to the right of the decimal place. or 1 m 1 m 2 2 875.45 ft = 875.45 ft X --------- X --------- 3.2808 ft. 3.2808 ft. = 81.3339 m2 Use 81.33 m2 Notice that the format of the units (sq. ft. vs: ft2) is changed. This is done for illustration purposes and for clarity. Convert 230,458.0 sq. ft. to hectares (ha): Please note that the factors for area or volume can be derived by using multiple factors for length such as: If you know that 1 m = 3.2808 ft., then you can derive a factor for area by using the following: 1 m 1 m 1 m2 --------- X ------- = ------- 3.2808 ft. 3.2808 ft. 10.7639 ft2 The new factor is used in this conversion problem. This concept is used in the next conversion problem to derive a factor for square meters vs. square yards. One can use this concept for volume or any other units of measure as necessary. 21
  61. 61. New Mexico State Highway & Transportation Department 1 m2 1 ha 230,458.0 ft2 = 230,458.0 ft2 X ---------- X -------- 10.7639 ft 2 10,000 m2 = 2.14103 ha Use 2.1 ha VOLUME Convert 175,468 square yard-inches to cubic meters (m3): 1 m2 1 m 175,468 yd2-in. = 175,468 yd2-in. X -------- X -------- 1.19599 yd 2 39.37 in. = 3,726.5329 m 3 Use 3,727 m3 OTHER COMMON UNITS OF MEASURE Convert 65 ft. per sec. to kilometers per hour (km/h): ft. ft. 1 mi. 1.609347 km 3,600 s 65 --- = 65 --- x ------- x ----------- x ------- sec. s 5280 ft. 1 mi. 1 h = 71. 3233 km/h Use 71 km/h Convert 3450 p.s.i. to pascals (Pa) using conversion factors: 3450 p.s.i. = 3450 p.s.i. x 6,894.757 = 23,786,911.65 Pa or 22
  62. 62. 23,786,911.65 Pa = 23,786,911.65 Pa x 1 MPa / 1,000,000 Pa = 23.78691165 Megapascals Use 23.787 MPa Convert 40 lbs. per square yard to kilograms per square meter: lbs 1 kg 1 yd2 40 lbs./sq. yd. = 40 --- X ------------ X ---------- yd2 2.204622 lbs 0.8361274 m2 = 21. 699683 kg/m2 Use 22 kg/m2 23
  63. 63. New Mexico State Highway & Transportation Department Convert 145.3 lbs. per cubic foot to kilograms per cubic meter using factors: 145.3 lbs./cu.ft. = 145.3 lbs./ft3 X 16.01846 = 2,327.482238 kg/m' Use 2,327.5 kg/m3 or using ratios: lbs. lbs. 1 kg 1 ft3 145.3 --- = 145.3 --- x ------------ x ---------- ft3 ft3 2.204622 lbs. 0.028317 m3 = 2,327.47677 kg/m3 Use 2,327.5 kg/m3 Convert the Prime Coat factor of 256.86 gal/ton to Liters/Tonne: gal. gal. 3.78541 L ton 256.86 --- = 256.86 --- X --------- X ----------- ton ton gal. 0.9071847 t = 1,071.7998359 Liters/tonne Use 1,071.80 L/t Determine the metric tons/m2 of PMBP using a depth of 10" and a unit weight of 3950 lbs. per cubic yard. For each square yard of PMBP, the following calculation applies: 1 yd 3950 lbs 0.9071847 t 1.1959854 yd2 101 = 10 X ---- X -------- X ----------- X ------------- 36" yd3 2000 lbs 1 m2 t (metric) = 0.5952319 --- m2 24
  64. 64. Use = 0.60 t/m2 or 0.60 t for each m2 of 10" PMBP 22 25
  65. 65. New Mexico State Highway & Transportation Department METRIC UNITS-OF-MEASUREMENT The New Mexico State Highway & Transportation Department units-of-measure used in the bidding documents are listed below. The proposed metric units-of-measure are shown here in both the abbre- viated form and also are spelled out with the recommended use of uppercase letters. Current Pay Units Proposed Metric Pay Units* (Abbr) (Spelled out) (Abbr) (Spelled out) Acre Acre ha hectare Acre-unit Ac-unit ha-unit hectare-unit Bale Bale Bale Bale Cal.Day Calendar Day Cal. Day Calendar Day Cu.Ft. Cubic foot Cu. m Cubic meter Cu.Yd. Cubic Yard Cu. m Cubic meter Each Each each Each Gallon Gallon L Liter Hour Hour hour Hour Lin.Ft. Linear Foot m meter L.S. Lump Sum LS Lump Sum Mile Mile km kilometer 1/ 4 M.Y. 1/ 4 Mile-Yard 1/ 4 km-m 1/ 4 kilometer-meter M-Gal Thousand Gallons Cu. m Cubic meter Pound Pound kg kilogram Sq.Ft. Square Foot Sq. m Square meter Sq.Yd. Square Yard Sq. m Square meter Sq.Yd.-In. Square Yard-Inch Cu. m Cubic meter Ton Ton t metric ton Tn-Mile Ton-Mile t-km ton-kilometer Ver.Ft. Vertical Foot Ver. m Vertical meter 26
  66. 66. * Please note that the metric units are in the recommended upper- /lower-case as defined by the Metric guidelines. 23 27

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